41

significant contributor to these area oscillations is the

interaction between the aeroshell wake and the parachute

flow fields [34].

From the parachute opening load and freestream flow

parameters, the curve of the parachute drag coefficient with

the Mach number can be obtained, as shown in Figure 15.

Table 4: Parachute deployment conditions.

Test Mach at mortar fire Dynamic pressure at mortar fire/Pa Recovery mass/kg Angle of attack/°

1 2:05 ± 0:25 550 ± 300 1285 ± 20 0±2

2 2:05 ± 0:25 550 ± 300 1285 ± 20 10 ± 2

3 2:3±0:25 100~500 1285 ± 20 10 ± 2

4 2:35 ± 0:25 250~950 1285 ± 20 13 ± 2

36 38 40 42 44 46 48 50 52 54 56 58 60 62

550

600

650

700

750

v (m/s)

800

850

h (km)

Test 1 and 2

Test 3

Test 4

Mortar Fire

Figure 11: Parachute deployment height and speed frame for different tests.

0 200 400 600 800 1000 1200

0

1

2

3

4

5

6

7

Test 01

Test 02

Test 03

Test 04

h (m)

×104

t (s)

Figure 12: Height versus time.

0

100

200

300

400

500

600

700

800

900

0 200 400 600 800 1000 1200

Test 01

Test 02

Test 03

Test 04

t (s)

v (m/s)

Figure 13: Velocity versus time.

8 Space: Science & Technology

The test results show that between Ma 0.2 and Ma 2.4, the

drag coefficient of the tapered DGB parachute increases first

and then decreases. The variation range of the drag coefficient is 0.39~0.70. At Ma 1.5, the drag coefficient reaches

the maximum value of about 0.7.

In the wind tunnel test of the drag coefficient, when the

parachute is at a Mach number of 0.21, 0.9, and 1.98, the

corresponding drag coefficients are 0.55, 0.50, and 0.47,

respectively. Except for Mach number 0.9, the drag coefficient in the wind tunnel test is consistent with the results

of the high-altitude drop parachute tests. Because parachutes

are in the wake of slender bodies in the high-altitude drop

parachute tests, its drag coefficient at Mach number 0.9 is

higher than that of the wind tunnel test. This behavior has

been observed in wind tunnel test data [35], and it is due

to the interaction between the blunt aeroshell and the parachute flow fields.

The oscillation angle of the parachute within 7 s after the

parachute inflation is shown in Figure 16. After the parachute inflation, the parachute shows repeated oscillation

within a small angle. The oscillation angle of test 03 is the

largest, about 20°

, and the maximum oscillation angle of

the other tests is 15°

. Since the dynamic pressure in the flight

tests is much smaller than that in the wind tunnel tests, the

oscillation angle of the parachute is larger than that in the

wind tunnel test results.

5. Conclusion

In this paper, the parachute of Tianwen-1 has been optimized and tested. According to the flight conditions of Mars

parachutes, five DGB parachutes with different geometries

were designed. In the wind tunnel tests, the change of drag

coefficient and oscillation angle under different Mach numbers were obtained. Based on the comprehensive performance of the parachute, the tapered DGB parachute is

selected as the priority parachute type. Then, the tapered

DGB parachute was verified by four high-altitude flight tests

using sounding rockets to reach the targeted conditions. The

test results indicate that the drag coefficient of the tapered

DGB parachute varied from 0.39 to 0.70 with the Mach

number increased from Ma 0.2-Ma 2.4 and reached the

maximum value of 0.7 at Ma 1.5; the maximum AOA after

parachute deployment is about 20°

, which have all demonstrated that the performance of the tapered DGB parachute

could meet the deceleration requirements of the Tianwen-1

Mars probe.

Data Availability

The data used to support the findings of this study are

available from the author upon request.

50 100 150 200 250 300 350 400

0

20

40

60

80

100

120

70 80 90

0

50

100

Test 01

Test 02

Test 03

Test 04

t (s)

F (kN)

Figure 14: Opening force versus time.

0 0.5 1 1.5 2 2.5

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

Test 01

Test 02

Test 03

Test 04

CD

Ma

Figure 15: Drag coefficient versus Mach number.

01234567

0

5

10

15

20

25

Test 01

Test 02

Test 03

Test 04

t (s)

Oscillation angle (°)

Figure 16: Oscillation angle versus time.

Space: Science & Technology 9

42

Geophysical Research: Planets, vol. 98, no. E4, pp. 7461–

7474, 1993.

[28] C. L. T. I. Chen, “Overview of the Mars 2020 parachute risk

reduction activity PPT,” in 2018 IEEE aerospace conference,

Big, Sky, MT, USA, 2018.

[29] J. C. Mcfall and H. N. Murrow, Summary of Experimental

Results Obtained from the NASA Planetary Entry Parachute

Program, NASA.AIAA PAPER 68-934, 1968.

[30] C. V. Eckstrom and J. S. Preisser, Flight Test of a 30-Foot

Nominal-Diameter Disk-Gap-Band Parachute Deployed at

Mach 1.56 and Dynamic Pressure of 11.4 Pounds per Square

Foot, National Aeronautics and Space Administration, 1967.

[31] C. Zumwalt, J. Cruz, C. O'Farrell, and D. Keller, “Wind Tunnel

Test of Subscale Ringsail and Disk-Gap-Band Parachutes,” in

34th AIAA Applied Aerodynamics Conference, Washington,

D.C., June 2016.

[32] R. C. Maydew and W. P. C. Orlik-Rueckemann, Design and

Testing of High-Performance Parachutes, ADVISORY GROUP

FOR AEROSPACE RESEARCH AND DEVELOPMENT,

FRANCE, 1991.

[33] M. X. Huang, S. Y. Gao, W. L. Wang, W. Q. Wang, and J. Li,

“Performance analysis and experimental study of Tianwen1,” Parachute Material, vol. 8, no. 5, pp. 478–485, 2021.

[34] A. Sengupta, “Temporal Characteristics of a Disk Gap Band

Parachute from Mach 2 to 2.5,”in AIAA Aerodynamic Decelerator Systems (ADS) Conference, Daytona Beach, Florida,

March 2013.

[35] D. E. A. Reichenau, Aerodynamic characteristics of disk-gapband parachutes in the wake of Viking entry forebodies at Mach

numbers from 0.2 to 2.6, AEDC.AEDC-TR-72-78, 1972.

Space: Science & Technology 11

Conflicts of Interest

All authors declare no conflicts of interest.

Authors’ Contributions

All authors participated in the research design and conducted the experiments. Mingxing Huang performed data

analysis and accomplished the writing of the manuscript.

Acknowledgments

This research was financially supported by the Beijing Institute of Space Mechanics & Electricity.

References

[1] M. X. Huagn, W. Q. Wang, J. Li, and L. W. Wang, “Analysis of

supersonic wind tunnel test results of Mars disk gap band

parachute,” Journal of Astronautics, vol. 42, no. 9, pp. 1178–

1186, 2021.

[2] Z. Yu, P. Cui, and J. L. Crassidis, “Design and optimization of

navigation and guidance techniques for Mars pinpoint landing: review and prospect,” Progress in Aerospace Sciences,

vol. 94, pp. 82–94, 2017.

[3] I. Clark and C. Tanner, “A historical summary of the design,

development, and analysis of the disk-gap-band parachute,”

in IEEE Aerospace Conference, pp. 4–11, Big Sky, MT, USA,

2017.

[4] J. R. Cruz and J. S. Lingard, “Aerodynamic Decelerators for

Planetary Exploration: Past, Present, and Future,” in AIAA

Guidance, Navigation, and Control Conference, pp. 21–24,

Keystone, Colorado, 2006.

[5] D. E. A. Reichenau, “Aerodynamic Characteristics of DiskGap-Band Parachutes in the Wake of Viking Entry Forebodies

at Mach Numbers from 0.2 to 2.6,” in Arnold Engineering

Development Center Arnold AFB TN, Defense Technical Information Center, 1972.

[6] S. Steinberg, P. M. I. Siemers, and R. G. Slayman, “velopment

of the Viking parachute configuration by Wind-Tunnel Investigation,” Journal of Spacecraft & Rockets, vol. 11, no. 2,

pp. 101–107, 1974.

[7] H. Murrow, C. Eckstrom, and D. Henke, “Development Flight

Tests of the Viking Decelerator System,” in 4th Aerodynamic

Deceleration Systems Conference, Palm Springs, CA, U.S.A,

1973.

[8] J. Raper, R. Lundstrom, and F. Michel, “The Viking Parachute

Qualification Test Technique,” in 4th Aerodynamic Deceleration Systems Conference, Palm Springs, CA, U.S.A, 1973.

[9] R. Reginald, J. L. R. Lundstrom, J. Richard, and A. E. W. S.

Bendura, “Flight Tests of Viking Parachute System in Three

Mach Number Regimes 1: Vehicle Description,” in Test operations, and Performance, Langley Research Cent. NASA TN D7692, 1974.

[10] R. J. Bendura, R. R. Lundstrom, P. G. Renfroe, and S. R.

LeCroy, Flight Tests of Viking Parachute System in Three Mach

Number Regimes 2: Parachute Test Results, NASA.NASA-TND-7734, 1975.

[11] R. D. Moog and F. C. Michel, Balloon Launched Viking Decelerator Test Program Summary Report, NASA.TR-3720359,

1974.

[12] S. Gao, S. Ge, and Y. Liang, “Research on transonic wind

tunnel tests of Mars disk-gap-band parachutes,” Chinese Space

Science and Technology, vol. 4, pp. 69–75, 2015.

[13] C. V. Eckstrom, Development and Testing of the Disk-GapBand Parachute Used for Low Dynamic Pressure Applications

at Ejection Altitudes at or above 200,000 Feet, NASA.NASA

CR-502, 1966.

[14] C. V. Eckstrom, Flight Test of a 40-Foot Nominal Diameter

Disk-Gap-Band Parachute Deployed at a Mach Number of

3.31 and a Dynamic Pressure of 10.6 Pounds per Square Foot,

NASA.NASA-TM-X-1924, 1970.

[15] C. ECKSTROM and D. R. BRANSCOME, High Altitude Flight

Test of a Disk Gap Band Parachute Deployed Behind a Bluff

Body at a Mach Number of 2.69, no. article 19730006315,

1972NASA Langley Research Center, Hampton, VA, United

States, 1972.

[16] C. V. Eckstrom, High-Altitude Flight test of a 40-Foot- Diameter/12.2-Meter/Ringsail Parachute at a Deployment Mach

Number of 2.95, NASA.NASA-TN-D-5796, 1970.

[17] D. A. Spencer, R. C. Blanchard, R. D. Braun, P. H. Kallemeyn,

and S. W. Thurman, “Mars Pathfinder entry, descent, and

landing reconstruction,” Journal of Spacecraft and Rockets,

vol. 36, no. 3, pp. 357–366, 1999.

[18] A. Witkowski, “Mars Pathfinder parachute system performance,” in 15th Aerodynamic Decelerator Systems Technology

Conference, Toulouse, France, June 1999.

[19] P. N. Desai, J. T. Schofield, and M. E. Lisano, “Flight reconstruction of the Mars pathfinder disk-gap-band parachute drag

coefficients,” Journal of Spacecraft and Rockets, vol. 42, no. 4,

pp. 672–676, 2005.

[20] I. G. Clark, J. C. Gallon, and A. Witkowski, “Parachute decelerator system performance during the low-density supersonic

decelerator program’s first supersonic flight dynamics test,”

in 23rd AIAA Aerodynamic Decelerator Systems Technology

Conference, Daytona Beach, FL, 2015.

[21] C. O'Farrell, E. J. Brandeau, C. Tanner, J. C. Gallon,

S. Muppidi, and I. G. Clark, “Reconstructed parachute system

performance during the second LDSD supersonic flight

dynamics test,”in AIAA Atmospheric Flight Mechanics Conference, Washington, D.C., 2016.

[22] C. O. Farrell, I. Clark, and M. Adler, “Overview of the ASPIRE

Project PPT,” in 14th International Planetary Probes Workshop, The Hague, NL., June 2017.

[23] B. S. Sonneveldt, I. G. Clark, and C. O'Farrell, “Summary of the

Advanced Supersonic Parachute Inflation Research Experiments (ASPIRE) Sounding Rocket Tests with a Disk-GapBand Parachute,” in AIAA Aviation 2019 Forum, Dallas,

Texas, June 2019.

[24] S. Dutta, C. D. Karlgaard, J. A. Tynis et al., “Advanced supersonic parachute inflation research experiment preflight trajectory modeling and postflight reconstruction,” Journal of

Spacecraft and Rockets, vol. 57, no. 6, pp. 1387–1407, 2020.

[25] C. O'Farrell, B. S. Sonneveldt, C. Karhgaard, J. A. Tynis, and

I. G. Clark, “Overview of the ASPIRE project's supersonic

flight tests of a strengthened DGB parachute,” in 2019 IEEE

Aerospace Conference, Big Sky, MT, USA, 2019.

[26] R. D. Braun and R. M. Manning, “Mars exploration entry,

descent, and landing challenges,” Journal of Spacecraft and

Rockets, vol. 44, no. 2, pp. 310–323, 2007.

[27] A. Seiff, “Mars atmospheric winds indicated by motion of

the Viking landers during parachute descent,” Journal of

10 Space: Science & Technology

&

43

Geophysical Research: Planets, vol. 98, no. E4, pp. 7461–

7474, 1993.

[28] C. L. T. I. Chen, “Overview of the Mars 2020 parachute risk

reduction activity PPT,” in 2018 IEEE aerospace conference,

Big, Sky, MT, USA, 2018.

[29] J. C. Mcfall and H. N. Murrow, Summary of Experimental

Results Obtained from the NASA Planetary Entry Parachute

Program, NASA.AIAA PAPER 68-934, 1968.

[30] C. V. Eckstrom and J. S. Preisser, Flight Test of a 30-Foot

Nominal-Diameter Disk-Gap-Band Parachute Deployed at

Mach 1.56 and Dynamic Pressure of 11.4 Pounds per Square

Foot, National Aeronautics and Space Administration, 1967.

[31] C. Zumwalt, J. Cruz, C. O'Farrell, and D. Keller, “Wind Tunnel

Test of Subscale Ringsail and Disk-Gap-Band Parachutes,” in

34th AIAA Applied Aerodynamics Conference, Washington,

D.C., June 2016.

[32] R. C. Maydew and W. P. C. Orlik-Rueckemann, Design and

Testing of High-Performance Parachutes, ADVISORY GROUP

FOR AEROSPACE RESEARCH AND DEVELOPMENT,

FRANCE, 1991.

[33] M. X. Huang, S. Y. Gao, W. L. Wang, W. Q. Wang, and J. Li,

“Performance analysis and experimental study of Tianwen1,” Parachute Material, vol. 8, no. 5, pp. 478–485, 2021.

[34] A. Sengupta, “Temporal Characteristics of a Disk Gap Band

Parachute from Mach 2 to 2.5,”in AIAA Aerodynamic Decelerator Systems (ADS) Conference, Daytona Beach, Florida,

March 2013.

[35] D. E. A. Reichenau, Aerodynamic characteristics of disk-gapband parachutes in the wake of Viking entry forebodies at Mach

numbers from 0.2 to 2.6, AEDC.AEDC-TR-72-78, 1972.

Space: Science & Technology 11

Conflicts of Interest

All authors declare no conflicts of interest.

Authors’ Contributions

All authors participated in the research design and conducted the experiments. Mingxing Huang performed data

analysis and accomplished the writing of the manuscript.

Acknowledgments

This research was financially supported by the Beijing Institute of Space Mechanics & Electricity.

References

[1] M. X. Huagn, W. Q. Wang, J. Li, and L. W. Wang, “Analysis of

supersonic wind tunnel test results of Mars disk gap band

parachute,” Journal of Astronautics, vol. 42, no. 9, pp. 1178–

1186, 2021.

[2] Z. Yu, P. Cui, and J. L. Crassidis, “Design and optimization of

navigation and guidance techniques for Mars pinpoint landing: review and prospect,” Progress in Aerospace Sciences,

vol. 94, pp. 82–94, 2017.

[3] I. Clark and C. Tanner, “A historical summary of the design,

development, and analysis of the disk-gap-band parachute,”

in IEEE Aerospace Conference, pp. 4–11, Big Sky, MT, USA,

2017.

[4] J. R. Cruz and J. S. Lingard, “Aerodynamic Decelerators for

Planetary Exploration: Past, Present, and Future,” in AIAA

Guidance, Navigation, and Control Conference, pp. 21–24,

Keystone, Colorado, 2006.

[5] D. E. A. Reichenau, “Aerodynamic Characteristics of DiskGap-Band Parachutes in the Wake of Viking Entry Forebodies

at Mach Numbers from 0.2 to 2.6,” in Arnold Engineering

Development Center Arnold AFB TN, Defense Technical Information Center, 1972.

[6] S. Steinberg, P. M. I. Siemers, and R. G. Slayman, “velopment

of the Viking parachute configuration by Wind-Tunnel Investigation,” Journal of Spacecraft & Rockets, vol. 11, no. 2,

pp. 101–107, 1974.

[7] H. Murrow, C. Eckstrom, and D. Henke, “Development Flight

Tests of the Viking Decelerator System,” in 4th Aerodynamic

Deceleration Systems Conference, Palm Springs, CA, U.S.A,

1973.

[8] J. Raper, R. Lundstrom, and F. Michel, “The Viking Parachute

Qualification Test Technique,” in 4th Aerodynamic Deceleration Systems Conference, Palm Springs, CA, U.S.A, 1973.

[9] R. Reginald, J. L. R. Lundstrom, J. Richard, and A. E. W. S.

Bendura, “Flight Tests of Viking Parachute System in Three

Mach Number Regimes 1: Vehicle Description,” in Test operations, and Performance, Langley Research Cent. NASA TN D7692, 1974.

[10] R. J. Bendura, R. R. Lundstrom, P. G. Renfroe, and S. R.

LeCroy, Flight Tests of Viking Parachute System in Three Mach

Number Regimes 2: Parachute Test Results, NASA.NASA-TND-7734, 1975.

[11] R. D. Moog and F. C. Michel, Balloon Launched Viking Decelerator Test Program Summary Report, NASA.TR-3720359,

1974.

[12] S. Gao, S. Ge, and Y. Liang, “Research on transonic wind

tunnel tests of Mars disk-gap-band parachutes,” Chinese Space

Science and Technology, vol. 4, pp. 69–75, 2015.

[13] C. V. Eckstrom, Development and Testing of the Disk-GapBand Parachute Used for Low Dynamic Pressure Applications

at Ejection Altitudes at or above 200,000 Feet, NASA.NASA

CR-502, 1966.

[14] C. V. Eckstrom, Flight Test of a 40-Foot Nominal Diameter

Disk-Gap-Band Parachute Deployed at a Mach Number of

3.31 and a Dynamic Pressure of 10.6 Pounds per Square Foot,

NASA.NASA-TM-X-1924, 1970.

[15] C. ECKSTROM and D. R. BRANSCOME, High Altitude Flight

Test of a Disk Gap Band Parachute Deployed Behind a Bluff

Body at a Mach Number of 2.69, no. article 19730006315,

1972NASA Langley Research Center, Hampton, VA, United

States, 1972.

[16] C. V. Eckstrom, High-Altitude Flight test of a 40-Foot- Diameter/12.2-Meter/Ringsail Parachute at a Deployment Mach

Number of 2.95, NASA.NASA-TN-D-5796, 1970.

[17] D. A. Spencer, R. C. Blanchard, R. D. Braun, P. H. Kallemeyn,

and S. W. Thurman, “Mars Pathfinder entry, descent, and

landing reconstruction,” Journal of Spacecraft and Rockets,

vol. 36, no. 3, pp. 357–366, 1999.

[18] A. Witkowski, “Mars Pathfinder parachute system performance,” in 15th Aerodynamic Decelerator Systems Technology

Conference, Toulouse, France, June 1999.

[19] P. N. Desai, J. T. Schofield, and M. E. Lisano, “Flight reconstruction of the Mars pathfinder disk-gap-band parachute drag

coefficients,” Journal of Spacecraft and Rockets, vol. 42, no. 4,

pp. 672–676, 2005.

[20] I. G. Clark, J. C. Gallon, and A. Witkowski, “Parachute decelerator system performance during the low-density supersonic

decelerator program’s first supersonic flight dynamics test,”

in 23rd AIAA Aerodynamic Decelerator Systems Technology

Conference, Daytona Beach, FL, 2015.

[21] C. O'Farrell, E. J. Brandeau, C. Tanner, J. C. Gallon,

S. Muppidi, and I. G. Clark, “Reconstructed parachute system

performance during the second LDSD supersonic flight

dynamics test,”in AIAA Atmospheric Flight Mechanics Conference, Washington, D.C., 2016.

[22] C. O. Farrell, I. Clark, and M. Adler, “Overview of the ASPIRE

Project PPT,” in 14th International Planetary Probes Workshop, The Hague, NL., June 2017.

[23] B. S. Sonneveldt, I. G. Clark, and C. O'Farrell, “Summary of the

Advanced Supersonic Parachute Inflation Research Experiments (ASPIRE) Sounding Rocket Tests with a Disk-GapBand Parachute,” in AIAA Aviation 2019 Forum, Dallas,

Texas, June 2019.

[24] S. Dutta, C. D. Karlgaard, J. A. Tynis et al., “Advanced supersonic parachute inflation research experiment preflight trajectory modeling and postflight reconstruction,” Journal of

Spacecraft and Rockets, vol. 57, no. 6, pp. 1387–1407, 2020.

[25] C. O'Farrell, B. S. Sonneveldt, C. Karhgaard, J. A. Tynis, and

I. G. Clark, “Overview of the ASPIRE project's supersonic

flight tests of a strengthened DGB parachute,” in 2019 IEEE

Aerospace Conference, Big Sky, MT, USA, 2019.

[26] R. D. Braun and R. M. Manning, “Mars exploration entry,

descent, and landing challenges,” Journal of Spacecraft and

Rockets, vol. 44, no. 2, pp. 310–323, 2007.

[27] A. Seiff, “Mars atmospheric winds indicated by motion of

the Viking landers during parachute descent,” Journal of

10 Space: Science & Technology

44

Research Article

Thermal Environment and Aeroheating Mechanism of

Protuberances on Mars Entry Capsule

Miao Wenbo ,

1,2 Li Qi,3 Li Junhong,1,2 Zhou Jingyun,1 and Cheng Xiaoli1,2

1

China Academy of Aerospace Aerodynamics, PO BOX 7201, Sub PO BOX 16, Beijing 100074, China

2

Key Laboratory of Aero-Thermal Protection of Aerospace Vehicles, China Aerospace Science and Technology Corporation,

Beijing 100074, China

3

Beijing Institute of Spacecraft System Engineering, China

Correspondence should be addressed to Miao Wenbo; tingles@126.com

Received 12 August 2021; Accepted 9 October 2021; Published 20 November 2021

Copyright © 2021 Miao Wenbo et al. Exclusive Licensee Beijing Institute of Technology Press. Distributed under a Creative

Commons Attribution License (CC BY 4.0).

Mars has only thin atmosphere composed mainly of carbon dioxide that differs significantly from the atmosphere of Earth in

terms of characteristics of reentry flows. To connect with the orbiter, the Mars entry capsule is provided with titanium pipes

and other units installed on the heat-shield. These units will create significant local interaction flow on the surface of the

capsule and cause additional heating on the surface of the shield during the entry of the capsule. With a view to interaction

thermal environment issues for the surface of the shield, in this paper, the characteristics of protrusion interaction flow on

different location of the shield were studied by means of numerical simulation. Heating mechanisms of protuberances on

different location were derived by analyzing characteristic parameters such as local flow velocity, pressure, and Mach number.

The results show that the interaction thermal environment of protuberances in the windward area is smaller than that of

protuberances in the leeward area, mainly because subsonic flow dominates in the windward area, and the interaction is weak,

while in the leeward area, the direction of flow intersects with protuberances to form a boundary layer shear flow, which

results in a stronger interaction before the protuberances.

1. Introduction

Mars is a planet that has the most Earth-like natural

environment currently explored by scientists. To adapt to

the reentry environment of Mars, the capsule normally

selects blunt body appearance, and the heat shield is subject

to the most crucial aeroheating in the Mars entry. During

the entry, the shield will retain mechanisms connected to

the orbital module such as titanium pipes and other units.

These units form a protrusion on the surface of the shield,

which creates a complex interaction thermal environment

on the shield, thus producing additional aeroheating on the

surface of the shield and seriously affecting the performance

of the thermal protection system.

Researches on protrusion interaction thermal environment have long been carried out. When protuberances

present on the surface of the vehicle, hypersonic inflow will

create a detached shock wave in front of protuberances,

which interacts with boundary layers to generate complex

shock wave-shock wave interaction around the protuberance

that leads to the separation and reattachment of flow, causing additional interaction heating. Back in the early 1970s,

Hung et al. [1, 2] classified and studied protrusion interaction. Based on the relationship between the height of protuberances and thickness of boundary layers, they divided the

protrusion into high column and short column for theoretical analysis and research and gave a rough distribution

diagram of the interaction flow. In addition to theoretical

analysis means, experimental research was realized to some

extent. Holden [3] roughly defined the range of the interaction area of protuberances (about 2-3times the diameter of

the cylinder). Suxun [4] conducted experimental research

on the thermal environment profile of circular cylinder, rectangular cylinder, compression corner, double ellipsoid, and

other flows and realized the mechanism of protrusion interaction thermal environment. With the development of

computer technology, numerical simulation has gradually

become an important means for studying the interaction

AAAS

Space: Science & Technology

Volume 2021, Article ID 9754068, 8 pages

https://doi.org/10.34133/2021/9754068

45

Research Article

Thermal Environment and Aeroheating Mechanism of

Protuberances on Mars Entry Capsule

Miao Wenbo ,

1,2 Li Qi,3 Li Junhong,1,2 Zhou Jingyun,1 and Cheng Xiaoli1,2

1

China Academy of Aerospace Aerodynamics, PO BOX 7201, Sub PO BOX 16, Beijing 100074, China

2

Key Laboratory of Aero-Thermal Protection of Aerospace Vehicles, China Aerospace Science and Technology Corporation,

Beijing 100074, China

3

Beijing Institute of Spacecraft System Engineering, China

Correspondence should be addressed to Miao Wenbo; tingles@126.com

Received 12 August 2021; Accepted 9 October 2021; Published 20 November 2021

Copyright © 2021 Miao Wenbo et al. Exclusive Licensee Beijing Institute of Technology Press. Distributed under a Creative

Commons Attribution License (CC BY 4.0).

Mars has only thin atmosphere composed mainly of carbon dioxide that differs significantly from the atmosphere of Earth in

terms of characteristics of reentry flows. To connect with the orbiter, the Mars entry capsule is provided with titanium pipes

and other units installed on the heat-shield. These units will create significant local interaction flow on the surface of the

capsule and cause additional heating on the surface of the shield during the entry of the capsule. With a view to interaction

thermal environment issues for the surface of the shield, in this paper, the characteristics of protrusion interaction flow on

different location of the shield were studied by means of numerical simulation. Heating mechanisms of protuberances on

different location were derived by analyzing characteristic parameters such as local flow velocity, pressure, and Mach number.

The results show that the interaction thermal environment of protuberances in the windward area is smaller than that of

protuberances in the leeward area, mainly because subsonic flow dominates in the windward area, and the interaction is weak,

while in the leeward area, the direction of flow intersects with protuberances to form a boundary layer shear flow, which

results in a stronger interaction before the protuberances.

1. Introduction

Mars is a planet that has the most Earth-like natural

environment currently explored by scientists. To adapt to

the reentry environment of Mars, the capsule normally

selects blunt body appearance, and the heat shield is subject

to the most crucial aeroheating in the Mars entry. During

the entry, the shield will retain mechanisms connected to

the orbital module such as titanium pipes and other units.

These units form a protrusion on the surface of the shield,

which creates a complex interaction thermal environment

on the shield, thus producing additional aeroheating on the

surface of the shield and seriously affecting the performance

of the thermal protection system.

Researches on protrusion interaction thermal environment have long been carried out. When protuberances

present on the surface of the vehicle, hypersonic inflow will

create a detached shock wave in front of protuberances,

which interacts with boundary layers to generate complex

shock wave-shock wave interaction around the protuberance

that leads to the separation and reattachment of flow, causing additional interaction heating. Back in the early 1970s,

Hung et al. [1, 2] classified and studied protrusion interaction. Based on the relationship between the height of protuberances and thickness of boundary layers, they divided the

protrusion into high column and short column for theoretical analysis and research and gave a rough distribution

diagram of the interaction flow. In addition to theoretical

analysis means, experimental research was realized to some

extent. Holden [3] roughly defined the range of the interaction area of protuberances (about 2-3times the diameter of

the cylinder). Suxun [4] conducted experimental research

on the thermal environment profile of circular cylinder, rectangular cylinder, compression corner, double ellipsoid, and

other flows and realized the mechanism of protrusion interaction thermal environment. With the development of

computer technology, numerical simulation has gradually

become an important means for studying the interaction

AAAS

Space: Science & Technology

Volume 2021, Article ID 9754068, 8 pages

https://doi.org/10.34133/2021/9754068

Thermal Environment and Aeroheating Mechanism of

Protuberances on Mars Entry Capsule

Wenbo Miao,1,2 Qi Li,3

Junhong Li,1,2 Jingyun Zhou,1

and Xiaoli Cheng1,2

1

China Academy of Aerospace Aerodynamics, PO BOX 7201, Sub PO BOX 16, Beijing 100074, China

2

Key Laboratory of Aero-Thermal Protection of Aerospace Vehicles, China Aerospace Science and Technology Corporation, Beijing

100074, China

3

Beijing Institute of Spacecraft System Engineering, China

Correspondence should be addressed to Wenbo Miao; tingles@126.com

Abstract: Mars has only thin atmosphere composed mainly of carbon dioxide that differs significantly from the atmosphere of Earth in

terms of characteristics of reentry flows. To connect with the orbiter, the Mars entry capsule is provided with titanium pipes and other units

installed on the heat-shield. These units will create significant local interaction flow on the surface of the capsule and cause additional

heating on the surface of the shield during the entry of the capsule. With a view to interaction thermal environment issues for the surface

of the shield, in this paper, the characteristics of protrusion interaction flow on different location of the shield were studied by means of

numerical simulation. Heating mechanisms of protuberances on different location were derived by analyzing characteristic parameters

such as local flow velocity, pressure, and Mach number. The results show that the interaction thermal environment of protuberances in the

windward area is smaller than that of protuberances in the leeward area, mainly because subsonic flow dominates in the windward area,

and the interaction is weak, while in the leeward area, the direction of flow intersects with protuberances to form a boundary layer shear

flow, which results in a stronger interaction before the protuberances.

46

thermal environment of protuberances. Pan [5] investigated

the scope of influence of the protrusion and the thermal

environment of its interaction region through combination

of theoretical analysis and numerical simulation and derived

the quantitative relationships between the range of separation

regions and the geometrical characteristics of protuberances.

Fuqun [6] researched the interaction thermal environment

of two types of typical protuberances-protrusions with a

single trapezoidal cross-section and conical bosses and discovered that the protrusion interaction thermal environment

of the conical boss is much bigger than that of the protuberance with a single trapezoidal cross-section. The developed

numerical technology provides strong support for the predication of protrusion interaction thermal environment and is

also applied in the prediction of thermal environment and

thermal protection system design. Current theoretical analysis and experimental research are mainly concentrated in protrusion interaction analysis for simple flow (flat-plate/slender

body). Despite allowing for simulation of complex flows,

numerical simulation now mainly takes Earth’s atmosphere

as principal subject of research, and there are few studies on

the thermal environment disturbed by protrusions in the

Mars entry.

The atmosphere of Mars is mainly comprised of carbon

dioxide and about 100 times thinner than Earth’s. Compared

with entry of Earth, Reynolds number for Mars entry is

smaller when flying at high speed due to the low density of

its atmosphere, and the characteristics of boundary layer of

Mars Lander are different from those of Earth’s. Pertinent

researches should be carried out on the protrusion interaction in the entry of Mars considering the differences of

thermo-chemical properties between CO2 and air in Earth.

The aeroheating mechanism of protrusion interaction on

the surface of shield is studied in this article and numerical

simulation method is involved to recognize the characteristics of interaction flow and profile of thermal environment

on the shield of Mars Lander.

2. Numerical Simulation Method

The protrusion interaction thermal environment of the Mars

capsule is analyzed by solving NS equations for multicomponent chemical reaction in this paper. The equations are

solved through discretization based on the finite volume

method, the spatial discretization scheme is AUSM+ scheme

which has higher computational accuracy [7], and the time

discretization scheme is LUSGS scheme. In calculation,

thermo nonequilibrium and chemical nonequilibrium

hypotheses are introduced; viscosity, conductivity, and diffusion models are given according to the methods for solving

the integral of collision cross-sections with reference to

Y

Z X

p (Pa)

5500

5000

4500

4000

3500

3000

2500

1500

2000

1000

500

Figure 2: Contours of temperature and pressure at plane of

symmetry.

800

CFD

Experiment

600

400

200

0.00 0.04 0.08 0.12

x (m)

0.16

Qw (kW/m2

)

Figure 3: Distribution of heat-flux on double-cone wall surface.

Radial location (m)

Qw (W/cm2

)

0 0.3 0.6 0.9 1.2 1.5

0

30

60

90

120

Present comp. 8 species

Mitcheltree and Gnoffo 8 species

Park etal. 18 species

Figure 1: Comparison of radial distributions of heat flux on the

shield of the Mars capsule.

2 Space: Science & Technology

literature [8]. For chemical reaction models, because the

atmosphere of Mars concludes 97% CO2 and 3% N2, eight

components and nine reaction models mentioned in literature [9] are used, and the components involved are O, O2,

CO2, CO, C, N, N2, and NO. In the process of computation,

set Tw ðtemperature of the surfaceÞ = 300 K and choose a

fully catalytic wall as a condition of the surface. For thermodynamic nonequilibrium models, a two-temperature model

is used, where T represents translational temperature and

rotational temperature and TV represents vibration temperature and electron temperature, and translation-vibration

energy relaxation models are taken into account. See literature [10] for specific models.

2.1. Validation and Verification. First, Mars Pathfinder [11]

entry vehicle is selected as the subject of verification, and

the comparison with data on heat flux of the shield included

in multiple literatures has verified the ability of this method

to simulate the flow of Mars entry. In this verification, only

the heat flux on the surface of the shield is compared. The

state of calculation is M = 32, T = 169 K, Tw = 2100 K, and

ρ = 2:8 × 10−4 kg/m3. The comparison of the calculation

results in this paper with the heat flux in the literatures at

the fully catalytic wall condition is shown in Figure 1. The

distribution of heat flux on the shield is essentially consistent, and the stagnation-point heat flux (109W/cm2

) is

slightly smaller than the stagnation-point heat flux in the

literatures (111.8W/cm2

).

Candler [12] 25-55°

angle double-cone typical compressioncorner interaction experiment is selected as the subject of

verification to verify the ability of this method to simulate the

thermal environment of complex shock wave boundary-layer

interaction region. Mach number of inflow Ma = 11:3, temperature T = 138:9 K, density ρ = 0:552 kg/m3, and temperature of

the surface Tw = 300 K.

The contours of temperature and pressure at plane of

symmetry are shown in Figure 2. It can be seen that a

remarkable separation and shock wave structure are located

at the corner. The comparison of the thermal environment

on the surface of the wall with the experimental data is

shown in Figure 3, and both match well with each other.

The separation region, dramatic decline caused by expansion, and quick rise of heat flux resulting from separation

and reattachment can be observed, and the size of the separation region and the peak heat-flux at the separation region

are captured accurately.

2.2. Analysis of Interaction Thermal Environment. With

Pathfinder as an example, interaction thermal environment

around the protuberances on the surface of the Mars capsule

shield is studied in this paper. The parameters of the outline of

Pathfinder are shown in Figure 4, including the direction of

flows and the schematic diagram of location of titanium pipes.

The titanium pipes are 70 mm in height, about 40 mm in

diameter, located at four generatrices of 45,135,225 and 315,

and 700 mm away from the central vertex.

Two typical flow conditions are analyzed. Two specific

calculation conditions are listed in Table 1. The two flight

conditions have the same angle of attack, so their flow structures are similar. Interaction flow structure and thermal

environment at the condition of H = 80 km are analyzed as

an example.

The distribution of the flow fields in the interaction

region of the titanium pipe and its nearby streamlines is

shown in Figure 5. At this point, the angle of attack is

10 degrees, and there is significant difference between

streamlines in the proximity of the titanium pipe Y1 in

the windward area and the titanium pipe B1 in the leeward area. The flow at the titanium pipe B1 is dominated

by boundary-layer flow that evolves from the stagnant

flow and creates apparent characteristics of boundaryY

Z X

Y

Z X

2.65 m 2.65 m

70

R = 0.66 m

Figure 4: Outline of the capsule and location of titanium pipes.

Table 1: Flow conditions.

Height (km) Speed (m/s) Temperature (K) Angle of attack

80 6000 131.9 10

60 5400 144.7 10

Space: Science & Technology 3

47

thermal environment of protuberances. Pan [5] investigated

the scope of influence of the protrusion and the thermal

environment of its interaction region through combination

of theoretical analysis and numerical simulation and derived

the quantitative relationships between the range of separation

regions and the geometrical characteristics of protuberances.

Fuqun [6] researched the interaction thermal environment

of two types of typical protuberances-protrusions with a

single trapezoidal cross-section and conical bosses and discovered that the protrusion interaction thermal environment

of the conical boss is much bigger than that of the protuberance with a single trapezoidal cross-section. The developed

numerical technology provides strong support for the predication of protrusion interaction thermal environment and is

also applied in the prediction of thermal environment and

thermal protection system design. Current theoretical analysis and experimental research are mainly concentrated in protrusion interaction analysis for simple flow (flat-plate/slender

body). Despite allowing for simulation of complex flows,

numerical simulation now mainly takes Earth’s atmosphere

as principal subject of research, and there are few studies on

the thermal environment disturbed by protrusions in the

Mars entry.

The atmosphere of Mars is mainly comprised of carbon

dioxide and about 100 times thinner than Earth’s. Compared

with entry of Earth, Reynolds number for Mars entry is

smaller when flying at high speed due to the low density of

its atmosphere, and the characteristics of boundary layer of

Mars Lander are different from those of Earth’s. Pertinent

researches should be carried out on the protrusion interaction in the entry of Mars considering the differences of

thermo-chemical properties between CO2 and air in Earth.

The aeroheating mechanism of protrusion interaction on

the surface of shield is studied in this article and numerical

simulation method is involved to recognize the characteristics of interaction flow and profile of thermal environment

on the shield of Mars Lander.

2. Numerical Simulation Method

The protrusion interaction thermal environment of the Mars

capsule is analyzed by solving NS equations for multicomponent chemical reaction in this paper. The equations are

solved through discretization based on the finite volume

method, the spatial discretization scheme is AUSM+ scheme

which has higher computational accuracy [7], and the time

discretization scheme is LUSGS scheme. In calculation,

thermo nonequilibrium and chemical nonequilibrium

hypotheses are introduced; viscosity, conductivity, and diffusion models are given according to the methods for solving

the integral of collision cross-sections with reference to

Y

Z X

p (Pa)

5500

5000

4500

4000

3500

3000

2500

1500

2000

1000

500

Figure 2: Contours of temperature and pressure at plane of

symmetry.

800

CFD

Experiment

600

400

200

0.00 0.04 0.08 0.12

x (m)

0.16

Qw (kW/m2

)

Figure 3: Distribution of heat-flux on double-cone wall surface.

Radial location (m)

Qw (W/cm2

)

0 0.3 0.6 0.9 1.2 1.5

0

30

60

90

120

Present comp. 8 species

Mitcheltree and Gnoffo 8 species

Park etal. 18 species

Figure 1: Comparison of radial distributions of heat flux on the

shield of the Mars capsule.

2 Space: Science & Technology

literature [8]. For chemical reaction models, because the

atmosphere of Mars concludes 97% CO2 and 3% N2, eight

components and nine reaction models mentioned in literature [9] are used, and the components involved are O, O2,

CO2, CO, C, N, N2, and NO. In the process of computation,

set Tw ðtemperature of the surfaceÞ = 300 K and choose a

fully catalytic wall as a condition of the surface. For thermodynamic nonequilibrium models, a two-temperature model

is used, where T represents translational temperature and

rotational temperature and TV represents vibration temperature and electron temperature, and translation-vibration

energy relaxation models are taken into account. See literature [10] for specific models.

2.1. Validation and Verification. First, Mars Pathfinder [11]

entry vehicle is selected as the subject of verification, and

the comparison with data on heat flux of the shield included

in multiple literatures has verified the ability of this method

to simulate the flow of Mars entry. In this verification, only

the heat flux on the surface of the shield is compared. The

state of calculation is M = 32, T = 169 K, Tw = 2100 K, and

ρ = 2:8 × 10−4 kg/m3. The comparison of the calculation

results in this paper with the heat flux in the literatures at

the fully catalytic wall condition is shown in Figure 1. The

distribution of heat flux on the shield is essentially consistent, and the stagnation-point heat flux (109W/cm2

) is

slightly smaller than the stagnation-point heat flux in the

literatures (111.8W/cm2

).

Candler [12] 25-55°

angle double-cone typical compressioncorner interaction experiment is selected as the subject of

verification to verify the ability of this method to simulate the

thermal environment of complex shock wave boundary-layer

interaction region. Mach number of inflow Ma = 11:3, temperature T = 138:9 K, density ρ = 0:552 kg/m3, and temperature of

the surface Tw = 300 K.

The contours of temperature and pressure at plane of

symmetry are shown in Figure 2. It can be seen that a

remarkable separation and shock wave structure are located

at the corner. The comparison of the thermal environment

on the surface of the wall with the experimental data is

shown in Figure 3, and both match well with each other.

The separation region, dramatic decline caused by expansion, and quick rise of heat flux resulting from separation

and reattachment can be observed, and the size of the separation region and the peak heat-flux at the separation region

are captured accurately.

2.2. Analysis of Interaction Thermal Environment. With

Pathfinder as an example, interaction thermal environment

around the protuberances on the surface of the Mars capsule

shield is studied in this paper. The parameters of the outline of

Pathfinder are shown in Figure 4, including the direction of

flows and the schematic diagram of location of titanium pipes.

The titanium pipes are 70 mm in height, about 40 mm in

diameter, located at four generatrices of 45,135,225 and 315,

and 700 mm away from the central vertex.

Two typical flow conditions are analyzed. Two specific

calculation conditions are listed in Table 1. The two flight

conditions have the same angle of attack, so their flow structures are similar. Interaction flow structure and thermal

environment at the condition of H = 80 km are analyzed as

an example.

The distribution of the flow fields in the interaction

region of the titanium pipe and its nearby streamlines is

shown in Figure 5. At this point, the angle of attack is

10 degrees, and there is significant difference between

streamlines in the proximity of the titanium pipe Y1 in

the windward area and the titanium pipe B1 in the leeward area. The flow at the titanium pipe B1 is dominated

by boundary-layer flow that evolves from the stagnant

flow and creates apparent characteristics of boundaryY

Z X

Y

Z X

2.65 m 2.65 m

70

R = 0.66 m

Figure 4: Outline of the capsule and location of titanium pipes.

Table 1: Flow conditions.

Height (km) Speed (m/s) Temperature (K) Angle of attack

80 6000 131.9 10

60 5400 144.7 10

Space: Science & Technology 3

48

layer flow on the surface of the titanium pipe. The flow at

the titanium pipe B1 mainly develops from outside of the

local shock layer and exhibits remarkable characteristics of

stagnant flow. This can be observed more clearly from the

angle between the direction of the flow before the titanium

pipes B1 and Y1 and the axis line of the titanium pipe. As

the axis line of the titanium pipe is parallel to the x-axis

and the semicone angle of the shield is 70 degrees, at this

point, the angle between the direction of flow in front of

the titanium pipe B1 and the axis line of the titanium pipe

is about 65 degrees, which means the direction of flow is

basically parallel to the conical surface; the angle between

the direction of flow velocity in front of the titanium pipe

Y1 and the axis line of the titanium pipe is about 45

degree, which means that the direction of flow and

the conical surface form an angle of attack with around

25 degrees.

From the research of Hung et al. [1, 2] on protrusion

interaction, it can be seen that the protrusion interaction

thermal environment in the hypersonic flow field is mainly

influenced by inflow Mach number, Reynolds number, and

the height of the protuberance, especially the relative height

of the protuberance to the boundary layer. If the protuberance is above the thickness of the boundary layer, external

flow will cause stronger interaction to the protuberance; if

the protuberance is hidden in the boundary layer, the interaction will be decreased significantly.

The Mach number isopleths for the cross-section of the

protrusions of two titanium pipes (Ma = 1) is shown in

Figure 6. It can be seen that, at the titanium pipe B1, most

areas of the titanium pipe are in the flow field with Mach

number more than 1, while at the titanium pipe Y1, the

entire titanium pipe is in the flow field with Mach number

less than 1. Therefore, it can be concluded that the interaction flow at the titanium pipe B1 on the leeward location is

significantly stronger than that at the titanium pipe Y1 on

the windward location, thus causing stronger interaction

heating at B1. This deviates from the general idea that the

heating in the windward area is stronger than that in the

leeward area.

The contours of pressure and heat-flux in the interaction

regions of two titanium pipes are shown in Figure 7. It can

be seen that the peak heat-flux at the titanium pipe mainly

locates at the upper end of the titanium pipe, and the

Y

ZX

X

ZY

X

Z

Y

P

100

90

80

70

60

50

40

30

20

10

0

Figure 5: Parameters of the flow field in the proximity of the titanium pipe and distribution of streamlines of flow around blunt body.

4 Space: Science & Technology

B1

X

P: 10 21 32 43 54 65 76 87 98 109 120

P: 10 21 32 43 54 65 76 87 98 109 120

Qw: 0 20 40 60 80 100 120 140 160 180 200

Qw: 0 20 40 60 80 100 120 140 160 180 200

Y

Z

Y1 Y1

B1

X

Y

Z

X

Y

Z

X

Y

Z

Figure 7: Distribution of pressure and heat flux on the surface of different titanium pipes.

X X

Y

Z

Z

Y

B1

Y1

Ma: 1 Ma: 1

Figure 6: Isopleths at the titanium pipe on different locations (Ma = 1).

Space: Science & Technology 5

49

layer flow on the surface of the titanium pipe. The flow at

the titanium pipe B1 mainly develops from outside of the

local shock layer and exhibits remarkable characteristics of

stagnant flow. This can be observed more clearly from the

angle between the direction of the flow before the titanium

pipes B1 and Y1 and the axis line of the titanium pipe. As

the axis line of the titanium pipe is parallel to the x-axis

and the semicone angle of the shield is 70 degrees, at this

point, the angle between the direction of flow in front of

the titanium pipe B1 and the axis line of the titanium pipe

is about 65 degrees, which means the direction of flow is

basically parallel to the conical surface; the angle between

the direction of flow velocity in front of the titanium pipe

Y1 and the axis line of the titanium pipe is about 45

degree, which means that the direction of flow and

the conical surface form an angle of attack with around

25 degrees.

From the research of Hung et al. [1, 2] on protrusion

interaction, it can be seen that the protrusion interaction

thermal environment in the hypersonic flow field is mainly

influenced by inflow Mach number, Reynolds number, and

the height of the protuberance, especially the relative height

of the protuberance to the boundary layer. If the protuberance is above the thickness of the boundary layer, external

flow will cause stronger interaction to the protuberance; if

the protuberance is hidden in the boundary layer, the interaction will be decreased significantly.

The Mach number isopleths for the cross-section of the

protrusions of two titanium pipes (Ma = 1) is shown in

Figure 6. It can be seen that, at the titanium pipe B1, most

areas of the titanium pipe are in the flow field with Mach

number more than 1, while at the titanium pipe Y1, the

entire titanium pipe is in the flow field with Mach number

less than 1. Therefore, it can be concluded that the interaction flow at the titanium pipe B1 on the leeward location is

significantly stronger than that at the titanium pipe Y1 on

the windward location, thus causing stronger interaction

heating at B1. This deviates from the general idea that the

heating in the windward area is stronger than that in the

leeward area.

The contours of pressure and heat-flux in the interaction

regions of two titanium pipes are shown in Figure 7. It can

be seen that the peak heat-flux at the titanium pipe mainly

locates at the upper end of the titanium pipe, and the

Y

ZX

X

ZY

X

Z

Y

P

100

90

80

70

60

50

40

30

20

10

0

Figure 5: Parameters of the flow field in the proximity of the titanium pipe and distribution of streamlines of flow around blunt body.

4 Space: Science & Technology

B1

X

P: 10 21 32 43 54 65 76 87 98 109 120

P: 10 21 32 43 54 65 76 87 98 109 120

Qw: 0 20 40 60 80 100 120 140 160 180 200

Qw: 0 20 40 60 80 100 120 140 160 180 200

Y

Z

Y1 Y1

B1

X

Y

Z

X

Y

Z

X

Y

Z

Figure 7: Distribution of pressure and heat flux on the surface of different titanium pipes.

X X

Y

Z

Z

Y

B1

Y1

Ma: 1 Ma: 1

Figure 6: Isopleths at the titanium pipe on different locations (Ma = 1).

Space: Science & Technology 5

50

Y B1

Y1 Y1

B1

Level Ma

H = 80 km

1 1

Z X

Y

Z X

Level Ma

1 1

H = 60 km

Figure 8: Distributions of isopleths at the titanium pipes on different heights (Ma = 1).

Y

X

H = 60 km

q0: q0:

q0: q0: 0.00 0.80 1.60 2.40 3.20 4.00 4.80 5.60 6.40 7.20 8.00 0 0.65 1.3 1.95 2.6 3.25 3.9 4.55 5.2 5.85 6.5

0 0.6 1.2 1.8 2.4 3 3.6 4.2 4.8 5.4 6 0 0.45 0.9 1.35 1.8 2.25 2.7 3.15 3.6 4.05 4.5

B1

Z

Y

X

Z

Y

X

Z

Y

X

Z

H = 60 km

Y1

H = 80 km

Y1

H = 80 km

B1

Figure 9: Distributions of dimensionless heat flux on the titanium pipes.

6 Space: Science & Technology

interaction thermal environment of the titanium pipe Y1 is

significantly smaller than that of the titanium pipe B1. As

the titanium pipe B1 is dominated by boundary-layer flow,

there is a noticeable high-pressure, high-temperature area

in the windward side of the titanium pipe, in addition to

the high-pressure, high-temperature area on the top of the

titanium pipe. For the titanium pipe Y1, the high-pressure,

high-temperature area is mainly on the top of the titanium

pipe and the pressure and heat-flux on the cylindrical segment decrease significantly. The peak heat-flux of the titanium pipe B1 is about 180 kW/m2

, and the peak heat-flux

of the titanium pipe B1 is about 150 kW/m2

.

Although the angles of attack at different heights are

consistent, flow Mach number and Reynolds number in different flight conditions vary greatly, and the thermal environment in the interference area of the titanium pipe will

be different due to the individual flight conditions. Whether

the local Mach number is more than 1 or not is the important basis for judging the strength of flow interference at this

location. It is also possible to analyze flow interaction that

could occur locally through the total enthalpy boundary

layer of flow field. The distributions of isopleths Ma equal

to 1 around the titanium pipe at different flight conditions

are shown in Figure 8. It can be seen that for different flight

conditions, velocities vary greatly, but the characteristics of

flow in the interaction area of the titanium pipe are consistent. The windward titanium pipe is dominated by stagnant

flow, and the leeward titanium pipe is dominated by shear

flow. The heights at the windward and leeward titanium

pipes (Ma = 1) are 160 mm and 12 mm, respectively, when

H = 60 km; the heights at the windward and leeward titanium pipes (Ma = 1) are 160 mm and 15 mm, respectively,

when H = 80 km.

The distributions of dimensionless heat-flux on the surface of the titanium pipes at two flight conditions are shown

in Figure 9. Dimensionless heat-flux is the ratio of interaction heat-flux to the local noninteraction heat-flux. At the

flight condition of H = 80 km and H = 60 km, noninteraction heat-flux of the shield are 22 kW/m2 and 50 kW/m2

.

Although interaction thermal environment at the titanium

pipe (H = 80 km) is lower, dimensionless heat flux there

is bigger.

3. Conclusions

In this paper, the mechanism of protrusion interaction thermal environment on the surface of the Mars entry capsule

was studied, the characteristics of flow at the typical flow

conditions were derived by means of numerical simulations,

and its generation mechanism and distribution rules were

analyzed. The results show that:

For the Mars entry capsule, there is difference between

interaction flow mechanisms of the titanium pipes at different locations on the shield. The titanium pipe in the windward area is dominated by strong subsonic compression

stagnant flow, and the titanium pipe in the leeward area is

dominated by supersonic boundary-layer shear flow. Therefore, the interaction flow of the titanium pipe in the leeward

area is stronger, and the interference thermal environment

is severe.

The titanium pipe B1 is dominated by boundary-layer

flow. In addition to high-pressure, high-temperature areas

on the top of the titanium pipe, there are remarkable highpressure, high-temperature areas in the windward side of

the titanium pipe. For the titanium pipe Y1, the high-pressure, high-temperature areas are mainly on the top of the

titanium pipe, and the pressure and heat-flux at the cylindrical segment are reduced significantly.

At the flight condition of H = 80 km, noninteraction

heat-flux is lower than flight condition of H = 60 km, but

the dimensionless heat-flux on the surface of the titanium

pipe is higher.

Data Availability

Some or all data, models, or code generated or used during

the study are proprietary or confidential in nature and may

only be provided with restrictions.

Disclosure

The views and conclusions contained herein are those of the

authors and should not be interpreted as necessarily representing the official policies or endorsements.

Conflicts of Interest

The authors declare that they have no competing interests.

Authors’ Contributions

The corresponding author is Miao Wenbo who contributed

to the literature review, data analysis, the writing of paper,

and the revision of the paper. The second author and the

third author contributed to the data acquisition, the data

analysis, and the writing of the paper. The fourth author

contributed to validation of method and the writing of the

paper. The fifth author contributed to the calculation planning and proofreading of the paper. The authors read and

approved the final manuscript.

Acknowledgments

This work was sponsored by the thermal protection system

research mission of TianWen Mars Exploration Project of

China and Joint Funds of National Natural Science Foundation of China (no. U20B2017).

References

[1] F. T. Hung, “Three-dimensional protuberance interference

heating in high speed flow,” in 18th Aerospace Sciences Meeting, Pasadena,CA,U.S.A, 1980.

[2] R. Sedney and C. W. Kitchens, “Separation ahead of protuberances in supersonic turbulent boundary layers,” AIAA Journal,

vol. 15, no. 4, pp. 546–552, 1977.

[3] M. S. Holden, “A study of flow separation in regions of shock

wave boundary layer interaction in hypersonic flow,” in 11th

Space: Science & Technology 7

51

Y B1

Y1 Y1

B1

Level Ma

H = 80 km

1 1

Z X

Y

Z X

Level Ma

1 1

H = 60 km

Figure 8: Distributions of isopleths at the titanium pipes on different heights (Ma = 1).

Y

X

H = 60 km

q0: q0:

q0: q0: 0.00 0.80 1.60 2.40 3.20 4.00 4.80 5.60 6.40 7.20 8.00 0 0.65 1.3 1.95 2.6 3.25 3.9 4.55 5.2 5.85 6.5

0 0.6 1.2 1.8 2.4 3 3.6 4.2 4.8 5.4 6 0 0.45 0.9 1.35 1.8 2.25 2.7 3.15 3.6 4.05 4.5

B1

Z

Y

X

Z

Y

X

Z

Y

X

Z

H = 60 km

Y1

H = 80 km

Y1

H = 80 km

B1

Figure 9: Distributions of dimensionless heat flux on the titanium pipes.

6 Space: Science & Technology

interaction thermal environment of the titanium pipe Y1 is

significantly smaller than that of the titanium pipe B1. As

the titanium pipe B1 is dominated by boundary-layer flow,

there is a noticeable high-pressure, high-temperature area

in the windward side of the titanium pipe, in addition to

the high-pressure, high-temperature area on the top of the

titanium pipe. For the titanium pipe Y1, the high-pressure,

high-temperature area is mainly on the top of the titanium

pipe and the pressure and heat-flux on the cylindrical segment decrease significantly. The peak heat-flux of the titanium pipe B1 is about 180 kW/m2

, and the peak heat-flux

of the titanium pipe B1 is about 150 kW/m2

.

Although the angles of attack at different heights are

consistent, flow Mach number and Reynolds number in different flight conditions vary greatly, and the thermal environment in the interference area of the titanium pipe will

be different due to the individual flight conditions. Whether

the local Mach number is more than 1 or not is the important basis for judging the strength of flow interference at this

location. It is also possible to analyze flow interaction that

could occur locally through the total enthalpy boundary

layer of flow field. The distributions of isopleths Ma equal

to 1 around the titanium pipe at different flight conditions

are shown in Figure 8. It can be seen that for different flight

conditions, velocities vary greatly, but the characteristics of

flow in the interaction area of the titanium pipe are consistent. The windward titanium pipe is dominated by stagnant

flow, and the leeward titanium pipe is dominated by shear

flow. The heights at the windward and leeward titanium

pipes (Ma = 1) are 160 mm and 12 mm, respectively, when

H = 60 km; the heights at the windward and leeward titanium pipes (Ma = 1) are 160 mm and 15 mm, respectively,

when H = 80 km.

The distributions of dimensionless heat-flux on the surface of the titanium pipes at two flight conditions are shown

in Figure 9. Dimensionless heat-flux is the ratio of interaction heat-flux to the local noninteraction heat-flux. At the

flight condition of H = 80 km and H = 60 km, noninteraction heat-flux of the shield are 22 kW/m2 and 50 kW/m2

.

Although interaction thermal environment at the titanium

pipe (H = 80 km) is lower, dimensionless heat flux there

is bigger.

3. Conclusions

In this paper, the mechanism of protrusion interaction thermal environment on the surface of the Mars entry capsule

was studied, the characteristics of flow at the typical flow

conditions were derived by means of numerical simulations,

and its generation mechanism and distribution rules were

analyzed. The results show that:

For the Mars entry capsule, there is difference between

interaction flow mechanisms of the titanium pipes at different locations on the shield. The titanium pipe in the windward area is dominated by strong subsonic compression

stagnant flow, and the titanium pipe in the leeward area is

dominated by supersonic boundary-layer shear flow. Therefore, the interaction flow of the titanium pipe in the leeward

area is stronger, and the interference thermal environment

is severe.

The titanium pipe B1 is dominated by boundary-layer

flow. In addition to high-pressure, high-temperature areas

on the top of the titanium pipe, there are remarkable highpressure, high-temperature areas in the windward side of

the titanium pipe. For the titanium pipe Y1, the high-pressure, high-temperature areas are mainly on the top of the

titanium pipe, and the pressure and heat-flux at the cylindrical segment are reduced significantly.

At the flight condition of H = 80 km, noninteraction

heat-flux is lower than flight condition of H = 60 km, but

the dimensionless heat-flux on the surface of the titanium

pipe is higher.

Data Availability

Some or all data, models, or code generated or used during

the study are proprietary or confidential in nature and may

only be provided with restrictions.

Disclosure

The views and conclusions contained herein are those of the

authors and should not be interpreted as necessarily representing the official policies or endorsements.

Conflicts of Interest

The authors declare that they have no competing interests.

Authors’ Contributions

The corresponding author is Miao Wenbo who contributed

to the literature review, data analysis, the writing of paper,

and the revision of the paper. The second author and the

third author contributed to the data acquisition, the data

analysis, and the writing of the paper. The fourth author

contributed to validation of method and the writing of the

paper. The fifth author contributed to the calculation planning and proofreading of the paper. The authors read and

approved the final manuscript.

Acknowledgments

This work was sponsored by the thermal protection system

research mission of TianWen Mars Exploration Project of

China and Joint Funds of National Natural Science Foundation of China (no. U20B2017).

References

[1] F. T. Hung, “Three-dimensional protuberance interference

heating in high speed flow,” in 18th Aerospace Sciences Meeting, Pasadena,CA,U.S.A, 1980.

[2] R. Sedney and C. W. Kitchens, “Separation ahead of protuberances in supersonic turbulent boundary layers,” AIAA Journal,

vol. 15, no. 4, pp. 546–552, 1977.

[3] M. S. Holden, “A study of flow separation in regions of shock

wave boundary layer interaction in hypersonic flow,” in 11th

Space: Science & Technology 7

52

Research Article

Numerical Simulation of Decompression Process of a Mars

Rover in the Launch Phase

Weizhang Wang,1 Wei Rao,2 Qi Li,2 Hao Yan,1 and Rui Zhao1

1

School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China

2

Beijing Institute of Spacecraft System Engineering (ISSE), Beijing 100094, China

Correspondence should be addressed to Rui Zhao; zr@bit.edu.cn

Received 29 July 2021; Accepted 24 November 2021; Published 2 February 2022

Copyright © 2022 Weizhang Wang et al. Exclusive Licensee Beijing Institute of Technology Press. Distributed under a Creative

Commons Attribution License (CC BY 4.0).

This paper performs numerical simulation on the decompression process of a Mars rover using FLUENT. The pressure

differential between the inside and outside of the Mars rover resulting from changes in ambient pressure of the rocket fairing

is investigated. In terms of numerical simulation, PROFILE outlet boundary conditions are developed and the impacts of

ambient pressure settings, time steps, and mesh density are investigated to improve the accuracy of simulation results. The

decompression process of the separate large module, large and small modules under two types of ambient pressures are

simulated. The results show that the largest pressure differential between the inside and outside of the module body is less than

2200 Pa. Because of the small size of the small module, the results for the separate large module and the large/small modules

are consistent. The pressure differential between the inside and outside of the rover is mainly influenced by the variation in

ambient pressure.

1. Introduction

In Mars exploration mission, the rover, which contains a

nonsealed module, uses heat sealing for aerodynamic thermal

protection. Nevertheless, it is difficult to conduct quantitative

analysis on the air permeability of the structure of the cabin.

Besides, the pressure-bearing capacity of the cover on the

top of the small end of the rover is limited. In the process of

launch, the ambient pressure in the rocket fairing drops dramatically and the pressure differential between the inside

and outside of the rover might exceed the bearing capacity of

the cover. Therefore, holes are made in the low heat flow area

on the surface of the rover to make sure that the pressure differential between the inside and outside in the launch phase

falls within the range of the bearing capacity of the cover.

The process of decompression in the module can be

reduced to the process of deflation in a container, which is

a complex unsteady-state process of variation in polytropic

indices and heat transfer coefficients. In the deflation process, velocity field, temperature field, and pressure field vary

over time. But on the real-world engineering issues, it is usually simplified as an adiabatic deflation process or isothermal

deflation process [1, 2]. Due to the complexity of the degassing process, a lot of experiments were mostly carried out on

the test bench to obtain systemic degassing characteristics on

different parameters [3]. With an increase in the level of

computer numerical simulation, Computational Fluid

Dynamics (CFD) greatly reduces the amount of experimental work, but some phenomena, such as complex physical

boundaries and the speed of gases reaching the speed of

sound or more in the degassing process, still exist. Therefore,

the calculation of the flow field inevitably involves multidimensional transient flow simulation, complex meshing and

massive amounts of meshes, and other issues [4]. In addition, the degassing performance of the degassing system is

influenced by many factors [5–7], such as the initial pressure

in the container, the length, inner diameter, inner wall

roughness of the tube, the effective bore, the length of the

bore, the inner wall roughness of the bore of the automatic

valve, the possibility of sudden changes to the gas path,

ambient conditions, and state of gas media. Jin et al.

[8–10] of Harbin Institute of Technology carried out

research on the inflation/deflation processes of the empty

container, put forward a method for modeling and determination of heat exchange coefficients based on experimental

and theoretical analysis, verified its accuracy through

AAAS

Space: Science & Technology

Volume 2022, Article ID 9827483, 12 pages

https://doi.org/10.34133/2022/9827483 Fluid and PlasmaDynamics Conference, Seattle,WA,U.S.A,

1978.

[4] L. Suxun, Complex flow dominated by shock waves and boundary layers, Science Press, Beijing, 2007.

[5] H. Pan, “Analysis on thermal environment of interaction

region around protuberance in high speed flows,” Chinese

Journal of Computational Physics, vol. 30, no. 6, pp. 825–832,

2013.

[6] L. Fuqun, “A study on characters of hypersonic multiprotuberance disturber,” Structure & Environment Engineering, vol. 45, no. 1, pp. 12–18, 2018.

[7] M. S. Liou, “A further development of the AUSM+ scheme

towards robust and accurate solutions for all speeds,” in 16th

AIAA Computational Fluid Dynamics Conference, Orlando,

Florida, 2013.

[8] P. A. Gnoffo, R. N. Gupta, and J. LShinn, Conservation equations and physical models for hypersonic air flows in thermal

and chemical non-equilibrium, NASA TP, 1989.

[9] C. Park, J. T. Howe, and R. L. Jaffe,“Review of chemical-kinetic

problems of future NASA missions, II: Mars entries,” Journal

of Thermo-physics and Heat Transfer, vol. 8, no. 1, pp. 9–23,

1994.

[10] M. Wenbo, “A study on the influence of thermodynamic

model on the thermal environment of Mars reentry,” Chinese

Journal of Computational Physics, vol. 32, no. 4, pp. 410–415,

2015.

[11] K. Sutton and R. A. Graves, A general stagnation-point

convective-heating equation for arbitrary gas mixtures, NASA

TR, 1990.

[12] G. V. Candler, “CFD validation for hypersonic flight: hypersonic double-cone flow simulations,” in 40th AIAA Aerospace

Sciences Meeting & Exhibit, Reno,NV,U.S.A, 2002.

8 Space: Science & Technology

&

&

53

Research Article

Numerical Simulation of Decompression Process of a Mars

Rover in the Launch Phase

Weizhang Wang,1 Wei Rao,2 Qi Li,2 Hao Yan,1 and Rui Zhao1

1

School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China

2

Beijing Institute of Spacecraft System Engineering (ISSE), Beijing 100094, China

Correspondence should be addressed to Rui Zhao; zr@bit.edu.cn

Received 29 July 2021; Accepted 24 November 2021; Published 2 February 2022

Copyright © 2022 Weizhang Wang et al. Exclusive Licensee Beijing Institute of Technology Press. Distributed under a Creative

Commons Attribution License (CC BY 4.0).

This paper performs numerical simulation on the decompression process of a Mars rover using FLUENT. The pressure

differential between the inside and outside of the Mars rover resulting from changes in ambient pressure of the rocket fairing

is investigated. In terms of numerical simulation, PROFILE outlet boundary conditions are developed and the impacts of

ambient pressure settings, time steps, and mesh density are investigated to improve the accuracy of simulation results. The

decompression process of the separate large module, large and small modules under two types of ambient pressures are

simulated. The results show that the largest pressure differential between the inside and outside of the module body is less than

2200 Pa. Because of the small size of the small module, the results for the separate large module and the large/small modules

are consistent. The pressure differential between the inside and outside of the rover is mainly influenced by the variation in

ambient pressure.

1. Introduction

In Mars exploration mission, the rover, which contains a

nonsealed module, uses heat sealing for aerodynamic thermal

protection. Nevertheless, it is difficult to conduct quantitative

analysis on the air permeability of the structure of the cabin.

Besides, the pressure-bearing capacity of the cover on the

top of the small end of the rover is limited. In the process of

launch, the ambient pressure in the rocket fairing drops dramatically and the pressure differential between the inside

and outside of the rover might exceed the bearing capacity of

the cover. Therefore, holes are made in the low heat flow area

on the surface of the rover to make sure that the pressure differential between the inside and outside in the launch phase

falls within the range of the bearing capacity of the cover.

The process of decompression in the module can be

reduced to the process of deflation in a container, which is

a complex unsteady-state process of variation in polytropic

indices and heat transfer coefficients. In the deflation process, velocity field, temperature field, and pressure field vary

over time. But on the real-world engineering issues, it is usually simplified as an adiabatic deflation process or isothermal

deflation process [1, 2]. Due to the complexity of the degassing process, a lot of experiments were mostly carried out on

the test bench to obtain systemic degassing characteristics on

different parameters [3]. With an increase in the level of

computer numerical simulation, Computational Fluid

Dynamics (CFD) greatly reduces the amount of experimental work, but some phenomena, such as complex physical

boundaries and the speed of gases reaching the speed of

sound or more in the degassing process, still exist. Therefore,

the calculation of the flow field inevitably involves multidimensional transient flow simulation, complex meshing and

massive amounts of meshes, and other issues [4]. In addition, the degassing performance of the degassing system is

influenced by many factors [5–7], such as the initial pressure

in the container, the length, inner diameter, inner wall

roughness of the tube, the effective bore, the length of the

bore, the inner wall roughness of the bore of the automatic

valve, the possibility of sudden changes to the gas path,

ambient conditions, and state of gas media. Jin et al.

[8–10] of Harbin Institute of Technology carried out

research on the inflation/deflation processes of the empty

container, put forward a method for modeling and determination of heat exchange coefficients based on experimental

and theoretical analysis, verified its accuracy through

AAAS

Space: Science & Technology

Volume 2022, Article ID 9827483, 12 pages

https://doi.org/10.34133/2022/9827483

Numerical Simulation of Decompression Process of a Mars

Rover in the Launch Phase

Weizhang Wang,1

Wei Rao,2

Qi Li,2

Hao Yan,1

and Rui Zhao1

1

School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China

2

Beijing Institute of Spacecraft System Engineering (ISSE), Beijing 100094, China

Correspondence should be addressed to Rui Zhao; zr@bit.edu.cn

Abstract: This paper performs numerical simulation on the decompression process of a Mars rover using FLUENT. The pressure

differential between the inside and outside of the Mars rover resulting from changes in ambient pressure of the rocket fairing is

investigated. In terms of numerical simulation, PROFILE outlet boundary conditions are developed and the impacts of ambient pressure

settings, time steps, and mesh density are investigated to improve the accuracy of simulation results. The decompression process of the

separate large module, large and small modules under two types of ambient pressures are simulated. The results show that the largest

pressure differential between the inside and outside of the module body is less than 2200 Pa. Because of the small size of the small module,

the results for the separate large module and the large/small modules are consistent. The pressure differential between the inside and

outside of the rover is mainly influenced by the variation in ambient pressure.

Fluid and PlasmaDynamics Conference, Seattle,WA,U.S.A,

1978.

[4] L. Suxun, Complex flow dominated by shock waves and boundary layers, Science Press, Beijing, 2007.

[5] H. Pan, “Analysis on thermal environment of interaction

region around protuberance in high speed flows,” Chinese

Journal of Computational Physics, vol. 30, no. 6, pp. 825–832,

2013.

[6] L. Fuqun, “A study on characters of hypersonic multiprotuberance disturber,” Structure & Environment Engineering, vol. 45, no. 1, pp. 12–18, 2018.

[7] M. S. Liou, “A further development of the AUSM+ scheme

towards robust and accurate solutions for all speeds,” in 16th

AIAA Computational Fluid Dynamics Conference, Orlando,

Florida, 2013.

[8] P. A. Gnoffo, R. N. Gupta, and J. LShinn, Conservation equations and physical models for hypersonic air flows in thermal

and chemical non-equilibrium, NASA TP, 1989.

[9] C. Park, J. T. Howe, and R. L. Jaffe,“Review of chemical-kinetic

problems of future NASA missions, II: Mars entries,” Journal

of Thermo-physics and Heat Transfer, vol. 8, no. 1, pp. 9–23,

1994.

[10] M. Wenbo, “A study on the influence of thermodynamic

model on the thermal environment of Mars reentry,” Chinese

Journal of Computational Physics, vol. 32, no. 4, pp. 410–415,

2015.

[11] K. Sutton and R. A. Graves, A general stagnation-point

convective-heating equation for arbitrary gas mixtures, NASA

TR, 1990.

[12] G. V. Candler, “CFD validation for hypersonic flight: hypersonic double-cone flow simulations,” in 40th AIAA Aerospace

Sciences Meeting & Exhibit, Reno,NV,U.S.A, 2002.

8 Space: Science & Technology

54

experiments, and discussed the heat exchange coefficient on

the state parameters of the system. In addition, Li et al. [2]

calculated the flow field of the aerodynamic inflation/deflation system and presented a calculation method for onedimensional unsteady flow field that takes into account friction and heat transfer. However, in the abovementioned

research, the simulation of the flow field in the deflation process is on pipes and the lumped parameter model used in the

container does not reflect variation in distribution and variation of temperature and speed in the intrinsic deflation process of the container. Li et al. [11] of the China Academy of

Engineering Physics investigated the deflation time it takes

for the deflation system, which consists of a larger container,

multiple segments of slender tubes of different diameters

and lengths, and automatic valves, when reducing the initial

pressure of 0.6 MPa to the residual pressure of 0.001 MPa

through deflation, deduced related calculation formulas,

and proposed that the whole deflation process be divided

into two phases: sonic and subsonic. Li et al. [12] of the

China Academy of Engineering Physics created a formula

for the variation of pressure in the container based on the

opening deflation system for the mechanism design of the

deflation system in low-pressure environments to simplify

the calculation process and shorten the calculation time.

Yang et al. [13] described the process of constant volume

inflation and deflation of high-pressure gases by creating

mathematical equations. The results show that the inflation

The small module

Vulnerability hatch

The large module

(a) The small/large module position diagram (b) Appearance of the non-sealed module

Figure 1: Model outline diagram.

0 20 40 60

Time (s)

(a) Condition 1 of pressure drop

80 100 120

0

20000

40000

60000

P (Pa)

80000

100000

120000

The upper limit of internal pressure

The lower limit of internal pressure

(b) Condition 2 of pressure drop

0 20 40 60

Time (s)

80 100 120

0

20000

40000

60000

P (Pa)

80000

100000

120000

Figure 2: Conditions of pressure drop.

Figure 3: Topology of the meshes.

2 Space: Science & Technology

and deflation process of gases matches with the results of the

ideal gas model. Huang et al. [14] investigated the regulation

characteristics of annular-slit pressure-regulating valves.

Results show that the annular-slit pressure-regulating valve

can better meet the requirements of pressure regulation of

transient wind tunnels. Kuptsov et al. [15] described the

parameters and conditions of vertical exhaust in the critical

and subcritical states and put forward two methods for calculating the draining time of the container.

This paper simulates the decompression process of the

Mars rover in the taking-off stage by means of numerical

simulation. The effects of environmental pressure setting,

time step, and mesh density on simulation results are studied to improve the accuracy of calculation results. The laws

of variation in the pressure differential between the inside

and outside of the module resulting from changes in the

ambient pressure in the rocket fairing are studied.

2. Model Design

The subject of research in this paper is a nonsealed module.

It has a maximum volume of less than 12 m3

, a maximum

outer diameter of 3401 mm, and a height of 2608 mm. The

cover is on the top of the module, and the opening is located

in the low heat flow area on the leeward surface of the module, with a diameter of 130 mm. The diameter of the opening

between the large module and the small module is 35 mm.

The cable that passes through the small opening is 20 mm.

This structure is simplified, with only the bodies of the

large/small modules, small holes between modules, cables,

openings on the large module, and baffles remained, as

shown in Figure 1.

By taking the inner pressure design belt of the fairing as

a condition of pressure drop in the environment outside of

the module, the conditions of pressure drop corresponding

to two operating conditions for the research in this paper

are shown in Figures 2(a) and 2(b), respectively.

3. Numerical Methods and Verification

3.1. Computational Meshes and Generation Methods. Mesh

generation techniques are an important part of CFD. Commercial software POINTWISE was used to generate fullstructure meshes, and the number of meshes is about 1.45

million. The computational domain consists of three parts:

large module body, small module body, and radiant outer

domain. To ensure the accuracy of the results, a radiant

outer domain along the direction of openings is added on

the outside of the opening of the large module and the

boundary of the outer domain serves as the pressure

Figure 4: Wall surface meshes of the large module.

Figure 5: Wall surface meshes of the small module.

Figure 6: Wall surface meshes of the small hole, intermediate

cable, and surrounding.

Space: Science & Technology 3

55

experiments, and discussed the heat exchange coefficient on

the state parameters of the system. In addition, Li et al. [2]

calculated the flow field of the aerodynamic inflation/deflation system and presented a calculation method for onedimensional unsteady flow field that takes into account friction and heat transfer. However, in the abovementioned

research, the simulation of the flow field in the deflation process is on pipes and the lumped parameter model used in the

container does not reflect variation in distribution and variation of temperature and speed in the intrinsic deflation process of the container. Li et al. [11] of the China Academy of

Engineering Physics investigated the deflation time it takes

for the deflation system, which consists of a larger container,

multiple segments of slender tubes of different diameters

and lengths, and automatic valves, when reducing the initial

pressure of 0.6 MPa to the residual pressure of 0.001 MPa

through deflation, deduced related calculation formulas,

and proposed that the whole deflation process be divided

into two phases: sonic and subsonic. Li et al. [12] of the

China Academy of Engineering Physics created a formula

for the variation of pressure in the container based on the

opening deflation system for the mechanism design of the

deflation system in low-pressure environments to simplify

the calculation process and shorten the calculation time.

Yang et al. [13] described the process of constant volume

inflation and deflation of high-pressure gases by creating

mathematical equations. The results show that the inflation

The small module

Vulnerability hatch

The large module

(a) The small/large module position diagram (b) Appearance of the non-sealed module

Figure 1: Model outline diagram.

0 20 40 60

Time (s)

(a) Condition 1 of pressure drop

80 100 120

0

20000

40000

60000

P (Pa)

80000

100000

120000

The upper limit of internal pressure

The lower limit of internal pressure

(b) Condition 2 of pressure drop

0 20 40 60

Time (s)

80 100 120

0

20000

40000

60000

P (Pa)

80000

100000

120000

Figure 2: Conditions of pressure drop.

Figure 3: Topology of the meshes.

2 Space: Science & Technology

and deflation process of gases matches with the results of the

ideal gas model. Huang et al. [14] investigated the regulation

characteristics of annular-slit pressure-regulating valves.

Results show that the annular-slit pressure-regulating valve

can better meet the requirements of pressure regulation of

transient wind tunnels. Kuptsov et al. [15] described the

parameters and conditions of vertical exhaust in the critical

and subcritical states and put forward two methods for calculating the draining time of the container.

This paper simulates the decompression process of the

Mars rover in the taking-off stage by means of numerical

simulation. The effects of environmental pressure setting,

time step, and mesh density on simulation results are studied to improve the accuracy of calculation results. The laws

of variation in the pressure differential between the inside

and outside of the module resulting from changes in the

ambient pressure in the rocket fairing are studied.

2. Model Design

The subject of research in this paper is a nonsealed module.

It has a maximum volume of less than 12 m3

, a maximum

outer diameter of 3401 mm, and a height of 2608 mm. The

cover is on the top of the module, and the opening is located

in the low heat flow area on the leeward surface of the module, with a diameter of 130 mm. The diameter of the opening

between the large module and the small module is 35 mm.

The cable that passes through the small opening is 20 mm.

This structure is simplified, with only the bodies of the

large/small modules, small holes between modules, cables,

openings on the large module, and baffles remained, as

shown in Figure 1.

By taking the inner pressure design belt of the fairing as

a condition of pressure drop in the environment outside of

the module, the conditions of pressure drop corresponding

to two operating conditions for the research in this paper

are shown in Figures 2(a) and 2(b), respectively.

3. Numerical Methods and Verification

3.1. Computational Meshes and Generation Methods. Mesh

generation techniques are an important part of CFD. Commercial software POINTWISE was used to generate fullstructure meshes, and the number of meshes is about 1.45

million. The computational domain consists of three parts:

large module body, small module body, and radiant outer

domain. To ensure the accuracy of the results, a radiant

outer domain along the direction of openings is added on

the outside of the opening of the large module and the

boundary of the outer domain serves as the pressure

Figure 4: Wall surface meshes of the large module.

Figure 5: Wall surface meshes of the small module.

Figure 6: Wall surface meshes of the small hole, intermediate

cable, and surrounding.

Space: Science & Technology 3

56

boundary condition. Figures 3–6 show the topology of the

entire computational meshes, the wall surface meshes of

the large/small modules, and the wall surface meshes of the

small hole and in its proximity. A fluid domain of a certain

size is provided on the outside of the large hole in the large

module, and the boundary condition is set as pressure outlet

to simulate the ambient pressure outside the module. In the

deflation process, the deflation system is in a sealed environment with stable temperature. Therefore, it is assumed that

the decompression process of the rover researched in this

paper is an isothermal deflation process [11], the wall surface of the module body uses an isothermal wall, and the

temperature of the wall surface is 300 K.

3.2. Verification of Numerical Schemes. The fluid simulation

module FLUENT in the commercial software package

ANSYS is used to perform numerical simulation on the

decompression process of the module. In this decompression process, the velocities in most areas are close to zero.

Therefore, a pressure-based solver is used to solve problems.

In the process of numerical discretization, advection

terms are discretized with a second-order upwind scheme

and least-squares construction based on cells is utilized for

diffusion terms; pressure-velocity coupling is performed

using the SIMPLE algorithm; a second-order implicit

scheme is used in time discretization, and the ideal gas

model and realizable k − ε turbulence model are applied.

There are three main factors that influence the accuracy

of calculations in this paper: ambient pressure boundary settings, time scheme, and computational meshes. In this section, numerical schemes are verified in these three aspects

to ensure the reliability of computation.

3.2.1. Mesh Independence. In this section, mesh independence verification is performed for the meshes of the large

module with the numbers of meshes of 1.18 million, 2.10

million, and 4.03 million, respectively, to research the

impact of the density of computational meshes on the

results. The lower limit of internal pressure in condition 1

where the pressure changes dramatically is selected as ambient pressure, and 0.02 s is selected as the maximum time

step.

The curves of variation in the mass and pressure inside

the large module with different numbers of meshes are

shown in Figures 7 and 8. The results suggest that the curves

14

12

10

8

m (kg)

t (s)

6

4

2

20 40 60 80 100 120

0

0

1.18 million meshes

2.10 million meshes

4.03 million meshes

Figure 7: Curves of variation in the quality inside the large module.

t (s)

0 20 40 60 80 100 120

12 ×104

10

8

p (Pa)

6

4

2

0

1.18 million meshes

ambient pressure

2.10 million meshes

4.03 million meshes

Figure 8: Curves of pressure inside the large module.

1000

800

p (Pa)

t (s)

600

400

200

–200

20 40 60 80 100 120

0

0

1.18 million meshes

2.10 million meshes

4.03 million meshes

Figure 9: Curves of variation in pressure differential between the

inside and outside of the large module.

0 20 40 60 80 100 120

12

×104

10

8

6

4

2

0

Original data

UDF polynomial fitting

Figure 10: Polynomial fitting of ambient pressure.

4 Space: Science & Technology

of variation in the mass and pressure inside the module are

basically consistent despite different densities of meshes.

The curves of variation in pressure differential between

the inside and outside of the module are shown in

Figure 9. The results show that the laws of variation in pressure differential between the inside and outside of the module are basically the same with no obvious difference and

there is only some difference in maximum values. In addition, the laws of variation in pressure differential are not

monotonic with an increase in the density of meshes. When

the number of meshes is 1.18 million, the respective pressure

differential between the inside and the outside is the largest

and the results are relatively conservative and it is also possible to save computational resources.

3.2.2. Ambient Pressure Simulation. It is crucial to simulate

the ambient pressure outside the module. On the one hand,

static pressure needs to be set at the boundary of the outlet

for pressure outlet boundary conditions. The setting of static

pressure is only used in subsonic flow. If the local flow velocity reaches the supersonic speed, the set pressure will no longer be used. Pressure is extrapolated from the inside of the

flow field, and other flow parameters are also extrapolated

from the inside. On the other hand, backflow conditions

need to be defined for pressure outlet boundaries in favor

of convergence calculation.

Change of ambient pressure outside the module is given

in Figure 2 and normally defined using UDF or PROFILE in

FLUENT software in calculation. This paper uses the two

methods, respectively, to fit and compare the ambient pressure outside the module and discusses the results.

First, use a user-defined function (UDF) to define variation in ambient pressure. UDF uses a polynomial to fit the variation characteristics of pressure. As shown in Figure 2(a), the

upper limit of internal pressure for ambient pressure 1 is easier

to fit; as shown in Figure 10, the fitted curves match well with

raw data when using a sixth-order polynomial to do the fittings. However, it can be seen from Figure 2 that there are sudden changes in the lower limit of internal pressure for ambient

pressure 1 and ambient pressure 2, which makes it difficult to

fit the variation characteristics of pressure. Therefore, UDF is

not suitable to simulate the outside complex pressure environment of the Mars rover.

(b) Pressure in the first 5s

×10 ×10 5 4

1234

1.002

1.004

1.006

1.008

1.01

1.012

1.014

P (Pa)

t (s)

(a) Pressure in the first 20s

0 5 10 15 20 25

9.5

9.6

9.7

9.8

9.9

10

10.1

10.2

P (Pa)

t (s)

dt = 0.001s, n = 20

dt = 0.002s, n = 20

dt = 0.005s, n = 20

dt = 0.01s, n = 50

dt = 0.01s, n = 20

dt = 0.05s, n = 50

dt = 0.05s, n = 30

dt = 0.05s, n = 20

dt = 0.1s, n = 50

dt = 0.1s, n = 30

dt = 0.001s, n = 20

dt = 0.002s, n = 20

dt = 0.005s, n = 20

dt = 0.01s, n = 50

dt = 0.01s, n = 20

dt = 0.05s, n = 50

dt = 0.05s, n = 30

dt = 0.05s, n = 20

dt = 0.1s, n = 50

dt = 0.1s, n = 30

Figure 11: Comparison of different time steps and the number of iterations.

Ambient pressure

The large module, dt = 0.01

The large module, dt = 0.02

Bottom wall of the small module, dt = 0.01

Bottom wall of the small module, dt = 0.02

Side wall of the small module, dt = 0.01

Side wall of the small module, dt = 0.02

t (s)

0 20 40 60 80 100 120

12 ×104

10

8

p (Pa)

6

4

2

0

Figure 12: Curves of pressure in the large and small modules.

Space: Science & Technology 5

57

boundary condition. Figures 3–6 show the topology of the

entire computational meshes, the wall surface meshes of

the large/small modules, and the wall surface meshes of the

small hole and in its proximity. A fluid domain of a certain

size is provided on the outside of the large hole in the large

module, and the boundary condition is set as pressure outlet

to simulate the ambient pressure outside the module. In the

deflation process, the deflation system is in a sealed environment with stable temperature. Therefore, it is assumed that

the decompression process of the rover researched in this

paper is an isothermal deflation process [11], the wall surface of the module body uses an isothermal wall, and the

temperature of the wall surface is 300 K.

3.2. Verification of Numerical Schemes. The fluid simulation

module FLUENT in the commercial software package

ANSYS is used to perform numerical simulation on the

decompression process of the module. In this decompression process, the velocities in most areas are close to zero.

Therefore, a pressure-based solver is used to solve problems.

In the process of numerical discretization, advection

terms are discretized with a second-order upwind scheme

and least-squares construction based on cells is utilized for

diffusion terms; pressure-velocity coupling is performed

using the SIMPLE algorithm; a second-order implicit

scheme is used in time discretization, and the ideal gas

model and realizable k − ε turbulence model are applied.

There are three main factors that influence the accuracy

of calculations in this paper: ambient pressure boundary settings, time scheme, and computational meshes. In this section, numerical schemes are verified in these three aspects

to ensure the reliability of computation.

3.2.1. Mesh Independence. In this section, mesh independence verification is performed for the meshes of the large

module with the numbers of meshes of 1.18 million, 2.10

million, and 4.03 million, respectively, to research the

impact of the density of computational meshes on the

results. The lower limit of internal pressure in condition 1

where the pressure changes dramatically is selected as ambient pressure, and 0.02 s is selected as the maximum time

step.

The curves of variation in the mass and pressure inside

the large module with different numbers of meshes are

shown in Figures 7 and 8. The results suggest that the curves

14

12

10

8

m (kg)

t (s)

6

4

2

20 40 60 80 100 120

0

0

1.18 million meshes

2.10 million meshes

4.03 million meshes

Figure 7: Curves of variation in the quality inside the large module.

t (s)

0 20 40 60 80 100 120

12 ×104

10

8

p (Pa)

6

4

2

0

1.18 million meshes

ambient pressure

2.10 million meshes

4.03 million meshes

Figure 8: Curves of pressure inside the large module.

1000

800

p (Pa)

t (s)

600

400

200

–200

20 40 60 80 100 120

0

0

1.18 million meshes

2.10 million meshes

4.03 million meshes

Figure 9: Curves of variation in pressure differential between the

inside and outside of the large module.

0 20 40 60 80 100 120

12

×104

10

8

6

4

2

0

Original data

UDF polynomial fitting

Figure 10: Polynomial fitting of ambient pressure.

4 Space: Science & Technology

of variation in the mass and pressure inside the module are

basically consistent despite different densities of meshes.

The curves of variation in pressure differential between

the inside and outside of the module are shown in

Figure 9. The results show that the laws of variation in pressure differential between the inside and outside of the module are basically the same with no obvious difference and

there is only some difference in maximum values. In addition, the laws of variation in pressure differential are not

monotonic with an increase in the density of meshes. When

the number of meshes is 1.18 million, the respective pressure

differential between the inside and the outside is the largest

and the results are relatively conservative and it is also possible to save computational resources.

3.2.2. Ambient Pressure Simulation. It is crucial to simulate

the ambient pressure outside the module. On the one hand,

static pressure needs to be set at the boundary of the outlet

for pressure outlet boundary conditions. The setting of static

pressure is only used in subsonic flow. If the local flow velocity reaches the supersonic speed, the set pressure will no longer be used. Pressure is extrapolated from the inside of the

flow field, and other flow parameters are also extrapolated

from the inside. On the other hand, backflow conditions

need to be defined for pressure outlet boundaries in favor

of convergence calculation.

Change of ambient pressure outside the module is given

in Figure 2 and normally defined using UDF or PROFILE in

FLUENT software in calculation. This paper uses the two

methods, respectively, to fit and compare the ambient pressure outside the module and discusses the results.

First, use a user-defined function (UDF) to define variation in ambient pressure. UDF uses a polynomial to fit the variation characteristics of pressure. As shown in Figure 2(a), the

upper limit of internal pressure for ambient pressure 1 is easier

to fit; as shown in Figure 10, the fitted curves match well with

raw data when using a sixth-order polynomial to do the fittings. However, it can be seen from Figure 2 that there are sudden changes in the lower limit of internal pressure for ambient

pressure 1 and ambient pressure 2, which makes it difficult to

fit the variation characteristics of pressure. Therefore, UDF is

not suitable to simulate the outside complex pressure environment of the Mars rover.

(b) Pressure in the first 5s

×10 ×10 5 4

1234

1.002

1.004

1.006

1.008

1.01

1.012

1.014

P (Pa)

t (s)

(a) Pressure in the first 20s

0 5 10 15 20 25

9.5

9.6

9.7

9.8

9.9

10

10.1

10.2

P (Pa)

t (s)

dt = 0.001s, n = 20

dt = 0.002s, n = 20

dt = 0.005s, n = 20

dt = 0.01s, n = 50

dt = 0.01s, n = 20

dt = 0.05s, n = 50

dt = 0.05s, n = 30

dt = 0.05s, n = 20

dt = 0.1s, n = 50

dt = 0.1s, n = 30

dt = 0.001s, n = 20

dt = 0.002s, n = 20

dt = 0.005s, n = 20

dt = 0.01s, n = 50

dt = 0.01s, n = 20

dt = 0.05s, n = 50

dt = 0.05s, n = 30

dt = 0.05s, n = 20

dt = 0.1s, n = 50

dt = 0.1s, n = 30

Figure 11: Comparison of different time steps and the number of iterations.

Ambient pressure

The large module, dt = 0.01

The large module, dt = 0.02

Bottom wall of the small module, dt = 0.01

Bottom wall of the small module, dt = 0.02

Side wall of the small module, dt = 0.01

Side wall of the small module, dt = 0.02

t (s)

0 20 40 60 80 100 120

12 ×104

10

8

p (Pa)

6

4

2

0

Figure 12: Curves of pressure in the large and small modules.

Space: Science & Technology 5

58

For PROFILE, the law of variation in ambient pressure

over time is written into a file and settings are made in pressure outlet boundary conditions. In the computation process, the program performs interpolation according to the

data in the file to derive ambient pressure in each time step

and update calculation. Therefore, this paper chooses PROFILE to set ambient pressure boundaries.

3.2.3. Time Step. When performing numerical simulation on

the process of decompression in the module, time step is a

key parameter that influences the accuracy of calculation.

To meet the requirements of accuracy and quickness, the

impact of time step on the results of calculation is explored.

First, create a two-dimensional axisymmetric model for

analysis. The volumes of the large/small modules, the sizes

of the opening between the large/small modules, and the

opening in the large module of this model are approximately

the same as those of the original model. In the computation

process, the initial pressure in the module is set to standard

atmospheric pressure and ambient pressure is defined using

the PROFILE file.

Calculation is carried out with different time steps. The

law of pressure variation in the module is shown in

Figure 11. As shown in Figure 11(a), the pressure drop

curves to which different time steps and the number of iterations correspond are overlapped after the flow state is created and the flow is stable. Therefore, the time steps and

the number of iterations have less influence; however, as

shown in Figure 11(b), the pressure curves which large time

steps correspond fluctuate greatly in the process of creation

of flow state in the initial stage.

Hence, smaller time steps are adopted to accurately simulate variation in velocity and pressure in the process of creation of flow state in the initial stage, with requirements of

accuracy and quickness in mind; with the advancement of

calculation time, time steps are gradually enlarged after the

flow state is created.

Comparative analysis shows that pressure already

changes slowly when the time step is 0.001 s during the creation of flow stage in the initial stage. After the creation of

flow state, it is still necessary to consider quickness and accuracy when choosing the final time step. Therefore, a threet (s)

0 20 40 60 80 100 120

The large module, dt = 0.01

The large module, dt = 0.02

Bottom wall of the small module, dt = 0.01

Bottom wall of the small module, dt = 0.02

Side wall of the small module, dt = 0.01

Side wall of the small module, dt = 0.02

1200

1000

800

p (Pa)600

400

200

–200

0

Figure 13: Curves of pressure differentials between the inside and

outside of the large and small modules.

t (s)

0 20 40 60 80 100 120

14

12

10

8

m (kg)

6

4

2

0

Figure 14: Curve of variation in the mass of air inside the large

module over time.

t (s)

0 20 40 60 80 100 120

12 ×104

10

8

p (Pa)

6

4

2

0

Ambient pressure

Internal pressure

Figure 15: Curves of pressure inside the large module over time.

t (s)

0 20 40 60 80 100 120

0

p (Pa)

600

500

400

300

200

100

–100

Figure 16: Curve of variation in pressure differential between the

inside and outside of the wall of the large module over time.

6 Space: Science & Technology

dimensional computational model for the large/small modules

is created and the final time steps of 0.01 s and 0.02 s are chosen. The ambient pressure is the lower limit of internal pressure in condition 1, and numerical simulation is performed

on variation of pressure inside the large/small modules.

The curves of variations in the ambient pressure and the

pressure in the wall surface of the large module and the bottom surface and the sidewall surface of the small module are

shown in Figure 12. The results show that pressure in the

large/small modules declines as the ambient pressure drops;

there is no significant difference of pressure in the large/

small modules when adopting different time steps.

The curves of pressure difference between the pressure in

the large/small modules and the ambient pressure are shown

in Figure 13. The results show that the differences between

the intensities of pressure in the bottom and side of the

large/small modules and the ambient pressure are almost

consistent when the maximum time steps are the same; the

differences between the intensities of pressure in various

modules and the ambient pressure are comparatively consistent initially (0-30 s) when the maximum time steps are different; the gap between the pressure differentials for various

modules to which different time steps correspond increases

gradually when the ambient pressure decreases more

quickly; the pressure differentials for various modules to

which different maximum time steps correspond tend to

be the same as the ambient pressure drops more slowly.

In summary, when the maximum time step selected is

larger, the value of the difference between the intensities of

pressure in various modules and the ambient pressure is relatively big and the results are more conservative. Therefore,

we choose 0.02 s as maximum time step to meet the requirements of quickness and accuracy.

4. Computational Results and Analysis

Simulate the process of decompression in the module. First,

simulate the decompression in the separate large module

and analyze the variation characteristics of pressure in the

large module when the ambient pressure is the upper and

lower limits of internal pressure in condition 1; then, simultaneously considering the impact of the large/small modules,

simulate the actual deflation process of the large/small modules and analyze the variation characteristics of pressure

inside the large/small modules when the ambient pressure

is the upper and lower limits of internal pressure in conditions 1 and 2.

4.1. Computation for the Separate Large Module

4.1.1. The Upper Limit of Internal Pressure in Pressure Drop

Condition 1 Is Selected as Ambient Pressure. When the upper

limit of internal pressure in condition 1 is selected as

t (s)

0 20 40 60 80 100 120

14

12

10

8

m (kg)

6

4

2

0

Figure 17: Curve of variation in the mass of air inside the large

module over time.

t (s)

0 20 40 60 80 100 120

12 ×104

10

8

p (Pa)

6

4

2

0

Ambient pressure

Internal pressure

Figure 18: Curves of pressure in the large module over time.

t (s)

0 20 40 60 80 100 120

0

p (Pa)

1200

1000

800

600

400

200

–200

Figure 19: Curve of variation in pressure differential between the

inside and outside of the large module over time.

Velocity

5.0

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Figure 20: Velocity contour in the center section of the large and

small modules at t = 18 s.

Space: Science & Technology 7

59

For PROFILE, the law of variation in ambient pressure

over time is written into a file and settings are made in pressure outlet boundary conditions. In the computation process, the program performs interpolation according to the

data in the file to derive ambient pressure in each time step

and update calculation. Therefore, this paper chooses PROFILE to set ambient pressure boundaries.

3.2.3. Time Step. When performing numerical simulation on

the process of decompression in the module, time step is a

key parameter that influences the accuracy of calculation.

To meet the requirements of accuracy and quickness, the

impact of time step on the results of calculation is explored.

First, create a two-dimensional axisymmetric model for

analysis. The volumes of the large/small modules, the sizes

of the opening between the large/small modules, and the

opening in the large module of this model are approximately

the same as those of the original model. In the computation

process, the initial pressure in the module is set to standard

atmospheric pressure and ambient pressure is defined using

the PROFILE file.

Calculation is carried out with different time steps. The

law of pressure variation in the module is shown in

Figure 11. As shown in Figure 11(a), the pressure drop

curves to which different time steps and the number of iterations correspond are overlapped after the flow state is created and the flow is stable. Therefore, the time steps and

the number of iterations have less influence; however, as

shown in Figure 11(b), the pressure curves which large time

steps correspond fluctuate greatly in the process of creation

of flow state in the initial stage.

Hence, smaller time steps are adopted to accurately simulate variation in velocity and pressure in the process of creation of flow state in the initial stage, with requirements of

accuracy and quickness in mind; with the advancement of

calculation time, time steps are gradually enlarged after the

flow state is created.

Comparative analysis shows that pressure already

changes slowly when the time step is 0.001 s during the creation of flow stage in the initial stage. After the creation of

flow state, it is still necessary to consider quickness and accuracy when choosing the final time step. Therefore, a threet (s)

0 20 40 60 80 100 120

The large module, dt = 0.01

The large module, dt = 0.02

Bottom wall of the small module, dt = 0.01

Bottom wall of the small module, dt = 0.02

Side wall of the small module, dt = 0.01

Side wall of the small module, dt = 0.02

1200

1000

800

p (Pa)600

400

200

–200

0

Figure 13: Curves of pressure differentials between the inside and

outside of the large and small modules.

t (s)

0 20 40 60 80 100 120

14

12

10

8

m (kg)

6

4

2

0

Figure 14: Curve of variation in the mass of air inside the large

module over time.

t (s)

0 20 40 60 80 100 120

12 ×104

10

8

p (Pa)

6

4

2

0

Ambient pressure

Internal pressure

Figure 15: Curves of pressure inside the large module over time.

t (s)

0 20 40 60 80 100 120

0

p (Pa)

600

500

400

300

200

100

–100

Figure 16: Curve of variation in pressure differential between the

inside and outside of the wall of the large module over time.

6 Space: Science & Technology

dimensional computational model for the large/small modules

is created and the final time steps of 0.01 s and 0.02 s are chosen. The ambient pressure is the lower limit of internal pressure in condition 1, and numerical simulation is performed

on variation of pressure inside the large/small modules.

The curves of variations in the ambient pressure and the

pressure in the wall surface of the large module and the bottom surface and the sidewall surface of the small module are

shown in Figure 12. The results show that pressure in the

large/small modules declines as the ambient pressure drops;

there is no significant difference of pressure in the large/

small modules when adopting different time steps.

The curves of pressure difference between the pressure in

the large/small modules and the ambient pressure are shown

in Figure 13. The results show that the differences between

the intensities of pressure in the bottom and side of the

large/small modules and the ambient pressure are almost

consistent when the maximum time steps are the same; the

differences between the intensities of pressure in various

modules and the ambient pressure are comparatively consistent initially (0-30 s) when the maximum time steps are different; the gap between the pressure differentials for various

modules to which different time steps correspond increases

gradually when the ambient pressure decreases more

quickly; the pressure differentials for various modules to

which different maximum time steps correspond tend to

be the same as the ambient pressure drops more slowly.

In summary, when the maximum time step selected is

larger, the value of the difference between the intensities of

pressure in various modules and the ambient pressure is relatively big and the results are more conservative. Therefore,

we choose 0.02 s as maximum time step to meet the requirements of quickness and accuracy.

4. Computational Results and Analysis

Simulate the process of decompression in the module. First,

simulate the decompression in the separate large module

and analyze the variation characteristics of pressure in the

large module when the ambient pressure is the upper and

lower limits of internal pressure in condition 1; then, simultaneously considering the impact of the large/small modules,

simulate the actual deflation process of the large/small modules and analyze the variation characteristics of pressure

inside the large/small modules when the ambient pressure

is the upper and lower limits of internal pressure in conditions 1 and 2.

4.1. Computation for the Separate Large Module

4.1.1. The Upper Limit of Internal Pressure in Pressure Drop

Condition 1 Is Selected as Ambient Pressure. When the upper

limit of internal pressure in condition 1 is selected as

t (s)

0 20 40 60 80 100 120

14

12

10

8

m (kg)

6

4

2

0

Figure 17: Curve of variation in the mass of air inside the large

module over time.

t (s)

0 20 40 60 80 100 120

12 ×104

10

8

p (Pa)

6

4

2

0

Ambient pressure

Internal pressure

Figure 18: Curves of pressure in the large module over time.

t (s)

0 20 40 60 80 100 120

0

p (Pa)

1200

1000

800

600

400

200

–200

Figure 19: Curve of variation in pressure differential between the

inside and outside of the large module over time.

Velocity

5.0

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Figure 20: Velocity contour in the center section of the large and

small modules at t = 18 s.

Space: Science & Technology 7

60

ambient pressure for pressure outlet boundary conditions,

the curve of variation in the mass of gas in the large module

over time is shown in Figure 14. The results show that the

gas is gradually expelled from the module and the mass of

gas inside the large module decreases gradually as the ambient pressure declines gradually.

Figure 15 shows the variation curve of wall pressure and

environmental pressure in the large module over time. The

pressure in the cabin decreases with the decrease of environmental pressure.

The curve of variation in the pressure differential

between the inside and outside of the wall of the large module over time is shown in Figure 16. At the initial moment

(t = 0 s), the pressure inside the module is standard atmospheric pressure and differs greatly from ambient pressure,

and in 1 s, the pressure inside the module falls quickly and

the pressure differential declines fast accordingly; subsequently, the environmental pressure gradually decreased,

and the decline rate gradually increased; the cabin wall

inside and outside the pressure difference gradually

increased; at last, ambient pressure drops at a gradually

decreasing speed and the pressure differential between the

inside and outside of the wall surface of the module

decreases gradually and accordingly again. The maximum

value of the pressure differential between the inside and outside of the wall surface of the module is smaller than 600 Pa.

4.1.2. The Lower Limit of Internal Pressure in Condition 1 Is

Selected as Ambient Pressure. When the lower limit of internal pressure in condition 1 is selected as ambient pressure

for pressure outlet boundary conditions, the curve of variation in the mass of gas inside the large module over time is

shown in Figure 17. The gas is gradually expelled from the

module, and the mass of gas inside the large module

decreases gradually as the ambient pressure declines

gradually.

The curves of pressure in the wall surface of the large

module and the ambient pressure over time are shown in

Figure 18. The pressure inside the module decreases as the

ambient pressure decreases.

Figure 19 shows the curve of variation in the pressure

differential between the inside and outside of the wall of

the large module over time. The results suggest that, at the

initial moment (0-60 s), this curve is similar to the curve of

variation in the pressure differential under the condition in

which the upper limit of internal pressure is selected as

ambient pressure in Section 4.1.1; after 60 s, ambient pressure plunges, leading to a sudden increase in pressure differential between the inside and outside of the module; then, as

the module continued to relieve pressure, the pressure difference gradually decreased. The maximum value of pressure

differential between the inside and outside of the wall of

the module does not exceed 1200 Pa.

4.2. Computation for the Large/Small Modules

4.2.1. The Upper Limit of Internal Pressure in Pressure Drop

Conditions Is Selected as Ambient Pressure. When the upper

limit of internal pressure in condition 1 is selected as ambient pressure for pressure outlet boundary conditions, the

t (s)

0 20 40 60 80 100 120

14

12

10

8

m (kg)

6

4

2

0

Figure 21: Curve of variation in the mass of air in the large

module.

t (s)

0 20 40 60 80 100 120

0.06

0.05

0.04

0.03

m (kg)

0.02

0.01

0

Figure 22: Curve of variation in the mass of air in the small

module.

t (s)

0 20 40 60 80 100 120

12 ×104

10

8

p (Pa)

6

4

2

0

Ambient pressure

The large module

Bottom wall of the small module

Side wall of the small module

Figure 23: Curves of pressure in the wall surfaces of the large/small

modules.

8 Space: Science & Technology

velocity contour in the center section of the large and small

modules at t = 18 s is shown in Figure 20. The results show

that the velocity increases gradually near the pressure relief

hole, and when reaching the exit, the velocity increases

sharply, and the maximum velocity is closed to Ma5, showing the outward jet shape, and then decreases gradually.

Figures 21 and 22 show the curves of variation in the

mass of gases inside the large and small modules. The results

show that the gas is expelled gradually from the module and

the masses of gases inside the large/small modules decrease

gradually as the ambient pressure declines gradually.

The curves of pressure in the inner wall surface of the large

module, the bottom and side of the inner wall of the small module, and the ambient pressure over time are shown in Figure 23.

It can be seen that the pressure inside the large/small modules is

consistent and decreases as ambient pressure drops.

The curves of variation in pressure differential between

the inside and outside of the inner wall surface of the large

module and the bottom surface and the sidewall surface of

the small module over time are shown in Figure 24. At the

initial moment (t = 0 s), the pressure inside the module is

standard atmospheric pressure, which has a certain pressure

difference from the ambient pressure; the pressure differential drops quickly as the module is deflated; thereafter, ambient pressure decreases gradually and at a gradually

increasing speed, and the pressure differential between the

inside and outside of the wall surface of the module increases

gradually; over time, ambient pressure goes down at a gradually decreasing speed and the pressure differential between

the inside and outside of the wall surface of the module

declines gradually. The maximum value of the pressure differential between the inside and outside of the wall surface

of the module is about 600 Pa.

4.2.2. The Lower Limit of Internal Pressure in Pressure Drop

Condition 1 Is Selected as Ambient Pressure. When the lower

t (s)

0 20 40 60 80 100 120

The large module

Bottom wall of the small module

Side wall of the small module

0

p (Pa)

600

700

500

400

300

200

100

–100

Figure 24: Curves of variation in pressure differential between the inside and outside of the large and small modules.

t (s)

0 20 40 60 80 100 120

14

12

10

8

m (kg)

6

4

2

0

Figure 25: Curve of variation in the mass of air in the large

module.

t (s)

0 20 40 60 80 100 120

0.06

0.05

0.04

0.03

m (kg)

0.02

0.01

0

Figure 26: Curve of variation in the mass of air in the small

module.

Space: Science & Technology 9

61

ambient pressure for pressure outlet boundary conditions,

the curve of variation in the mass of gas in the large module

over time is shown in Figure 14. The results show that the

gas is gradually expelled from the module and the mass of

gas inside the large module decreases gradually as the ambient pressure declines gradually.

Figure 15 shows the variation curve of wall pressure and

environmental pressure in the large module over time. The

pressure in the cabin decreases with the decrease of environmental pressure.

The curve of variation in the pressure differential

between the inside and outside of the wall of the large module over time is shown in Figure 16. At the initial moment

(t = 0 s), the pressure inside the module is standard atmospheric pressure and differs greatly from ambient pressure,

and in 1 s, the pressure inside the module falls quickly and

the pressure differential declines fast accordingly; subsequently, the environmental pressure gradually decreased,

and the decline rate gradually increased; the cabin wall

inside and outside the pressure difference gradually

increased; at last, ambient pressure drops at a gradually

decreasing speed and the pressure differential between the

inside and outside of the wall surface of the module

decreases gradually and accordingly again. The maximum

value of the pressure differential between the inside and outside of the wall surface of the module is smaller than 600 Pa.

4.1.2. The Lower Limit of Internal Pressure in Condition 1 Is

Selected as Ambient Pressure. When the lower limit of internal pressure in condition 1 is selected as ambient pressure

for pressure outlet boundary conditions, the curve of variation in the mass of gas inside the large module over time is

shown in Figure 17. The gas is gradually expelled from the

module, and the mass of gas inside the large module

decreases gradually as the ambient pressure declines

gradually.

The curves of pressure in the wall surface of the large

module and the ambient pressure over time are shown in

Figure 18. The pressure inside the module decreases as the

ambient pressure decreases.

Figure 19 shows the curve of variation in the pressure

differential between the inside and outside of the wall of

the large module over time. The results suggest that, at the

initial moment (0-60 s), this curve is similar to the curve of

variation in the pressure differential under the condition in

which the upper limit of internal pressure is selected as

ambient pressure in Section 4.1.1; after 60 s, ambient pressure plunges, leading to a sudden increase in pressure differential between the inside and outside of the module; then, as

the module continued to relieve pressure, the pressure difference gradually decreased. The maximum value of pressure

differential between the inside and outside of the wall of

the module does not exceed 1200 Pa.

4.2. Computation for the Large/Small Modules

4.2.1. The Upper Limit of Internal Pressure in Pressure Drop

Conditions Is Selected as Ambient Pressure. When the upper

limit of internal pressure in condition 1 is selected as ambient pressure for pressure outlet boundary conditions, the

t (s)

0 20 40 60 80 100 120

14

12

10

8

m (kg)

6

4

2

0

Figure 21: Curve of variation in the mass of air in the large

module.

t (s)

0 20 40 60 80 100 120

0.06

0.05

0.04

0.03

m (kg)

0.02

0.01

0

Figure 22: Curve of variation in the mass of air in the small

module.

t (s)

0 20 40 60 80 100 120

12 ×104

10

8

p (Pa)

6

4

2

0

Ambient pressure

The large module

Bottom wall of the small module

Side wall of the small module

Figure 23: Curves of pressure in the wall surfaces of the large/small

modules.

8 Space: Science & Technology

velocity contour in the center section of the large and small

modules at t = 18 s is shown in Figure 20. The results show

that the velocity increases gradually near the pressure relief

hole, and when reaching the exit, the velocity increases

sharply, and the maximum velocity is closed to Ma5, showing the outward jet shape, and then decreases gradually.

Figures 21 and 22 show the curves of variation in the

mass of gases inside the large and small modules. The results

show that the gas is expelled gradually from the module and

the masses of gases inside the large/small modules decrease

gradually as the ambient pressure declines gradually.

The curves of pressure in the inner wall surface of the large

module, the bottom and side of the inner wall of the small module, and the ambient pressure over time are shown in Figure 23.

It can be seen that the pressure inside the large/small modules is

consistent and decreases as ambient pressure drops.

The curves of variation in pressure differential between

the inside and outside of the inner wall surface of the large

module and the bottom surface and the sidewall surface of

the small module over time are shown in Figure 24. At the

initial moment (t = 0 s), the pressure inside the module is

standard atmospheric pressure, which has a certain pressure

difference from the ambient pressure; the pressure differential drops quickly as the module is deflated; thereafter, ambient pressure decreases gradually and at a gradually

increasing speed, and the pressure differential between the

inside and outside of the wall surface of the module increases

gradually; over time, ambient pressure goes down at a gradually decreasing speed and the pressure differential between

the inside and outside of the wall surface of the module

declines gradually. The maximum value of the pressure differential between the inside and outside of the wall surface

of the module is about 600 Pa.

4.2.2. The Lower Limit of Internal Pressure in Pressure Drop

Condition 1 Is Selected as Ambient Pressure. When the lower

t (s)

0 20 40 60 80 100 120

The large module

Bottom wall of the small module

Side wall of the small module

0

p (Pa)

600

700

500

400

300

200

100

–100

Figure 24: Curves of variation in pressure differential between the inside and outside of the large and small modules.

t (s)

0 20 40 60 80 100 120

14

12

10

8

m (kg)

6

4

2

0

Figure 25: Curve of variation in the mass of air in the large

module.

t (s)

0 20 40 60 80 100 120

0.06

0.05

0.04

0.03

m (kg)

0.02

0.01

0

Figure 26: Curve of variation in the mass of air in the small

module.

Space: Science & Technology 9

62

limit of internal pressure in condition 1 is selected as ambient pressure for pressure outlet boundary conditions, the

curves of variation in the mass of gas inside the large and

small modules are shown in Figures 25 and 26. The results

show that with the decrease of the ambient pressure, the

gas in the module is gradually expelled, and the mass of

the gas in both the large and small modules decreases

gradually.

The curves of pressure in the inner wall surface of the

large module, the bottom surface and the side of the inner

wall of the small module, and the ambient pressure over

time are shown in Figure 27. The pressure inside the large

and small modules declines as ambient pressure drops.

The curves of variation in the pressure differential

between the inside and outside of the inner wall surface of

the large module and the bottom surface and the sidewall

surface of the small module over time are shown in

Figure 28. At the initial moment (0-62 s), the pressure differential between the inside and outside of the wall of the module increases gradually over time; after 62 s, the pressure

differential reaches a brief peak due to an accelerated decline

in ambient pressure; thereafter, the increase in the pressure

differential causes a rise in the speed of decompression, thus

leading to a quick drop in the pressure differential. The maximum value of the pressure differential is less than 1200 Pa.

4.2.3. Pressure Drop Condition 2 Is Selected as Ambient

Pressure. When pressure condition 2 is selected as ambient

pressure in pressure outlet boundary conditions, the curves

of variation in the mass of gas in the large/small modules

are shown in Figures 29 and 30. The results suggest that

the gas is expelled gradually from the module and the masses

of gas inside the large/small modules decline gradually as the

ambient pressure decreases gradually.

The curves of pressure in the inner wall surface of the

large module, the bottom and the side of the inner wall of

the small module, and the ambient pressure over time are

shown in Figure 31. It can be seen that the pressure inside

the large/small modules decreases as ambient pressure goes

down.

t (s)

0 20 40 60 80 100 120

12 ×104

10

8

p (Pa)

6

4

2

0

Ambient pressure

The large module

Bottom wall of the small module

Side wall of the small module

Figure 27: Curves of pressure in the wall surfaces of the large and

small modules.

t (s)

0 20 40 60 80 100 120

0

p (Pa)

1200

1000

800

600

400

200

–200

The large module

Bottom wall of the small module

Side wall of the small module

Figure 28: Curves of variation in pressure differential for the large

and small modules.

t (s)

0 20 40 60 80 100 120

14

12

10

8

m (kg)

6

4

2

0

Figure 29: Curve of variation in the mass of air in the large

module.

t (s)

0 20 40 60 80 100 120

0.06

0.05

0.04

0.03

m (kg)

0.02

0.01

0

Figure 30: Curve of variation in the mass of air in the small

module.

10 Space: Science & Technology

The curves of variation in the pressure differential

between the inside and outside of the inner wall surface of

the large module and the bottom surface and the sidewall

surface of the small module over time are shown in

Figure 32. At the initial moment (t = 0 s), the pressure inside

the module is standard atmospheric pressure, which has a

certain pressure difference from the ambient pressure; the

pressure differential drops quickly as the module is deflated;

thereafter, ambient pressure goes down gradually and at a

gradually increasing speed, and the pressure differential

between the inside and outside of the wall surface of the

module increases gradually and accordingly; over time,

ambient pressure declines at a gradually decreasing speed,

and the pressure differential between the inside and outside

of the wall of the module falls gradually and accordingly.

When t = 65 s, ambient pressure drops dramatically to

6381 Pa in 1 s and the pressure differential between the

inside and outside of the wall surface of the small module

reaches a maximum, at around 2150 Pa.

5. Conclusion

This paper uses FLUENT to perform numerical simulation

on the decompression process of the Mars rover, develops

outlet boundary conditions for PROFILE, and investigates

the impact of ambient pressure settings, time steps, and the

density of meshes on the results of simulation to improve

the accuracy of computational results. The decompression

process of the separate large module and the large/small

modules under the ambient pressure of conditions 1 and 2

is simulated. The results show that when the ambient pressure is the upper limit and lower limit of internal pressure

in condition 1 and condition 2, respectively, the maximum

internal and external pressure difference is less than

600 Pa, 1200 Pa, and 2200 Pa. Due to the small volume of

the small module, the results for the separate large module

and the large/small modules are basically consistent. The

pressure differential between the inside and outside of the

rover is mainly affected by changes in ambient pressure. In

subsequent researches, on the one hand, the area of the

opening should be increased and the following performance

of pressure inside the module be sped up. On the other hand,

the distortion of ambient pressure inside the fairing should

be cut down to further reduce the pressure differential

between the inside and outside of the rover.

Data Availability

The data used to support the findings of this study are

available from the corresponding author upon request.

Conflicts of Interest

All authors declare no possible conflicts of interest.

Authors’ Contributions

Wei Rao, Qi Li, and Rui Zhao participated in the research

design. Weizhang Wang and Rui Zhao performed data analysis. Weizhang Wang and Hao Yan contributed to the writing of the manuscript.

Acknowledgments

The authors would like to acknowledge the support of the

National Natural Science Foundation of China (Grant No.

11902025).

References

[1] J. Yingzi, Z. Zuchao, and Y. Qingjun, “Simplification and

determination of polytropic exponent of THER- modynamic

process in the filling and exhausting process in a pneumaitic

system,” Chinese Journal of Mechanical Engineering, vol. 41,

no. 6, pp. 76–79, 2005.

[2] L. Jun, L. Yujun, and W. Zuwen, “Flow field calculation of

pneumatic charging and discharging system,” Machine Tool

& Hydraulics, vol. 2, pp. 24–26, 1999.

t (s)

0 20 40 60 80 100 120

12 ×104

10

8

p (Pa)

6

4

2

0

Ambient pressure

The large module

Bottom wall of the small module

Side wall of the small module

Figure 31: Curves of pressure in the wall surface of the large and

small modules.

t (s)

0 20 40 60 80 100 120

0

p (Pa)

2500

2000

1500

1000

500

–500

The large module

Bottom wall of the small module

Side wall of the small module

Figure 32: Curves of variation in the pressure differential between

the inside and outside of the large module.

Space: Science & Technology 11

63

limit of internal pressure in condition 1 is selected as ambient pressure for pressure outlet boundary conditions, the

curves of variation in the mass of gas inside the large and

small modules are shown in Figures 25 and 26. The results

show that with the decrease of the ambient pressure, the

gas in the module is gradually expelled, and the mass of

the gas in both the large and small modules decreases

gradually.

The curves of pressure in the inner wall surface of the

large module, the bottom surface and the side of the inner

wall of the small module, and the ambient pressure over

time are shown in Figure 27. The pressure inside the large

and small modules declines as ambient pressure drops.

The curves of variation in the pressure differential

between the inside and outside of the inner wall surface of

the large module and the bottom surface and the sidewall

surface of the small module over time are shown in

Figure 28. At the initial moment (0-62 s), the pressure differential between the inside and outside of the wall of the module increases gradually over time; after 62 s, the pressure

differential reaches a brief peak due to an accelerated decline

in ambient pressure; thereafter, the increase in the pressure

differential causes a rise in the speed of decompression, thus

leading to a quick drop in the pressure differential. The maximum value of the pressure differential is less than 1200 Pa.

4.2.3. Pressure Drop Condition 2 Is Selected as Ambient

Pressure. When pressure condition 2 is selected as ambient

pressure in pressure outlet boundary conditions, the curves

of variation in the mass of gas in the large/small modules

are shown in Figures 29 and 30. The results suggest that

the gas is expelled gradually from the module and the masses

of gas inside the large/small modules decline gradually as the

ambient pressure decreases gradually.

The curves of pressure in the inner wall surface of the

large module, the bottom and the side of the inner wall of

the small module, and the ambient pressure over time are

shown in Figure 31. It can be seen that the pressure inside

the large/small modules decreases as ambient pressure goes

down.

t (s)

0 20 40 60 80 100 120

12 ×104

10

8

p (Pa)

6

4

2

0

Ambient pressure

The large module

Bottom wall of the small module

Side wall of the small module

Figure 27: Curves of pressure in the wall surfaces of the large and

small modules.

t (s)

0 20 40 60 80 100 120

0

p (Pa)

1200

1000

800

600

400

200

–200

The large module

Bottom wall of the small module

Side wall of the small module

Figure 28: Curves of variation in pressure differential for the large

and small modules.

t (s)

0 20 40 60 80 100 120

14

12

10

8

m (kg)

6

4

2

0

Figure 29: Curve of variation in the mass of air in the large

module.

t (s)

0 20 40 60 80 100 120

0.06

0.05

0.04

0.03

m (kg)

0.02

0.01

0

Figure 30: Curve of variation in the mass of air in the small

module.

10 Space: Science & Technology

The curves of variation in the pressure differential

between the inside and outside of the inner wall surface of

the large module and the bottom surface and the sidewall

surface of the small module over time are shown in

Figure 32. At the initial moment (t = 0 s), the pressure inside

the module is standard atmospheric pressure, which has a

certain pressure difference from the ambient pressure; the

pressure differential drops quickly as the module is deflated;

thereafter, ambient pressure goes down gradually and at a

gradually increasing speed, and the pressure differential

between the inside and outside of the wall surface of the

module increases gradually and accordingly; over time,

ambient pressure declines at a gradually decreasing speed,

and the pressure differential between the inside and outside

of the wall of the module falls gradually and accordingly.

When t = 65 s, ambient pressure drops dramatically to

6381 Pa in 1 s and the pressure differential between the

inside and outside of the wall surface of the small module

reaches a maximum, at around 2150 Pa.

5. Conclusion

This paper uses FLUENT to perform numerical simulation

on the decompression process of the Mars rover, develops

outlet boundary conditions for PROFILE, and investigates

the impact of ambient pressure settings, time steps, and the

density of meshes on the results of simulation to improve

the accuracy of computational results. The decompression

process of the separate large module and the large/small

modules under the ambient pressure of conditions 1 and 2

is simulated. The results show that when the ambient pressure is the upper limit and lower limit of internal pressure

in condition 1 and condition 2, respectively, the maximum

internal and external pressure difference is less than

600 Pa, 1200 Pa, and 2200 Pa. Due to the small volume of

the small module, the results for the separate large module

and the large/small modules are basically consistent. The

pressure differential between the inside and outside of the

rover is mainly affected by changes in ambient pressure. In

subsequent researches, on the one hand, the area of the

opening should be increased and the following performance

of pressure inside the module be sped up. On the other hand,

the distortion of ambient pressure inside the fairing should

be cut down to further reduce the pressure differential

between the inside and outside of the rover.

Data Availability

The data used to support the findings of this study are

available from the corresponding author upon request.

Conflicts of Interest

All authors declare no possible conflicts of interest.

Authors’ Contributions

Wei Rao, Qi Li, and Rui Zhao participated in the research

design. Weizhang Wang and Rui Zhao performed data analysis. Weizhang Wang and Hao Yan contributed to the writing of the manuscript.

Acknowledgments

The authors would like to acknowledge the support of the

National Natural Science Foundation of China (Grant No.

11902025).

References

[1] J. Yingzi, Z. Zuchao, and Y. Qingjun, “Simplification and

determination of polytropic exponent of THER- modynamic

process in the filling and exhausting process in a pneumaitic

system,” Chinese Journal of Mechanical Engineering, vol. 41,

no. 6, pp. 76–79, 2005.

[2] L. Jun, L. Yujun, and W. Zuwen, “Flow field calculation of

pneumatic charging and discharging system,” Machine Tool

& Hydraulics, vol. 2, pp. 24–26, 1999.

t (s)

0 20 40 60 80 100 120

12 ×104

10

8

p (Pa)

6

4

2

0

Ambient pressure

The large module

Bottom wall of the small module

Side wall of the small module

Figure 31: Curves of pressure in the wall surface of the large and

small modules.

t (s)

0 20 40 60 80 100 120

0

p (Pa)

2500

2000

1500

1000

500

–500

The large module

Bottom wall of the small module

Side wall of the small module

Figure 32: Curves of variation in the pressure differential between

the inside and outside of the large module.

Space: Science & Technology 11

&

64

Research Article

Ballistic Range Testing Data Analysis of Tianwen-1 Mars

Entry Capsule

Haogong Wei ,

1 Xin Li,2 Jie Huang,2 Qi Li,1 and Wei Rao1

1

Beijing Institute of Spacecraft System Engineering, Beijing, China

2

China Aerodynamics Research and Development Center, Mianyang, Sichuan, China

Correspondence should be addressed to Haogong Wei; weihaogong@aliyun.com

Received 22 July 2021; Accepted 11 November 2021; Published 3 December 2021

Copyright © 2021 Haogong Wei et al. Exclusive Licensee Beijing Institute of Technology Press. Distributed under a Creative

Commons Attribution License (CC BY 4.0).

A typical blunt body such as Tianwen-1 Mars entry capsule suffers dynamic instability in supersonic regime. To investigate the

unstable Mach range of flight and to confirm the design of aerodynamic shape and mass properties, a ballistic range test was

carried out aiming at capturing supersonic dynamic characteristics of Tianwen-1. Aerodynamic coefficients of free-flight scaled

models were derived by modified linear regression method based on position and attitude data, while the dynamic coefficients

were established under the assumption of small angle linearization. The static moment coefficients and dynamic derivatives

were identified thereafter. Results show that models in untrimmed configuration are dynamically unstable at certain Mach

numbers, whereas models in trimmed configuration are dynamically stable at other Mach numbers tested. Both trimmed and

untrimmed configurations are statically stable in all testing cases.

1. Introduction

The Tianwen-1 Mars entry capsule successfully landed on

the surface of Mars in southern Utopia planitia on May

14th, 2021 at 23 : 18 UTC. Launched aboard CZ-5B from

WenChang on July 23th, 2020, the Tianwen-1 Mars exploration mission aims at orbiting, landing, and roving in one

trip. The Tianwen-1 spacecraft was injected into Mars

orbit in February, 2021, and stayed two and a half months

in orbit for optical observations of the landing site before

the final touchdown.

Tianwen-1 was programmed to unfold a trim tab at

Mach 2.8 to trim the angle of attack (AoA) towards 0° before

parachute deployment at Mach 1.8. A free-flight ballistic

range test was conducted in order to obtain the static and

dynamic aerodynamic characteristics of Tianwen-1 in

trimmed and untrimmed configurations under typical

supersonic conditions and to verify the numerical calculation results of supersonic static and dynamic aerodynamic

characteristics of the capsule.

Transonic and supersonic dynamic characteristics of

blunt body entry vehicles are difficult to calculate by numerical methods, since transient and unsteady flow phenomena

such as separation, reattachment, wake, and time-delay are

hard to capture accurately. Therefore, researchers prefer

studying flight dynamics via ground testing methods. There

are three types of tests, i.e., forced oscillation, free oscillation,

and free-flight. Blunt bodies, such as Tianwen-1 Mars entry

capsule itself, are sensitive to disturbances in transonic and

supersonic flows.

It is difficult to capture accurate dynamic characteristics

by forced oscillation tests as this method induces considerable disturbance to the flow field unavoidably. The free oscillation method can only be used to obtain the dynamic

response in a single degree of freedom, which is considered

as a simplified free-flight method. The free-flight method

retains all six degrees of freedom of the model under no

external disturbance after launching, which reflects the real

dynamic characteristics of the model [1].

Chapman et al. studied the limit cycle analysis method of

general blunt bodies, and derived the limit cycle expression

for different cases [2]. Chapman et al. completed the

dynamic stability test of the Stardust sample return capsule

in the Aeroballistic Research Facility at Eglin Air Force Base

(ARFAFB) and obtained the data from Mach 1.2 to 2.8. It is

found that the limit cycle phenomenon is caused by the high

nonlinearity of pitch damping and angle of attack [3].

Cheatwood et al. completed the dynamic stability test of

AAAS

Space: Science & Technology

Volume 2021, Article ID 9830415, 6 pages

[3] C. S. Landram, “Heat transfer during vessel discharge: mean https://doi.org/10.34133/2021/9830415

and fluctuating gas temperature,” Journal of Heat Transfer,

vol. 95, no. 1, pp. 101–106, 1973.

[4] H. Zhanzhong, Z. Futang, and L. Yaofeng, “Numerical simulation of air flow in an engine inlet port,” Vehicle & Power Technology, vol. 2, pp. 49–53, 2001.

[5] Y. Lihong, Y. Qian, and L. Chengliang, “Study on measuring

flow rate characteristics of pneumatic solenoid valves by isothermal chamber discharge,” Mechanical Science and Technology, vol. 20, no. 10, pp. 1170–1172, 2005.

[6] J. C. Harley, Y. Huang, H. H. Bau, and J. N. Zemel,“Gas flow in

micro-channels,” Journal of Fluid Mechanics, vol. 284,

pp. 257–274, 1995.

[7] D. Dongxing, T. Liyan, L. Zhixin, and G. Zengyuan, “Further

research on the resistance characteristics of gas flow in micro

tubes,” Journal of Engineering Thermophysics, vol. 20, no. 5,

pp. 603–607, 1999.

[8] J. Yingzi, Research on Condensation Of Pneumatic System,

[Ph.D. thesis], Harbin Institute of Technology, 1998.

[9] L. Jun, Study on the Internal Condensation of Water Vapor in

Pneumatic System, [Ph.D. thesis], Harbin Institute of Technology, 1999.

[10] J. Yingzi, L. Jun, B. Gang, and W. Zuwen, “Measurement and

influence of propagation coefficient in the charging and releasing process in a pneumaitic system,” Journal of Harbin Institute of Technology, vol. 30, no. 1, pp. 15–19, 1998.

[11] L. Chao, L. Hao, W. Fei, and Y. Xia, “A study of the outgassing

characteristics of a vessel,” Mechanical Science and Technology

for Aerospace Engineering, vol. 1, 2011.

[12] L. Minghai, Z. Liqing, L. Chao, S. Guangmei, and C. Jun,

“Analysis of pressure drop characteristics of deflation system

under low atmospheric pressure environment,” Acta Armamentarii, vol. 28, 2007.

[13] Y. Gang, X. Xiaowei, G. Longlong, and L. Baoren, “Characteristics of isovolumetric charging and releasing of high-pressure

gas,” Journal of Lanzhou University of Technology, vol. 36,

no. 3, pp. 42–46, 2010.

[14] X. Huang Zhilong and Z. G. Dachuan, “Aerodynamic design

and characteristic test of large intermittent wind tunnel control value,” Journal of Experiments in Fluid Mechanics,

vol. 26, no. 6, pp. 87–90, 2012.

[15] A. I. Kuptsov, R. R. Akberov, and F. M. Gimranov, “Calculation of gas parameters at the exit from a gas vent stack by

means of calculating duration of emptying of the processing

equipment,” Contemporary Engineering Sciences, vol. 9,

pp. 103–111, 2016.

12 Space: Science & Technology

&

65

Research Article

Ballistic Range Testing Data Analysis of Tianwen-1 Mars

Entry Capsule

Haogong Wei ,

1 Xin Li,2 Jie Huang,2 Qi Li,1 and Wei Rao1

1

Beijing Institute of Spacecraft System Engineering, Beijing, China

2

China Aerodynamics Research and Development Center, Mianyang, Sichuan, China

Correspondence should be addressed to Haogong Wei; weihaogong@aliyun.com

Received 22 July 2021; Accepted 11 November 2021; Published 3 December 2021

Copyright © 2021 Haogong Wei et al. Exclusive Licensee Beijing Institute of Technology Press. Distributed under a Creative

Commons Attribution License (CC BY 4.0).

A typical blunt body such as Tianwen-1 Mars entry capsule suffers dynamic instability in supersonic regime. To investigate the

unstable Mach range of flight and to confirm the design of aerodynamic shape and mass properties, a ballistic range test was

carried out aiming at capturing supersonic dynamic characteristics of Tianwen-1. Aerodynamic coefficients of free-flight scaled

models were derived by modified linear regression method based on position and attitude data, while the dynamic coefficients

were established under the assumption of small angle linearization. The static moment coefficients and dynamic derivatives

were identified thereafter. Results show that models in untrimmed configuration are dynamically unstable at certain Mach

numbers, whereas models in trimmed configuration are dynamically stable at other Mach numbers tested. Both trimmed and

untrimmed configurations are statically stable in all testing cases.

1. Introduction

The Tianwen-1 Mars entry capsule successfully landed on

the surface of Mars in southern Utopia planitia on May

14th, 2021 at 23 : 18 UTC. Launched aboard CZ-5B from

WenChang on July 23th, 2020, the Tianwen-1 Mars exploration mission aims at orbiting, landing, and roving in one

trip. The Tianwen-1 spacecraft was injected into Mars

orbit in February, 2021, and stayed two and a half months

in orbit for optical observations of the landing site before

the final touchdown.

Tianwen-1 was programmed to unfold a trim tab at

Mach 2.8 to trim the angle of attack (AoA) towards 0° before

parachute deployment at Mach 1.8. A free-flight ballistic

range test was conducted in order to obtain the static and

dynamic aerodynamic characteristics of Tianwen-1 in

trimmed and untrimmed configurations under typical

supersonic conditions and to verify the numerical calculation results of supersonic static and dynamic aerodynamic

characteristics of the capsule.

Transonic and supersonic dynamic characteristics of

blunt body entry vehicles are difficult to calculate by numerical methods, since transient and unsteady flow phenomena

such as separation, reattachment, wake, and time-delay are

hard to capture accurately. Therefore, researchers prefer

studying flight dynamics via ground testing methods. There

are three types of tests, i.e., forced oscillation, free oscillation,

and free-flight. Blunt bodies, such as Tianwen-1 Mars entry

capsule itself, are sensitive to disturbances in transonic and

supersonic flows.

It is difficult to capture accurate dynamic characteristics

by forced oscillation tests as this method induces considerable disturbance to the flow field unavoidably. The free oscillation method can only be used to obtain the dynamic

response in a single degree of freedom, which is considered

as a simplified free-flight method. The free-flight method

retains all six degrees of freedom of the model under no

external disturbance after launching, which reflects the real

dynamic characteristics of the model [1].

Chapman et al. studied the limit cycle analysis method of

general blunt bodies, and derived the limit cycle expression

for different cases [2]. Chapman et al. completed the

dynamic stability test of the Stardust sample return capsule

in the Aeroballistic Research Facility at Eglin Air Force Base

(ARFAFB) and obtained the data from Mach 1.2 to 2.8. It is

found that the limit cycle phenomenon is caused by the high

nonlinearity of pitch damping and angle of attack [3].

Cheatwood et al. completed the dynamic stability test of

AAAS

Space: Science & Technology

Volume 2021, Article ID 9830415, 6 pages

https://doi.org/10.34133/2021/9830415

Ballistic Range Testing Data Analysis of Tianwen-1 Mars

Entry Capsule

Haogong Wei,1

Xin Li,2

Jie Huang,2

Qi Li,1

and Wei Rao1

1

Beijing Institute of Spacecraft System Engineering, Beijing, China

2

China Aerodynamics Research and Development Center, Mianyang, Sichuan, China

Correspondence should be addressed to Haogong Wei; weihaogong@aliyun.com

Abstract: A typical blunt body such as Tianwen-1 Mars entry capsule suffers dynamic instability in supersonic regime. To investigate the

unstable Mach range of flight and to confirm the design of aerodynamic shape and mass properties, a ballistic range test was carried out

aiming at capturing supersonic dynamic characteristics of Tianwen-1. Aerodynamic coefficients of free-flight scaled models were derived

by modified linear regression method based on position and attitude data, while the dynamic coefficients were established under the

assumption of small angle linearization. The static moment coefficients and dynamic derivatives were identified thereafter. Results show

that models in untrimmed configuration are dynamically unstable at certain Mach numbers, whereas models in trimmed configuration are

dynamically stable at other Mach numbers tested. Both trimmed and untrimmed configurations are statically stable in all testing cases.

[3] C. S. Landram, “Heat transfer during vessel discharge: mean

and fluctuating gas temperature,” Journal of Heat Transfer,

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[4] H. Zhanzhong, Z. Futang, and L. Yaofeng, “Numerical simulation of air flow in an engine inlet port,” Vehicle & Power Technology, vol. 2, pp. 49–53, 2001.

[5] Y. Lihong, Y. Qian, and L. Chengliang, “Study on measuring

flow rate characteristics of pneumatic solenoid valves by isothermal chamber discharge,” Mechanical Science and Technology, vol. 20, no. 10, pp. 1170–1172, 2005.

[6] J. C. Harley, Y. Huang, H. H. Bau, and J. N. Zemel,“Gas flow in

micro-channels,” Journal of Fluid Mechanics, vol. 284,

pp. 257–274, 1995.

[7] D. Dongxing, T. Liyan, L. Zhixin, and G. Zengyuan, “Further

research on the resistance characteristics of gas flow in micro

tubes,” Journal of Engineering Thermophysics, vol. 20, no. 5,

pp. 603–607, 1999.

[8] J. Yingzi, Research on Condensation Of Pneumatic System,

[Ph.D. thesis], Harbin Institute of Technology, 1998.

[9] L. Jun, Study on the Internal Condensation of Water Vapor in

Pneumatic System, [Ph.D. thesis], Harbin Institute of Technology, 1999.

[10] J. Yingzi, L. Jun, B. Gang, and W. Zuwen, “Measurement and

influence of propagation coefficient in the charging and releasing process in a pneumaitic system,” Journal of Harbin Institute of Technology, vol. 30, no. 1, pp. 15–19, 1998.

[11] L. Chao, L. Hao, W. Fei, and Y. Xia, “A study of the outgassing

characteristics of a vessel,” Mechanical Science and Technology

for Aerospace Engineering, vol. 1, 2011.

[12] L. Minghai, Z. Liqing, L. Chao, S. Guangmei, and C. Jun,

“Analysis of pressure drop characteristics of deflation system

under low atmospheric pressure environment,” Acta Armamentarii, vol. 28, 2007.

[13] Y. Gang, X. Xiaowei, G. Longlong, and L. Baoren, “Characteristics of isovolumetric charging and releasing of high-pressure

gas,” Journal of Lanzhou University of Technology, vol. 36,

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[15] A. I. Kuptsov, R. R. Akberov, and F. M. Gimranov, “Calculation of gas parameters at the exit from a gas vent stack by

means of calculating duration of emptying of the processing

equipment,” Contemporary Engineering Sciences, vol. 9,

pp. 103–111, 2016.

12 Space: Science & Technology

66

the Genesis sample return capsule at ARF and found that the

shape is dynamically unstable in the range of Mach 1.0 to

4.5, and the angle of attack range of dynamic unstable

expands as Mach number decreasing [4]. Kiritani et al. analyzed the transonic flow field of the Hayabusa sample return

capsule from Mach 0.77 to 1.52 using the ballistic range test

equipment at Tohoku University [5]. Schoenberger et al.

obtained static and dynamic aerodynamic characteristics of

the Mars Pathfinder entry capsule from Mach 1.5 to 3.5 at

ARFAFB [6]. Brown et al. carried out the free-flight ballistic

range test of the Mars Science Laboratory entry capsule [7].

Schoenberger et al. completed the ballistic range test of the

Perseverance Mars entry capsule at the Aberdeen Test Center in Maryland and obtained data in support of the second

generation of Mars Entry Descent and Landing Instrumentation (MEDLI 2) [8]. Murman et al. carried out the forced

oscillation, free oscillation, and free-flight simulation analyses of the general blunt bodies and investigated the nonlinear

coupling characteristics [9]. Song et al. studied the motion

and aerodynamic characteristics of Soyuz-like capsule with

large blunt nose and small lift-drag ratio during free flight

in transonic flow [10].

In this paper, a study in dynamic stability of Tianwen-1

entry capsule is discussed regarding the special application

of a trim table A typical blunt body such as Tianwen-1 Mars

entry capsule suffers dynamic instability in supersonic

regime. To investigate the unstable Mach range of flight

and to confirm the design of aerodynamic shape and mass

properties, a ballistic range test was carried out aiming at

capturing supersonic dynamic characteristics of Tianwen-1.

The position and attitude data was obtained by binocular

vision technique, from which the aerodynamic coefficients

were derived from. Static and dynamic coefficients are established under the assumption of small angle linearization.

The supersonic aerodynamic characteristics of the entry capsule in trimmed and untrimmed configurations are studied

in the end.

2. Test Description

The tests were carried out in the 200 m Free-Flight Ballistic

Range of China Aerodynamics Research and Development

Center. The test medium in the chamber was air. The binocular measurement stations were installed besides the room

along the model flying direction, which would be calibrated

and aligned to the global base reference coordinate system

before the test. There are two configurations of scaled test

models: trimmed (with trim tab deployed) and untrimmed

(with trim tab folded). The reduce frequency of the oscillating model should be consistent with that in actual flight, i.e.,

ϖm = ϖr, where

ω�i = ωi

D

V =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

mα

i ρV2SD

2Ii

s

⋅

D

V =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

− πmα

i ρD5

8Ii

s

, ð1Þ

where ω�i is the reduce frequency, ωi is the original frequency, D is the diameter, V is the velocity, mα

i is static

momentum coefficient, ρ is the density, S = π · ðD/2Þ

2 is the

area, and Ii is the inertia.

The two configurations of the scaled models are shown

in Figure 1. When the flying model with coded marking

points on surface entered the measurement field, it would

be illuminated by the extended laser beam with the pulse

width of smaller than 10 ns; meanwhile, the two images of

the target were obtained by the cameras [11]. Mass properties are shown in Table 1. The ratio of momenta of three

axes is consistent with that of the actual capsule. However,

the nominal mass of these scaled models is designed much

heavier than it should be to retain altitude and to produce

more data in one shot. If a lighter mass is adopted, the model

will lose altitude quickly in flight and thus cannot reach the

end of the testing chamber. Less data will be acquired if

fewer cameras are passed. Small variations due to manufacture could be noticed in mass properties.

Two typical free-flight test cases are shown in Table 2,

with one trimmed and the other not. The test conditions

of the two cases were selected based on nominal trajectory,

namely, HX01 is aiming at Mach 1.5 average and HX02 at

Mach 2.5. The average speed is computed here only for reference purpose. The initial velocity is higher than this average to compensate speed loss due to drag. Density is

determined according to reduce frequency. Pressure is governed by density and temperature. The release angle of

attack is set to 5 degree for an initial turbulence.

3. Methods

The supersonic aerodynamics of the capsule in the free flight

is characterized as follows: the weak nonlinearity of the static

stability derivative coefficient can be identified by an aerodynamic model which is dominated by linear term

ðCmq + Cmα_Þ

0 at small angle of attacks and by nonlinear term

ðCmq + Cmα_Þ

2

α2 at high angle of attacks. The range of angle

of attack oscillation is within ±10° in most cases; thus, the

linearization assumption for small angle of attack is

applicable.

By minimizing the error variance sum of each motion

equation, the corresponding aerodynamic coefficients can

be obtained. The aerodynamic coefficients cannot be measured directly by flight test and need to be calculated according to the acceleration measurements

Cx = max

�qS ,

Cy = may

�qS ,

Cz = maz

�qS ,

ð2Þ

where Cx is the axial force coefficient, Cy is the normal force

coefficient, and Cz is the lateral force coefficient; m is the

mass, ax, ay, and az are accelerations in three axes, �q is the

dynamic pressure, S is the reference area, and l is the reference length. After the sensor error was corrected by the

2 Space: Science & Technology

trajectory reconstruction, the aerodynamic coefficients can

be calculated. The lift coefficient CL and drag coefficient

CD can be converted from the following equations:

CL = Cy cos α − Cx sin α,

CD = Cy sin α + Cx cos α: ð3Þ

Because the products of inertia cannot be measured

directly, the definition of the body axes should be coincide

with the inertial principal axes of the vehicle, so that the

products of inertia are Ixy = Iyz = Izx = 0. The products of

inertia are considered ignorable in engineering practice

and retain sufficient accuracy if the angle between the

body x-axis and the true x-axis of inertia align with Ix is

less than one degree. The total moment coefficients can

be expressed as

Cmx = 1

�qSl Ixω_ x + Iz − Iy

 ωzωy

 ,

Cmy = 1

�qSl Iyω_ y + Ix − Iz ð Þωxωz

 ,

Cmz = 1

�qSl Izω_ z + Iy − Ix

 ωyωx

 ,

ð4Þ

Figure 1: Scaled model of the capsule with coded marking points (left: trimmed; right: untrimmed).

Table 1: Mass properties (partial).

Shot Model Mass

(g)

Diameter

(mm)

Length

(mm)

Roll momentum

(g·cm2

)

Yaw momentum

(g·cm2

)

Pitch momentum

(g·cm2

)

HX01 Trimmed 451.96 100.00 76.66 5009.71 3756.75 4036.43

HX02 Untrimmed 454.90 99.98 76.68 5018.13 3799.07 4002.96

Table 2: Test cases (partial).

Shot Model Mass (g) Average speed (m/s) Pressure (kPa) Temperature (°

C) Mach Release AoA (°

)

HX01 Trimmed 451.96 500 14.940 13.7 1.47 5

HX02 Untrimmed 456.30 848 2.582 25.0 2.45 5

150 200 250 300 350 400 450

−10

−8

−6

−4

−2

0

2

4

6

8

10

Time (ms)

Angle (deg)

??exp

??rgs

??exp

??rgs

Figure 2: Angle of attack and sideslip of the model with trim tab

(Shot HX01).

Space: Science & Technology 3

67

the Genesis sample return capsule at ARF and found that the

shape is dynamically unstable in the range of Mach 1.0 to

4.5, and the angle of attack range of dynamic unstable

expands as Mach number decreasing [4]. Kiritani et al. analyzed the transonic flow field of the Hayabusa sample return

capsule from Mach 0.77 to 1.52 using the ballistic range test

equipment at Tohoku University [5]. Schoenberger et al.

obtained static and dynamic aerodynamic characteristics of

the Mars Pathfinder entry capsule from Mach 1.5 to 3.5 at

ARFAFB [6]. Brown et al. carried out the free-flight ballistic

range test of the Mars Science Laboratory entry capsule [7].

Schoenberger et al. completed the ballistic range test of the

Perseverance Mars entry capsule at the Aberdeen Test Center in Maryland and obtained data in support of the second

generation of Mars Entry Descent and Landing Instrumentation (MEDLI 2) [8]. Murman et al. carried out the forced

oscillation, free oscillation, and free-flight simulation analyses of the general blunt bodies and investigated the nonlinear

coupling characteristics [9]. Song et al. studied the motion

and aerodynamic characteristics of Soyuz-like capsule with

large blunt nose and small lift-drag ratio during free flight

in transonic flow [10].

In this paper, a study in dynamic stability of Tianwen-1

entry capsule is discussed regarding the special application

of a trim table A typical blunt body such as Tianwen-1 Mars

entry capsule suffers dynamic instability in supersonic

regime. To investigate the unstable Mach range of flight

and to confirm the design of aerodynamic shape and mass

properties, a ballistic range test was carried out aiming at

capturing supersonic dynamic characteristics of Tianwen-1.

The position and attitude data was obtained by binocular

vision technique, from which the aerodynamic coefficients

were derived from. Static and dynamic coefficients are established under the assumption of small angle linearization.

The supersonic aerodynamic characteristics of the entry capsule in trimmed and untrimmed configurations are studied

in the end.

2. Test Description

The tests were carried out in the 200 m Free-Flight Ballistic

Range of China Aerodynamics Research and Development

Center. The test medium in the chamber was air. The binocular measurement stations were installed besides the room

along the model flying direction, which would be calibrated

and aligned to the global base reference coordinate system

before the test. There are two configurations of scaled test

models: trimmed (with trim tab deployed) and untrimmed

(with trim tab folded). The reduce frequency of the oscillating model should be consistent with that in actual flight, i.e.,

ϖm = ϖr, where

ω�i = ωi

D

V =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

mα

i ρV2SD

2Ii

s

⋅

D

V =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

− πmα

i ρD5

8Ii

s

, ð1Þ

where ω�i is the reduce frequency, ωi is the original frequency, D is the diameter, V is the velocity, mα

i is static

momentum coefficient, ρ is the density, S = π · ðD/2Þ

2 is the

area, and Ii is the inertia.

The two configurations of the scaled models are shown

in Figure 1. When the flying model with coded marking

points on surface entered the measurement field, it would

be illuminated by the extended laser beam with the pulse

width of smaller than 10 ns; meanwhile, the two images of

the target were obtained by the cameras [11]. Mass properties are shown in Table 1. The ratio of momenta of three

axes is consistent with that of the actual capsule. However,

the nominal mass of these scaled models is designed much

heavier than it should be to retain altitude and to produce

more data in one shot. If a lighter mass is adopted, the model

will lose altitude quickly in flight and thus cannot reach the

end of the testing chamber. Less data will be acquired if

fewer cameras are passed. Small variations due to manufacture could be noticed in mass properties.

Two typical free-flight test cases are shown in Table 2,

with one trimmed and the other not. The test conditions

of the two cases were selected based on nominal trajectory,

namely, HX01 is aiming at Mach 1.5 average and HX02 at

Mach 2.5. The average speed is computed here only for reference purpose. The initial velocity is higher than this average to compensate speed loss due to drag. Density is

determined according to reduce frequency. Pressure is governed by density and temperature. The release angle of

attack is set to 5 degree for an initial turbulence.

3. Methods

The supersonic aerodynamics of the capsule in the free flight

is characterized as follows: the weak nonlinearity of the static

stability derivative coefficient can be identified by an aerodynamic model which is dominated by linear term

ðCmq + Cmα_Þ

0 at small angle of attacks and by nonlinear term

ðCmq + Cmα_Þ

2

α2 at high angle of attacks. The range of angle

of attack oscillation is within ±10° in most cases; thus, the

linearization assumption for small angle of attack is

applicable.

By minimizing the error variance sum of each motion

equation, the corresponding aerodynamic coefficients can

be obtained. The aerodynamic coefficients cannot be measured directly by flight test and need to be calculated according to the acceleration measurements

Cx = max

�qS ,

Cy = may

�qS ,

Cz = maz

�qS ,

ð2Þ

where Cx is the axial force coefficient, Cy is the normal force

coefficient, and Cz is the lateral force coefficient; m is the

mass, ax, ay, and az are accelerations in three axes, �q is the

dynamic pressure, S is the reference area, and l is the reference length. After the sensor error was corrected by the

2 Space: Science & Technology

trajectory reconstruction, the aerodynamic coefficients can

be calculated. The lift coefficient CL and drag coefficient

CD can be converted from the following equations:

CL = Cy cos α − Cx sin α,

CD = Cy sin α + Cx cos α: ð3Þ

Because the products of inertia cannot be measured

directly, the definition of the body axes should be coincide

with the inertial principal axes of the vehicle, so that the

products of inertia are Ixy = Iyz = Izx = 0. The products of

inertia are considered ignorable in engineering practice

and retain sufficient accuracy if the angle between the

body x-axis and the true x-axis of inertia align with Ix is

less than one degree. The total moment coefficients can

be expressed as

Cmx = 1

�qSl Ixω_ x + Iz − Iy

 ωzωy

 ,

Cmy = 1

�qSl Iyω_ y + Ix − Iz ð Þωxωz

 ,

Cmz = 1

�qSl Izω_ z + Iy − Ix

 ωyωx

 ,

ð4Þ

Figure 1: Scaled model of the capsule with coded marking points (left: trimmed; right: untrimmed).

Table 1: Mass properties (partial).

Shot Model Mass

(g)

Diameter

(mm)

Length

(mm)

Roll momentum

(g·cm2

)

Yaw momentum

(g·cm2

)

Pitch momentum

(g·cm2

)

HX01 Trimmed 451.96 100.00 76.66 5009.71 3756.75 4036.43

HX02 Untrimmed 454.90 99.98 76.68 5018.13 3799.07 4002.96

Table 2: Test cases (partial).

Shot Model Mass (g) Average speed (m/s) Pressure (kPa) Temperature (°

C) Mach Release AoA (°

)

HX01 Trimmed 451.96 500 14.940 13.7 1.47 5

HX02 Untrimmed 456.30 848 2.582 25.0 2.45 5

150 200 250 300 350 400 450

−10

−8

−6

−4

−2

0

2

4

6

8

10

Time (ms)

Angle (deg)

??exp

??rgs

??exp

??rgs

Figure 2: Angle of attack and sideslip of the model with trim tab

(Shot HX01).

Space: Science & Technology 3

68

where Cmx is the rolling moment coefficient, Cmy is the

yawing moment coefficient, Cmz is the pitching moment

coefficient, and Ix, Iy, and Iz are the three-axis inertia,

respectively. The aerodynamic moment coefficients cannot

be measured directly and need to be calculated according

to the measured value of the angular velocity.

The aerodynamic model of the vehicle assumes that the

aerodynamic parameters are functions of the flight state

parameters and control inputs. Let the aerodynamic parameters Cx, Cy, Cz, Cmx, Cmy, and Cmz be the aerodynamic

forces and moments on the system axes, respectively, and

let the flight state parameters and control inputs be x =

ðx1, x2, ⋯, xnÞ

T. Taking the aerodynamic moment coefficient Cmz ðtÞ as an example, the general form of the mathematical model of the aerodynamic parameters is as follows,

Cmzð Þt = 〠

N1

i1=0

⋯ 〠

Np

ip=0

Cxπi

k mz Y

p

k=1

x

ik

k ð Þt , ð5Þ

where xk is one of the flight state parameters (k = 1, 2, …, n),

such as α, β, ωz, …, δz, and ik is the power of xk, and Cxπi

k mz is

the derivative of Cmz corresponding to Qp

k=1x

ik

k ðtÞ, where ik

= 0, 1, …, Nk. Usually, each term is the product of 1 to 3

state parameters, and the highest power is thus normally

taken as 3 or 4, except for a few individual terms that can

be selected with higher powers based on a priori knowledge,

theoretical calculations, or ground test results.

The six-degree-of-freedom dynamic equation is linearized in plane, and the force and moment are linearized with

small angle assumption [6].

α€ − ρVS

2m −CLα + Cmq + Cmα_

� � D2

2σ2

� �α_ − ρV2SD

2I

Cmαα = 0,

ð6Þ

where for the coefficient of constant term, the solution of the

above equation is in damped resonant form.

αð Þt = α0e

γt cos ð Þ ωt , ð7Þ

−15 −10 −5 0 5 10 15

1.34

1.36

1.38

1.4

1.42

1.44

1.46

AoA (deg)

CD

−5 0 5 10 15

−0.025

−0.02

−0.015

−0.01

−0.005

0

0.005

0.01

AoA (deg)

CMZ

(a) Drag coefficient (b) Pitching moment

M = 1.5

Figure 3: Static aerodynamic coefficients of free-flight model in trimmed configuration.

Table 3: Static and dynamic moment derivatives of model in

trimmed configuration.

Pitch Yaw

Cα

mz Cωz

mz Cβ

my Cωy

my

-0.113 1.28 -0.092 0.292

120 140 160 180 200 220 240 260 280

−30

−25

−20

−15

−10

−5

0

5

10

15

Time (ms)

Angle (deg)

??exp

??rgs

??exp

??rgs

Figure 4: Results of angle of attack and sideslip of untrimmed

configuration (Shot HX02).

4 Space: Science & Technology

where

γ = ρVS

4m −CLα + Cmq + Cmα_

� � D2

2σ2

� �, ð8Þ

ω =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ρV2SD

2I

Cmα − γ2

r

, ð9Þ

where in equation (6), γ is the damping term and dominated

by ðCmq + Cmα_Þ. When γ is positive (so that ðCmq + Cmα_Þ is

positive), the amplitude increases; when γ is negative, the

amplitude decreases. ω is the frequency term, which is

determined by the square root of the static stability coefficient Cmα.

It is important to extract static coefficients in order to

obtain the dynamic derivative. The lift coefficient can be

expressed by the aerodynamic coefficient as

CL = −CA sin αT + CN cos αT: ð10Þ

The derivative of CL with respect to αT is written as

CLα = −CA cos αT − CN sin αT: ð11Þ

The axial force coefficient and the static stability coefficient are the key parameters to extract the pitching dynamic

derivative in combination with equation (6).

4. Results and Analysis

4.1. Trimmed Configuration. The angle of attack and sideslip

results of shot HX01 (trimmed configuration) are shown in

Figure 2. There are diverge oscillations of angle of attack

and sideslip, indicating that the trimmed configuration is

dynamically unstable in pitch and yaw directions between

Mach 1.2 and 1.6.

The results of drag coefficient and pitch moment curve

of trimmed configuration in shot HX01 are shown in

Figure 3. The maximum drag of Shot HX01, the trimmed

configuration, appears at AoA = 1° ~ 2° Mach 1.5, with the

maximum value of 1.45. According to Figure 3(b), the line

of pitch moment passes zero at AoA = 1°

, suggesting that

there is no pitch moment when AoA = 1°

; hence, the trim

angle of attack is 1°

. Theoretically, both angle of attack of

the maximum drag and zero pitch moment should be 0°

.

This small deviation in trim angle of attack is caused by

two likely reasons. On one hand, the selection of parameters

in Eq. (5) affects the result considerably (the parameters are

selected cautiously and each with evaluations accordingly).

On the other hand, small variations in shape and mass

property of the model might exist after manufacturing

and assembling, which leads to the deviation in trim angle

of attack.

The results of the static and dynamic derivatives of the

aerodynamic moment in pitch and yaw directions of the

model in trimmed configuration are shown in Table 3,

where Cα

mz and Cβ

my represent the static derivatives, and

Cωz

mz and Cωy

my the dynamic derivatives, of the pitch and yaw

moments relative to the angle of attack and sideslip angle,

respectively. It can be seen from Table 3 that the static derivatives are negative in the pitch and yaw directions for the

model in trimmed configuration in shot HX01, whereas

the dynamic derivatives are positive. In summary, the model

in trimmed configuration is statically stable but dynamically

unstable at Mach 1.5.

4.2. Untrimmed Configuration. The results of angle of attack

and sideslip angle of shot HX02 in untrimmed configuration

are shown in Figure 4. It is difficult to evaluate dynamic stability simply from the angular motion history since insufficient period exists during test run.

The drag coefficient and pitch moment curve of the

model in untrimmed configuration in shot HX02 are

shown in Figure 5. The results show that the maximum

axial force on the capsule in untrimmed configuration

appears near Mach 2.5 at around 0° of angle of attack,

and the maximum axial force is 1.47; the pitch moment

0 5 10 15 20

1.34

1.36

1.38

1.4

1.42

1.44

1.46

1.48

AoA (deg)

M = 2.5

−25 −20 −15 −10 −5 0 5 10

−0.03

−0.025

−0.02

−0.015

−0.01

−0.005

0

0.005

0.01

0.015

0.02

AoA (deg)

CMZ

CD

(a) Damping coefficient (b) Pitching moment

Figure 5: Aerodynamic coefficient curve of free flight of the untrimmed configuration.

Space: Science & Technology 5

69

where Cmx is the rolling moment coefficient, Cmy is the

yawing moment coefficient, Cmz is the pitching moment

coefficient, and Ix, Iy, and Iz are the three-axis inertia,

respectively. The aerodynamic moment coefficients cannot

be measured directly and need to be calculated according

to the measured value of the angular velocity.

The aerodynamic model of the vehicle assumes that the

aerodynamic parameters are functions of the flight state

parameters and control inputs. Let the aerodynamic parameters Cx, Cy, Cz, Cmx, Cmy, and Cmz be the aerodynamic

forces and moments on the system axes, respectively, and

let the flight state parameters and control inputs be x =

ðx1, x2, ⋯, xnÞ

T. Taking the aerodynamic moment coefficient Cmz ðtÞ as an example, the general form of the mathematical model of the aerodynamic parameters is as follows,

Cmzð Þt = 〠

N1

i1=0

⋯ 〠

Np

ip=0

Cxπi

k mz

Y

p

k=1

x

ik

k ð Þt , ð5Þ

where xk is one of the flight state parameters (k = 1, 2, …, n),

such as α, β, ωz, …, δz, and ik is the power of xk, and Cxπi

k mz is

the derivative of Cmz corresponding to Qp

k=1x

ik

k ðtÞ, where ik

= 0, 1, …, Nk. Usually, each term is the product of 1 to 3

state parameters, and the highest power is thus normally

taken as 3 or 4, except for a few individual terms that can

be selected with higher powers based on a priori knowledge,

theoretical calculations, or ground test results.

The six-degree-of-freedom dynamic equation is linearized in plane, and the force and moment are linearized with

small angle assumption [6].

α€ − ρVS

2m −CLα + Cmq + Cmα_

� � D2

2σ2

� �

α_ − ρV2SD

2I

Cmαα = 0,

ð6Þ

where for the coefficient of constant term, the solution of the

above equation is in damped resonant form.

αð Þt = α0e

γt cos ð Þ ωt , ð7Þ

−15 −10 −5 0 5 10 15

1.34

1.36

1.38

1.4

1.42

1.44

1.46

AoA (deg)

CD

−5 0 5 10 15

−0.025

−0.02

−0.015

−0.01

−0.005

0

0.005

0.01

AoA (deg)

CMZ

(a) Drag coefficient (b) Pitching moment

M = 1.5

Figure 3: Static aerodynamic coefficients of free-flight model in trimmed configuration.

Table 3: Static and dynamic moment derivatives of model in

trimmed configuration.

Pitch Yaw

Cα

mz Cωz

mz Cβ

my Cωy

my

-0.113 1.28 -0.092 0.292

120 140 160 180 200 220 240 260 280

−30

−25

−20

−15

−10

−5

0

5

10

15

Time (ms)

Angle (deg)

??exp

??rgs

??exp

??rgs

Figure 4: Results of angle of attack and sideslip of untrimmed

configuration (Shot HX02).

4 Space: Science & Technology

where

γ = ρVS

4m −CLα + Cmq + Cmα_

� � D2

2σ2

� �, ð8Þ

ω =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ρV2SD

2I

Cmα − γ2

r

, ð9Þ

where in equation (6), γ is the damping term and dominated

by ðCmq + Cmα_Þ. When γ is positive (so that ðCmq + Cmα_Þ is

positive), the amplitude increases; when γ is negative, the

amplitude decreases. ω is the frequency term, which is

determined by the square root of the static stability coefficient Cmα.

It is important to extract static coefficients in order to

obtain the dynamic derivative. The lift coefficient can be

expressed by the aerodynamic coefficient as

CL = −CA sin αT + CN cos αT: ð10Þ

The derivative of CL with respect to αT is written as

CLα = −CA cos αT − CN sin αT: ð11Þ

The axial force coefficient and the static stability coefficient are the key parameters to extract the pitching dynamic

derivative in combination with equation (6).

4. Results and Analysis

4.1. Trimmed Configuration. The angle of attack and sideslip

results of shot HX01 (trimmed configuration) are shown in

Figure 2. There are diverge oscillations of angle of attack

and sideslip, indicating that the trimmed configuration is

dynamically unstable in pitch and yaw directions between

Mach 1.2 and 1.6.

The results of drag coefficient and pitch moment curve

of trimmed configuration in shot HX01 are shown in

Figure 3. The maximum drag of Shot HX01, the trimmed

configuration, appears at AoA = 1° ~ 2° Mach 1.5, with the

maximum value of 1.45. According to Figure 3(b), the line

of pitch moment passes zero at AoA = 1°

, suggesting that

there is no pitch moment when AoA = 1°

; hence, the trim

angle of attack is 1°

. Theoretically, both angle of attack of

the maximum drag and zero pitch moment should be 0°

.

This small deviation in trim angle of attack is caused by

two likely reasons. On one hand, the selection of parameters

in Eq. (5) affects the result considerably (the parameters are

selected cautiously and each with evaluations accordingly).

On the other hand, small variations in shape and mass

property of the model might exist after manufacturing

and assembling, which leads to the deviation in trim angle

of attack.

The results of the static and dynamic derivatives of the

aerodynamic moment in pitch and yaw directions of the

model in trimmed configuration are shown in Table 3,

where Cα

mz and Cβ

my represent the static derivatives, and

Cωz

mz and Cωy

my the dynamic derivatives, of the pitch and yaw

moments relative to the angle of attack and sideslip angle,

respectively. It can be seen from Table 3 that the static derivatives are negative in the pitch and yaw directions for the

model in trimmed configuration in shot HX01, whereas

the dynamic derivatives are positive. In summary, the model

in trimmed configuration is statically stable but dynamically

unstable at Mach 1.5.

4.2. Untrimmed Configuration. The results of angle of attack

and sideslip angle of shot HX02 in untrimmed configuration

are shown in Figure 4. It is difficult to evaluate dynamic stability simply from the angular motion history since insufficient period exists during test run.

The drag coefficient and pitch moment curve of the

model in untrimmed configuration in shot HX02 are

shown in Figure 5. The results show that the maximum

axial force on the capsule in untrimmed configuration

appears near Mach 2.5 at around 0° of angle of attack,

and the maximum axial force is 1.47; the pitch moment

0 5 10 15 20

1.34

1.36

1.38

1.4

1.42

1.44

1.46

1.48

AoA (deg)

M = 2.5

−25 −20 −15 −10 −5 0 5 10

−0.03

−0.025

−0.02

−0.015

−0.01

−0.005

0

0.005

0.01

0.015

0.02

AoA (deg)

CMZ

CD

(a) Damping coefficient (b) Pitching moment

Figure 5: Aerodynamic coefficient curve of free flight of the untrimmed configuration.

Space: Science & Technology 5

70

passes through zero near -10° of angle of attack; hence, the

trim angle of attack is -10°

.

The results of the aerodynamic moment static and

dynamic derivatives in pitch and yaw directions of the

untrimmed configuration are shown in Table 4, where Cα

mz

and Cβ

my represent the static derivatives of pitch and yaw

moment relative to the angle of attack and sideslip, respectively. The results shows that both static and dynamic derivatives of the untrimmed configuration in shot HX02 are

negative, which indicates that both pitch and yaw directions

of the untrimmed configuration are statically and dynamically stable at Mach 2.45 with small angle of attack.

5. Conclusion

The identification algorithm of the aerodynamic parameters

for the free-flight ballistic range test is established, and the

aerodynamic parameters for the free-flight ballistic range

test results of Tianwen-1 Mars entry capsule are completed.

The static and dynamic aerodynamic characteristics of the

free-flight capsule in both trimmed and untrimmed configurations are acquired under typical supersonic conditions.

Based on analysis of the position and attitude, attitude

oscillation, aerodynamic force, static and dynamic stability

of the capsule, it is demonstrated that the ballistic range test

captures the attitude behaviors and aerodynamic characteristics of Tianwen-1 Mars entry capsule. The results of the

pitch and yaw moment coefficients exhibit the aerodynamic

characteristics of the capsule. The capsule in trimmed configuration is dynamically unstable in the pitch and yaw

directions, whereas the untrimmed configuration is dynamically stable. In both cases, the capsule is statically stable in

pitch and yaw directions.

Data Availability

The experimental data used to support the findings of this

study are available from the corresponding author upon

request.

Conflicts of Interest

The authors declare that there are no conflicts of interest

regarding the publication of this article.

References

[1] D. Bogdanoff, Design guide for aerodynamics testing of earth

and planetary entry vehicles in a ballistic range, 2017, NASA/

TM-2017-219473.

[2] G. Chapman and L. Yates, “Limit Cycle Analysis of Planetary

Probes,” in 37th AIAA Aerospace Sciences Meeting and Exhibit,

Reno, NV, 1999.

[3] G. Chapman, R. Mitcheltree, and W. Hathaway, “Transonic

and low supersonic static and dynamic aerodynamic characteristics of the Stardust sample return capsule,” in 37th Aerospace Sciences Meeting and Exhibit, Reno, NV, 1999.

[4] F. Cheatwood, G. Winchenbach, W. Hathaway, and

G. Chapman, “Dynamic stability testing of the genesis sample

return capsule,” in 38th Aerospace Sciences Meeting and

Exhibit, Reno, NV, 2000.

[5] H. Kiritani, N. Tanaka, K. Ohtani, K. Fujita, and H. Nagai,

“Transonic flow field analysis of a free-flight capsule using ballistic range,” in AIAA Scitech 2020 Forum, Orlando, FL, 2020.

[6] M. Schoenenberger, W. Hathaway, L. Yates, and P. Desai,

“Ballistic Range Testing of the Mars Exploration Rover Entry

Capsule,” in 43rd AIAA Aerospace Sciences Meeting and

Exhibit, Reno, NV, 2005.

[7] J. Brown, L. Yates, D. Bogdanoff, G. Chapman, M. Loomis, and

T. Tam, “Free-flight testing in support of the Mars science laboratory aerodynamics database,” Journal of Spacecraft and

Rockets, vol. 43, no. 2, pp. 293–302, 2006.

[8] M. Schoenenberger, G. Brown, and L. Yates, “Surface pressure

ballistic range test of Mars 2020 capsule in support of

MEDLI2,” in 35th AIAA Applied Aerodynamics Conference,

Denver, Colorado, 2017.

[9] S. Murman and M. Aftosmis, “Dynamic Analysis of

Atmospheric-Entry Probes and Capsules,” in 45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 2007.

[10] W. Song, B. Ai, Z. Jiang, and W. Lu, “Free-flight static and

dynamic aerodynamic characteristics for re-entry capsule at

transonic speed,” Journal of Experiments in Fluid Mechanics,

vol. 33, no. 4, pp. 89–94, 2019.

[11] F. Ke, J. Huang, X. Li et al., “Vision measurement technique of

model position and its widespread application on the ballistic

range,” Measurement, vol. 140, pp. 486–496, 2019.

Table 4: Static and dynamic moment derivatives of the untrimmed

configuration.

Pitch Yaw

Cα

mz Cωz

mz Cβ

my Cωy

my

-0.084 -1.563 -0.083 -1.755

6 Space: Science & Technology

Research Article

Study on Effect of Aerodynamic Configuration on Aerodynamic

Performance of Mars Ascent Vehicles

Qi Li,1 Wu Yuan,2 Rui Zhao,3 and Haogong Wei 1

1

Beijing Institute of Spacecraft System Engineering, CAST, Beijing, China 100094

2

Computer Network Information Center, Chinese Academy of Sciences, Beijing, China 100190

3

School of Aeronautics and Astronautics, Beijing Institute of Technology, Beijing, China 100081

Correspondence should be addressed to Qi Li; qi-ge-ge@163.com

Received 10 August 2021; Accepted 29 November 2021; Published 29 January 2022

Copyright © 2022 Qi Li et al. Exclusive Licensee Beijing Institute of Technology Press. Distributed under a Creative Commons

Attribution License (CC BY 4.0).

The Mars surface take-off and ascent technology is one of the key technologies for realizing the Mars sample return mission.

Different from that on the moon, the gravity acceleration on the surface of Mars is 3.71 m/s2

, so that the gravity loss is larger

than that on the moon; a rarefied atmosphere is found on the surface of Mars, and although it is only about 1% of the Earth’s

atmosphere, its effect on aerodynamic drag in the process of ascent shall also be considered. In this paper, the aerodynamic

performance demand of ascent vehicles is analyzed in light of the mission requirements for take-off and ascent from the

surface of Mars. Based on the results of literature research and supersonic CFD static simulation, the influence of forebody and

afterbody shapes of ascent vehicles on aerodynamic drag and static stability is studied, respectively. The forebody shape of

ascent vehicles with better aerodynamic performance is proposed, and the subsequent improvement direction of aerodynamic

configuration is clarified, providing necessary theoretical and data support for the aerodynamic selection of Mars ascent vehicles.

1. Introduction

According to the white paper, “China’s Space Activities in

2016” [1], the Mars sample return mission represents one

of the main tasks to be implemented in China’s deep space

exploration field in the next 10 years. As the key technologies to be developed for Mars sample return, the design,

analysis, and verification for Mars take-off and ascent can

play a very important support role in the engineering design

and implementation of the rover. Moreover, the shape

design of Mars ascent vehicles (MAV for short) is the key

link of the Mars take-off and ascent technology, which has

an important impact on the design of the power system, attitude control system, structure, and loading system.

In accordance with the published literature, countries all

over the world mainly adopt two routes for the shape design

of Mars ascent vehicles. One is the slender body similar to

the missile/rocket [2–4], and the other is the short blunt

body with a high loading volume ratio [5, 6]. The former

is mainly developed for the solid propulsion system, while

the latter is mainly developed for the liquid propulsion

system.

The thickness of the Martian atmosphere is about

100 km, and the atmospheric density at the same altitude is

only 1%~10% of the earth’s atmosphere [7, 8]. However,

due to the severe quality restriction of the propulsion system, the speed loss of the MAV caused by the atmospheric

resistance of Mars cannot be ignored. To minimize the

velocity loss, save the fuel for the propulsion system, and

improve safety during the ascent, we should strictly constrain and optimize the drag characteristics of the ascent

vehicle.

According to a similar design abroad, the supersonic

region is the region with the largest dynamic pressure and

the most obvious velocity loss of the ascent vehicle during

take-off and ascent from Mars [9]. Tang et al. [10] studied

the influence of different slenderness ratio on MAV resistance characteristics based on the shape of slender body.

Miao et al. [11] studied the resistance variation characteristics of a variety of rotating warheads with different

AAAS

Space: Science & Technology

Volume 2022, Article ID 9790131, 11 pages

https://doi.org/10.34133/2022/9790131

71

passes through zero near -10° of angle of attack; hence, the

trim angle of attack is -10°

.

The results of the aerodynamic moment static and

dynamic derivatives in pitch and yaw directions of the

untrimmed configuration are shown in Table 4, where Cα

mz

and Cβ

my represent the static derivatives of pitch and yaw

moment relative to the angle of attack and sideslip, respectively. The results shows that both static and dynamic derivatives of the untrimmed configuration in shot HX02 are

negative, which indicates that both pitch and yaw directions

of the untrimmed configuration are statically and dynamically stable at Mach 2.45 with small angle of attack.

5. Conclusion

The identification algorithm of the aerodynamic parameters

for the free-flight ballistic range test is established, and the

aerodynamic parameters for the free-flight ballistic range

test results of Tianwen-1 Mars entry capsule are completed.

The static and dynamic aerodynamic characteristics of the

free-flight capsule in both trimmed and untrimmed configurations are acquired under typical supersonic conditions.

Based on analysis of the position and attitude, attitude

oscillation, aerodynamic force, static and dynamic stability

of the capsule, it is demonstrated that the ballistic range test

captures the attitude behaviors and aerodynamic characteristics of Tianwen-1 Mars entry capsule. The results of the

pitch and yaw moment coefficients exhibit the aerodynamic

characteristics of the capsule. The capsule in trimmed configuration is dynamically unstable in the pitch and yaw

directions, whereas the untrimmed configuration is dynamically stable. In both cases, the capsule is statically stable in

pitch and yaw directions.

Data Availability

The experimental data used to support the findings of this

study are available from the corresponding author upon

request.

Conflicts of Interest

The authors declare that there are no conflicts of interest

regarding the publication of this article.

References

[1] D. Bogdanoff, Design guide for aerodynamics testing of earth

and planetary entry vehicles in a ballistic range, 2017, NASA/

TM-2017-219473.

[2] G. Chapman and L. Yates, “Limit Cycle Analysis of Planetary

Probes,” in 37th AIAA Aerospace Sciences Meeting and Exhibit,

Reno, NV, 1999.

[3] G. Chapman, R. Mitcheltree, and W. Hathaway, “Transonic

and low supersonic static and dynamic aerodynamic characteristics of the Stardust sample return capsule,” in 37th Aerospace Sciences Meeting and Exhibit, Reno, NV, 1999.

[4] F. Cheatwood, G. Winchenbach, W. Hathaway, and

G. Chapman, “Dynamic stability testing of the genesis sample

return capsule,” in 38th Aerospace Sciences Meeting and

Exhibit, Reno, NV, 2000.

[5] H. Kiritani, N. Tanaka, K. Ohtani, K. Fujita, and H. Nagai,

“Transonic flow field analysis of a free-flight capsule using ballistic range,” in AIAA Scitech 2020 Forum, Orlando, FL, 2020.

[6] M. Schoenenberger, W. Hathaway, L. Yates, and P. Desai,

“Ballistic Range Testing of the Mars Exploration Rover Entry

Capsule,” in 43rd AIAA Aerospace Sciences Meeting and

Exhibit, Reno, NV, 2005.

[7] J. Brown, L. Yates, D. Bogdanoff, G. Chapman, M. Loomis, and

T. Tam, “Free-flight testing in support of the Mars science laboratory aerodynamics database,” Journal of Spacecraft and

Rockets, vol. 43, no. 2, pp. 293–302, 2006.

[8] M. Schoenenberger, G. Brown, and L. Yates, “Surface pressure

ballistic range test of Mars 2020 capsule in support of

MEDLI2,” in 35th AIAA Applied Aerodynamics Conference,

Denver, Colorado, 2017.

[9] S. Murman and M. Aftosmis, “Dynamic Analysis of

Atmospheric-Entry Probes and Capsules,” in 45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 2007.

[10] W. Song, B. Ai, Z. Jiang, and W. Lu, “Free-flight static and

dynamic aerodynamic characteristics for re-entry capsule at

transonic speed,” Journal of Experiments in Fluid Mechanics,

vol. 33, no. 4, pp. 89–94, 2019.

[11] F. Ke, J. Huang, X. Li et al., “Vision measurement technique of

model position and its widespread application on the ballistic

range,” Measurement, vol. 140, pp. 486–496, 2019.

Table 4: Static and dynamic moment derivatives of the untrimmed

configuration.

Pitch Yaw

Cα

mz Cωz

mz Cβ

my Cωy

my

-0.084 -1.563 -0.083 -1.755

6 Space: Science & Technology

Research Article

Study on Effect of Aerodynamic Configuration on Aerodynamic

Performance of Mars Ascent Vehicles

Qi Li,1 Wu Yuan,2 Rui Zhao,3 and Haogong Wei 1

1

Beijing Institute of Spacecraft System Engineering, CAST, Beijing, China 100094

2

Computer Network Information Center, Chinese Academy of Sciences, Beijing, China 100190

3

School of Aeronautics and Astronautics, Beijing Institute of Technology, Beijing, China 100081

Correspondence should be addressed to Qi Li; qi-ge-ge@163.com

Received 10 August 2021; Accepted 29 November 2021; Published 29 January 2022

Copyright © 2022 Qi Li et al. Exclusive Licensee Beijing Institute of Technology Press. Distributed under a Creative Commons

Attribution License (CC BY 4.0).

The Mars surface take-off and ascent technology is one of the key technologies for realizing the Mars sample return mission.

Different from that on the moon, the gravity acceleration on the surface of Mars is 3.71 m/s2

, so that the gravity loss is larger

than that on the moon; a rarefied atmosphere is found on the surface of Mars, and although it is only about 1% of the Earth’s

atmosphere, its effect on aerodynamic drag in the process of ascent shall also be considered. In this paper, the aerodynamic

performance demand of ascent vehicles is analyzed in light of the mission requirements for take-off and ascent from the

surface of Mars. Based on the results of literature research and supersonic CFD static simulation, the influence of forebody and

afterbody shapes of ascent vehicles on aerodynamic drag and static stability is studied, respectively. The forebody shape of

ascent vehicles with better aerodynamic performance is proposed, and the subsequent improvement direction of aerodynamic

configuration is clarified, providing necessary theoretical and data support for the aerodynamic selection of Mars ascent vehicles.

1. Introduction

According to the white paper, “China’s Space Activities in

2016” [1], the Mars sample return mission represents one

of the main tasks to be implemented in China’s deep space

exploration field in the next 10 years. As the key technologies to be developed for Mars sample return, the design,

analysis, and verification for Mars take-off and ascent can

play a very important support role in the engineering design

and implementation of the rover. Moreover, the shape

design of Mars ascent vehicles (MAV for short) is the key

link of the Mars take-off and ascent technology, which has

an important impact on the design of the power system, attitude control system, structure, and loading system.

In accordance with the published literature, countries all

over the world mainly adopt two routes for the shape design

of Mars ascent vehicles. One is the slender body similar to

the missile/rocket [2–4], and the other is the short blunt

body with a high loading volume ratio [5, 6]. The former

is mainly developed for the solid propulsion system, while

the latter is mainly developed for the liquid propulsion

system.

The thickness of the Martian atmosphere is about

100 km, and the atmospheric density at the same altitude is

only 1%~10% of the earth’s atmosphere [7, 8]. However,

due to the severe quality restriction of the propulsion system, the speed loss of the MAV caused by the atmospheric

resistance of Mars cannot be ignored. To minimize the

velocity loss, save the fuel for the propulsion system, and

improve safety during the ascent, we should strictly constrain and optimize the drag characteristics of the ascent

vehicle.

According to a similar design abroad, the supersonic

region is the region with the largest dynamic pressure and

the most obvious velocity loss of the ascent vehicle during

take-off and ascent from Mars [9]. Tang et al. [10] studied

the influence of different slenderness ratio on MAV resistance characteristics based on the shape of slender body.

Miao et al. [11] studied the resistance variation characteristics of a variety of rotating warheads with different

AAAS

Space: Science & Technology

Volume 2022, Article ID 9790131, 11 pages

https://doi.org/10.34133/2022/9790131

Study on Effect of Aerodynamic Configuration on Aerodynamic

Performance of Mars Ascent Vehicles

Qi Li,1

Wu Yuan,2

Rui Zhao,3

and Haogong Wei1

1

Beijing Institute of Spacecraft System Engineering, CAST, Beijing, China 100094

2

Computer Network Information Center, Chinese Academy of Sciences, Beijing, China 100190

3

School of Aeronautics and Astronautics, Beijing Institute of Technology, Beijing, China 100081

Correspondence should be addressed to Qi Li; qi-ge-ge@163.com

Abstract: The Mars surface take-off and ascent technology is one of the key technologies for realizing the Mars sample return mission.

Different from that on the moon, the gravity acceleration on the surface of Mars is 3.71 m/s2

, so that the gravity loss is larger than that on

the moon; a rarefied atmosphere is found on the surface of Mars, and although it is only about 1% of the Earth’s atmosphere, its effect

on aerodynamic drag in the process of ascent shall also be considered. In this paper, the aerodynamic performance demand of ascent

vehicles is analyzed in light of the mission requirements for take-off and ascent from the surface of Mars. Based on the results of literature

research and supersonic CFD static simulation, the influence of forebody and afterbody shapes of ascent vehicles on aerodynamic drag

and static stability is studied, respectively. The forebody shape of ascent vehicles with better aerodynamic performance is proposed, and

the subsequent improvement direction of aerodynamic configuration is clarified, providing necessary theoretical and data support for the

aerodynamic selection of Mars ascent vehicles.

72

generatrix lines. According to the author’s preliminary

study, it is found that the influence of the forebody generatrix of slender body and short blunt body on the resistance

characteristics is not consistent.

In this paper, the RANS numerical simulation method is

used to calculate and analyze the aerodynamic characteristics of two types of MAV, i.e., slender body and short blunt

cone cylinder. The influence law and efficiency of the change

of forebody generatrix parameters on the aerodynamic performance of different types of Mars risers are explored,

which can provide design basis and data basis for the aerodynamic selection of MAV.

2. Aerodynamic Performance Demands of MAV

2.1. Drag Performance. The ascent vehicle mainly relies on

the main engine to provide the power, and the velocity loss

caused by aerodynamic drag, gravity, and other factors in the

process of ascent directly affects the design of a propulsion system. In light of the rarefied atmosphere on Mars, the aerodynamic loss on the Mars surface during take-off and ascent is

much smaller than that on the Earth during launch. However,

according to the previous analysis, the velocity loss caused by

aerodynamic drag accounts for 18% of the total velocity loss

for a short blunt ascent vehicle, while it accounts for about

6.67% in the total velocity loss for a slender ascent vehicle,

both of which cannot be ignored. Therefore, the aerodynamic

drag of Mars ascent vehicles still needs to be reduced.

Through the preliminary aerodynamic configuration

design and drag performance budget, the optimization indicators for the drag performance of ascent vehicles are proposed:

(1) When the maximum windward section is taken as

the reference area, the zero-attack-angle drag coefficient of an ascent vehicle with a short blunt body

shall not be higher than 1.02 at Ma2.0 and 0.8 at

Ma4.1, respectively

(2) When the maximum windward section is taken as

the reference area, the zero-attack-angle drag coefficient of an ascent vehicle with a slender body shall

not be higher than 0.9 at Ma2.0 and 0.44 at Ma4.1,

respectively

2.2. Static Stability. For the ascent vehicle with a smalltorque attitude control system, its static stability within the

main flight attitude range is indispensable. If the ascent vehicle is statically unstable in trimmed flight, a little disturbance

such as crosswinds and asymmetric jets will cause the ascent

vehicle to deviate from the designed trimmed attitude and

result in large attitude drift, thereby increasing aerodynamic

drag and inducing large oscillation. The attitude drift caused

by static instability can be resisted only when the thrust of

the attitude control system is large enough, but the large

thrust will also lead to the overall increase in dry weight of

the control system and additional consumption of propellant. Therefore, the ascent vehicle should be capable of static

stability in the atmosphere.

Similar to rockets, missiles, and other flight vehicles, the

static stability of ascent vehicles can be characterized by the

relative position between the center of mass and the center

of pressure on the centroid axis. When the center of pressure

is behind the center of mass, namely, ðXcp‐XcgÞ > 0, the

ascent vehicle will be statically stable; otherwise, it will be

statically unstable; the shorter distance between the center

of pressure and the center of mass indicates the lower static

stability. Generally, ðXcp‐XcgÞ/L characterizes the static stability of flight vehicles, and L is the reference length of a

flight vehicle. According to the design criteria for missiles,

ðXcp‐XcgÞ/L is generally required to be between 0.03 and

0.06 for normal or tailless missiles [12]. If the static stability

is too high, the maneuverability will be poor, and it will be

difficult to adjust the flight trajectory by changing the flight

attitude through the rudder surface or RCS jets; if the static

stability is too small, the antidisturbance ability will be poor,

and additional resources will be required for ensuring the

trimmed flight.

To sum up, the static stability of Mars ascent vehicles can

be achieved by aerodynamic configuration, mass configuration, and the attitude control system by reference to the

design ideas of rockets or missiles.

3. Selection of Shape Parameters of the

Forebody of MAV

During the ascent of an ascent vehicle from the surface of

Mars, its aerodynamic drag mainly comes from shock wave

drag, wall friction drag, and pressure drag and is proportional

to the inflow pressure. The preliminary trajectory analysis

reveals that the maximum dynamic pressure during the ascent

of the vehicle occurs when Ma is between 1.5 and 4.5, which is

the supersonic region. According to the previous research, the

shock wave drag of a flight vehicle in the supersonic region

accounts for more than 70% of the total drag [10]. Therefore,

reducing the shock wave drag of the ascent vehicle is crucial to

the lower energy consumption and system cost.

Since the ascent vehicle mainly flies at a small attack

angle during ascent, its shock wave drag is mainly caused by

the nose shock. Therefore, the supersonic shock wave drag

can be significantly reduced by controlling the forebody shape

of the ascent vehicle and changing the direction of shock force,

and this method has good engineering applicability. For example, in the supersonic aerospace vehicle demonstrator X-51A

launched in 2010, the forebody shape is optimized. The wave

rider configuration is adopted, which ensures that when the

vehicle passes through the air at a hypersonic velocity, the

sharp cone weakens the strength of normal shock wave, and

all the pressure generated by the shock wave system is directly

applied under the body to provide the lift so that the supersonic aerodynamic drag of the vehicle is greatly reduced [13].

With the aerodynamic configuration design of the warhead as a reference, the shape of the warhead is determined

by the generatrix curve type. With the theoretical vertex of

the cone as the coordinate origin, the x-axis is along the symmetry axis of the projectile and points to the bottom of the

projectile, and r is the radius of the revolutionary body. As

for the five common generatrix curve types, namely, spherical-conical, circular arc, parabolic, exponential, and von Karman curves, the equations can be written as follows [13]:

2 Space: Science & Technology

(1) Spherical-conical shape: r = ðRd/LÞx

(2) Circular arc shape: r = ρ½

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1 − ððL − xÞ/RÞ

2

q

− 1� + Rd

(3) Parabolic shape: r = ðRd/LÞð2x − ðx2/LÞÞ

(4) Exponential shape: r = Rdðx/LÞ

n

(5) von Karman curve shape: r = ðRd/ ffiffiffi

π p Þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

φ − ð1/2Þ sin 2φ p , φ = arccos ð1 − 2ðx/LÞÞ

where L is the theoretical length of the curve segment, Rd is

the maximum radius of the curve segment, ρ is the curvature

radius of the arc curve, and n is the exponent of the exponential curve, which can be taken between 0 and 1. When

n = 1, it is a cone.

4. Description and Verification of

the Algorithm

4.1. Algorithm Description. Three-dimensional compressible

viscous gas dynamic equations are used as the governing equations of flow field. The governing equation is expressed as follows:

∂

∂t

ð

Ω

QdV +

ð

∂Ω

F⋅ n̂dS =

ð

∂Ω

G ⋅ n̂dS, ð1Þ

where Ω is the control body, ∂Ω is the control surface, Q is the

conservation variable vector, F is the convection term, and G is

the viscous diffusion term.

Q =

ρ

ρu

ρv

ρw

E

0

BBBBBBBB@

1

CCCCCCCCA

,

F=

ρu

ρu2 + p

ρuv

ρuw

u Eð Þ + p

0

BBBBBBBB@

1

CCCCCCCCA

̂i +

ρv

ρvu

ρv2 + p

ρvw

v Eð Þ + p

0

BBBBBBBB@

1

CCCCCCCCA

̂j +

ρw

ρwu

ρwv

ρw2 + p

w Eð Þ + p

0

BBBBBBBB@

1

CCCCCCCCA

k̂,

G =

0

τxx

τxy

τxz

uτxx + vτxy + wτxz − qx

0

BBBBBBBBBB@

1

CCCCCCCCCCA

� ̂i +

0

τyx

τyy

τyz

uτyx + vτyy + wτyz − qy

0

BBBBBBBBBB@

1

CCCCCCCCCCA

� ̂j +

0

τzx

τzy

τzz

uτzx + vτzy + wτzz − qz

0

BBBBBBBBBB@

1

CCCCCCCCCCA

k̂:

ð2Þ

In the above formula, ρ is the density, p is the pressure, u, v,

and w are velocities in three directions, and E is total energy.

(a) (b)

∅4.500

∅3.001 ∅1.529

0.519

0.579

0.997

2.875

R0.126

Reference Dimensions

Nominal Measured

dref = 4.500 m dref = 4.519 m

Sref = 15.904 m2 Sref = 16.039 m2

Mass: m = 3152.5 kg

R1.125 29° 36.90° 59.73°

65°

20°

∅1.307

∅0.731

Figure 1: Aerodynamic shape and grid diagram of forebody of Mars Laboratory (MSL). (a) Main body dimension parameters of MSL. (b)

Grid representation of forebody.

Table 1: Incoming flow conditions for MSL supersonic

aerodynamic calculation.

M∞ α (

°

) V∞ (m/s) ρ∞ (kg/m3

) T∞ (K) γeff

2.09 0, 6, 11,

16, 20, 24 472 4:634E − 03 190.2 1.24822

Space: Science & Technology 3

73

generatrix lines. According to the author’s preliminary

study, it is found that the influence of the forebody generatrix of slender body and short blunt body on the resistance

characteristics is not consistent.

In this paper, the RANS numerical simulation method is

used to calculate and analyze the aerodynamic characteristics of two types of MAV, i.e., slender body and short blunt

cone cylinder. The influence law and efficiency of the change

of forebody generatrix parameters on the aerodynamic performance of different types of Mars risers are explored,

which can provide design basis and data basis for the aerodynamic selection of MAV.

2. Aerodynamic Performance Demands of MAV

2.1. Drag Performance. The ascent vehicle mainly relies on

the main engine to provide the power, and the velocity loss

caused by aerodynamic drag, gravity, and other factors in the

process of ascent directly affects the design of a propulsion system. In light of the rarefied atmosphere on Mars, the aerodynamic loss on the Mars surface during take-off and ascent is

much smaller than that on the Earth during launch. However,

according to the previous analysis, the velocity loss caused by

aerodynamic drag accounts for 18% of the total velocity loss

for a short blunt ascent vehicle, while it accounts for about

6.67% in the total velocity loss for a slender ascent vehicle,

both of which cannot be ignored. Therefore, the aerodynamic

drag of Mars ascent vehicles still needs to be reduced.

Through the preliminary aerodynamic configuration

design and drag performance budget, the optimization indicators for the drag performance of ascent vehicles are proposed:

(1) When the maximum windward section is taken as

the reference area, the zero-attack-angle drag coefficient of an ascent vehicle with a short blunt body

shall not be higher than 1.02 at Ma2.0 and 0.8 at

Ma4.1, respectively

(2) When the maximum windward section is taken as

the reference area, the zero-attack-angle drag coefficient of an ascent vehicle with a slender body shall

not be higher than 0.9 at Ma2.0 and 0.44 at Ma4.1,

respectively

2.2. Static Stability. For the ascent vehicle with a smalltorque attitude control system, its static stability within the

main flight attitude range is indispensable. If the ascent vehicle is statically unstable in trimmed flight, a little disturbance

such as crosswinds and asymmetric jets will cause the ascent

vehicle to deviate from the designed trimmed attitude and

result in large attitude drift, thereby increasing aerodynamic

drag and inducing large oscillation. The attitude drift caused

by static instability can be resisted only when the thrust of

the attitude control system is large enough, but the large

thrust will also lead to the overall increase in dry weight of

the control system and additional consumption of propellant. Therefore, the ascent vehicle should be capable of static

stability in the atmosphere.

Similar to rockets, missiles, and other flight vehicles, the

static stability of ascent vehicles can be characterized by the

relative position between the center of mass and the center

of pressure on the centroid axis. When the center of pressure

is behind the center of mass, namely, ðXcp‐XcgÞ > 0, the

ascent vehicle will be statically stable; otherwise, it will be

statically unstable; the shorter distance between the center

of pressure and the center of mass indicates the lower static

stability. Generally, ðXcp‐XcgÞ/L characterizes the static stability of flight vehicles, and L is the reference length of a

flight vehicle. According to the design criteria for missiles,

ðXcp‐XcgÞ/L is generally required to be between 0.03 and

0.06 for normal or tailless missiles [12]. If the static stability

is too high, the maneuverability will be poor, and it will be

difficult to adjust the flight trajectory by changing the flight

attitude through the rudder surface or RCS jets; if the static

stability is too small, the antidisturbance ability will be poor,

and additional resources will be required for ensuring the

trimmed flight.

To sum up, the static stability of Mars ascent vehicles can

be achieved by aerodynamic configuration, mass configuration, and the attitude control system by reference to the

design ideas of rockets or missiles.

3. Selection of Shape Parameters of the

Forebody of MAV

During the ascent of an ascent vehicle from the surface of

Mars, its aerodynamic drag mainly comes from shock wave

drag, wall friction drag, and pressure drag and is proportional

to the inflow pressure. The preliminary trajectory analysis

reveals that the maximum dynamic pressure during the ascent

of the vehicle occurs when Ma is between 1.5 and 4.5, which is

the supersonic region. According to the previous research, the

shock wave drag of a flight vehicle in the supersonic region

accounts for more than 70% of the total drag [10]. Therefore,

reducing the shock wave drag of the ascent vehicle is crucial to

the lower energy consumption and system cost.

Since the ascent vehicle mainly flies at a small attack

angle during ascent, its shock wave drag is mainly caused by

the nose shock. Therefore, the supersonic shock wave drag

can be significantly reduced by controlling the forebody shape

of the ascent vehicle and changing the direction of shock force,

and this method has good engineering applicability. For example, in the supersonic aerospace vehicle demonstrator X-51A

launched in 2010, the forebody shape is optimized. The wave

rider configuration is adopted, which ensures that when the

vehicle passes through the air at a hypersonic velocity, the

sharp cone weakens the strength of normal shock wave, and

all the pressure generated by the shock wave system is directly

applied under the body to provide the lift so that the supersonic aerodynamic drag of the vehicle is greatly reduced [13].

With the aerodynamic configuration design of the warhead as a reference, the shape of the warhead is determined

by the generatrix curve type. With the theoretical vertex of

the cone as the coordinate origin, the x-axis is along the symmetry axis of the projectile and points to the bottom of the

projectile, and r is the radius of the revolutionary body. As

for the five common generatrix curve types, namely, spherical-conical, circular arc, parabolic, exponential, and von Karman curves, the equations can be written as follows [13]:

2 Space: Science & Technology

(1) Spherical-conical shape: r = ðRd/LÞx

(2) Circular arc shape: r = ρ½

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1 − ððL − xÞ/RÞ

2

q

− 1� + Rd

(3) Parabolic shape: r = ðRd/LÞð2x − ðx2/LÞÞ

(4) Exponential shape: r = Rdðx/LÞ

n

(5) von Karman curve shape: r = ðRd/ ffiffiffi

π p Þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

φ − ð1/2Þ sin 2φ p , φ = arccos ð1 − 2ðx/LÞÞ

where L is the theoretical length of the curve segment, Rd is

the maximum radius of the curve segment, ρ is the curvature

radius of the arc curve, and n is the exponent of the exponential curve, which can be taken between 0 and 1. When

n = 1, it is a cone.

4. Description and Verification of

the Algorithm

4.1. Algorithm Description. Three-dimensional compressible

viscous gas dynamic equations are used as the governing equations of flow field. The governing equation is expressed as follows:

∂

∂t

ð

Ω

QdV +

ð

∂Ω

F⋅ n̂dS =

ð

∂Ω

G ⋅ n̂dS, ð1Þ

where Ω is the control body, ∂Ω is the control surface, Q is the

conservation variable vector, F is the convection term, and G is

the viscous diffusion term.

Q =

ρ

ρu

ρv

ρw

E

0

BBBBBBBB@

1

CCCCCCCCA

,

F=

ρu

ρu2 + p

ρuv

ρuw

u Eð Þ + p

0

BBBBBBBB@

1

CCCCCCCCA

̂i +

ρv

ρvu

ρv2 + p

ρvw

v Eð Þ + p

0

BBBBBBBB@

1

CCCCCCCCA

̂j +

ρw

ρwu

ρwv

ρw2 + p

w Eð Þ + p

0

BBBBBBBB@

1

CCCCCCCCA

k̂,

G =

0

τxx

τxy

τxz

uτxx + vτxy + wτxz − qx

0

BBBBBBBBBB@

1

CCCCCCCCCCA

� ̂i +

0

τyx

τyy

τyz

uτyx + vτyy + wτyz − qy

0

BBBBBBBBBB@

1

CCCCCCCCCCA

� ̂j +

0

τzx

τzy

τzz

uτzx + vτzy + wτzz − qz

0

BBBBBBBBBB@

1

CCCCCCCCCCA

k̂:

ð2Þ

In the above formula, ρ is the density, p is the pressure, u, v,

and w are velocities in three directions, and E is total energy.

(a) (b)

∅4.500

∅3.001 ∅1.529

0.519

0.579

0.997

2.875

R0.126

Reference Dimensions

Nominal Measured

dref = 4.500 m dref = 4.519 m

Sref = 15.904 m2 Sref = 16.039 m2

Mass: m = 3152.5 kg

R1.125 29° 36.90° 59.73°

65°

20°

∅1.307

∅0.731

Figure 1: Aerodynamic shape and grid diagram of forebody of Mars Laboratory (MSL). (a) Main body dimension parameters of MSL. (b)

Grid representation of forebody.

Table 1: Incoming flow conditions for MSL supersonic

aerodynamic calculation.

M∞ α (

°

) V∞ (m/s) ρ∞ (kg/m3

) T∞ (K) γeff

2.09 0, 6, 11,

16, 20, 24 472 4:634E − 03 190.2 1.24822

Space: Science & Technology 3

74

There are

E = p

γ − 1

+

1

2

ρ u2 + v2 + w2 � �,

τ = μ

2ux uy + vx uz + wx

uy + vx 2vy vz + wy

uz + wx vz + wy 2wz

2

6

6

4

3

7

7

5 − 2

3

μ ux + vy + wz

� �I:

ð3Þ

In this paper, the finite volume method of grid center

based on structural grid was used to solve the above governing equations. Among them, Roe’s FDS scheme [14] was

used to discretize the flow term, and MUSUL interpolation

and Min-mod limiter were used to obtain the second-order

accuracy. Term was iterated in LU-SGS format. The turbulent model of viscous diffusion term adopts an equation

model based on SA [15].

4.2. Verification of an Example. The aerodynamic parameters of windward outsole supersonic in Mars Science Laboratory (MSL for short) [16] are selected as an example in this

paper and compared with the literature data. The geometric

dimensions of MSL are shown in Figure 1(a). Because the

strong expansion of the rear body has a weak influence on

the force coefficient, only the windward outsole is taken for

calculation. Because there is no sideslip in the calculation,

half-mode calculation is adopted. The calculated total grid

number is about 309,000, with 106 points in the normal

direction, and the height of the first layer grid in the normal

direction is 0.15 mm. Figure 1(b) shows the grid distribution

(a) (b)

(c)

Ref

Cal

Ref

Cal

1.4

1.35

Cx

1.3

1.25

1.2

0 5 10 15

α (°)

20 25

Cy

0.06

0.05

0.04

0.03

0.02

0.01

0

0 5 10 15

α (°)

20 25

Ref

Cal

0.06

0.05

0.04

0.03

0.02

0.01

0

Mz

0 5 10 15

α (°)

20 25

Figure 2: Comparison between the calculated data of Mars Laboratory (MSL) aerodynamics and the literature data. (a) Axial force

coefficient. (b) Normal force coefficient. (c) Pitching moment coefficient.

Spherical-conical

Circular arc

Base shape Configuration

constraints

Figure 3: Comparison between the basic configuration and the

improved spherical-conical and circular arc shapes of the slender

ascent vehicle.

4 Space: Science & Technology

of symmetry plane and object plane of the windward outsole

model.

The calculated inflow conditions are shown in Table 1,

in which the local equivalent specific heat ratio of the atmospheric inflow from Mars is obtained by the formula γeff =

ððη + 1Þ/ðη − 1ÞÞ − ð2η/ðη − 1ÞM2

∞Þ [17].

As shown in Figure 2, under the above calculation conditions, the aerodynamic coefficients obtained by the algorithm in this paper are consistent with the trend of

literature results, and the relative deviation is less than 1%.

Therefore, the effectiveness of the aerodynamic algorithm

used in this paper for calculating the aerodynamic characteristics of aircraft in the Martian atmosphere is verified.

5. Calculation Result Analysis

5.1. Influence Analysis of Aerodynamic Performance of

Forebody Configuration of the Slender Ascent Vehicle. As

shown in the figure below Figure 3, the Base shape is drawn

first according to the minimum envelope contour of configuration constraints, in which the forebody is rounded and

the radius of the bulbous is 115 mm. Then, the sphericalconical and circular arc cones are designed, respectively.

The theoretical length of 2.1 m is adopted for these two

shapes; the contour line of the circular arc nose is the arc

from the top of the spherical cone to the end of the third

spherical-conical surface, and the radius is 848.7 mm; the

radius of both spherical-conical and arc noses is 50 mm.

Based on CFD numerical simulation, the axial force

coefficient and pressure center coefficient of the Base shape

and the two improved shapes (namely, spherical-conical

and circular arc noses) at Ma2.0 and Ma4.1 are obtained,

as shown in Figure 4. By comparison, the following conclusions are obtained:

(1) After the Base shape is changed to the sphericalconical or the circular arc nose, the CA decreases

slightly. The drag reduction effects of the two

improved shapes are different at different Ma, but

the difference is subtle in general

(2) The zero-attack-angle CA of the spherical-conical

nose is less than 0.58 at Ma2.0 and less than 0.44 at

(a) (b) Xcp/L

0 5 10 15 20 25 30

alf (°)

0.45

0.5

0.55

Base shape

Spherical-conical nose

Circular arc nose

Ma2.0

Ma4.1

0 5

CA

10 15 20 25 30

alf (°)

0.45

0.5

0.55

0.6

0.65

Base shape

Spherical-conical nose

Circular arc nose

Ma2.0

Ma4.1

Figure 4: Comparison of supersonic aerodynamic characteristic curves between the basic shape and the improved spherical-conical and

circular arc shapes of the slender ascent vehicle. (a) Axial force coefficient. (b) Pressure center coefficient.

(a)

(b) (c)

500

500

X (mm)

1000

Y (mm)

0

0

Base shape

power_n=0.19

power_n=0.26

Figure 5: Optimization result of exponential noses of the slander

ascent vehicle. (a) Comparison of optimized shape and

configuration constraint contour of two exponential noses. (b)

Exponential nose with n = 0:19. (c) Exponential nose with n = 0:26.

Space: Science & Technology 5

75

There are

E = p

γ − 1

+

1

2

ρ u2 + v2 + w2 � �,

τ = μ

2ux uy + vx uz + wx

uy + vx 2vy vz + wy

uz + wx vz + wy 2wz

2

6

6

4

3

7

7

5 − 2

3

μ ux + vy + wz

� �I:

ð3Þ

In this paper, the finite volume method of grid center

based on structural grid was used to solve the above governing equations. Among them, Roe’s FDS scheme [14] was

used to discretize the flow term, and MUSUL interpolation

and Min-mod limiter were used to obtain the second-order

accuracy. Term was iterated in LU-SGS format. The turbulent model of viscous diffusion term adopts an equation

model based on SA [15].

4.2. Verification of an Example. The aerodynamic parameters of windward outsole supersonic in Mars Science Laboratory (MSL for short) [16] are selected as an example in this

paper and compared with the literature data. The geometric

dimensions of MSL are shown in Figure 1(a). Because the

strong expansion of the rear body has a weak influence on

the force coefficient, only the windward outsole is taken for

calculation. Because there is no sideslip in the calculation,

half-mode calculation is adopted. The calculated total grid

number is about 309,000, with 106 points in the normal

direction, and the height of the first layer grid in the normal

direction is 0.15 mm. Figure 1(b) shows the grid distribution

(a) (b)

(c)

Ref

Cal

Ref

Cal

1.4

1.35

Cx

1.3

1.25

1.2

0 5 10 15

α (°)

20 25

Cy

0.06

0.05

0.04

0.03

0.02

0.01

0

0 5 10 15

α (°)

20 25

Ref

Cal

0.06

0.05

0.04

0.03

0.02

0.01

0

Mz

0 5 10 15

α (°)

20 25

Figure 2: Comparison between the calculated data of Mars Laboratory (MSL) aerodynamics and the literature data. (a) Axial force

coefficient. (b) Normal force coefficient. (c) Pitching moment coefficient.

Spherical-conical

Circular arc

Base shape Configuration

constraints

Figure 3: Comparison between the basic configuration and the

improved spherical-conical and circular arc shapes of the slender

ascent vehicle.

4 Space: Science & Technology

of symmetry plane and object plane of the windward outsole

model.

The calculated inflow conditions are shown in Table 1,

in which the local equivalent specific heat ratio of the atmospheric inflow from Mars is obtained by the formula γeff =

ððη + 1Þ/ðη − 1ÞÞ − ð2η/ðη − 1ÞM2

∞Þ [17].

As shown in Figure 2, under the above calculation conditions, the aerodynamic coefficients obtained by the algorithm in this paper are consistent with the trend of

literature results, and the relative deviation is less than 1%.

Therefore, the effectiveness of the aerodynamic algorithm

used in this paper for calculating the aerodynamic characteristics of aircraft in the Martian atmosphere is verified.

5. Calculation Result Analysis

5.1. Influence Analysis of Aerodynamic Performance of

Forebody Configuration of the Slender Ascent Vehicle. As

shown in the figure below Figure 3, the Base shape is drawn

first according to the minimum envelope contour of configuration constraints, in which the forebody is rounded and

the radius of the bulbous is 115 mm. Then, the sphericalconical and circular arc cones are designed, respectively.

The theoretical length of 2.1 m is adopted for these two

shapes; the contour line of the circular arc nose is the arc

from the top of the spherical cone to the end of the third

spherical-conical surface, and the radius is 848.7 mm; the

radius of both spherical-conical and arc noses is 50 mm.

Based on CFD numerical simulation, the axial force

coefficient and pressure center coefficient of the Base shape

and the two improved shapes (namely, spherical-conical

and circular arc noses) at Ma2.0 and Ma4.1 are obtained,

as shown in Figure 4. By comparison, the following conclusions are obtained:

(1) After the Base shape is changed to the sphericalconical or the circular arc nose, the CA decreases

slightly. The drag reduction effects of the two

improved shapes are different at different Ma, but

the difference is subtle in general

(2) The zero-attack-angle CA of the spherical-conical

nose is less than 0.58 at Ma2.0 and less than 0.44 at

(a) (b) Xcp/L

0 5 10 15 20 25 30

alf (°)

0.45

0.5

0.55

Base shape

Spherical-conical nose

Circular arc nose

Ma2.0

Ma4.1

0 5

CA

10 15 20 25 30

alf (°)

0.45

0.5

0.55

0.6

0.65

Base shape

Spherical-conical nose

Circular arc nose

Ma2.0

Ma4.1

Figure 4: Comparison of supersonic aerodynamic characteristic curves between the basic shape and the improved spherical-conical and

circular arc shapes of the slender ascent vehicle. (a) Axial force coefficient. (b) Pressure center coefficient.

(a)

(b) (c)

500

500

X (mm)

1000

Y (mm)

0

0

Base shape

power_n=0.19

power_n=0.26

Figure 5: Optimization result of exponential noses of the slander

ascent vehicle. (a) Comparison of optimized shape and

configuration constraint contour of two exponential noses. (b)

Exponential nose with n = 0:19. (c) Exponential nose with n = 0:26.

Space: Science & Technology 5

76

Ma4.1, which can meet the requirements for optimized drag performance

(3) The pressure center coefficient of the Base shape and

the two improved shapes is less than 0.45 at a small

attack angle. The spherical-conical nose has the largest pressure center coefficient, but it is difficult to

maintain static stability because the pressure center

is too close to the nose

In addition to the spherical-conical and circular arc

noses, this study also attempts to use the parabolic, von Karman, and exponential curves to optimize the nose of the

slender ascent vehicle. However, the parabolic and von Karman curves cannot be generated because the configuration

constraint contour cannot be broken through. Only the

exponential curve can generate the blunt shape with a small

n value. The value of n is set as 0.19 and 0.26, respectively,

and the latter has slightly deviated from the contour constraint, as shown in Figure 5.

Through CFD numerical simulation, the axial force coefficient and pressure center coefficient of spherical-conical

and two optimized exponential noses at Ma2.0 and Ma4.1

are obtained, as shown in Figure 6. Comparative analysis

reveals that as compared with that of the previous improved

spherical-conical nose, the axial force of the two optimized

exponential noses increases, while the pressure center coefficient decreases. Accordingly, the two optimized exponential

noses fail to achieve the desired drag reduction and stability

enhancement.

As indicated by the mechanism analysis, for the slender

shape, the greater nose bluntness can result in the greater

shock wave intensity and the stronger drag. In addition,

the corner of the exponential nose with small n is obvious,

so that the pressure distribution on the surface changes rapidly. Therefore, the pressure center moves forward, and the

slope increases with the attack angle. To sum up, the degradation of the stability can be predicted.

5.2. Influence Analysis of Aerodynamic Performance of

Forebody Configuration of the Short Blunt Ascent Vehicle.

The aerodynamic performance of the short blunt ascent

vehicle is analyzed. As shown in Figure 7, firstly, the Base

shape is drawn according to the minimum envelope contour

of configuration constraints. In the figure, the nose is

rounded, and the radius of bulbous is 336 mm. Secondly,

spherical-conical and circular arc noses are designed, respectively. The theoretical length of 1.0 m is adopted for these

two shapes; the arc radius of the circular arc nose is

1990.6 mm, and that of spherical-conical and circular arc

noses is 50 mm.

Through CFD numerical simulation, the axial force coefficient and pressure center coefficient of the Base shape and

(a) (b) Xcp/L

0 5 10 15 20 25 30

alf (°)

0.45

0.4

0.5

0.55

Spherical-conical nose

Exponential nose with n = 0.19

Exponential nose with n = 0.26

Ma2.0

Ma4.1

0 5

CA

10 15 20 25 30

alf (°)

0.45

0.5

0.55

0.6

0.65

Spherical-conical nose

Exponential nose with n = 0.19

Exponential nose with n = 0.26

Ma2.0

Ma4.1

Figure 6: Comparison between supersonic aerodynamic characteristic curves of the spherical-conical nose and optimized exponential noses

of the slender ascent vehicle. (a) Axial force coefficient. (b) Pressure center coefficient.

Spherical-conical

Circular arc

Base shape

Configuration

constraints

Figure 7: Comparison between the Base shape and improved

spherical-conical and circular arc noses of the short blunt ascent

vehicle.

6 Space: Science & Technology

improved spherical-conical and circular arc noses at Ma2.0

and Ma4.1 are obtained, as shown in Figure 8. L in the pressure center coefficient Xcp/L is the total height of the short

blunt body. By comparison, the following conclusions can

be drawn:

(1) The pressure center coefficient of the Base shape and

the two improved noses is less than 0.45 at a small

attack angle. The spherical-conical nose has the largest pressure center coefficient, but it is difficult to

maintain static stability because the pressure center

is too close to the nose

(2) After the Base shape is changed to the sphericalconical or circular arc nose, the CA decreases

slightly, but the drag reduction effect of the

spherical-conical nose becomes stronger

(3) Compared with that of the Base shape, the zeroattack-angle CA of circular arc nose decreases by

about 3.5% to 1.232 at Ma2.0 and drops by about

0.5% to 1.083 at Ma4.1, so that the zero-attackangle drag reduction at a large Mach number is weak

(4) The static stability margin of the two improved noses

is reduced as compared with that of the Base shape,

but the pressure center coefficient is still above 0.7,

which makes it easier to achieve static stability

A group of parabolic curves is designed, and k is set as

0.62, 0.75, and 1.0, respectively. When k is 0.62, the generatrix passes through the inner contour point. The parabolic

shape has a sharp nose so that it is rounded, and the radius

of the spherical nose is 50 mm. The results of shape optimization are shown in Figure 9.

Through CFD numerical simulation, the axial force coefficient and pressure center coefficient of the three optimized

parabolic noses at Ma2.0 and Ma4.1 are obtained. They are

compared with the corresponding parameters of the circular

(a) (b)

0 5

CA

10 15 20 25 30

alf (°)

0.85

0.95

0.9

1.1

1.05

1

1.2

1.15

1.3

1.25

Base shape

Spherical-conical

Circular arc

Ma2.0

Ma4.1

Xcp/L

0 5 10 15 20 25 30

alf (°)

0.75

0.8

0.85

Base shape

Spherical-conical

Circular arc

Ma2.0

Ma4.1

Figure 8: Comparison between supersonic aerodynamic characteristic curves of the Base shape and improved spherical-conical and circular

arc noses of the short blunt ascent vehicle. (a) Axial force coefficient. (b) Pressure center coefficient.

(a)

(b) (c) (d)

500

400

300

200

100

600

200

X (mm)

400 600

Y (mm)

0

0

Base shape

parabolic_k=0.62

parabolic_k=0.75

parabolic_k=1

Figure 9: Optimization results of parabolic noses of the short blunt

ascent vehicle. (a) Comparison of optimized shape and

configuration constraint contour of three parabolic noses. (b)

Parabolic nose with k = 0:62. (c) Parabolic nose with k = 0:75. (d)

Parabolic nose with k = 1.

Space: Science & Technology 7

77

Ma4.1, which can meet the requirements for optimized drag performance

(3) The pressure center coefficient of the Base shape and

the two improved shapes is less than 0.45 at a small

attack angle. The spherical-conical nose has the largest pressure center coefficient, but it is difficult to

maintain static stability because the pressure center

is too close to the nose

In addition to the spherical-conical and circular arc

noses, this study also attempts to use the parabolic, von Karman, and exponential curves to optimize the nose of the

slender ascent vehicle. However, the parabolic and von Karman curves cannot be generated because the configuration

constraint contour cannot be broken through. Only the

exponential curve can generate the blunt shape with a small

n value. The value of n is set as 0.19 and 0.26, respectively,

and the latter has slightly deviated from the contour constraint, as shown in Figure 5.

Through CFD numerical simulation, the axial force coefficient and pressure center coefficient of spherical-conical

and two optimized exponential noses at Ma2.0 and Ma4.1

are obtained, as shown in Figure 6. Comparative analysis

reveals that as compared with that of the previous improved

spherical-conical nose, the axial force of the two optimized

exponential noses increases, while the pressure center coefficient decreases. Accordingly, the two optimized exponential

noses fail to achieve the desired drag reduction and stability

enhancement.

As indicated by the mechanism analysis, for the slender

shape, the greater nose bluntness can result in the greater

shock wave intensity and the stronger drag. In addition,

the corner of the exponential nose with small n is obvious,

so that the pressure distribution on the surface changes rapidly. Therefore, the pressure center moves forward, and the

slope increases with the attack angle. To sum up, the degradation of the stability can be predicted.

5.2. Influence Analysis of Aerodynamic Performance of

Forebody Configuration of the Short Blunt Ascent Vehicle.

The aerodynamic performance of the short blunt ascent

vehicle is analyzed. As shown in Figure 7, firstly, the Base

shape is drawn according to the minimum envelope contour

of configuration constraints. In the figure, the nose is

rounded, and the radius of bulbous is 336 mm. Secondly,

spherical-conical and circular arc noses are designed, respectively. The theoretical length of 1.0 m is adopted for these

two shapes; the arc radius of the circular arc nose is

1990.6 mm, and that of spherical-conical and circular arc

noses is 50 mm.

Through CFD numerical simulation, the axial force coefficient and pressure center coefficient of the Base shape and

(a) (b) Xcp/L

0 5 10 15 20 25 30

alf (°)

0.45

0.4

0.5

0.55

Spherical-conical nose

Exponential nose with n = 0.19

Exponential nose with n = 0.26

Ma2.0

Ma4.1

0 5

CA

10 15 20 25 30

alf (°)

0.45

0.5

0.55

0.6

0.65

Spherical-conical nose

Exponential nose with n = 0.19

Exponential nose with n = 0.26

Ma2.0

Ma4.1

Figure 6: Comparison between supersonic aerodynamic characteristic curves of the spherical-conical nose and optimized exponential noses

of the slender ascent vehicle. (a) Axial force coefficient. (b) Pressure center coefficient.

Spherical-conical

Circular arc

Base shape

Configuration

constraints

Figure 7: Comparison between the Base shape and improved

spherical-conical and circular arc noses of the short blunt ascent

vehicle.

6 Space: Science & Technology

improved spherical-conical and circular arc noses at Ma2.0

and Ma4.1 are obtained, as shown in Figure 8. L in the pressure center coefficient Xcp/L is the total height of the short

blunt body. By comparison, the following conclusions can

be drawn:

(1) The pressure center coefficient of the Base shape and

the two improved noses is less than 0.45 at a small

attack angle. The spherical-conical nose has the largest pressure center coefficient, but it is difficult to

maintain static stability because the pressure center

is too close to the nose

(2) After the Base shape is changed to the sphericalconical or circular arc nose, the CA decreases

slightly, but the drag reduction effect of the

spherical-conical nose becomes stronger

(3) Compared with that of the Base shape, the zeroattack-angle CA of circular arc nose decreases by

about 3.5% to 1.232 at Ma2.0 and drops by about

0.5% to 1.083 at Ma4.1, so that the zero-attackangle drag reduction at a large Mach number is weak

(4) The static stability margin of the two improved noses

is reduced as compared with that of the Base shape,

but the pressure center coefficient is still above 0.7,

which makes it easier to achieve static stability

A group of parabolic curves is designed, and k is set as

0.62, 0.75, and 1.0, respectively. When k is 0.62, the generatrix passes through the inner contour point. The parabolic

shape has a sharp nose so that it is rounded, and the radius

of the spherical nose is 50 mm. The results of shape optimization are shown in Figure 9.

Through CFD numerical simulation, the axial force coefficient and pressure center coefficient of the three optimized

parabolic noses at Ma2.0 and Ma4.1 are obtained. They are

compared with the corresponding parameters of the circular

(a) (b)

0 5

CA

10 15 20 25 30

alf (°)

0.85

0.95

0.9

1.1

1.05

1

1.2

1.15

1.3

1.25

Base shape

Spherical-conical

Circular arc

Ma2.0

Ma4.1

Xcp/L

0 5 10 15 20 25 30

alf (°)

0.75

0.8

0.85

Base shape

Spherical-conical

Circular arc

Ma2.0

Ma4.1

Figure 8: Comparison between supersonic aerodynamic characteristic curves of the Base shape and improved spherical-conical and circular

arc noses of the short blunt ascent vehicle. (a) Axial force coefficient. (b) Pressure center coefficient.

(a)

(b) (c) (d)

500

400

300

200

100

600

200

X (mm)

400 600

Y (mm)

0

0

Base shape

parabolic_k=0.62

parabolic_k=0.75

parabolic_k=1

Figure 9: Optimization results of parabolic noses of the short blunt

ascent vehicle. (a) Comparison of optimized shape and

configuration constraint contour of three parabolic noses. (b)

Parabolic nose with k = 0:62. (c) Parabolic nose with k = 0:75. (d)

Parabolic nose with k = 1.

Space: Science & Technology 7

78

(a) (b)

0 5

CA

10 15 20 25 30

alf (°)

0.85

0.95

0.9

1.1

1.05

1

1.2

1.15

Ma2.0

parabolic_k=0.62 Ma4.1

parabolic_k=0.75

parabolic_k=1

Spherical-conical

0 5 10 15 20 25 30

alf (°)

0.72

0.74

0.76

0.78

0.8

0.82

Xcp/L

Ma2.0

parabolic_k=0.62 Ma4.1

parabolic_k=0.75

parabolic_k=1

Spherical-conical

Figure 10: Comparison between supersonic aerodynamic characteristic curves of the circular arc nose and optimized parabolic noses of the

short blunt ascent vehicle. (a) Axial force coefficient. (b) Pressure center coefficient.

(a)

(b) (c) (d) (e)

500

400

300

200

100

600

100 200

X (mm)

300 400 500

Y (mm)

0

0

Base shape

power_n=0.2

power_n=0.4

power_n=0.6

power_n=0.73

Figure 11: Optimization results of exponential noses of the short blunt ascent vehicle. (a) Comparison of optimized shape and configuration

constraint contour of four exponential noses. (b) Exponential nose with n = 0:2. (c) Exponential nose with n = 0:4. (d) Exponential nose with

n = 0:6. (e) Exponential nose with n = 0:73.

8 Space: Science & Technology

arc nose under the same conditions, as shown in Figure 10.

By comparison, the following conclusions can be drawn:

(1) Compared with the circular arc nose, the parabolic

nose has better drag characteristics at a low supersonic velocity; the drag characteristics better than

those of the circular arc nose can also be obtained

through reasonable k at a large Mach number.

Among the three curves with k = 0:62/0:75/1:0,

when k is 0.75, the optimal drag characteristics are

obtained and are better than those of the circular

arc nose under the calculation conditions

(2) Compared with the circular arc nose, the zeroattack-angle CA of the parabolic nose with k = 0:75

declines by about 5.5% to 1.164 at Ma2.0 and drops

by about 1.4% to 1.068 3 at Ma4.1, so that the

zero-attack-angle drag reduction at a large Mach

number is weak

(3) The static stability margin of the parabolic nose is

less than that of the circular arc nose, but it is easier

to ensure static stability

Based on a comprehensive comparison, the aerodynamic

performance of the parabolic nose is better than that of the

previous two improved noses.

Another group of exponential curves is designed, and n

is set as 0.2, 0.4, 0.6, and 0.73, respectively. When k is 0.73,

the generatrix passes through the inner contour point. The

optimization results for the exponential nose are shown in

Figure 11.

Through CFD numerical simulation, the axial force coefficient and pressure center coefficient of the four optimized

exponential noses at Ma2.0 and Ma4.1 are obtained. They

are compared with the corresponding parameters of the parabolic nose with k = 0:75 under the same conditions, as

shown in Figure 12. By comparison, the following conclusions can be drawn:

(1) Compared with the parabolic nose, the exponential

nose with n ≤ 0:6 has better drag characteristics at a

low supersonic velocity, and the smaller n will lead

to the smaller CA

(2) The CA curves at different Mach numbers approach

gradually with the smaller n. When n = 0:2, the difference between the CA curves at Ma2.0 and Ma4.1 is less

than 2% within the range of attack angle (0°

–5°

).

(3) Compared with the parabolic nose with k = 0:75, the

zero-attack-angle CA of the exponential nose

(n = 0:2) decreases by about 19.8% to 0.933 at

Ma2.0 and drops by about 14.0% to 0.918 at Ma4.1,

with evident drag reduction

(4) The exponential nose with n = 0:4 is close to that

with n = 0:2 in the supersonic drag reduction. It

can be inferred that, when n = 0:2 – 0:4, the aerodynamic performance of the exponential nose still

requires optimization

(5) The static stability margin of the exponential nose is

less than that of the parabolic nose. The minimum

pressure center coefficient of the exponential nose

with n = 0:2 is 0.6 so that it is difficult to maintain

static stability

The comprehensive comparison demonstrates that the

drag reduction by the exponential nose with n = 0:2 – 0:4 is

visible. Since the pressure center coefficient is higher when

n = 0:2, the in-depth optimization shall be carried out for

the exponential nose with 0:2 < n ≤ 0:4 in the actual design.

(a) (b)

0 5

CA

10 15 20 25 30

alf (°)

0.85

0.8

0.95

0.9

1.1

1.05

1

1.2

1.25

1.15

Parabolic_k=0.75

Exponential_n= 0.2

Exponential_n= 0.4

Exponential_n= 0.6

Exponential_n= 0.73

Ma2.0

Ma4.1

0 5 10 15 20 25 30

alf (°)

0.55

0.6

0.65

0.7

0.75

0.8

Xcp/L

Parabolic_k=0.75

Exponential_n= 0.2

Exponential_n= 0.4

Exponential_n= 0.6

Exponential_n= 0.73

Ma2.0

Ma4.1

Figure 12: Comparison between supersonic aerodynamic characteristic curves of the parabolic nose and optimized exponential noses of the

short blunt ascent vehicle. (a) Axial force coefficient. (b) Pressure center coefficient.

Space: Science & Technology 9

79

(a) (b)

0 5

CA

10 15 20 25 30

alf (°)

0.85

0.95

0.9

1.1

1.05

1

1.2

1.15

Ma2.0

parabolic_k=0.62 Ma4.1

parabolic_k=0.75

parabolic_k=1

Spherical-conical

0 5 10 15 20 25 30

alf (°)

0.72

0.74

0.76

0.78

0.8

0.82

Xcp/L

Ma2.0

parabolic_k=0.62 Ma4.1

parabolic_k=0.75

parabolic_k=1

Spherical-conical

Figure 10: Comparison between supersonic aerodynamic characteristic curves of the circular arc nose and optimized parabolic noses of the

short blunt ascent vehicle. (a) Axial force coefficient. (b) Pressure center coefficient.

(a)

(b) (c) (d) (e)

500

400

300

200

100

600

100 200

X (mm)

300 400 500

Y (mm)

0

0

Base shape

power_n=0.2

power_n=0.4

power_n=0.6

power_n=0.73

Figure 11: Optimization results of exponential noses of the short blunt ascent vehicle. (a) Comparison of optimized shape and configuration

constraint contour of four exponential noses. (b) Exponential nose with n = 0:2. (c) Exponential nose with n = 0:4. (d) Exponential nose with

n = 0:6. (e) Exponential nose with n = 0:73.

8 Space: Science & Technology

arc nose under the same conditions, as shown in Figure 10.

By comparison, the following conclusions can be drawn:

(1) Compared with the circular arc nose, the parabolic

nose has better drag characteristics at a low supersonic velocity; the drag characteristics better than

those of the circular arc nose can also be obtained

through reasonable k at a large Mach number.

Among the three curves with k = 0:62/0:75/1:0,

when k is 0.75, the optimal drag characteristics are

obtained and are better than those of the circular

arc nose under the calculation conditions

(2) Compared with the circular arc nose, the zeroattack-angle CA of the parabolic nose with k = 0:75

declines by about 5.5% to 1.164 at Ma2.0 and drops

by about 1.4% to 1.068 3 at Ma4.1, so that the

zero-attack-angle drag reduction at a large Mach

number is weak

(3) The static stability margin of the parabolic nose is

less than that of the circular arc nose, but it is easier

to ensure static stability

Based on a comprehensive comparison, the aerodynamic

performance of the parabolic nose is better than that of the

previous two improved noses.

Another group of exponential curves is designed, and n

is set as 0.2, 0.4, 0.6, and 0.73, respectively. When k is 0.73,

the generatrix passes through the inner contour point. The

optimization results for the exponential nose are shown in

Figure 11.

Through CFD numerical simulation, the axial force coefficient and pressure center coefficient of the four optimized

exponential noses at Ma2.0 and Ma4.1 are obtained. They

are compared with the corresponding parameters of the parabolic nose with k = 0:75 under the same conditions, as

shown in Figure 12. By comparison, the following conclusions can be drawn:

(1) Compared with the parabolic nose, the exponential

nose with n ≤ 0:6 has better drag characteristics at a

low supersonic velocity, and the smaller n will lead

to the smaller CA

(2) The CA curves at different Mach numbers approach

gradually with the smaller n. When n = 0:2, the difference between the CA curves at Ma2.0 and Ma4.1 is less

than 2% within the range of attack angle (0°

–5°

).

(3) Compared with the parabolic nose with k = 0:75, the

zero-attack-angle CA of the exponential nose

(n = 0:2) decreases by about 19.8% to 0.933 at

Ma2.0 and drops by about 14.0% to 0.918 at Ma4.1,

with evident drag reduction

(4) The exponential nose with n = 0:4 is close to that

with n = 0:2 in the supersonic drag reduction. It

can be inferred that, when n = 0:2 – 0:4, the aerodynamic performance of the exponential nose still

requires optimization

(5) The static stability margin of the exponential nose is

less than that of the parabolic nose. The minimum

pressure center coefficient of the exponential nose

with n = 0:2 is 0.6 so that it is difficult to maintain

static stability

The comprehensive comparison demonstrates that the

drag reduction by the exponential nose with n = 0:2 – 0:4 is

visible. Since the pressure center coefficient is higher when

n = 0:2, the in-depth optimization shall be carried out for

the exponential nose with 0:2 < n ≤ 0:4 in the actual design.

(a) (b)

0 5

CA

10 15 20 25 30

alf (°)

0.85

0.8

0.95

0.9

1.1

1.05

1

1.2

1.25

1.15

Parabolic_k=0.75

Exponential_n= 0.2

Exponential_n= 0.4

Exponential_n= 0.6

Exponential_n= 0.73

Ma2.0

Ma4.1

0 5 10 15 20 25 30

alf (°)

0.55

0.6

0.65

0.7

0.75

0.8

Xcp/L

Parabolic_k=0.75

Exponential_n= 0.2

Exponential_n= 0.4

Exponential_n= 0.6

Exponential_n= 0.73

Ma2.0

Ma4.1

Figure 12: Comparison between supersonic aerodynamic characteristic curves of the parabolic nose and optimized exponential noses of the

short blunt ascent vehicle. (a) Axial force coefficient. (b) Pressure center coefficient.

Space: Science & Technology 9

80

[16] A. A. Dyakonov, J. W. MarkSchoenenberger, and V. Norman,

“Hypersonic and supersonic static aerodynamics of Mars science laboratory entry vehicle,” in 43rd AIAA Thermophysics

Conference, p. 2999, New Orleans, LA, 2012.

[17] P. A. Gnoffo, K. J. Weilmuenster, R. D. Braun, and C. I. Cruz,

“Influence of sonic-line location on Mars pathfinder probe

aerothermodynamics,” Journal of Spacecraft and Rockets,

vol. 33, no. 2, pp. 169–177, 1996.

Space: Science & Technology 11

According to the mechanism analysis based on the flow

field analysis, the characteristic that the exponential nose

with small n has the most evident drag reduction and the

worst static stability can be explained as follows: the smaller

n of the exponential nose will lead to the larger bluntness at

the crown, but the smaller crown area will lead to the smaller

taper of the rear curved surface of the crown. When there is

a crown with large bluntness and small area, the detached

shock wave will only exist in the crown with a small area,

with low intensity; the flow on the surface with a small taper

will be smoother, and the pressure and friction on it will be

very small. However, the smaller n of the exponential nose

will lead to the larger flow transition between the crown

and its adjacent surface, so that the pressure will change fast

and the pressure center will move forward rapidly. Therefore, the static stability of the exponential nose with small

n will become lower.

6. Conclusions

The paper analyzed the requirements of supersonic aerodynamic performance of MAV, and the influence laws and

numerical values of bus parameters of different types of

MAV on supersonic drag characteristics and static stability

were calculated and analyzed. Finally, the following conclusions can be drawn:

(1) For slender ascent vehicle, the shape of conical forebody can play a better role in drag reduction, and the

drag performance after drag reduction can meet the

demand. However, the slender body has poor static

stability due to its front center of pressure, and the

improvement of forebody shape has little effect on

static stability

(2) For the short blunt body riser, the exponential forebody with 0:2 < n ≤ 0:4 can greatly improve the

resistance performance and reduce the resistance

coefficient. Meanwhile, the static stability margin of

the short blunt body is easy to meet because the center of pressure at a small angle of attack is closer to

the tail end, so the drag reduction design of the forebody shape should be emphasized

Further research will be carried out on the influence of

the tail shape optimization of the ascent vehicle on aerodynamic stability, the optimization design of the forebody

resistance reduction structure, and the aerodynamic performance, so as to explore more effective methods for reducing

energy consumption and improving the bearing capacity of

the system of the Mars ascent vehicle.

Conflicts of Interest

All authors declare no possible conflicts of interests.

Authors’ Contributions

Li Qi completed the conception and compilation of the

manuscript. Yuan Wu completed the aerodynamic layout

optimization design of the Mars ascent vehicles. Zhao Rui

contributed to the calculation of static aerodynamic data of

the Mars ascent vehicles. Wei Haogong performed the data

analysis.

Acknowledgments

This is supported by the Major Planetary Exploration Projects and the National Natural Science Foundation of China

11902025.

References

[1] Strategy CM, “The State Council Information Office of the

People’s Republic of China. China’s space actives in 2016,”

Aerospace China, vol. 1, pp. 10–17, 2017.

[2] A. Karp, B. Nakazono, R. Shotwell et al., “A hybrid mars ascent

vehicle design and FY 2016 technology development,” in 2017

IEEE Aerospace Conference, pp. 1–10, Big Sky, MT, USA, 2017.

[3] I. J. Dux, J. A. Huwaldt, R. S. McKamey, and J. W. Dankanich,

“Mars ascent vehicle gross lift-off mass sensitivities for robotic

Mars sample return,” in 2011 Aerospace Conference, pp. 1–16,

Big Sky, MT, USA, 2011.

[4] B. G. Drake and K. D. Watts, Human exploration of Mars

design reference architecture 5.0, Addendum 2, NASA,

2009.

[5] A. A. Gonzales, C. R. Stoker, L. G. Lemke et al., “Mars sample

return using commercial capabilities: mission architecture

overview,” in 2014 IEEE Aerospace Conference, pp. 1–15, Big

Sky, MT, USA, 2014.

[6] B. Gardini and A. Santovincenzo, “The Aurora Mars sample

return mission,” in 54th International Astronautical Congress

of the International Astronautical Federation, the International

Academy of Astronautics, and the International Institute of

Space Law, Bremen, Germany, 2003.

[7] J. S. Martin, Mars engineering model, NASA, 1975.

[8] W. Rong and G. L. Chen, “The characters of deceleration and

landing technology on Mars explorer,” Spacecraft Recovery &

Remote Sensing, vol. 31, no. 4, pp. 1–6, 2010.

[9] J. V. Bowles, L. C. Huynh, V. M. Hawke, and X. J. Jiang, Mars

sample return: Mars ascent vehicle mission and technology

requirements, NASA, 2013.

[10] W. Tang, D. W. Jiang, and Y. W. Gui, “Study on generatrix

curvetypes of axis-symmetric missiles,” Acta Aerodynamica

Sinica, vol. 28, no. 2, pp. 218–221, 2010.

[11] R. S. Miao, J. M. Ju, and J. S. Wu, Missile Aerodynamics,

National Defense Industry Press, 2006.

[12] B. B. Feng, D. R. Chen, J. D. Wang, and X. T. Yang, “Effect of

nose shape on flight dynamics of supersonic vehicles,” Flight

Dynamics, vol. 30, no. 6, pp. 537–540, 2012.

[13] W. L. Wang, H. Li, F. Liu, and S. Pan, “Research on drag

characteristics of supersonic vehicle influenced by different

base flows,” Computer Simulation, vol. 33, no. 5, pp. 105–

110, 2016.

[14] P. I. Roe, “Approximate Riemann solvers, parameter vectors,

and difference schemes,” Journal of Computational Physics,

vol. 43, no. 2, pp. 357–372, 1981.

[15] C. Yan, Computational fluid dynamics methods and applications, Beijing University of Aeronautics and Astronautics

Press, Beijing, China, 2006.

10 Space: Science & Technology

&

81

[16] A. A. Dyakonov, J. W. MarkSchoenenberger, and V. Norman,

“Hypersonic and supersonic static aerodynamics of Mars science laboratory entry vehicle,” in 43rd AIAA Thermophysics

Conference, p. 2999, New Orleans, LA, 2012.

[17] P. A. Gnoffo, K. J. Weilmuenster, R. D. Braun, and C. I. Cruz,

“Influence of sonic-line location on Mars pathfinder probe

aerothermodynamics,” Journal of Spacecraft and Rockets,

vol. 33, no. 2, pp. 169–177, 1996.

Space: Science & Technology 11

According to the mechanism analysis based on the flow

field analysis, the characteristic that the exponential nose

with small n has the most evident drag reduction and the

worst static stability can be explained as follows: the smaller

n of the exponential nose will lead to the larger bluntness at

the crown, but the smaller crown area will lead to the smaller

taper of the rear curved surface of the crown. When there is

a crown with large bluntness and small area, the detached

shock wave will only exist in the crown with a small area,

with low intensity; the flow on the surface with a small taper

will be smoother, and the pressure and friction on it will be

very small. However, the smaller n of the exponential nose

will lead to the larger flow transition between the crown

and its adjacent surface, so that the pressure will change fast

and the pressure center will move forward rapidly. Therefore, the static stability of the exponential nose with small

n will become lower.

6. Conclusions

The paper analyzed the requirements of supersonic aerodynamic performance of MAV, and the influence laws and

numerical values of bus parameters of different types of

MAV on supersonic drag characteristics and static stability

were calculated and analyzed. Finally, the following conclusions can be drawn:

(1) For slender ascent vehicle, the shape of conical forebody can play a better role in drag reduction, and the

drag performance after drag reduction can meet the

demand. However, the slender body has poor static

stability due to its front center of pressure, and the

improvement of forebody shape has little effect on

static stability

(2) For the short blunt body riser, the exponential forebody with 0:2 < n ≤ 0:4 can greatly improve the

resistance performance and reduce the resistance

coefficient. Meanwhile, the static stability margin of

the short blunt body is easy to meet because the center of pressure at a small angle of attack is closer to

the tail end, so the drag reduction design of the forebody shape should be emphasized

Further research will be carried out on the influence of

the tail shape optimization of the ascent vehicle on aerodynamic stability, the optimization design of the forebody

resistance reduction structure, and the aerodynamic performance, so as to explore more effective methods for reducing

energy consumption and improving the bearing capacity of

the system of the Mars ascent vehicle.

Conflicts of Interest

All authors declare no possible conflicts of interests.

Authors’ Contributions

Li Qi completed the conception and compilation of the

manuscript. Yuan Wu completed the aerodynamic layout

optimization design of the Mars ascent vehicles. Zhao Rui

contributed to the calculation of static aerodynamic data of

the Mars ascent vehicles. Wei Haogong performed the data

analysis.

Acknowledgments

This is supported by the Major Planetary Exploration Projects and the National Natural Science Foundation of China

11902025.

References

[1] Strategy CM, “The State Council Information Office of the

People’s Republic of China. China’s space actives in 2016,”

Aerospace China, vol. 1, pp. 10–17, 2017.

[2] A. Karp, B. Nakazono, R. Shotwell et al., “A hybrid mars ascent

vehicle design and FY 2016 technology development,” in 2017

IEEE Aerospace Conference, pp. 1–10, Big Sky, MT, USA, 2017.

[3] I. J. Dux, J. A. Huwaldt, R. S. McKamey, and J. W. Dankanich,

“Mars ascent vehicle gross lift-off mass sensitivities for robotic

Mars sample return,” in 2011 Aerospace Conference, pp. 1–16,

Big Sky, MT, USA, 2011.

[4] B. G. Drake and K. D. Watts, Human exploration of Mars

design reference architecture 5.0, Addendum 2, NASA,

2009.

[5] A. A. Gonzales, C. R. Stoker, L. G. Lemke et al., “Mars sample

return using commercial capabilities: mission architecture

overview,” in 2014 IEEE Aerospace Conference, pp. 1–15, Big

Sky, MT, USA, 2014.

[6] B. Gardini and A. Santovincenzo, “The Aurora Mars sample

return mission,” in 54th International Astronautical Congress

of the International Astronautical Federation, the International

Academy of Astronautics, and the International Institute of

Space Law, Bremen, Germany, 2003.

[7] J. S. Martin, Mars engineering model, NASA, 1975.

[8] W. Rong and G. L. Chen, “The characters of deceleration and

landing technology on Mars explorer,” Spacecraft Recovery &

Remote Sensing, vol. 31, no. 4, pp. 1–6, 2010.

[9] J. V. Bowles, L. C. Huynh, V. M. Hawke, and X. J. Jiang, Mars

sample return: Mars ascent vehicle mission and technology

requirements, NASA, 2013.

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82

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