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CFD MODELING OF THRUST VECTOR CONTROL THROUGH JET VANE

Article · May 2016

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Sci.Int.(Lahore),28(2),1151-1156,2016 ISSN 1013-5316; CODEN: SINTE 8 1151
CFD MODELING OF THRUST VECTOR CONTROL THROUGH JET VANE
Madiha Imdad1, Mukkarum Hussain2, Mirza Mehmood Baig3, Tabinda Kanwal4
1,3,4
Department of Mathematics, NEDUET, Karachi, Pakistan
2
Institute of Space Technology (IST), Karachi, Pakistan
Corresponding Author: madiha.imdad@gmail.com
ABSTRACT: Nozzle thrust vectoring is used for active controlling and maneuverability of the vehicle. Thrust vectoring can
be achieved through flexible nozzle, secondary injection, and plume deflection through jet vanes. Experimental setup for
design and analysis of thrust vectoring is very costly while numerical simulation of these cases is a challenging task. In
present study numerical computations of a test case which is very much similar to thrust vectoring through jet vanes are
carried out. The nozzle used for the test case has rectangular cross section and an obstacle is placed at lower wall of nozzle
exit for thrust vectoring. 2D density based Roe’s scheme with kw-SST turbulence model is used. Computed pressure profiles
at upper and lower nozzle walls are compared with available experimental data. Present results reinforce the concept of
numerical test rig and depicts that CFD would be very helpful for future development of thrust vector control system by
minimizing the expensive and time consuming wind tunnel tests.
Keywords: Convergent-divergent nozzle, Wall pressure distribution, Roe’s method, RANS k-w SST, 2D flow

INTRODUCTION numerical prediction. Results are very encouraging and

In gas power systems combustion chamber is used to depicts that CFD would be very helpful for future
convert chemical energy of gases into thermal energy. After development of thrust vector control system by minimizing
the expensive and time consuming wind tunnel tests.
combustion chamber a nozzle is placed to expand gases
where the temperature and pressure of gas decreases and TEST CASE
velocity of gas increases drastically which generates Rectangular cross-section nozzle with an obstacle placed at
required thrust force [1]. Due to their compactness gas lower wall of nozzle exit for thrust vectoring is used in
power systems are used in flying vehicles like airplanes, present study. Experimental data of this test case is available
rockets, missiles etc [2]. A flying vehicle is in mission, it is in literature [10] [19]. Wind tunnel tests for this test case
sometimes needed to control its flight path and speed due to were performed in VTI Žarkovo (Belgrade) by the joint team
outside disturbance or for a particular purpose. Thrust Vector from the Faculty of Mechanical Engineering, University of
Control (TVC) is a technique to adjust direction of flight Belgrade and Aeronautical Technical Institute Žarkovo.
path of the propulsion system [3] [4]. Geometrical description of test case used, grid generation
In addition to providing a thrust force to a flying vehicle, and solver setting details are given in following sections.
nozzle of gas power systems can be used to generate Geometry Model and Grid Generation
moments to rotate the flying vehicle and thus provide Geometry modeling and grid generation are done through
control of the vehicle's attitude and flight path [5]. Many Gridgen software. Detailed dimension of nozzle model used
different mechanisms have been used successfully for in present study are shown in Fig. 1 and Fig. 2. Grid
controlling the direction of the thrust vector which causes independence study is also carried out. Details of grids are
vehicle maneuvering. Commonly used mechanisms for given in Table 1 and Table 2 while shown from Fig. 4 to Fig.
controlling the direction of the thrust vector are mechanical 7.
deflection of the nozzle known as flexi-nozzle [6], injection Table 1. Nozzle without obstacle mesh description
of fluid into the side of the diverging nozzle section causing Grid First Cell Height (mm) Mesh size (Cells)
an asymmetrical distortion of the supersonic exhaust flow
known as secondary injection [7] [8], and thrust vector Coarse 0.1 13094
control by deflection of exhaust gases through jet vanes [9]
[10] [11]. Table 2. Nozzle with obstacle mesh description
For preliminary design and analysis numerical predictions Grid First Cell Height(mm) Mesh size (Cells)
are always recommended for quick estimation. The
Coarse 0.1 16885
capability to numerically simulate these test conditions
containing complex geometry and physical feature and Medium 0.05 37695
generate precise results is a challenging task [12] [13]. Fine 0.01 128902
Numerical predictions give researchers a chance to spread
the investigation to many other possible geometry and flow
conditions without performing expensive and time
consuming wind tunnel tests [14].
Computational Fluid Dynamics (CFD) is a technology that
enables to study the dynamics of things that flow [15] [16]
[17]. CFD as a computational technology is eminently suited
to develop the concept of numerical test rig or virtual wind
tunnel [18]. In present study CFD computations are carried
out to capture flow physics that take place in thrust vector
controlling by deflection of exhaust gases through jet vanes.
Test case nozzle cross-section is rectangular and an obstacle
is placed at lower wall of nozzle exit for thrust vectoring
[10]. Computed results are compared with available
experimental data to investigate limitations and capability of Fig. 1. Nozzle without Obstacle Geometry (dimensions are
in millimeters)
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Boundary Conditions
Boundary conditions applied in present study are shown in
Fig. 7 and tabulated in Table 3. Solver setting used in
Fluent solver is given in Table 4.

Fig. 2. Nozzle with Obstacle Geometry (dimensions are in

millimeters)

Fig. 7. Boundary Conditions used for

Convergent-Divergent Nozzle

Table 3. Details of Boundary Conditions used in Present Study

Minlet 0.086
Tinlet (K) 286.75
Pinlet(total) (Pascal) 101054.2
Pinlet(static)(Pascal) 100532.3
Fig. 3. Mesh used for Nozzle without Pexit (Pascal) 500
Obstacle Tw (K) Adiabatic Wall
R (J/kg-K) 287
Γ 1.4

Table 4. Ansys fluent solver setting

ANSYS FLUENT
Numerical Method
Algorithm RANS
Fig. 4. Coarse Mesh for Nozzle with Obstacle
Method FDS
Solver Density Based
Linear Algebra and Accuracy ILU
Multigrid AMG
Spatial Discretization
Convective terms TVD (Second order upwind)
Pressure interpolation First Order
Scheme Temporal Discretization
Scheme Implicit
Fig. 5. Medium Mesh for Nozzle with Obstacle Thermodynamics
Compressibility Ideal gas law
Dynamic Viscosity Sutherland (three coefficients)
Turbulence Model
Modified k-omega k-omega SST
Boundary Conditions
Inlet Pressure Inlet
Outlet Pressure Outlet
Walls Stationary walls , No-slip
Fig. 6. Fine Mesh for Nozzle with Obstacle
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RESULTS AND DISCUSSION in good agreement and depict that center line lies within
Computations are carried out for rectangular cross-section influence region of disturbance generated by obstacle.
nozzle without obstacle and with an obstacle placed at the Overall results are not only satisfactory but also very
end of lower wall of divergent section. Test case of nozzle encouraging. Results for nozzle without obstacle and an
with an obstacle placed at the end of lower wall of divergent obstacle placed at the end of lower wall of divergent section
section is very much similar to the thrust vector controlling are in good agreement with experimental data and previous
through jet vanes. Although nozzles used for thrust vector CFD studies.
controlling through jet vanes have mostly circular cross
section area but the physical behavior of flow deflection
through jet vanes and obstacle are almost similar.
In present study Roe’s density-based solver is used to solve
RANS system of equations. Turbulence effect is modeled
through k-omega SST turbulence model. Three different
grid spacing and sizes are used to investigate results
dependency on grid quality. Experimental data of pressure
profile at upper and lower wall of nozzle without obstacle
and with an obstacle placed at the end of lower wall of Fig. 8. Static pressure profile at upper divergent
divergent section are used for validation purpose [10][19]. wall of nozzle (without obstacle)
Nozzle central line results for both cases are also compared
with previous numerical studies.
Initially computations are run for smooth nozzle without any
obstacle. Fig. 8 and Fig. 9 present comparison of pressure
profile at upper and lower walls of nozzle. Results are in
good agreement with experimental data. Flow is attached
though out the nozzle. Separation and formation of shock
and vortex are not found as shown in Fig. 14 to Fig. 16.
Central line Mach number is also compared with CFD
computations of Ivan A. Kostic [19] and presented in Fig. 10.
Recently computed and previously predicted results are Fig. 9. Static pressure profile at lower divergent wall
compared well. Mach number at the exit of nozzle plane is of nozzle (without obstacle)
precisely predicted and is same as determined through
experiment, i.e. M = 2.6. Overall results for smooth nozzle
without obstacle are very satisfactory.
Furthermore, computations are carried out for nozzle with an
obstacle placed at the end of the lower wall of divergent
section. As compared to former problem, it is a challenging
task. Flow separations, vortex and shock formation are basic
characteristics of this type of flow which were not present in
prior problem. Computed pressure profile at upper wall of
nozzle is compared with experimental data in Fig. 11.
Computed and experimental values are similar and are same
as for smooth nozzle without obstacle. Flow at nozzle exit is
supersonic, as shown in Fig. 17. Supersonic flow has certain
regions namely, region of influence and region of
dependence. Disturbance at a location transmit their effect
within region of influence. Region of influence become
shorter as Mach number is increased. Distance between
upper and lower wall of nozzle divergent section is large
enough and hence upper wall is outside from lower wall’s
region of influence. If same disturbance was produced at Fig. 10. Mach number along the nozzle axis, from throat to
convergent section then it must be transmitted its effect on divergent section exit (without obstacle)
upper wall. Computed pressure profile at lower wall of
nozzle is compared with experimental data in Fig. 12.
Pressure profile is predicted well qualitatively as well as
quantitatively. Sudden increase in pressure at lower wall
near obstacle is computed precisely. Unsymmetrical flow
pattern inside divergent section is also well predicted
through numerical computations and presented in Fig. 17. A
high speed flow decelerates when it reaches near solid
surface. Its kinetic energy converts into potential energy and
its pressure, temperature and density increases. Pressure,
density and temperature raised due to stagnation are evident
in Fig. 18 to Fig. 20, respectively. Fig. 11. Static pressure profile at upper divergent wall of
Computed center line Mach number is also compared with nozzle (with 15mm obstacle)
previous CFD studies [19] and shown in Fig. 13. Results are

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Fig. 15. Pressure Distribution Obtained through CFD

Computation (without obstacle)

Fig. 12. Static pressure profile at lower divergent wall of

nozzle (with 15mm obstacle)

Fig. 16. Density Distribution obtained through CFD

Computation (without obstacle)

Fig. 13. Mach number along the Nozzle Axis, from

Throat (with obstacle)

Fig. 17. Mach number Distribution Obtained through CFD

Computation (with obstacle)

Fig. 14. Mach number Distribution Obtained through

CFD Computation (without obstacle) Fig. 18. Static Pressure Distribution Obtained through
CFD Computation (with obstacle)

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[4] M.Ryan Schaefermeyer, "Aerodynamics Thrust
Vectoring for Attitude Control," 2011.
[5] Zeamer, Robert F.H. Woodberry , and Richard J.,
"Solid Rocket Thrust Vector Control," Cleveland,
Ohio, December 1974.
[6] Nauparac, D.Prsić, D. Miloš, M. Samadžić, and
Isaković, J , "Design Criterion to Select Adequate
Control Algorithm for Electro-Hydraulic Actuator
Applied to Rocket Engine Flexible Nozzle Thrust
Vector Control Under Specific Load," vol. 41, No 1,
pp. 33-40, 2013.
[7] Dan Miller, Pat Yagle, and Jeff Hamstra, "Fluidic
Fig. 19. Density Distribution Obtained through CFD Throat Skewing for Thrust Vectoring in Fixed
Computation (with obstacle) Geometry Nozzle," 2015,.
[8] Erdem and Erinc, "Thrust Vector Control by
Secondary Injection," 2006.
[9] Lloyd, R. and Thorp, G., "A review of Thrust Vector
Control System for Tactical Missiles," in 14th Joint
Propulsion Conference.
[10] Zoran S. Marko M. Ivana T. and Milan P.,
"Ivestigation of Pressure Distribution in 2D Rocket
Nozzle with a Mechanical System for Thrust Vector
Control.," 2011.
[11] Chakraborty, M.S.R Chandra Murty, and Debasis,
"Numerical Characteristics of Jet-vane based Thrust
Vector Control System," Defence Science Journal, vol.
Fig. 20. Temperature Distribution Calculated through 65, No.4, pp. 261-264, July 2015.
CFD Computation (with obstacle) [12] Jhon C. Tannehill, Dale A. Anderson, and H. Pletcher,
Computational Fluid Mechanics and Heat Transfer,
CONCLUSION Second Edition. United States of America: Taylor &
CFD is a numerical tool to predict flows. Its results before Francis, 1984.
validation cannot be used with confidence. Validation of [13] Professor Eleuterio F. Toro, Riemann Solvers and
numerical computation of highly separated flow is presented Numerical Methods for Fluid Dynamics, A Practical
in this study. Test case used in the present study is very much Introduction,Third Edition. University of Trento, Italy:
similar to thrust vector controlling through jet vanes. Results Springer Dordrecht Heidelberg London New York,
conclude that CFD is an appropriate tool to predict this type 2009.
of complex flow. It will not only decrease design and
analysis time but also reduce costs by minimizing costly [14] H. K. Versteeg and W. Malalasekera, An Introduction
wind tunnel tests. to Computational Fluid Dynamics,The Finite Volume
Method, Second Edition. England, United Kingdom:
ACKNOWLEDGMENT PEARSON Prentice Hall, 2007.
Authors are thankful to Department of Mathematics, [15] Jr. John D. Anderson, Computational Fluid Dynamics:
NEDUET, Karachi, Pakistan for their support throughout The Basics with Applications. University of Maryland
the work. ,United States of America.: McGraw-Hill, Inc., 1976.
[16] Klauss A. Hoffmann and Steve T. Chiang,
REFERENCES Computational Fluid Dynamics. Wichita, Kansas:
[1] George. P. Sutton and Biblarz Oscar, Rocket Engineering Education System, 2001.
Propulsion Elements, 7th ed.: JOHN WILEY & [17] Klaus A. Hoffmann and Steve T. Chiang,
SONS, INC., 2001. Computational Fluid Dynamics,Fourth Edition,Volume
[2] M. Haluk Aksel and O.Cahit Eralp, Gas Dynamics.: I. Wichita,Kansas,USA.: Engineering Education
Prentice Hall, 1994. System(EES), August 2000.
[3] B. Jojić and Z. Stefanović, "Theoretical Analysis and [18] Culbert B. Laney, Computational Gasdynamics.
Design of 2D TVC Model for Wind Tunnel Testing, University ofColorado, New York, United States of
PhD thesis," Belgrade, 1986. America: Cambridge University Press, 1998.
[19] Olivera P. Kostić, Zoran A. Stefanović , and Ivan A. K,
"CFD Modeling of Supersonic Airflow Generated by
2D Nozzle With and Without an Obstacle at the Exit
Section," 2015.

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