Effect of jets interaction on the static stability for a launch vehicle
Sanjoy Kumar Saha, Navin Kumar kessop and Dipankar Das
Aerodynamics and Aerothermal Group
Vikram Sarabhai Space Centre, Thiruvanthapuram, India.
(sanjoy_kumar@vssc.gov.in, sanjoy_254@gmail.com)
ABSTRACT
Multi-jet interactions are associated with very complex flow involving turbulent flow mixing, shock-shock
interaction, shear layer interaction, external air jet interaction and mutual interaction between jets. CFD simulations have
been carried out for a typical multi-strapon launch vehicle configuration corresponding to flight conditions to investigate the
twin jets interaction phenomena and the associated effect on the load distribution. Numerical simulations were carried out for
Mach number ranging from 0.60 to 4.0. The simulations are carried out at 40 angle of attack in a plane perpendicular to
strapon plane. The jet pressure ratio was varied from 0.73 to 61.91. The free-stream pressure reduces with altitude, which
results in higher jet pressure ratio. With the increase in the jet pressure ratio, jets spread more and results in jets interaction.
This will lead to reverse flow and alters the pressure distribution at the base of the vehicle. Hence, the load distribution over
the vehicle base region will change especially at very high pressure ratio. A reduction of 16% in overall vehicle load is
noticed at Mach number 4.0. As all these changes occur at the base of the vehicle, the centre of pressure of the vehicle shifts
towards vehicle nose. This makes the vehicle more unstable. Around 0.72D reduction is stability margin is observed at Mach
number 4.0 due to the presence of jet interaction.
Key Words: Jet interaction, CFD, Mach number, base pressure, reverse flow, stability.
1. INTRODUCTION
Multi-jet interactions have extensive applications in a wide variety of fields. The
developments of high performance aircraft, rocket, launch vehicle, industrial gas burner etc are the application
areas where multi-jet interaction is getting increased attention. Multi-jet interaction associated with the launch
vehicles during their flight through the atmosphere poses severe heat transfer problem in the rear part, especially
at the base region of the vehicle. As the launch vehicle gains altitude, the jet boundary continues to spread till
the jet pressure at the boundary matches with the external pressure. As the altitude increases, the ambient
pressure reduces and as a consequence the spreading or expansion of jet boundary increases. Depending on the
lateral distance between the nozzles, continuous widening or spreading of jet plumes with increasing altitude
results in the interception of jet boundaries at certain point of flight. The initial contact of jets may not produce
any significant consequences. However, as the altitude increases, further spreading of jets plume results into the
reversal of a portion of the jet shear layer towards the base region. The portion of the shear layer of the jet,
which does not have sufficient energy to pass through the shock at the jet plume interaction point, traverses back
towards the vehicle base region along with the external base flow in between the nozzles. The reverse flow
towards the base increases the pressure and temperature at the vehicle base region. Higher the altitude is, higher
is the reverse flow and hence, higher is the base pressure to ambient pressure ratio. This change in base pressure
will affect the load distribution at the base region.
Nomenclature:
M
D
X, Y, Z
P
XCP
CN
CD
Mach number
core diameter, m
coordinate directions, m
pressure, Pascal
location of centre of pressure in meter, measured from the vehicle nose
slope of the normal force coefficient
coefficient of drag
Subscripts
j
∞
jet
free stream
The main parameters that govern the flow field of a high-speed twin free jets are jet pressure to ambient
pressure ratio & nozzle spacing[1]. Several studies have been carried out so far to understand the jet interaction
phenomena[2-4] and its effect on the base thermal properties. In the present study, effort is made to understand
and quantify the effects of jet interaction on the vehicle load.
2. Methodology:
CFD code PARAS[5,6] is used to simulate the flow over the body. PARAS can simulate viscous,
turbulent, three-dimensional flow over an arbitrary body. It can solve both viscous and inviscid flow using finite
volume methods on Cartesian grids. Fluxes at the interface of the cell are computed by means of an approximate
Rieman solver. The explicit scheme is second order accurate in space and of TVD(Total Variation Diminishing)
type. Grids get adapted automatically based on the body geometry during grid generation. As the solution
proceeds, adding some more grids at the region of high flow gradients can refine the flow and at the same time
the extra cells are removed around the region of low gradients. Standard K- turbulence model has been used
here for simulation of the flow.
Grids and computational domain:
The configuration studied has a core vehicle with two strapon motors attached to it. The core nozzle
base is 0.75D ahead of the strapon nozzle base [Figure 1]. Co-ordinate system followed is given in Figure 2. The
origin is considered at the heat-shield nose tip location of the vehicle. The longitudinal, lateral and traverse
direction are represented by X, Y and Z direction respectively. X direction is positive towards vehicle base. The
domain selected for the simulations is shown in Figure 3 and is as followsUpstream
Downstream
Top, bottom and lateral
-2D (-7.5D for M ≤ 1.20)
+25D
±15D
Simulation has started with initial grids of 500 X 250 X 200 in longitudinal, lateral and transverse
directions respectively. Special attention has been taken for the base region of the vehicle to capture the reverse
flow and associated phenomena. Simulations have been carried out till good convergence in results is achieved.
Grid and domain independence tests have been done for the vehicle. Final grids are about 34-40 million for
different cases.
Simulations parameter:
The variation of ambient conditions considered for numerical simulations are listed in Table-1 below.
Table-1: Free stream properties used in simulations
Ambient pressure
Density
Mach Number
(Pascal)
(kg/m3)
0.60
76458.10
0.92946
0.80
60700.51
0.76407
0.90
51682.02
0.66791
0.95
47145.45
0.61874
1.10
34953.54
0.48542
1.20
28808.24
0.41736
1.50
18172.24
0.29399
2.00
9343.48
0.16760
2.50
4442.82
0.07353
3.00
2314.59
0.03617
3.50
1258.86
0.01892
4.00
687.36
0.00995
Jet exit properties at the nozzle exit are enforced. Care was taken to align the velocity vector with
respect to nozzle axis across the nozzle, i.e. the velocity vector close to the nozzle inside surface is parallel to
the nozzle surface and at the nozzle center, and the velocity is along the nozzle axis. Flow simulations are
carried out at an angle of attack 40.
3. RESULTS AND DISCUSSION
3.1 Jet Plume shape and Interaction Event:
The main factor that governs the jet plume shape is the jet pressure ratio at nozzle exit plane. The
pressure ratio at different Mach numbers is given in Table 2. At lower Mach numbers, the average pressure at
the nozzle exit is less as compared to that of free-stream pressure. Hence, the jets are over-expanded [Figure
3a]. As the altitude increases, the free stream pressure falls. The jet becomes gradually under-expanded for free
stream Mach number of 1.10 and above. The growth of plume shape is evident as Mach number increases
[Figure 3b]. The jets start interacting beyond Mach number 2.50 onward. As the altitude increase further, the
individual jet continues to spread further, resulting in upstream movement of jet interaction point towards base
[7]. A typical jet interaction event is plotted in Figure 3c for Mach number 4.0.
Table 2: Variation of jet pressure ratio with Mach number
M∞
Pj / P∞
0.60
0.73
0.80
0.77
0.90
0.83
0.95
0.87
1.10
1.10
1.20
1.34
1.50
2.30
2.00
4.87
2.50
10.79
3.00
20.71
3.50
38.07
4.00
61.91
Pressure distribution:
Jet interaction results in change in the flow field around the base. More the pluming, the stronger is the
jet interaction. This results in the stronger shock at the jet interaction plane. Hence more and more reverse flow
occurs. All this will change the pressure distribution at the base region of the vehicle. In Figure 4, the pressure
distribution over the strap-on is plotted. It is clear that at lower Mach numbers (M=0.80), the pressure
distribution does not show any difference. But at higher Mach numbers, jet-on pressure is more than the jet-off
pressure especially close to the base region. With increase of the jet pressure ratio, the zone of influence
increases. At Mach number 4.0, zone of influence is about 3.5D from the vehicle base.
In Figure 5, the ratio of base pressure to the ambient pressure for both core and strap-on at different
Mach numbers(0.60 to 4.0) for both jet-on and jet-off conditions is shown. For jet-on conditions, the core base
pressure is lower than the ambient pressure till Mach number 2.0. Both jet-on and jet-off data till Mach number
1.0 show a very close match. The base pressure becomes higher than the ambient pressure above Mach number
2.0. This is due to the reverse flow above Mach numbers 2.0. At higher Mach numbers (>2.0) base region of the
vehicle will experience thrusting effect due to increase of base pressure than the ambient pressure. The core base
pressure becomes 1.82 times the ambient pressure at Mach number 4.0. The same for strapon base pressure is
1.9 times of free stream pressure.
Axial force distribution:
It is already mentioned that due to the jet interaction and subsequent reverse flow the base pressure
increases. The increase in base pressure is more attributed to increase of jet pressure ratio. With the increase of
vehicle Mach number, the ratio of core base pressure to free stream pressure increases. This will help in
reduction of the vehicle base drag. For Mach numbers greater than 2.0, the core base pressure is more than the
free stream pressure (Figure 5). Hence, the base drag is no more present, instead of that the vehicle will
experience base thrust. In Figure 6, the variations of the vehicle drag with Mach numbers are plotted for both
jets on and off conditions. A maximum reduction of 25% in vehicle drag is noticed at Mach number 4.0.
Normal force distribution:
The change in pressure distribution in the base region will change the load distribution over the vehicle.
Load distributions at different Mach numbers 0.60 to 4.0 along the vehicle length is shown in Figure 7. It is
noticed that till M=2.0, the load distribution under jet-on and jet-off conditions are almost identical. Above
M=2.50, a difference is noticed in load distribution at the base region which is maximum at M=4.0. This is due
to the reverse flow at the base region.
The cumulative co-efficient of normal force (CN) and XCP are plotted in Figure 8 and Figure 9 at Mach
number 2.0 for both core and strapon. Whereas, the same are depicted in Figure 10 and Figure 11 for Mach
number 4.0. It is clear from the figures that at M=2.0, the jet does not have any significant influence on the load
either on the core or strapon. Whereas, at higher Mach number (M=4.0), a significant influence is noticed for
both the core and strapon, especially beyond core-boat tail (X/D = 9.5). The reduction in load at the base region
of the vehicle will shift the XCP towards vehicle nose. In Figure 12, the variation of CN and XCP with Mach
number is plotted for the complete vehicle. It is clear from the figure that till M=2.50, there is negligible change
in CN due to jet. Above M=2.5, CN reduces and XCP moves towards vehicle nose. The maximum reduction in
CN is of 16% and an XCP shift of 0.72D towards vehicle nose is noticed at Mach number 4.0.
To understand the reason behind the reduction in load, pressure distribution at the base region is closely
monitored. Different longitudinal sections are selected and the Cp values are plotted. In Figure 13, these data are
shown along the circumferential locations for Mach number 0.80 at X/D =9.75 over strapon. It is observed that
the presence of jet increases the pressure as compared to jet-off case. This increase is uniform. Hence, the net
effective change in load distribution is negligible. But as the Mach number increases, the scenario changes. In
Figure 14, circumferential pressure distribution over strapons is plotted for Mach number 4.0. It is observed that
for strapons, the presence of jet does not alter the pressure distribution in wind-ward side. But the pressure
distribution on the leeward side increases. Increase in pressure on the leeward side will reduce the normal forces
acting on strapons. This is true for the core also. As a result, a reduction in normal force is observed.
All these results show that the presence of jet affects the base region of the vehicle. As the load reduces
from the base, Xcp of the vehicle moves towards vehicle nose. This will make the vehicle more unstable. With
altitude, the jet plumes more. This will result in severe jet interaction. All this will increase instability of the
vehicle with increase in altitude. Maximum increase in instability of 0.72D is observed at Mach number 4.0. So
the control force requirement also more due to this jet interaction.
4. CONCLUSION
The CFD simulations have been carried out for a launch vehicle with strapon jet-on conditions. It is
noticed that strap-on jets are over-expanded jet till Mach number 1.10. Above that the jet pressure being more
than the ambient pressure, the jets expands as they come out of the nozzles. They interact at some point downstream from the nozzle exit plane and cause reverse flow. The flow properties at the base region alter due to
reverse flow. Base pressure is less than the ambient pressure until Mach number is 2.0 and becomes higher than
ambient pressure as the Mach number increases. At Mach number 4.0, the base pressure to ambient pressure
ratio is 1.82, which is maximum among all the cases considered for numerical simulations. The load distribution
over the base region of the vehicle changes owing to the changes in base pressure distribution above Mach
numbers 2.50. A maximum reduction of 16% in overall normal force coefficients and 0.72D forward shifts of
XCP are noticed at Mach number 4.0. This makes the vehicle more unstable in presence of jet. Vehicle drag also
reduces due to the jet interactions.
Acknowledgment
Authors are very much thankful to Thomas C babu of computing facility for his continuous support
during computation. We want to express our sincere gratitude to Shri A E Sivaramakrishnan, Dr M M Patil, Dr
V Ashok, Shri S Pandian and Dr S Swaminathan, for their valuable remarks and suggestions.
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NASA TND 3698
Figure 1: Launch vehicle configuration
Figure 2: Co-ordinate system followed
Figure 3: Initial grid distribution
Jet off
Jet off
Jet on
Figure 4a: Pressure palette at M=0.80
Jet on
Figure 4b: Pressure palette at M=1.50
Jet off
Jet on
Figure 4c: Pressure palette at M=4.0
Core base
Strap-on base
Figure 5: Variation of base pressure with Mach numbers
4.0
Jet-on
Jet-off
3.5
3.0
CD
2.5
2.0
1.5
1.0
0.5
0.0
0.0
1.0
2.0
3.0
4.0
Mach No
Figure 6: Variation of vehicle drag with Mach numbers
M=0.60
M=1.10
M=0.80
M=1.50
M=2.0
M=3.0
Figure 7: Load distribution over vehicle
M=2.50
M=4.0
Core
Strapon
Figure 8: Variation of cumulative load along the length at M=2.0
Core
Strapon
Figure 9: Variation of cumulative Xcp along the length at M=2.0
Core
Strapon
Figure 10: Variation of cumulative load along the length at M=4.0
Core
Strapon
Figure 11: Variation of cumulative Xcp along the length at M=4.0
Force coefficients (CNα)
Centre of pressure (Xcp)
Figure 11: Variation of overall coefficient with Mach numbers
Load distribution
Pressure distribution
Figure 13: load and pressure distribution over strap-on at M=0.80
Load distribution
Pressure distribution
Figure 14: load and pressure distribution over strap-on at M=4.0