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The main focus of the present paper is to computational fluid dynamics analysis and design of payload fairing of
satellite launch vehicle at freestream Mach number range of 0.6 - 3.0. Initially, time-dependent compressible three-
dimensional Euler equations are solved employing a finite volume discretization method with a multi-stage Runge-
Kutta time-stepping scheme to compute surface pressure and aerodynamic coefficients at various payload fairing and
at angle of attack up to 5o with an increment of 1o. Payload fairing dimensions are selected that satisfies permissible
structure load on satellite launch vehicle. Detailed flowfield simulation is carried out on the selected payload fairing
employing axisymmetric compressible Reynolds-average Navier-Stokes equations to assess unsteady flowfield
characteristics. The numerical simulations are used to locate terminal shock on the payload fairing at transonic Mach
number. Unsteady flow characteristics are used to compute acoustic load. Shock standoff distances at supersonic
speeds are tabulated and compared with the analytical solution. Schlieren images and oil flow pictures are compared
with experimental results and in good agreement. Aerodynamic shape optimization of satellite launch vehicle payload
fairing shape has been performed to satisfy structural load at maximum drag and dynamic pressure.
Keywords: CFD; compressible flow; satellite launch vehicle; transonic flow; supersonic flow; shock wave;
aerodynamic forces and moments; separated flow.
Copyright © 2022 The Author(s): This is an open-access article distributed under the terms of the Creative Commons Attribution 4.0 International
License (CC BY-NC 4.0) which permits unrestricted use, distribution, and reproduction in any medium for non-commercial use provided the original
author and source are credited.
© 2022 Scholars Journal of Engineering and Technology | Published by SAS Publishers, India 17
Rakhab C. Mehta., Sch J Eng Tech, Apr, 2022; 10(4): 16-34
Fig 1(a): Schematic sketch of flow field over payload shroud at transonic speed
Fig 1(b): Schematic sketch of flow field over payload shroud at supersonic speed
© 2022 Scholars Journal of Engineering and Technology | Published by SAS Publishers, India 18
Rakhab C. Mehta., Sch J Eng Tech, Apr, 2022; 10(4): 16-34
2. NUMERICAL ANALYSIS forces. The high-speed flow over the payload fairing is
Governing Equations expressed by Euler equations of motion in a flux vector
The fluid motion of governed by time form as:
dependent three-dimensional compressible inviscid U F G H
0 ………….. (1)
equations which express the conservation of mass, t x y z
momentum and energy in the absence of external
Where
u v w
u uv
u p
2
uw
U v ' F u v
, G v p , H vw
2
w u w v w w p
2
e ( e p ) u ( e p ) v ( e p ) w
are the U state vector conserved quantities solver. The numerical scheme is advanced in time with
with , u, v, w and e denoting the density, Cartesian a third order Runge-Kutta method [22]. AUSM+
velocity components, and the specific total energy, scheme is employed here to evaluate the inviscid fluxes
respectively, and inviscid flux vectors, F, G and H in by splitting them as a convective and pressure terms.
the Cartesian coordinates x, y and z. With the ideal gas The spatial discretization described above reduces the
assumption, the pressure and total enthalpy can be integral equation to semi-discrete ordinary differential
expressed as: equations. The numerical algorithm is second-order
p 1 accurate in space discretization and time integration.
e u 2 v 2 w 2 …………. (2) The numerical scheme is stable for a Courant number
1 2 2. Local time steps are used to accelerate to a steady-
here is the ratio of specific heats. state solution by setting the time-step at each point to
the maximum value allowed by the local Courant-
Numerical algorithm Friedrichs-Lewy (CFL) condition.
To simplify the spatial discretization in
numerical technique, Eq. (1) can be written in the Initial and boundary conditions
integral form over a finite computational domain Ω with To solve the equations of motion, one has to
the boundary Γ as: have the initial boundary conditions, which defines a
Ud E F G d Hd ………. (3)
particular problem. At the inflow, all the flow variables
are taken at the freestream values as tabulated in Table
1.
Here Ω is a control volume with surface Γ. The
contour integration around the boundary of the cell is At a solid wall, the velocity tangential to the
performed in anticlockwise sense in order to keep flux boundary is applied since the flow is inviscid. At
vectors normal to boundary of the cell. The transonic freestream Mach number, the computational
computational domain has a finite number of non- domain of dependence is unbounded, and the
overlapping hexahedral cells. In a cell centred finite implementation of boundary and initial conditions
volume method, the flux variables are stored at the become critical, the known physically acceptance of
centroid of the grid cell and the control volume is far-field boundary conditions usually limit the flow
formed by the cell itself. The conservation variables variables to asymptotic values at large distance from the
within the computational cell are represented by their payload fairing. Therefore, suitable coordinate
average values at the cell centre. stretching and placement of the far-field boundary
condition have been considered in numerical
The inviscid fluxes are computed at the cell- simulations. The freestream conditions are prescribed
centre resulting in flux balance. The summation is on the outer boundary. For supersonic flow, all of the
carried out over the eight edges of the cell. The space flow variables are extrapolated from the vector of
discretization scheme shares the reconstruction of the conserved variables U. An image cell is imposed to the
conservative variables of cell interfaces but differ in the solved variables at the line of symmetry ahead of the
evaluation of fluxes in time stepping. The inviscid vehicle.
fluxes are obtained from Roe’s approximate Reimann
© 2022 Scholars Journal of Engineering and Technology | Published by SAS Publishers, India 19
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Table 1: Initial conditions
M p 105 Pa T K
0.8 0.83 266
0.9 0.787 258
0.95 0.766 254
1.0 0.93 250
1.1 0.68 241
1.2 0.64 232
1.5 0.45 207
1.75 0.36 186
2.0 0.285 166
2.5 0.184 134
3.0 0.122 107
© 2022 Scholars Journal of Engineering and Technology | Published by SAS Publishers, India 20
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2.5 Dimension of Payload Shroud and computational boundary is about 6 - 9 times the
Computational Grid diameter of the module; D. The computational domain
Table 2 and Fig 2 shows the NASA depends on freestream Mach number. Figures 3 show
recommended geometrical dimensions for payload three-dimensional view of grid over the payload fairing.
shroud. The geometrical parameters 1, 2, l1, l1, RN, D The grid arrangement is found to yield a relative
and d are employed to compute the aerodynamic loads. difference of about ± 3% in the pressure peak, which is
The dimensions of the payload shroud are in the range in the same range as the stagnation pressure
of the NASA recommended criteria. We have carried measurement error in the wind-tunnel. The convergence
out numerical simulations of several configurations and criterion is based on the difference in density values at
the dimensions are tabulated in Table 3. any of the grid points, between two successive
iterations │ρn+1 − ρn│≤ 10-5 where n is time-step
The body-oriented grids are generated using a counter. The numerical computations were carried out
homotopy one-to-one and onto technique in conjunction with various grid arrangements in order to meet a grid
with finite element method [23]. The stretched grids are independency check. Grids typically contained 46 cells
generated in an orderly manner. Efficient computation in the longitudinal direction, 45 cells in the transverse
of cell volume in flow prediction is used as described in direction, and 15 – 25 cells in the body-normal
Ref. [24]. A non-uniform and non-overlapping direction. The minimum grid size in the normal
structured computational cell is generated for numerical direction of the payload fairing is about 1.70 × 10-4 m.
simulations. The grid-stretching factor is selected as 4, The internal grid cells were constructed so that all of the
and the outer boundary of the computational domain is nose pressure ports coincide with the center of a finite
maintained as 3.5 − 4.5 times maximum diameter D of volume cell face.
the payload fairing. In the downstream direction, the
1.5
M = 3.00
M = 2.50
1.0 M = 1.50
M = 1.20
M = 0.98
M = 0.90
0.5 M = 0.80
CP
-0.5
-1.0
-0.5 0 0.5 1.0 1.5 2.0 2.5
x/D
Fig 5 (a): Variation of windward pressure coefficient at angle of attack α = 1o
1.5
M = 3.0
M = 2.5
1.0 M = 1.5
M = 1.2
M= 0.98
M= 0.90
0.5 M = 0.8
CP
-0.5
-1.0
-0.5 0 0.5 1.0 1.5 2.0 2.5
x/D
Fig 5(b): Variation of leeward pressure coefficient at angle of attack α = 1o
© 2022 Scholars Journal of Engineering and Technology | Published by SAS Publishers, India 22
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The centre of aerodynamic pressure is evaluated using In the next section we will compute viscous
the following expression flow over SLV-1, SLV-5 and SLV-7. The viscous
solution will compute the effect of shock wave
Cp, xr cos dxdx
L
boundary layer interaction over the payload and
X CP 0 0
geometrical induced flow separation in the boat tail
Cp, xr cos ddx …………….. (7)
L
region. This analysis will also compute unsteady flow
0 0 caused by shock wave boundary layer interaction.
© 2022 Scholars Journal of Engineering and Technology | Published by SAS Publishers, India 23
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Table 4: Aerodynamic forces and moment for various payload shroud of satellite launch vehicle
M SLV-1 SLV-2 SLV-3 SLV-4 SLV-5 SLV-6 SLV-7
CN, XCP CN, XCP CN, XCP CN, XCP CN, XCP CN, XCP CN, XCP
0.75 1.67 5.40 0.94 1.25 1.12 1.31 0.94 1.23 0.94 1.25 1.12 3.31 1.12 1.31
0.80 2.03 5.03 1.28 1.75 1.13 1.56 1.28 1.75 1.28 1.75 1.13 1.58 1.13 1.58
0.90 - - 2.34 2.35 2.36 2.35 2.34 2.35 2.34 2.35 2.36 2.35 2.36 2.35
0.95 4.62 4.82 2.50 1.86 2.54 2.13 2.50 1.86 2.50 1.86 2.84 2.13 2.54 2.13
0.98 - - 3.03 2.04 2.74 2.07 3.03 2.04 3.03 2.04 2.74 2.07 2.74 2.06
1.00 4.70 4.21 3.27 2.05 3.10 3.73 3.27 2.05 3.27 2.05 3.10 2.33 3.10 2.38
1.20 4.85 3.23 3.78 2.96 2.80 2.13 3.78 2.96 3.87 2.96 3.23 2.85 3.73 2.85
1.40 4.10 2.84 2.90 2.96 3.22 2.49 2.90 2.29 2.90 2.29 2.80 2.13 2.80 2.13
1.60 3.74 2.60 3.38 3.38 2.90 2.27 3.38 2.70 2.38 2.70 3.23 1.49 2.32 2.49
1.80 3.48 2.43 3.87 2.48 2.69 2.12 3.07 2.28 3.07 2.48 2.90 2.27 2.90 2.27
2.00 3.48 2.43 2.81 2.27 2.83 2.32 2.81 2.27 2.82 2.27 2.69 2.12 2.69 2.12
3.00 3.30 2.36 2.81 2.29 3.12 3.29 2.72 2.29 2.72 2.29 2.83 2.35 2.83 2.34
4
CN/rad
1
0.5 1.0 1.5 2.0 2.5 3.0
M
Fig 7(a): Variation of normal force vs. Mach number for SLV-7
© 2022 Scholars Journal of Engineering and Technology | Published by SAS Publishers, India 24
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3.5
2.8
XCP m
2.1
1.4
0.5 1.0 1.5 2.0 2.5 3.0
M
Fig 7(b): Variation of aerodynamic centre of pressure vs. Mach number for SLV-7
© 2022 Scholars Journal of Engineering and Technology | Published by SAS Publishers, India 25
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At the line of symmetry ahead of the heat shield, an arrangement is found to yield a relative difference of
image cell is imposed to the solved variables. about ± 3% in the pressure peak, which is in the same
range as the pressure measurement error in the wind
tunnel with a blockage ratio of about 0.3%. The
Model and Computational Grid convergence criterion is based on the difference in
The body-oriented grids are generated using a density values at any of the grid points, between two
homotopy scheme in conjunction with finite element successive iterations │ρn+1 − ρn│≤ 10-5 where n is time-
method [23]. The stretched grids are generated in an step counter. The numerical computations were carried
orderly manner. A non-uniform and non-overlapping out with different grid arrangements in order to get a
structured grid is generated for numerical simulations. grid independency check. The computation is
The grid-stretching factor is selected as 5, and the outer performed using 132 × 62 grid points over the
boundary of the computational domain is maintained as hemisphere-cylinder. The finer grid near the wall helps
3.5 − 4.5 times maximum diameter D of the heat shield. to resolve the boundary layer. The coarse grid
In the downstream direction, the computational economizes the computer time. The minimum grid size
boundary is about 6 − 9 times the diameter of the in the normal direction of the heat shield is about 1.70
module; D. Figure 8 shows view of grid over the 10-4 m. A global time-step ∆t is used rather than the grid
payload shroud of SLV-7. We have displayed grid with varying time-step to simulate time accurate solution.
one-plane rotation in order to check the axisymmetry of
grid distribution over the heat shield. The grid
© 2022 Scholars Journal of Engineering and Technology | Published by SAS Publishers, India 26
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Fig 13: Comparison between density contour and schlieren picture SLV-7
© 2022 Scholars Journal of Engineering and Technology | Published by SAS Publishers, India 29
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Table 7: Location of terminal shock on payload shroud SLV-7
M∞ LT/D, measured LT/D, computed
0.80 1.19 1.186
0.90 1.54 1.538
0.95 2.17 2.15
1.00 2.59 2.581
Table 8: Separation length (LH) in boat tail region for various scale model of payload shroud of SLV-7
M∞ Model 1:52 Model 1:26 Model 1:14 Flight
0.80 6.87 6.90 7.10 7.0
0.85 7.11
0.88 7.30 7.30 7.83 7.50
0.90 7.66 7.70 8.55 8.00
0.95 8.30 9.50 11.22 10.42
0.98 10.22 10.68 11.88 10.94
1.00 11.10 12.00 13.12 12.77
1.10 7.00 7.22 7.70 7.45
1.20 6.54 6.88 7.44 7.30
1.30 6.33 6.47 7.00 6.88
1.40 6.00 6.33 6.70 6.48
1.50 5.90 6.50
1.60 5.66 5.80 6.25 6.12
2.00 5.11 5.25 5.45 5.40
ReD 1.5106 3.0106 4.0106 40.0106
Table 9: Bow shock wave standoff distance for payload shroud of SLV-7
M∞ ∆/RN, computed ∆/RN, Zierep et al.,
1.2 1.15 0.122
1.4 0.55 0.559
1.6 0.30 0.348
1.8 0.26 0.236
2.0 0.24 0.171
2.5 0.18 0.097
3.0 0.10 0.045
RESULTS AND DISCUSSION 0.94, α1 = 15o and M∞ = 0.94, α1 = 20o. Figure 14 shows
Flowfield characteristics over axisymmetric payload oil flow simulation over payload shroud of SLV-7. The
fairing flow attachment can be noticed by the accumulation of
Figures 9–11 show density contours over oil and it compares well with the experimental results.
payload shroud of SLV-5, SLV-6 and SLV-7. The
density contours have captured all the essential flow Wall Pressure fluctuations
field characteristic of transonic and supersonic Mach Figure 15 shows variation of pressure
numbers. The density contours are function of payload coefficient along payload shroud of SLV-7. The surface
dimensions as well as freestream Mach number. pressure coefficient shows the effect of freestream
Nomenclature of the terminal shock distance, length of Mach numbers.
separated flow in the boat tail and bow shock standoff
distance is shown in Fig. 1(a) and (b). Table 7 shows Shock induced separation. All the essential
the location of terminal shock on payload shroud SLV- features of transonic flow are well captured and a
7. It can be observed the shock movement is non-linear separation zone is observed in the cylinder region. The
function of freestream Mach number. It increases with unsteady flow computation is continued till some
increasing freestream Mach number. Table 8 shows anticipated periodicity in the flow variables is observed.
separation length (LH) in boat tail region for various The study of the flow field in the cylinder region, the
scale model of payload shroud of SLV-7. Figure 12 shock locations, computed the surface pressure levels
shows the vector field over payload shroud of SLV-7 and the frequency content.
and Table 9 shows the standoff distance of the bow
shock from the blunt-nose. Figure 13(a), (b) and (c) The figure depicts a close-up view of the
shows comparison between density contour and velocity field in the hemisphere-cylinder body. It can be
schlieren picture SLV-7 for M∞ = 0.90, α1 = 15o, M∞ = seen from the velocity vector plots that the flow
separates at the junction of the hemisphere-cylinder
© 2022 Scholars Journal of Engineering and Technology | Published by SAS Publishers, India 30
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enclosing a recirculation region of low velocity. The Payload fairing of SLV exhibits high levels of
comparison between present results with experimental pressure fluctuations at transonic speeds attributed to
data shows some disagreement on the cylindrical region shock-wave/turbulent boundary-layer interactions
of the heat shield at M = 1.2. This is attributed to (SWTBLI) and associated with separated flow and
pressure loss along the expansion fan, poor recovery of formation of a vortex pair. One of the main attributed to
the pressure and separated flow on the boat tail region transonic shock-wave/boundary-layer interactions
of the heat shield. featuring intermittently attached separated flows over
the payload shroud region of a satellite launch vehicle.
Figure 16 shows variation of pressure
coefficient along payload shroud of SLV-7 at It has been found that the nose-cone semi-
supersonic speeds. The pressure coefficient in the boat angle is an important parameter that influences the
tail region shows formation of bucket that will influence development of unsteady flow over the payload region
reattachment point of the separated flow. of a launch-vehicle model. We will discussed
computation of acoustic load in the next section.
© 2022 Scholars Journal of Engineering and Technology | Published by SAS Publishers, India 31
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Fig 16: Variation of pressure coefficient along payload shroud of SLV-7 at supersonic speeds
Fig 17: Variation of unsteady pressure coefficient at M∞ = 0.90 payload shroud of SLV-7
Table 10: Sound pressure level (SPL) for payload shroud of SLV-7
M∞ 0.80 0.85 0.90 0.95 1.0 1.1
SPL dB 158.6 158.0 157.6 153.7 158.2 158.4
© 2022 Scholars Journal of Engineering and Technology | Published by SAS Publishers, India 32
Rakhab C. Mehta., Sch J Eng Tech, Apr, 2022; 10(4): 16-34
Sound pressure level analysis terminal shock and separated region adds in a
The main focus of solving RANS equations is systematic understanding of the unsteady flow
to analysis unsteady flow field [26] behaviour over characteristics under various freestream Mach numbers
SLV-7. Digital spectrum analysis associates with and various payload shroud geometry. The terminal
computed pressure coefficient is carried out using Fast shock moves downstream with increasing freestream
Fourier Transform of MATLAB [27]. Figure 17 shows Mach number. The location of the terminal shock is
variation of unsteady pressure coefficient at M∞ = 0.90 tabulated as a function of freestream Mach number. The
payload shroud of SLV-7. The characteristic time of the separation zone in the boat tail region is found as a
flow is D/u∞ = 2.68 × 10-4 s function of freestream Mach number and Reynolds
number.
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