Aerodynamics of Fragment in Spacecraft Wake
P. Vashchenkov, A. Kashkovsky and M. Ivanov
Institute of Theoretical and Applied Mechanics SB RAS,
630090 Novosibirsk Russia
Abstract. Forces acting on spacecraft fragments located at different points of the aerodynamic wake of the
spacecraft are considered in the present paper. Special attention is paid to aerodynamic parameters of the fragment
directly interacting with the shock wave generated by the spacecraft. The computations are performed by the
DSMC method.
INTRODUCTION
During deorbiting, the spacecraft experiences a considerable force and thermal action of the atmosphere, which usually
leads to its gradual destruction. The process of spacecraft destruction is accompanied by separation of a large number
of small fragments from the spacecraft surface, the size of the fragments being much smaller than the size of the
spacecraft.
One of the important problems is simulation of spacecraft destruction during its reentry is the analysis of motion
of the products of spacecraft disintegration. It is necessary to determine the region where the fragments hit the Earth
surface. If the spacecraft contains chemically active or radioactive materials, it is particularly important to know the
region where such fragments fall down onto the Earth.
The problem of motion of a cloud of fragments is difficult because of the aerodynamic influence of some fragments
on others [1]. It becomes even more complicated by the fact that the fragments separated from the spacecraft surface
are entrained downstream and enter the disturbed region bounded by the bow shock from the spacecraft. This region
is characterized by significant gradients of flow parameters, especially near the shock wave.
The main objective of the present work was to study the aerodynamic forces acting on a spacecraft fragment
located in the spacecraft wake. These aerodynamic characteristics will be later used to study the process of spacecraft
destruction and the motion of the cloud of fragments.
APPROACH TO THE SOLUTION
The aerodynamic characteristics of the fragment in the spacecraft wake were examined in a two-dimensional steady
model formulation. The spacecraft model was a cylindrical body with a base radius R. This is admissible since this
model is necessary to generate a shock wave, and the body shape has no significant influence on the shock-wave
structure further downstream. The wake behind the body was considered at very large distances 50R. A total of
69 points were chosen in the wake (predominantly, in the region of high gradients), where the fragment model was
located, and its aerodynamic characteristics were computed.
Two fragment models were used. As the spacecraft model, they were cylinders with base radii r 0 1R and
r 0 001R.
The wake can be divided into three zones:
•
•
Near wake: a subsonic zone is formed directly behind the spacecraft, and all perturbations that enter this zone are
transferred to the spacecraft and can affect its aerodynamic characteristics.
Far wake: a flow region bounded by the bow shock. This is a supersonic flow region characterized by small
gradients of flow parameters. The flow around the fragment in this region almost corresponds to a uniform flow
CP663, Rarefied Gas Dynamics: 23rd International Symposium, edited by A. D. Ketsdever and E. P. Muntz
© 2003 American Institute of Physics 0-7354-0124-1/03/$20.00
226
•
with parameters taken for this point in the spacecraft wake.
Vicinity of the shock wave: flow region characterized by high gradients of flow parameters. This region attracts
the major attention, since the shock wave from the fragment located in this region has a complicated interaction
with the shock wave generated by the spacecraft, which leads to specific variations in aerodynamic characteristics
of the fragment.
NUMERICAL METHOD AND FLOW CONDITIONS
The DSMC computations were performed using a two-dimensional variant of the SMILE code [2] developed at ITAM.
The variable hard sphere (VHS) model was used for computations of particle collisions. The energy exchange between
internal and translational degrees of freedom of molecules was simulated by the Larsen-Borgnakke model. The TCE
model [2] was used to model chemical reactions.
The gas–surface interaction was simulated using the Nocilla model. In this model, the values of the tangential and
normal momentum are calculated as functions of the angle of particle incidence, based on experimental data for widely
used construction materials. It was assumed that the spacecraft surface is made of an aluminum–magnesium alloy.
The atmospheric parameters correspond to conditions at an altitude of 95 km: temperature T∞ 178 K, static
pressure p∞ 8 1 10 2 Pa, and velocity V 7400 m/s (M 27 5). As was mentioned previously, the spacecraft
model was a cylinder of radius R 1 m, and the fragments were cylinders of radii r 0 1 m and r 0 001 m. The
surface temperature in all cases was TW 800 K. The free-stream Knudsen number based on the spacecraft diameter
was Kn∞ 0 018.
N
O
N2
O2
NO
Chemical composition of the gas:
0.0 0.01 0.77 0.22 0.0
COMPUTATIONAL TECHNIQUE
First, an undisturbed flow around the spacecraft was calculated in a computational domain of rather large dimensions
(52R 17R). To improve the efficiency, the computational domain was divided into subdomains. In the first subdomain
(x
2R 30R), the spacecraft nose was located at the point (0; 0). The parameters at the output boundary of this
domain were used as the free-stream parameters in the second subdomain (x 30R 50R).
In the case of such a division of the flow region, one can use different time steps in each subdomain, and the solution
converges to the steady state more rapidly than in the case without domain division. The reason is that the gas density
in the second subdomain is significantly lower than in the first one. Thus, greater cells and time step can be used in the
second subdomain.
After that, new subdomains were cut in the resultant flow fields, where the fragments were located. The data
computed for the flow around the spacecraft were used as the boundary conditions in solving the problem of the flow
around the fragment. Locating the fragments to different points of the wake, it is possible to obtain their aerodynamic
characteristics and construct the field of their values.
Figure 1 shows the pressure field near the main body of the spacecraft and the locations of points where the
fragments were placed. Flow subdomains can also be seen in the figure. The discontinuity of the isobars at the boundary
of subdomains in Fig. 1 is caused by the specific features of the graphical program.
Special attention was paid to aerodynamic characteristics of fragments near the shock wave (SW): the gradients of
gas-dynamic parameters are very large in the vicinity of the shock wave, and an insignificant change in the fragment
position to either side involves a substantial change in aerodynamic characteristics.
The gas-dynamic parameters across the flow in the far wake vary without significant gradients, and the values of
aerodynamic characteristics in this region can be interpolated with a smaller number of points; therefore, the grid is
coarser here.
FIELDS OF AERODYNAMIC PARAMETERS
Interpolating the coefficients at the chosen points to the entire computational domain, one can obtain the fields of the
Fy
Mz
drag coefficient CA S ρ FVx 2 2 , lift coefficient CN
, and pitching moment Cm
. The reference
S ρ V2 2
S Lρ V 2 2
∞ ∞
∞ ∞
227
∞ ∞
P/P_inf
15
10
5
0
0
5
10
15
FIGURE 1.
20
25
30
35
40
45
50
1.5
3.1
4.9
6.8
8.9
11.3
13.8
16.7
19.9
23.5
27.5
32.2
37.6
43.8
51.2
60.1
70.9
84.5
101.9
125.2
157.7
206.5
287.9
450.6
Pressure field and locations of the spacecraft and fragments
area S and the reference length L are equal to the mid-section area and the diameter of the corresponding fragment,
respectively. The pitching moment was calculated relative to the centerline of the cylindrical fragments. These fields
are plotted in Figs. 2, 3, and 4, respectively.
The values of aerodynamic coefficients for the fragment with r 0 1R are significantly lower than for a smaller
fragment with r 0 001R. The reason is that the flow around a smaller fragment is closer to the free-molecular regime
than the flow around a larger fragment, the free-stream conditions being identical. In the former case, energy losses in
the bow shock wave ahead of the fragments are smaller, and greater values of the aerodynamic force coefficients are
obtained.
It is seen in the figures that the changes in aerodynamic coefficients actually repeat the wake structure. As was
expected, the greatest influence on the aerodynamic characteristics of the fragments is observed in the vicinity of the
shock wave. The changes in the drag and lift forces are caused by the changes in flow parameters. Some effect is also
exerted by the angle of attack. The changes in the pitching moment of a cylindrical fragment can only be induced by
an asymmetric flow around its lower and upper parts, which is observed in Fig. 4. In the region of the far aerodynamic
wake behind the spacecraft, where the gradients of flow parameters are small, the pitching moment is m z 0, and the
maximum values are observed in the vicinity of the shock wave.
However, even in this region with low gradients of flow parameters, the changes in the pitching moment are small
in magnitude. The reason is that the flow around the fragment is supersonic, and there is always a shock wave ahead
of the fragment, which levels out the flow asymmetry.
For a smaller fragment, the pitching moment equals zero within the entire domain, since the fragment size is too
small as compared to the shock-wave thickness ( 30 cm), and the flow parameters at the opposite sides of the fragment
remain almost unchanged.
EFFECT OF THE SHOCK WAVE ON THE FRAGMENT AND ITS POSSIBLE MOTION
Based on the values of the drag and lift coefficients and on Fig. 3, one can conclude that Cy is always positive inside
the shock wave and in the wake in the vicinity of the shock wave, except for a section directly behind the body, i.e.,
all fragments in the wake experience the action of forces that try to shift the fragments to the periphery. This fact is
explained by the general character of the flow, which expands behind the shock wave.
The resultant aerodynamic force in the far wake is directed along the streamline at a given point. The gradients
of flow parameters in this region are very small, and the flow may be considered as uniform. The aerodynamic
characteristics of the fragment in the far wake behind the spacecraft can be calculated by engineering methods.
In the vicinity of the shock wave and inside it, the shock wave from the spacecraft interacts with the bow shock from
the fragment; as a result, the latter becomes significantly deformed. Figure 6 shows the flow around the spacecraft
without and with a fragment located in the shock wave generated by the spacecraft. Comparing these two fields, one
can note that the upper and lower branches of the wave formed by the fragment enter flow regions with different
parameters. The fragment experiences the action of a very asymmetric flow, and the pressure on the lower part of the
228
r=0.1R
10
0
0
10
20
30
40
50
20
30
40
50
r=0.001R
10
C_A
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
3.6
4.0
4.4
4.8
5.2
5.6
6.0
6.4
6.8
7.2
7.6
8.0
8.4
8.8
9.2
9.6
0
0
10
FIGURE 2.
Flow field of the drag coefficient of the fragments.
r=0.1R
10
0
0
10
20
30
40
50
20
30
40
50
r=0.001R
10
C_N
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
0
0
10
FIGURE 3.
Flow field of the lift coefficient of the fragments.
10
0
0
10
FIGURE 4.
20
30
40
Flow field of the pitching moment of the fragment (r
229
50
0 1R).
Cm
-0.17
-0.16
-0.15
-0.14
-0.13
-0.12
-0.11
-0.10
-0.09
-0.08
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0.0
0.01
0.02
0.03
0.04
0.05
0.06
FIGURE 5. Streamlines in the spacecraft wake.
fragment is significantly greater than the pressure on the upper part. In a larger scale, the shock-wave deformation
is depicted in Fig. 7. The picture shows both the pressure isolines in the spacecraft wake without the fragment and
the pressure isolines changed by the fragment introduced into the flow. Significant asymmetry of the flow around the
fragment can be noted. Because of the asymmetry of pressure distribution, a lift force arises even in the flow around
an axisymmetric fragment, and the resultant force deflects from the streamlines.
Let us consider the change in the direction of the resultant aerodynamic force acting on the fragment along the
line perpendicular to the plane of symmetry (see Fig. 8). The solid curve shows the slope of the streamlines in the
spacecraft wake in the absence of the fragment versus the function of the distance from the plane of symmetry in three
cross sections: x 3 29, and 49 m. The markers indicate the slope of the resultant force acting on the fragment of
radius r 0 1R. The dashed curve shows the pressure distribution in the same cross section.
Far away from the plane of symmetry, the fragment is in a uniform flow, and the resultant aerodynamic force is
directed along the streamlines.
In the zone of the smeared shock wave, the fragment experiences the action of a flow with significant gradients of
gas-dynamic parameters; as a consequence, the resultant aerodynamic force deviates from the streamlines toward the
free-stream direction.
At the lower boundary of the shock wave, the flow around the fragment becomes symmetric again. In this case, the
direction of the resultant force coincides with the streamlines.
As the distance from the plane of symmetry further decreases, the fragment enters the region of a gradient flow.
This leads to deviation of the resultant force from the direction of the streamlines toward the plane of symmetry.
Flow gradients in the vicinity of the plane of symmetry are insignificant, and the flow around the fragment is almost
symmetric. Thus, the resultant force in this region is directed along the streamlines.
The trajectory of fragment motion in the wake can be calculated only by means of dynamic modeling. Nevertheless,
the results considered above allow one to assume that the fragment should have a certain kinetic energy to leave the
shock-wave region. Otherwise, it will be cast away to the far wake. If the fragment still overcomes the “barrier" of
the shock wave, it will be thrown to a certain distance into the external flow. Later on, however, it will experience the
action of the free stream, which, possibly (depending on the fragment mass), will press it to the shock wave. In this
case, the fragment will “slide" over the fore front of the shock wave.
The smaller fragment of radius r 0 001R does not experience the flow nonuniformity in the smeared shock wave
because of the large difference between the fragment size and the shock-wave thickness. This means that the magnitude
of aerodynamic forces changes only with changing flow parameters, and the direction of aerodynamic forces coincides
with the streamlines at all points of the wake. The streamlines are plotted in Fig. 5.
Thus, it is reasonable to assume that the cloud of small fragments formed by spacecraft destruction expands with
distance downstream from the spacecraft and is bounded by branches of the shock wave induced by the spacecraft.
Since the shock wave degenerates with time and disappears at a certain distance (a uniform flow is again established),
the maximum size of the cloud remains commensurable with the width of the disturbed flow region after vanishing of
the shock wave. The cloud changes its shape from conical (in the three-dimensional case) to cylindrical.
230
12
Normalized
density
10
8
16
14
6
4
22
2
12
0
−2
0
2
4
6
8
10 12 14
16 18
12
20 22
22
10
14
8
6
4
22
18
22
16
18
14
2
12
0
−2
0
2
4
0.04
0.08
0.12
4 0.17
0.22
6 0.27
0.34
8 0.40
10
0.48
10 0.57
0.67
24 26 28 30 12 0.78
0.91
14 1.06
1.24
16 1.46
18 1.72
2.05
20 2.47
3.03
12
3.82
22 5.01
6.98
24 10.92
2
14
12
12
6
8
10 12 14
16 18
20 22
24
26 28 30
FIGURE 6. Perturbations introduced into the mass-density field by the fragment with r 0 1R: interaction of the fragment with
the shock wave induced by the spacecraft (top) and the flow disturbed by the spacecraft only (bottom).
P/P_inf
1.5
3.1
4.9
6.8
8.9
11.3
13.8
16.7
19.9
23.5
27.5
32.2
37.6
43.8
51.2
60.1
70.9
84.5
101.9
125.2
157.7
206.5
287.9
450.6
6
4
2
0
−2
0
FIGURE 7.
2
4
6
8
Effect of the fragment on pressure distribution.
EFFECT OF THE FRAGMENT ON AERODYNAMIC CHARACTERISTICS OF THE
SPACECRAFT
As was shown above, the spacecraft exerts a significant effect on aerodynamic characteristics of the fragment.
Nevertheless, the opposite situation is possible, i.e., the aerodynamic coefficients of the spacecraft can be changed
under the influence of the fragment. This can occur in two cases:
•
Perturbations induced by the fragment affect the spacecraft directly;
231
0
angle of stream
8
16
0
24
32 40
12
P/P_inf Y
11
angle of force
Pressure
5
10
15
20 25
16
P/P_inf Y
14
10
0 25 50 75 100 125 150
4.5
12
9
P/P_inf Y
4.0
8
3.5
7
3.0
6
2.5
5
2.0
4
1.5
3
1.0
2
0.5
1
10
8
6
4
2
0
10
0
0
0.0
-10
Angle
Angle
Angle
-20
0
20
x=3m
5
10
15
0
20
5
15
20
x=49m
x=29m
FIGURE 8.
10
Slope of the flow and resultant force.
Mach_number
1.0
3 2.0
3.0
5 4.0
5.0
7 6.0
7.0
9 8.0
9.0
11 10.0
11.0
13 12.0
13.0
15 14.0
15.0
17 16.0
17.0
19 18.0
19.0
21 20.0
21.0
23 22.0
23.0
25 24.0
1
6
4
25
5
2
3
1
0
−2
0
2
4
6
8
FIGURE 9. Mach number field.
The gray line shows the influence region of the fragment on aerodynamic characteristics of the spacecraft body.
•
Perturbations induced by the fragment affect the subsonic near wake and lead to its deformation, which alters the
aerodynamic characteristics of the spacecraft.
The subsonic flow in the aerodynamic wake is observed only in some region near the spacecraft. The size of this
subsonic region is comparable with the size of the spacecraft itself. The gas in the remaining part of the wake moves
with a supersonic velocity, and the perturbations from the fragment located rather far from the body cannot reach the
subsonic region. Thus, the region of fragment influence on the spacecraft is limited. The boundaries of this region for
the fragment with r 0 1R are plotted in Fig. 9.
The aerodynamic coefficients of the spacecraft for various positions of the fragment with r 0 1R are listed in
Table 1. The position x f y f ∞ corresponds to the flow around the spacecraft with no allowance for the fragment.
Owing to its small size, the fragment of radius r 0 001R generates significantly smaller perturbations and does
not change the aerodynamic characteristics of the spacecraft.
232
TABLE 1.
Aerodynamic coefficients of the spacecraft
Coordinates
of the fragment
xf , m
Aerodynamic characteristics of the spacecraft
yf , m
CA
CN
CM
∞
∞
1.430
0.0
1
1.1
1.5
1.75
2.25
2.5
1.43
1.42
1.39
1.41
1.43
-0.10
-0.09
-0.04
0.00
0.0
-0.01
0.01
0.01
0.0
0.0
2
0.46
1.0
2.0
2.6
2.8
1.43
1.40
1.40
1.42
1.43
-0.00
-0.01
0.00
0.00
0.00
0.0
0.00
0.0
0.0
0.0
3
0.0
1.0
2.4
3.2
1.42
1.41
1.42
1.43
0.0
0.00
0.0
0.0
0.0
0.0
0.0
0.0
4
0.0
1.0
1.5
1.42
1.42
1.43
0.0
0.0
0.0
0.0
0.0
0.0
6
0.0
1.43
0.0
0.0
0.0
CONCLUSIONS
The present study yields the following results.
•
The variation of flow parameters around fragments of various sizes in the spacecraft wake is considered, and
the distributions of aerodynamic characteristics in the flow with the Knudsen numbers based on the free-stream
parameters and spacecraft diameter Kn 0 02 is constructed. These data can be used in modeling the trajectory
of individual fragments of different mass.
It is not at all points of the spacecraft wake that the direction of the resultant force acting on the fragment
coincides with the streamlines obtained in computations with no allowance for the fragment. This should be
taken into account in computing aerodynamics of the cloud.
In calculating the aerodynamic characteristics of the fragments, the most careful analysis should be performed in
the vicinity of the smeared shock wave, and the use of the DSMC method is preferable. Engineering methods can
be used in the far wake.
The fragments formed during spacecraft destruction are mainly located inside the wake formed by the shock
wave.
It is shown that the influence of fragments on the aerodynamic characteristics of the spacecraft is small and
decreases as the fragment size becomes smaller. The influence region of the fragments on the spacecraft is mainly
determined by the size of the subsonic flow region behind the spacecraft.
•
•
•
•
REFERENCES
1.
2.
3.
Ivanov M.S., Kashkovsky A.V., Grinberg E.I. Statistical Simulation of space debris cloud aerodynamics in the free-molecular
and transitional regimes // Proc. XIX Intern. Conf. on Rarefied Gas Dynamics. -Oxford University Press. -1995. -Vol.2.
-P.1401-1408.
Ivanov M.S., Markelov G.N., Gimelshein S.F., Statistical Simulation of Reactive Rarefied Flows: Numerical Approach and
Applications AIAA Paper 98-2669, Albuquerque, 1998.
G. Koppenwallner, M. Ivanov, D. Johannsmeier, A. Kashkovsky
Executive Summary of Free Molecular and Transitional Aerodynamics of Spacecraft. HTG Report 94-1.
233