Aerodynamics of Space Station "Mir" during
Aeroassisted Controlled Descent
Gennady N. Markelov, Alexander V. Kashkovsky, and Mikhail S. Ivanov
Computational Aerodynamics Laboratory
Institute of Theoretical and Applied Mechanics
Siberian Division of Russian Academy of Sciences, Novosibirsk, Russia
Abstract. Future descent of space station "Mir" requires the choice of an optimal configuration (positions
of solar arrays) which allows one to minimize the disturbing aerodynamic torques and maximize the drag.
The aerodynamic characteristics of two configurations with required positions of solar arrays are studied
by engineering and statistical methods along the descent trajectory. The study showed that a decrease in
the flight altitude from 200 to 130 km does not exert a noticeable effect on the magnitude of the force and
moment coefficients and also revealed the reasons decreasing the accuracy of the engineering prediction.
INTRODUCTION
Space objects operating on LEO have a certain lifetime and shall be deorbited after completion of their
missions. To reduce possible adverse consequences of collision of unburned fragments, which are often rather
heavy and fall down with a large velocity, with the Earth's surface, controlled descent to water area of the
ocean or deserted lands is preferable. During the controlled descent the object enters the dense layers of the
atmosphere with a certain attitude, for which the aerodynamic forces and torques are determined; then, the
regions of descent can be predicted rather accurately.
For the planned descent of the space station (SS) "Mir", it is necessary to determine the solar array positions
which would allow one to minimize the disturbing aerodynamic torques and maximize the drag. This allows
a significant reduction of fuel consumption for maintaining a given orientation of the SS by the Reactive
Control System. Therefore, the precise knowledge of the aerodynamic forces and torques of the SS "Mir"
from the orbital phase flight down to the disintegration altitude is indispensable. The proper definition of the
SS disintegration altitude is beyond the scope of the given paper. Based on the accumulated experience on
descent of various space objects, in particular, "Salyut-7", the beginning of the SS "Mir" disintegration process
into separate parts is expected at an altitude of about 120-130 km. Choosing an optimal orientation of the
SS "Mir" requires multiparametric calculations of its aerodynamic characteristics for various configurations,
determined by positions of the solar arrays, both in the free-molecular and transitional regimes of rarefied gas
flows. With the use of exact statistical methods (Test Particle and Direct Simulation Monte Carlo methods
for free-molecular and transitional regimes, respectively), these calculations require significant computational
resources. Therefore, the most rational procedure is the joint use of engineering and statistical methods.
Such an approach was used in [1] for choosing configurations of the SS "Mir" having required aerodynamic
characteristics in free-molecular regime and for an analysis the aerodynamics of these configurations in the
transitional regime along the descent trajectory. It was found that the engineering approach (local bridging)
taking into account the shadowing of SS elements by means of geometrical optics does not allow the prediction
of aerodynamic characteristics of the SS "Mir" with a required accuracy.
The main objective of the present work is a detailed analysis of the aerodynamic characteristics of the SS
"Mir" in the free-molecular (above 200 km) and transitional regimes by engineering and statistical methods.
Particular attention was paid to investigation of applicability and modification of the local bridging method
for such a space object with a very complex shape.
CP585, Rarefied Gas Dynamics: 22nd International Symposium, edited by T. J. Bartel and M. A. Gallis
© 2001 American Institute of Physics 0-7354-0025-3/01/$18.00
745
a) configuration chosen with diffuse reflecton
b) configuration chosen with Nocilla model
FIGURE 1. Configurations of SS "Mir" and its module composition (1- Progress spacecraft, 2- Kvant, 3- Base Block,
4- Spektr, 5- Kristall, 6- Kvant-2, 7- Priroda).
TABLE 1. Preestream conditions
Altitude,
km
110
120
130
140
160
200
Poo,
kg/m3
9.67e-8
2.27e-8
8.23e-9
3.86e-9
1.32e-9
3.29e-10
T
•*- oo,
K
247
368
500
625
822
1026
Mole fraction
0.123
0.085
0.071
0.062
0.049
0.032
0.770
0.733
0.691
0.652
0.581
0.455
X0
0.106
0.183
0.238
0.286
0.370
0.514
M,
g/mol
27.22
26.14
25.43
24.81
23.75
21.96
m
0.599
2.681
7.724
16.920
50.330
196.700
FLOW CONDITIONS AND CONFIGURATIONS OF SS "MIR"
The numerical studies were conducted within the altitude range from 200 down to 110 km for two configurations of SS "Mir" which differ by positions of solar arrays (Fig. 1). Both configurations satisfy above-mentioned
requirements (maxmimum drag and minimum distrubing torques) for future descent and were chosen in [1] using diffuse reflection and Nocilla model for gas/surface interaction, respectively. The configurations are greatly
simplified as compared to the real SS, but they retain all the basic features important for aerodynamic studies.
They consist of about 200 elementary geometrical surfaces that are triangulated into about 70000 panels.
The RAMSES [2] and SMILE [3] software systems were used to study the aerodynamics of the SS "Mir".
The first system has codes for calculation of free-molecular and transitional aerodynamics of re-entry vehicles
with the Test Particle Monte Carlo (TPMC) and Local Bridging methods. The latter system is based on the
DSMC method [4] and an exact majorant frequency scheme [5] for modeling collision processes.
The parameters of the atmosphere are listed in Table 1 [6]. The wall temperature was constant for all parts
of the SS "Mir" and equal to Tp^ = 350 K. Diffuse reflection with complete energy accommodation and Nocilla
model were used as a gas/surface interaction model. The cross-sectional area of the Base Block (BB) module
S = 13.5 m2 was used as the reference area, and the reference length was equal to L = 13.6 m.
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35*
120
140
160
H,km
180
200
140
160
H, km
160
H, km
FIGURE 2. Aerodynamic characteristics of the first configuration (left - axial force coefficient, center - yawing moment
coefficient, right - pitching moment coefficient).
RESULTS AND DISCUSSIONS
Comparison of the Local Bridging and DSMC predictions
The aerodynamic characteristics of the first configuration versus the flight altitude are plotted in Fig. 2,
which shows that the force and torque characteristics are almost constant within the altitude range from 200
to 140 km for two angles of attack a = 0 and —5 deg. Significant changes are observed only for the altitudes
below 140 km where the mean free path significantly decreases (see Table 1). The prediction of the LB method
differs significantly from the DSMC results except for the yawing moment coefficient Cn for a zero angle of
attack. Nevertheless, this good coincidence is most likely accidental. Since the aerodynamic characteristics
vary little within the range of 200-140 km, the accuracy of the LB prediction depends mainly on the accuracy
of determining the free-molecular limit used in bridging relations. Figure 2 also shows the forces and torques
obtained in the free-molecular flow around the SS "Mir" using the TPMC method. Some difference between
the LB results for free-molecular limits and the TPMC results is observed.
The LB method [2] was constructed using available experimental data for blunted bodies, and for such bodies
(for example, the Soyus reentry capsule [7]) the LB method produces rather accurate data on aerodynamic
characteristics. To take into account the shadow effect, the LB code of the RAMSES system uses geometric
optics. The shadowed parts of the space object are determined by calculating the geometric shadow of all
triangular panels in a plane perpendicular to the flow velocity and checking mutual shadowing by comparing
the distance to the shadow plane in the case of overlapping shadows. The shadowed parts of the surface are
ignored in determining the aerodynamic forces and torques. However, the SS "Mir" has a very complicated
shape: there are many concave corners, some elements of the station are shaded by other elements, etc.
Thus, the use of geometrical optics for determining the shadow effect of SS elements is insufficient for such a
complex geometry. It is necessary to take into account the finite Mach number and multiple reflection effects
in determining free-molecular limit for the LB method.
Simple examples shown in Fig. 3 clearly demonstrate the finite Mach number effects: semishadow and
shielding. The semishadow effect is manifested by the fact that, having a transverse thermal velocity, the
molecules can hit the surface of the aft plate located in the geometrical shadow (Fig. 3a). For this position
of the plate, the neglect of the semishadow effect yields a zero force acting on the aft plate. Therefore, the
calculation of free-molecular aerodynamics of the SS "Mir" has to take into account the semishadow effects.
The account of the finite Mach number can also lead to a decrease in the flux of incident particles. For example,
in the flow at zero incidence around a body consisting of two coaxial cylinders of different diameters (Fig. 3b),
shielding of flux against downstream body parts is observed, i.e., the flux of particles onto the end-face part of
the backward cylinder decreases.
These effects exert a significant influence, for example, on the distribution of CA over the surface of the SS
"Mir" (Fig. 3c). Thus, there are regions with the zero value of the axial force on solar arrays of the BB "shadows" of the "Kvant" solar arrays. The use of the TPMC method allows one to take into account both the
finite Mach number effects and the influence of reflected molecules (multiple reflection). The distribution of
747
0.005
0.010
0.020
0.030
0.040
0.060
0.080
0.100
0.150
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0.900
1.000
1.200
1.400
1.600
1.800
2.000
2.200
a) Semishadow
b) Shielding
c) Axial force distribution
FIGURE 3. Finite Mach number effects and axial force distribution without accounting for these effects (LB, 200 km,
zero angle of attack).
0.005
0.010
0.020
0.030
0.040
0.060
0.080
0.100
0.150
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0.900
1.000
1.200
1.400
1.600
1.800
2.000
2.200
a) TPMC method
b) LBM (200 km)
FIGURE 4. Axial force distribution with accounting for finite Mach number effects (zero angle of attack).
CA obtained by the TPMC method is shown in Fig. 4a. It is characterized by the absence of dramatic changes
in CA such as those observed in the LB prediction. Note, the shielding effect decreases the axial force in the
region of docking of the "Progress" spacecraft and "Kvant" module (cf. Figs 3c and 4a).
Modification of the Local Bridging code
A comparison of the total aerodynamic characteristics obtained with the use of the LB and TPMC methods
shows that the contribution of the finite Mach number effects is ten fold higher than multiple reflection contribution for the configuration of the SS "Mir" under consideration (Table 2). Therefore, the modification of
the LB code was aimed at taking into account semishadow and shielding.
Taking into account these effects by means of computational geometry methods is a complicated problem,
which requires significant computational resources. The most rational method of solving this problem is the
use of test particles as in the TPMC method. In the case of particle collisions with the body surface, bridging
relations that take into account the angle of incidence of the particle on the surface are used to determine the
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TABLE 2. Contribution of different effects into total aerodynamics characteristics of the first configuration (zero angle of attack)
____Geometric shadow
48.35
CA
-0.004
Cn
0.846
120
140
160
H,km
180
200
Semishadow and shielding
2.36
0.024
-0.756
140
Multiple reflection
-0.237
0.003
-0.082
160
H, km
160
H, km
FIGURE 5. Prediction of axial force (left), yawing (center) and pitching moment (right) coefficients for zero angle of
attack.
forces and moments acting on a surface element. Thus, the use of random trajectories of the TPMC method
allows us to compute the aerodynamics in the transitional regime.
Figure 4b shows the distribution of CA obtained using a modified LB (MLB) code. It is in good agreement
with the TPMC prediction. Note, the computational efficiency of the MLB method was comparable with the
efficiency of traditional local bridging in studying the aerodynamics of the SS "Mir".
The axial force coefficient and yawing and pitching moment coefficients versus the altitude are plotted in
Fig. 5. Taking into account the semishadow and shielding effects allowed a significant increase in the accuracy
of the LB prediction of the aerodynamic characteristics for altitude higher than 140 km. However, the MLB
prediction for lower altitudes still differs from the DSMC results.
Consideration of the contribution of pressure and friction forces to CA (Fig. 6) shows that LB and DSMC
methods yield almost identical values of the contribution of the friction forces to CA- At the same time,
LB predicts a decrease in the contribution of pressure forces with decreasing flight altitude below 140 km.
This behavior is typical of the flow over reentry vehicles of convex shape [7], which was used in deriving the
bridging relations. However, the contribution of pressure forces increases with decreasing flight altitude of the
SS "Mir". This is caused by a significant reconstruction of the flow structure near the SS "Mir". For example,
at an altitude of 200 km, the shape of the disturbed region is almost independent of the SS shape and looks
like a sphere (see Fig. 7, which shows the pressure flowfields). At a low altitude (110 km), the disturbed region
repeats the SS shape.
Aerodynamics of the second configuration
It was shown in [1] that the gas/surface interaction has a considerable effect on the aerodynamic characteristics of the SS "Mir". For example, the use of the Nocilla model leads to a 10% increase in CA as compared to
diffuse reflection. At the same time, the values of the moments can change by more than an order of magnitude
at high altitudes. Such a strong effect of the gas/surface interaction model made the authors of [1] choose the
configuration of the SS "Mir" using the Nocilla model. The parameters of this model were determined for
engineering surfaces in experiments [8].
Figure 8 shows a comparison of the LB prediction and DSMC results for the second configuration with the
Nocilla model. As for the first configuration, the LB method does not allow one to predict the aerodynamic
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120
140
160
H, km
180
200
FIGURE 6. Pressure and friction contribution into axial force coefficient.
,P/Poo
1.5
3.0
4.5
I 6.0
i.O
I 10.0
12.5
15.0
18.0
|21.0
24.5
29.0
34.0
40.0
45.0
54.0
63.0
75.0
91.0
110.0
140.0
185.0
255.0
400.0
FIGURE 7. Pressure flowfield (left - 200 km, right - 110 km, the DSMC method).
characteristics with a required accuracy. Consideration of the finite Mach number effects yields a more accurate
prediction of the moments Cn and Cm versus the altitude. However, the MLB method gives a higher value of
CA as compared to the DSMC results, whereas the value given by the LB method is lower (Fig. 8).
Such a situation is caused not by the influence of the gas/surface interaction model, but by the special features
of the configuration considered. Solar arrays of Base Block and Kvant modules are located perpendicular to
the incoming stream (see Fig. 1). Therefore, the molecules reflected from solar arrays of the Base Block occur
on Kvant solar arrays in the free-molecular regime, leading to a decrease in the axial force (see Figure 9, which
shows the reflected molecule flux over the SS "Mir" configurations obtained by the TPMC method). Table 3
750
160
H, km
FIGURE 8. Aerodynamic characteristics of the second configuration (left - axial force coefficient, center - yawing
moment coefficient, right - pitching moment coefficient, zero angle of attack).
1.Oe-05
2.0e-05
3.Oe-05
4.Oe-05
5.Oe-05
6.Oe-05
7.Oe-05
8.Oe-05
9.Oe-05
l.Oe-04
l.le-04
1.2e-04
1.3e-04
1.4e-04
1.5e-04
1.6e-04
1.7e-04
1.8e-04
1.9e-04
2.0e-04
2.1e-04
2.2e-04
2.3e-04
2.4e-04
FIGURE 9. Molecular flux due to multiple reflection (values in #/m2sec, TPMC method)
TABLE 3. Contribution of different effects into total aerodynamics characteristics of the second configuration (zero angle of attack)
____Geometric shadow
58.52
CA
0.253
Cn
0.805
Semishadow and shielding
3.65
-0.203
-0.683
Multiple reflection
-1.20
-0.002
-0.065
lists the contributions of the geometric shadow, finite Mach number effects, and multiple reflection to the
aerodynamic characteristics of this configuration of the SS "Mir". In contrast to the first configuration, the
contribution of multiple reflection to the axial force is comparable with the contribution of finite Mach number
effects but has the opposite sign. Therefore, for the configuration considered, it is insufficient to take into
account semishadow and shielding for reasonable prediction of the SS "Mir" aerodynamics, and it is necessary
to take into account multiple molecule reflection effects on free-molecular aerodynamics of the SS "Mir".
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CONCLUSIONS
The DSMC studies of aerodynamics of the Space Station "Mir" along the descent trajectory showed that
the change in its aerodynamic characteristics is small down to an altitude of 140 km. A further decrease in
the altitude leads to a reconstruction of the flow near the SS "Mir" and significant changes in its aerodynamic
characteristics.
The use of the traditional LB method, which takes into account only the geometric shadowing of some
elements of the SS by others, does not allow one to predict, with a required accuracy, the aerodynamic
characteristics of the SS "Mir" at small angles of attack and sideslip. The reasons for the low accuracy of the
LB prediction are the neglect of the finite Mach number (semishadow and shielding) and multiple molecule
reflection effects.
A modified LB code was developed, which allows on to take into account semishadow and shielding and
significantly increase the accuracy of predicting the aerodynamics of complex-shaped bodies. However, for
some configurations of the SS "Mir", multiple molecule reflection exerts an effect of the aerodynamics of the
SS "Mir", which is comparable with the finite Mach number effects. A further increase in the accuracy of the
LB prediction requires the use of the TPMC method for determining free-molecular limit.
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