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Performance analysis and flowfield characterization of secondary injection thrust vector control (SITVC) for a 2DCD nozzle
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Performance analysis and flowfield characterization of secondary injection thrust vector control (SITVC) for a 2DCD nozzle
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Content
PERFORMANCE ANALYSIS AND FLOWFIELD CHARACTERIZATION
OF SECONDARY INJECTION THRUST VECTOR CONTROL (SITVC)
FOR A 2DCD NOZZLE
by
Muhammad Usman Sadiq
A Thesis Presented to the
FACULTY OF THE VITERBI SCHOOL OF ENGINEERING
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
(ASTRONAUTICAL ENGINEERING)
August 2007
Copyright 2007 Muhammad Usman Sadiq
ii
Acknowledgements
At University of Southern California (USC), I had many opportunities to learn
from the renowned scholars both from academia and industry. I would like to extend my
gratitude to all of them for their motivation and encouragement; in particular I would like
to thank Professor Keith Goodfellow for boosting my interests in spacecraft propulsion.
This master’s thesis was completed at Astronautics Division, under the auspices
of supervising committee composed of Professor Daniel Erwin (Astronautics Division),
Professor Paul Ronney (Aerospace & Mechanical Engineering Department), Professor
Keith Goodfellow (Lockheed Martin), and Professor Mike Gruntman (Astronautics
Division). I would like to extend my special gratitude to all of the thesis committee
members for the freedom and the support I enjoyed during this work, especially for their
cooperation, inspiration and the technical discussions about our research.
I would like to specially thank Professor Paul Ronney for providing the necessary
computational resources to conduct my research work. I am also deeply indebted by the
extensive technical assistance provided by Professor Daniel Erwin. Without their
generous assistance this work would have not been accomplished. Rocket Propulsion
Laboratory at USC is thanked for numerous discussions and help with numerical setup; in
particular I would like to acknowledge the help of Ian Whittinghill for his support.
I also would like to thank my sponsoring organization, Institute of Space
Technology (IST) for their continuing support and guidance throughout my masters
program. Finally, I am everlastingly gratified to my parents and wife for their
understanding, endless patience and encouragement when it was most required.
iii
Contents
Acknowledgements ii
List of Tables v
List of Figures vi
Nomenclature xi
Abbreviations xiii
Abstract xiv
Chapter 1: Introduction 1
1.1) Secondary Injection Thrust Vector Control (SITVC) Mechanism 2
1.2) Research Review 4
1.2.1) Review of Analytical & Empirical Studies 4
1.2.2) Review of Numerical Studies 10
1.2.3) Common Observations & Discussion of Pertinent Literature 13
1.3) Current Research Approach 17
1.4) Thesis Outlines 18
Chapter 2: Computational Model 20
2.1) Geometrical Configuration 20
2.2) Grid Generation 22
2.3) Grid Sensitivity Analysis 25
2.4) Computational Solver Characteristics 30
2.5) Flow Characteristics 35
2.6) Conical Nozzle Configurations 36
2.7) Test Matrices 40
Chapter 3: Flowfield Structure 43
3.1) Flowfield Structure Elements 43
3.2) Flowfield Structure: Observations & Discussion 47
3.2.1) Effects of Secondary Stagnation Pressure & Injection Slot Area 47
3.2.2) Effects of Injection Location 55
3.2.3) Effects of Angular Injection 62
3.2.4) Effects of Primary Nozzle Profile 69
iv
Chapter 4: Performance Analysis 77
4.1) SITVC Performance Parameters 77
4.2) Performance Calculations 82
4.3) Performance Analysis: Results & Discussion 85
4.3.1) Effects of Secondary Stagnation Pressure & Injection Slot Area 85
4.3.2) Effects of Injection Location 99
4.3.3) Effects of Angular Injection 109
4.3.4) Effects of Primary Nozzle Profile 119
4.4) Safe Injection Limits 129
4.5) Results Verification 131
Chapter 5: Summary and Conclusions 137
5.1) Research Summary 137
5.2) Conclusions & Recommendations 143
5.3) Proposed Future Studies 144
Bibliography 145
v
List of Tables
Table 2-1: Geometrical properties of primary nozzle 20
Table 2-2: Geometrical properties of bell & conical shaped primary nozzles 36
Table 2-3: Summary of test runs to estimate the influence of injectant pressure,
injection slot area, injection location and angle of injection 41
Table 2-4: Summary of test runs to estimate the influence of injectant mass flow rate 42
Table 2-5: Summary of test runs to estimate the influence of primary nozzle profile 42
vi
List of Figures
Figure 1-1: Flowfield structure setup by secondary injection into primary nozzle flow 3
Figure 1-2: Flowfield structure setup by secondary injection into primary nozzle flow
(Linearized Model) 6
Figure 1-3: Flowfield structure setup by secondary injection into primary nozzle flow
(Boundary Layer Separation Model) 8
Figure 1-4: Flowfield structure setup by secondary injection into primary nozzle flow
(Blunt Body Model) 10
Figure 2-1: Primary nozzle profile coordinates 21
Figure 2-2: Primary Flow Axial Mach # 21
Figure 2-3: Two dimensional 250x75 grid configuration of primary nozzle with
10x10 grid configuration of injector 22
Figure 2-4: Two dimensional 10x10 grid configuration of injector 23
Figure 2-5: Two dimensional 250x75 grid configurations for different
injection configurations 24
Figure 2-6: Candidate two dimensional grid configurations used for grid
sensitivity analysis 26
Figure 2-7: Effect of grid resolution on injector upstream wall static pressure
distribution 29
Figure 2-8: Effect of grid resolution on injector downstream wall static
pressure distribution 29
Figure 2-9: Geometrical configuration of nozzle studied by Guhse 32
Figure 2-10: Grid configuration of nozzle transformed from the experimental
setup of Guhse 33
Figure 2-11: Injector upstream & downstream wall static pressure distribution
comparison for various viscous models & Guhse’s experimental data 34
vii
Figure 2-12: Flowfield structure (Mach number contours) obtained from numerical
solution of Guhse’s experimental configuration
(Viscous Model: rk-ε with enhanced wall treatment) 34
Figure 2-13: Geometrical configuration of bell & conical shaped nozzles 37
Figure 2-14: Two dimensional grid configuration of primary bell and conical shaped
nozzles (Showing relative positions of same injection location at M
P
= 2) 38
Figure 2-15: Two dimensional grid configuration of primary bell and conical shaped
nozzles (Showing relative positions of same injection location at M
P
= 3) 39
Figure 3-1: Flowfield structure (Mach number contours) setup by secondary
injection into primary nozzle flow 46
Figure 3-2: Effect of injection pressure on flowfield structure (Mach # contours) 50
Figure 3-3: Effect of secondary (injection) mass flow rate on injector upstream
wall static pressure distribution 52
Figure 3-4: Effect of secondary (injection) mass flow rate on injector downstream
wall static pressure distribution 53
Figure 3-5: Effect of secondary (injection) mass flow rate on down
(opposite wall static pressure distribution 54
Figure 3-6: Effect of injection location on flowfield structure (Mach # contours) 57
Figure 3-7: Effect of injection location on flowfield structure (Mach # contours) 58
Figure 3-8: Effect of injection location on injector upstream wall static
pressure distribution 59
Figure 3-9: Effect of injection location on injector downstream wall static
pressure distribution 60
Figure 3-10: Effect of injection location on down (opposite) wall static
pressure distribution 61
Figure 3-11: Effect of angle of injection on flowfield structure (Mach # contours) 64
Figure 3-12: Effect of angle of injection on flowfield structure (Mach # contours) 65
Figure 3-13: Effect of angle of injection on injector upstream wall static
pressure distribution 66
viii
Figure 3-14: Effect of angle of injection on injector downstream wall static
pressure distribution 67
Figure 3-15: Effect of angle of injection on down (opposite) wall static
pressure distribution 68
Figure 3-16: Effect of primary nozzle profile on flowfield structure (Mach # contours) 72
Figure 3-17: Effect of primary nozzle profile on flowfield structure (Mach # contours) 73
Figure 3-18: Effect of primary nozzle profile on injector upstream wall static
pressure distribution 74
Figure 3-19: Effect of primary nozzle profile on injector downstream wall static
pressure distribution 75
Figure 3-20: Effect of primary nozzle profile on down (opposite) wall static
pressure distribution 76
Figure 4-1: Effect of secondary stagnation pressure & injection slot area on
secondary mass flow rate 88
Figure 4-2: Effect of secondary stagnation pressure & injection slot area on
axial thrust 89
Figure 4-3: Effect of secondary stagnation pressure & injection slot area on
interaction force 90
Figure 4-4: Effect of secondary stagnation pressure & injection slot area on
jet reaction force 91
Figure 4-5: Effect of secondary stagnation pressure & injection slot area on
net side thrust 92
Figure 4-6: Effect of secondary stagnation pressure & injection slot area on
amplification factor 93
Figure 4-7: Effect of secondary stagnation pressure & injection slot area on
system specific impulse 94
Figure 4-8: Dependence of secondary mass flow rate on secondary stagnation pressure 95
Figure 4-9: Effect of secondary mass flow rate on axial thrust augmentation 95
Figure 4-10: Effect of secondary mass flow rate on interaction force 96
ix
Figure 4-11: Effect of secondary mass flow rate on jet reaction force 96
Figure 4-12: Effect of secondary mass flow rate on net side thrust 97
Figure 4-13: Effect of secondary mass flow rate on amplification factor 97
Figure 4-14: Effect of secondary mass flow rate on system specific impulse 98
Figure 4-15: Effect of injection location on secondary mass flow rate 102
Figure 4-16: Effect of injection location on axial thrust augmentation 103
Figure 4-17: Effect of injection location on interaction force 104
Figure 4-18: Effect of injection location on jet reaction force 105
Figure 4-19: Effect of injection location on net side thrust 106
Figure 4-20: Effect of injection location on amplification factor 107
Figure 4-21: Effect of injection location on system specific impulse 108
Figure 4-22: Effect of angle of injection on secondary mass flow rate 112
Figure 4-23: Effect of angle of injection on axial thrust augmentation 113
Figure 4-24: Effect of angle of injection on interaction force 114
Figure 4-25: Effect of angle of injection on jet reaction force 115
Figure 4-26: Effect of angle of injection on net side thrust 116
Figure 4-27: Effect of angle of injection on amplification factor 117
Figure 4-28: Effect of angle of injection on system specific impulse 118
Figure 4-29: Effect of primary nozzle shape on secondary mass flow rate 122
Figure 4-30: Effect of primary nozzle shape on axial thrust augmentation 123
Figure 4-31: Effect of primary nozzle shape on interaction force 124
Figure 4-32: Effect of primary nozzle shape on jet reaction force 125
Figure 4-33: Effect of primary nozzle shape on net side thrust 126
x
Figure 4-34: Effect of primary nozzle shape on amplification factor 127
Figure 4-35: Effect of primary nozzle shape on system specific impulse 128
Figure 4-36: Safe injection limits for bell shaped nozzle 130
Figure 4-37: Effect of injection pressure & injection slot area
(Comparison b/w Analytical & Computational Results) 134
Figure 4-38: Effect of injection location
(Comparison b/w Analytical & Computational Results) 135
Figure 4-39: Effect of angle of injection
(Comparison b/w Analytical & Computational Results) 136
Figure 4-40: Effect of primary nozzle profile
(Comparison b/w Analytical & Computational Results) 136
Nomenclature
F
p
Primary Axial Thrust [N]
F
s
Net Side Thrust [N]
F
n
Interaction Force (Side Thrust-Pressure Component) [N]
F
j
Jet Reaction Force (Side Thrust-Momentum Component) [N]
o
p
F Primary (Axial) Thrust – No Injection Condition [N]
Isp
p
Primary Specific Impulse [sec]
Isp
p
Secondary Specific Impulse [sec]
Isp
sys
System Specific Impulse [sec]
δIsp
sys
System Specific Impulse Loss [sec]
AK Amplification Factor
o
p
Isp
Primary Specific Impulse – No Injection Condition [sec]
P
op
Primary Stagnation Pressure (Primary Nozzle Inlet Pressure) [Pa]
P
ep
Primary Exit Pressure at Primary Nozzle Exit [Pa]
P
ap
Primary Ambient Pressure (Atmospheric Pressure) [Pa]
P
os
Secondary Stagnation Pressure (Injection Slot Inlet Pressure) [Pa]
P
es
Secondary Exit Pressure at Injection Slot Exit [Pa]
P
as
Secondary Ambient Pressure at Injection Slot Exit [Pa]
PR Secondary to Primary Stagnation Pressure Ratio
T
op
Primary Stagnation Temperature [K]
T
os
Secondary Stagnation Temperature [K]
xi
V
p
Primary Flow Exit Velocity at Primary Nozzle Exit [m/s]
V
px
Primary Flow Exit Velocity Axial Component at Primary Nozzle Exit [m/s]
V
py
Primary Flow Exit Velocity Normal Component at Primary Nozzle Exit [m/s]
V
s
Secondary Flow (Injectant) Exit Velocity at Injection Slot Exit [m/s]
V
sx
Secondary Flow Exit Velocity Axial Component at Injection Slot Exit [m/s]
V
sy
Secondary Flow Exit Velocity Normal Component at Injection Slot Exit [m/s]
A
e
Primary Nozzle Exit Area [m
2
]
A
s
Injection Slot Area [m
2
]
ΔA
x
X-Face Area of Grid Cell [m
2
]
ΔA
y
Y-Face Area of Grid Cell [m
2
]
H* Height of Primary Nozzle Throat [m]
A* Primary Nozzle Throat Area [m
2
]
AR Injection Slot to Primary Nozzle Throat Areas Ratio
p m
•
Primary Mass Flow Rate [kg/s]
s m
•
Secondary (Injectant) Mass Flow Rate [kg/s]
MW
p
Molecular Weight of Primary Gas
MW
s
Molecular Weight of Secondary Gas (Injectant)
α
inj
Angle of Injection [deg]
(Angle between injection slot axis and normal to the primary nozzle axis)
β
inj
Wall Angle at Point of Injection [deg]
(Angle between normal to the wall at point of injection and the normal
to the primary nozzle axis)
M
P
Injection Location (in terms of Primary Flow Axial Mach # corresponding
to Injection Point located on Primary Nozzle Wall)
xii
xiii
Abbreviations
2D Two Dimensional
2DCD Two Dimensional Convergent Divergent
3D Three Dimensional
AR Area Ratio (Injection Slot to Primary Nozzle Throat Area Ratio)
CFD Computational Fluid Dynamics
PR Pressure Ratio (Primary to Secondary Stagnation Pressure Ratio)
LITVC Liquid Injection Thrust Vector Control
SITVC Secondary Injection Thrust Vector Control
TVC Thrust Vector Control
xiv
Abstract
A numerical study was conducted to investigate the effects of secondary gaseous
injection into primary supersonic gas stream by characterizing the resulting flowfield and
estimating the thrust vector control performance for a 2DCD nozzle. Flowfield structure
and performance parameters were systematically investigated for several variables such
as secondary (injectant) stagnation pressure, injection slot area, angle of injection, and
primary nozzle profile. FLUENT, a commercial CFD software was employed for current
numerical investigation. 2D coupled-implicit solver with realizable k-ε viscous model
was used throughout the research. The results showed that flowfield structure and
performance parameters were primarily influenced by injectant mass flow rate, injection
location, and primary nozzle profile whereas injection angle was less influential for the
range of parameters investigated. An important aspect of the research was the
identification of the safe injection limits for a specific configuration. Numerical
estimations were found to have fairly close agreement with analytical results.
1
Chapter 1
Introduction
Thrust Vector Control (TVC) is intended to provide the control moments required for
keeping the attitude and trajectory of the flying vehicle. A number of mechanisms have
been proposed and implemented to accomplish the task for various aerospace systems.
TVC mechanisms can be broadly classified as mechanical deflection and secondary
injection systems. Gimbaled nozzles, flexible nozzle joints, jet vanes, and jetavators are
some commonly employed means of mechanical operated TVC systems. All such
systems primarily deflect the main flow at certain angle to obtain required side thrust.
These systems require high temperature resistant mechanical components that increase
the overall system complexity and cost. In contrast to this, secondary injection into the
primary nozzle flow causing net side thrust owing to asymmetrical pressure distribution
on the nozzle walls & momentum exchange requires no moving components and is
governed by simple flow regulations.
Secondary Injection Thrust Vector Control (SITVC) has a long history of exploration
both in academia and industry. Due to its advantages over conventional means of thrust
vectoring, STIVC technique has immense technological importance for high altitude
flying vehicles including both the air-breathing and rocket engines. The main interest lies
2
in the SITVC performance estimation and flowfield characterization for various flying
configurations such as supersonic jet fighters, rockets, and hypersonic vehicles.
1.1) Secondary Injection Thrust Vector Control (SITVC)
Mechanism
The physical process involved in the secondary fluidic (gas or liquid) injection to obtain
an asymmetric thrust distribution in the primary (main) nozzle for thrust vectoring is
quite complex and many analytical & computational models have been proposed as an
explanation to this. A generalized approach is discussed as follows.
Upon injection into the nozzle, the secondary fluid (injectant) induces a complex
flowfield. The injectant acts as an obstruction and introduces a strong bow shock
upstream of the injector. This strong bow shock, in turn, interacts with the boundary layer
and causes the flow to separate introducing a separation shock. Under certain injection
conditions, a relatively weak bow shock may also be present originating downstream of
the injector. Part of the primary flow is deflected through these bow and separation
shocks. The characteristics of the separation region are dependent on the nature of the
boundary layer. The injected secondary fluid expands isentropically through Prandtl-
Meyer fan until it achieves the static pressure of the primary flow. The undisturbed
primary flow and disturbed mixing flow is separated by a jet streamline.
Figure 1.1 [1] schematically depicts the flowfield structure inside the nozzle setup as a
result of secondary injection.
Figure 1-1: Flowfield structure setup by secondary injection into primary nozzle flow
This complex shock structure creates regions of high & low pressure in the vicinity of the
injector. The nature and strength of the shock structure is controlled by aero-thermo-
chemical processes such as mixing, reaction, heat, and momentum exchange resulting
from the interaction of the primary flow with the secondary jet. The net side thrust
produced is a combined effect of a) jet reaction force, caused by the momentum of the
secondary fluid (injectant), and b) interaction (induced) force, due to pressure rise along
the wall. Also, a substantial axial thrust augmentation is produced owing to the additional
mass, momentum and energy carried by the injectant. It is interesting to note that under
3
4
certain conditions the secondary injection may lead the impingement of strong bow shock
on the opposite side of the nozzle wall and, in turn, results into reduced net side thrust or
in worst cases, vectoring the system into entirely undesired direction.
1.2) Research Review
Characterization of the complex flowfield and prediction of SITVC performance has
always been a problem of great engineering interest. In past, numerous theoretical and
experimental studies have been performed to characterize the complex flowfield setup in
the nozzle by the interaction of the secondary injection into supersonic flow and
subsequent performance analysis of SITVC. In this section, a brief review of some of
these models is presented.
1.2.1) Review of Analytical & Empirical Studies
As mentioned earlier, several analytical & empirical models have been proposed as an
explanation of the processes associated with the secondary injection into a supersonic
flow. An overview of some of these analytical models is presented below.
5
a) Linearized Model
Walker, Stone and Shandor [8] studied the processes associated and characterized the
phenomena using linearized theory for supersonic flows. The authors examined the aero-
thermo-chemical aspects of the fluidic injectant interaction with the primary supersonic
flow for six groups of injectants: inert gases, inert liquids, reactive gases, dissociatve
liquids, reactive liquids, and liquid bipropellants. In the analysis, however, the effects of
atomization and evaporation, droplet drag and trajectory are not discussed. Boundary
layer effects are neglected and the analytical model is developed for two dimensional
flows only. The model idealizes the problem as a constant area mixing between a trace of
injectant and a portion of supersonic flow. That is why, proposed model is valid only for
very small injectant mass flow rates and is useful for comparing the relative merits of
different injectants. Thermo-chemical effects (mixing, phase changes, chemical reactions,
etc.) are assumed to be instantaneous.
The model provides a very simple approach to determine both the components of the total
side force i.e. jet reaction force and interaction force. Based on this, effective side
specific impulse (net side force divided by injectant weight flow rate) is determined. The
authors provide a very comprehensive analysis of the predicted values with the
experimental data. The comparison is primarily based on the predicted side specific
impulse value (calculated from analytical model) and experimentally determined side
specific impulse for the same flow conditions for a given injectant to primary weight flow
ratio. Figure 1-2 shows the flowfield structure as proposed in linearized model.
Figure 1-2: Flowfield structure setup by secondary injection into primary nozzle flow (Linearized Model)
b) Blast Wave Analogy Model
This model is due to James E. Broadwell [2]. The model treats the flow as inviscid and is
limited to two dimension analyses only. Broadwell applied blast wave analogy to
characterize the flow field and associated side force due to secondary injection. Blast
wave theory is based on an analogy between the cylindrical unsteady flow produced by
the explosion of a line charge and an axi-symmetric steady flow. The analogy has been
successfully applied to characterize the flow about blunt bodies at high supersonic
speeds. The flowfield is determined by the energy added per unit length of gas. The
energy released by the explosion is set equal to the momentum of the secondary jet. The
6
7
shape and strength of the resulting shock waves are approximated by the well-known
solutions of a blast wave. Since the momentum of the secondary jet is considered as a
gross parameter, the effect of important injection parameters, such as injection orifice
size and geometry and flow properties cannot be accounted for by this model [7]. This
model also discusses the effects if a liquid or reactive fluid is injected into the supersonic
gas stream. A serious defect of blast wave theory is that it is strictly valid only for high
Mach numbers of the primary stream and becomes increasingly inaccurate quantitatively
as the value of the Mach number decreased as commented by [6]. Analytical model by
Broadwell was employed for results verification in present research.
c) Boundary Layer Separation Model
The model is proposed by Wu, Chapkis and Mager [9]. The interaction of the primary
supersonic flow causes the formation of a conical shock and separated region originating
upstream the injection point. The position of the conical shock depends upon the main
stream conditions, the flow rate and physical properties of the injectant. The conical
shock angle, the separation angle, and the conditions behind the shock and in the
separated flow region are determined from knowledge of upstream Mach number. The
side force results from the higher pressure behind the shock acting on the projected area
of the shock and the separated region. The side force produced by the injection of a gas is
shown to be the sum of three components. The first results form the pressure increase in
the separated region. The second is due to similar increase in pressure occurring between
the shock and the separated region. The third component is due to the momentum of the
injected gas. The authors neglect any possible contribution to the side force downstream
of the injection port. However, the model does not treat the three dimensional nature of
the shock and separated region [6]. Figure 1-3 shows the flowfield structure as proposed
in boundary layer separation model.
Figure 1-3: Flowfield structure setup by secondary injection into primary nozzle flow (Boundary Layer
Separation Model)
d) Blunt Body Model
In 1964, Zukoski and Spaid [10] proposed an empirical model based on experimental
data consisted of wind tunnel test section flow conditions, Schlieren photographs, static
pressure distribution on the test section wall in the region of injection, concentration
8
9
measurements in the flow downstream of the injection port, and injectant total pressure
and mass flow rate. It is observed that the injection of the secondary gas into the primary
supersonic flow produced the similar flowfield as a blunt body placed in a supersonic
flow. The separated region, shock structure and pressure distributions are observed to be
similar in both the cases. The empirical model is developed on the basis of a single
characteristic parameter “h”, the penetration height. A systematic approach to determine
this height is developed in the model as well. This penetration height is considered to be
the radius of the equivalent blunt body sphere. The total side force is the sum of the
interaction force and the jet reaction. The authors also derive the scaling laws based on
the penetration height for the total side force on the wall. The author assumes the
injection is sonic with no wall boundary layer and no mixing occurs between the flows.
Since the experimentation performed employed the injection of various inert gases into a
supersonic stream of air that is why this model is not qualified for the reactive gaseous
and inert or reactive liquid secondary injection that involve complex mixing and heat
exchange processes. Also, according to Guhse
[6], the data used in developing the models
involve flow rate ratios of the secondary to primary streams which are considerably less
than the minimum practical values for thrust vector control by secondary injection.
Figure 1-4 shows the flowfield structure as proposed in blunt body model.
Figure 1-4: Flowfield structure setup by secondary injection into primary nozzle flow (Blunt Body Model)
1.2.2) Review of Numerical Studies
Modern computing resources have made it possible to obtain the numerical solutions of
otherwise impossible to solve analytical Navier-Stokes equations for complex flowfields.
Such flowfields involving complex interactions can be effectively investigated using the
advanced CFD techniques for a wide range of configurations. Like other research
domains of fluid dynamics problems, secondary injection thrust vector control systems
are also extensively investigated through CFD techniques. Based on these numerical
models, more accurate SITVC performance can be predicted. Such numerical techniques
have become strong alternative to previous theoretical models and a complimentary
element to experiments. A few studies have been presented in this section on the
numerical treatment of the SITVC problem.
10
11
a) R. Balu, A. G. Marathe, P. J. Paul, and H.S. Mukunda
Balu, Marathe, and Mukunda
[1] numerically investigated the flowfield induced due to
interaction of secondary hot gas injection into a supersonic hot gas stream. Primary fluid
is main rocket hot gas while the secondary fluid is also the hot gas taken from the main
rocket motor. SITVC performance parameters such as amplification factor, injectant
specific impulse and axial thrust augmentation have been predicted by solving unsteady
three dimensional Euler equations and integrating the resulting wall pressure distribution.
The governing equations are discretized using a finite volume concept, and the resulting
difference equations are integrated in time using the explicit two level MacCormack’s
predictor-corrector scheme. An inviscid model is justified by claiming the insignificant
effects of boundary layer on the side force.
b) Numerical Investigation by Hyun Ko and Woong-Sup Yoon
Ko and Yoon [7] have presented a three dimensional viscous flow analysis of the
secondary injection thrust vector control system for a conical rocket nozzle. Thermally &
calorically perfect air is used both as primary & secondary fluid in the investigation. The
flow solver is based on the strong conservation law form of full Navier-Stokes equations
in curvilinear coordinates. Ko & Yoon analyzed the problem employing two turbulent
models, namely, algebraic Baldwin-Lomax model & two equation turbulence closure (k-
ε) model with low Reynolds number treatment. Parameters investigated by the
12
researchers include injection location, nozzle divergent cone angle, and secondary to
primary stagnation pressure ratio. Performance parameters estimated include thrust ratio,
axial thrust augmentation, and amplificatation factor (secondary to primary specific
impulse ratio). The characteristic curves are plotted to evaluate performance parameters
based on the stagnation pressure ratio for various configurations of injection location,
nozzle divergent angle and injectant flow rates.
c) Numerical Investigation by Erinc Erdem, Kahraman Albayrak, and
H. Turgrul Tinaztepe
In a recent study by Erdem, Albayrak and Tinaztepe
[3] numerical analysis of the
secondary injection thrust vector control is performed using commercially available CFD
software, FLUENT. Realizable k-ε turbulent model with enhanced wall treatment
approach is used to investigate the three dimensional flowfield. Essentially this
investigation is an extension of the study conducted by Ko & Yoon [7]. FLUENT, a
commercially available CFD package was employed for this study. The study consists of
two parts. The first part includes the simulation of three dimensional flowfield inside a
test case nozzle for validating the solver and more importantly, for selection of
parameters associated with both computational grid and the CFD solver such as mesh
size, turbulence model and solver type. In the second part a typical rocket nozzle with
conical diverging cone is picked for the parametric study. Both fluids are air and the
effects on thrust ratio, axial thrust augmentation and amplification factor are estimated
with variation in injection location and mass flow rate.
13
1.2.3) Common Observations & Discussion of Pertinent Literature
a) Analytical & Empirical Studies
The common observations made while reviewing the analytical and empirical models are
as follows:
- In all the analytical and empirical models 2-dimensional flow is focused.
- Flow is often times considered inviscid, however, there are some experimental
and analytical studies that treats the boundary layer effects.
- Most of the studies are performed for flat plates to describe the phenomenon of
secondary injection and generalization of the flat plate models is required to suit
nozzle shapes. Some of the models, however, focus the conical nozzle. Only one
study has been found on the flow characterization and performance evaluation for
contoured nozzles.
- In most of the cases normal injection and fixed injectant locations are analyzed.
However, we find quiet a few studies that considered some of these factors.
- In most of the models the fluid for primary and secondary flows is gas. Physical
properties of primary gas and secondary liquid interactions are less investigated.
The reason associated is the complex processes involved in liquid atomization,
evaporation, droplet drag and trajectory etc. Reactive flows are least investigated.
14
- Effects of strong bow shock impingement & safe injection limits of secondary
injection leading to desired net side thrust and direction have not been explicitly
investigated.
b) Numerical Studies
The common observations made while reviewing the numerical models are as follows:
- All studies are limited in investigation of the flow inside conical rocket nozzle.
No investigation has been performed for the flow characterization and
performance evaluation of the contoured nozzles.
- In all of the studies the performance variation with injectant locations are
analyzed. However, angle of injection is not discussed.
- No numerical model has been proposed investigating the interaction of the liquid
injectant with the supersonic gas flows and predicting the subsequent performance
of such Liquid Injection Thrust Vector Control (LITVC) systems.
- Effects of strong bow shock impingement & safe injection limits of secondary
injection leading to desired net side thrust and direction have not been explicitly
investigated.
15
c) SITVC Performance Parameters
The review of pertinent literature shows that the following parameters have been
explored for the estimation of SITVC system performance.
- Axial Thrust Augmentation
- Net Side Thrust (Side Thrust)
- Amplification Factor (Secondary to Primary Specific Impulse Ratio)
In the current study, however, after performing the detailed analyses it was felt that the
following additional performance parameters must be explicitly studied for the better
understanding of the overall system performance. The discussion on these parameter is
provided in the following chapters.
- Interaction Force (Pressure Component of the Side Thrust)
- Jet Reaction Force (Momentum Component of Side Thrust)
- System Specific Impulse Loss
d) Flowfield Characterization
The flowfield inside the nozzle is characterized by the complex shock structure
accompanied by asymmetric pressure distribution. Discussion on various aspects of the
16
flowfield is found in the SITVC literature, most importantly on the formation and
parameterization of the following:
- Primary Bow Shock
- Secondary Bow Shock
- Separation Shock
- Asymmetric Wall Pressure Regions
A detailed qualitative analysis of the flowfield structure in perspective of the SITVC
control parameter has been presented in this thesis.
e) SITVC Control Parameters
The following parameters have been identified from the literature that govern the
flowfield structure and affect SITVC system performance.
- Secondary (Injectant) Mass Flow Rate
o Injection Stagnation Pressure
o Injection Slot Area
- Injection Location
- Injector Shape (Geometry)
- Angle of Injection
- Primary (Main) Nozzle Shape
- Physical Properties of Primary & Secondary Fluids
17
In present research all parameters except injector geometry & physical properties are
investigated.
1.3) Current Research Approach
The research presented herein was primarily meant for the numerical investigation of the
interaction of the gaseous injection into supersonic gas stream to characterize the
flowfield, and estimate the SITVC performance parameters for a two dimensional
contoured (bell-shaped) converging diverging rocket nozzle. Calorifically perfect air has
been employed as both the primary & secondary fluids. FLUENT, a commercially
available CFD software has been employed for the analyses. The primary nozzle flow
conditions were kept constant for all the test runs performed. Throughout course of the
research, results were verified through suitable analytical & empirical models.
An important aspect of this research was the qualitative and quantitative investigation of
the primary bow shock impingement and its effects on flowfield structure and
performance parameters. In the same perspective, safe injection limits were also
identified for a specific configuration.
As stated earlier, investigation was primarily conducted for a bell shaped rocket nozzle,
however, an interesting extension to this study was the performance comparison between
conical and bell shaped rocket nozzles. In the same context, the flowfields structures
18
were also compared for conical and bell shaped rocket nozzles. No such attempts have
been made earlier and comparative study was intended to develop the understanding
about the advantages and disadvantages of using either of the configurations from thrust
vectoring viewpoint.
Current research results would provide the performance data for thrust vector planning
and design of future experimental rocket systems planned by Rocket Propulsion
Laboratory (RPL) at University of Southern California (USC).
1.4) Thesis Outlines
This report presents the numerical study performed to investigate the secondary injection
thrust vector control technique for a two dimensional convergent divergent nozzle. In
particular, the flowfield structure and performance estimation is investigated.
Chapter two encompasses computational setup including the geometrical configurations,
grid generation, grid independence studies, numerical solver characteristics and
systematic description of flow models investigated in this study.
Flowfield structure and effects of various SITVC control parameters on flowfield
structure are provided in chapter three. Flowfield structure in perspective of the SITVC
performance parameters is also discussed in the same chapter.
19
Description of performance parameters, performance calculations & subsequent
performance analyses under the influence of various SITVC control parameters are
presented in chapter four. The chapter also includes the discussion on the verification of
numerical estimations in perspective of analytical results and a note on safe injection
limits.
Summary and conclusions derived from the study are presented in chapter five.
Chapter 2
Computational Model
2.1) Geometrical Configuration
The geometrical characteristics of the primary nozzle employed in current research are
given in Table 2-1. The nozzle geometry has been shown in figure 2-1.
Primary Nozzle Characteristics
Profile 2-D Contoured (Bell Shaped)
Contour Slope Angle 30 deg
Exit Divergence Angle 6 deg
Nozzle Height 0.02 m
Throat Area 0.02 m
2
Area Ratio 10
Nozzle Length to Dia Ratio 17.5
Table 2-1: Geometrical properties of primary nozzle
Secondary injection was carried out through a two dimensional slot injector extended
throughout the primary nozzle depth (z-axis). The geometrical configuration of the slot
injectors employed in this research are detailed in section 2.7. Figure 2-2 shows the axial
flow Mach number for the primary bell shaped nozzle employed in present study.
20
-0.10
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
-0.05
-0.04
-0.03
-0.02
-0.01
0.01
0.02
0.03
0.05
0.06
0.08
0.09
0.10
0.12
0.13
0.15
0.16
0.18
0.19
0.21
0.22
0.24
0.25
0.27
0.28
0.30
Axial Location (m)
Height (m)
x
y
Figure 2-1: Primary nozzle profile coordinates
Figure 2-2: Primary Flow Axial Mach #
21
2.2) Grid Generation
The computational grid for the primary nozzle including the injector has been shown in
figure 2-3. A typical grid configuration employed in present study for injection slot is
shown in figure 2-4. The primary or main nozzle has been assigned 250x75 grid points
while for all the injector configurations a 10x10 grid has been employed throughout the
investigation. Two dimensional rectangular (quad) elements were generated using the
structured solver in the GAMBIT®, a popular geometry and mesh generation software,
typically used with FLUENT.
Figure 2-3: Two dimensional 250x75 grid configuration of primary nozzle with 10x10 grid configuration of
injector
22
Figure 2-4: Two dimensional 10x10 grid configuration of injector
The same meshing approach has been employed in case of a different injection slot size,
injection location or injector angle. Figure 2-5 depict some of the grid configurations
employed in present study. In all the cases, mesh size and meshing technique were
identical both for the primary nozzle and injector. Following the mesh generation, each
mesh was examined thoroughly for aspect ratio, equi-size, and equi-angle skews to
ensure the mesh quality. It can be observed that the grid density is kept higher near the
injection location in order to better resolve the flowfield structure and complex flow
interactions in the injector vicinity.
23
a) Injection Location, M
P
= 2, Injection Angle = 0
o
, AR = 5%
b) Injection Location, M
P
= 3, Injection Angle = 45
o
, AR = 5%
Figure 2-5: Two dimensional 250x75 grid configurations for different injection configurations
24
c) Injection Location, M
P
= 3.75, Injection Angle = 0
o
, AR = 2%
Figure 2-5 (continued): Two dimensional 250x75 grid configurations for different injection configurations
2.3) Grid Sensitivity Analysis
A grid independence study was carried out for the primary nozzle prior to selection of the
grid configuration described in previous section. The study included the following grid
configurations:
a) 150x75
b) 250x75
c) 350x75
d) 300x100
25
The grid configurations studied are depicted in figure 2-6.
a) 150x75 grid configuration
b) 250x75 grid configuration
Figure 2-6: Candidate two dimensional grid configurations used for grid sensitivity analysis
26
c) 350x75 grid configuration
d) 300x100 grid configuration
Figure 2-6 (continued): Candidate two dimensional grid configurations used for grid sensitivity
analysis
27
28
Numerical test runs were performed for each of the above grids for the following flow
model:
Primary Stagnation Pressure, P
op
= 3.45 MPa
Primary Stagnation Temperature, T
op
= 3000 K
Primary Nozzle Throat Area, A* = 0.02 m
2
Primary Nozzle Area Ratio, A
e
/A* = 10
Primary Nozzle Exit Pressure, P
ep
= 0.1 MPa
Axial Primary Flow Mach # @ Injection Location, M
P
= 3
Secondary to Primary Stagnation Pressure Ratio, P
os
/P
op
= 0.75
Secondary Inj Slot to Primary Throat Area Ratio, A
s
/A* = 0.01
Angle of Injection, α
inj
= 0
Secondary (Injectant) Temperature, T
os
= 300 K
2-D, coupled implicit solver with realizable k-ε viscous model was employed for the
numerical solution of the given flow model for all the grid configurations. It was
observed that compared to 250x75 grid configuration:
- upstream wall pressure distribution was almost identical for all grids. In case of
300x100 grid, the pressure distribution was slightly off but not significantly.
- downstream wall pressure distribution was identical for all grids.
- primary axial thrust was identical in all cases. Maximum difference for all grids
for this value was less than 0.2 %.
- the integral of the pressure times area had a maximum difference less than 0.2%
for upper wall (containing injector) whereas for lower (opposite) wall this
difference was less than 0.16 % for all grid configurations.
Based on the grid sensitivity analysis, 250x75 grid was used throughout the research. The
static pressure distribution for the upstream & downstream of the injector for the upper
wall (containing injector) has been given in figures 2-7 & 2-8.
Figure 2-7: Effect of grid resolution on injector upstream wall static pressure distribution
Figure 2-8: Effect of grid resolution on injector downstream wall static pressure distribution
29
30
2.4) Computational Solver Characteristics
In terms of solver, FLUENT provides two choices; a) segregated solver, b) coupled
solver. The most important difference between the two is coupling of the flow equations.
For solving compressible flow with shocks, coupled solver is recommended because
coupling of energy equation with continuity and momentum is essential. Implicit
formulation converges faster compared to explicit formulation. Also, implicit
formulation is capable of providing time accurate solutions. The downside is high
memory requirement, which is not an issue keeping in view the size of the problem at
hand
[4,5].
The flow problem under consideration was inherently turbulent. In this specific problem,
the interaction of the secondary jet with the main flow is actually boundary layer-shock
wave interaction occurring in the neighborhood of injection location. This boundary
layer-shock wave interaction results into flow separation that directly influences the
SITVC performance as described earlier. Thus, selection & subsequent implementation
of a suitable viscous model was critical for accurate resolution of flowfield and flow
parameters. In terms of viscous model choices, FLUENT provides a wide range of
solvers. As we know, the physics of turbulence is not fully understood, so there is not any
universally accepted viscous model. Certain viscous models perform better in certain
conditions. Typically suitability of a specific model for a given flow problem is
determined by comparing the numerical results with available experimental data. In
31
current study, the experimental results by Guhse [6] were used for the selection of
viscous model. The geometrical & experimental configuration reported by Guhse in his
study was first transformed into computational domain. The flow model was then solved
using FLUENT for various viscous models and finally numerical results were compared
with the experimental data provided by Guhse. The numerical solution was obtained for
the following viscous models:
- Inviscid Flow
- Laminar Flow
- Spalart Allmaras (SA)
- k-ω with Enhanced Wall Treatment
- Realizable k-ε with Enhanced Wall Treatment
All numerical test runs were solved using 2-D Coupled Implicit solver for each of the
above viscous model for the following configuration:
Primary Fluid Air
Primary Stagnation Pressure, P
op
= 100 psig
Primary Stagnation Temperature, T
op
= 465
0
R
Primary Nozzle Throat Height, H* = 3.556 in
Primary Nozzle Throat Area, A* = 7.112 in
2
Primary Nozzle Area Ratio, A
e
/A* = 1.687
Primary Nozzle Exit Pressure, P
ep
= 12.7 psi
Secondary Fluid Air
Axial Primary Flow Mach # @ Injection Location, M
P
= 1.904
Secondary to Primary Stagnation Pressure Ratio, P
os
/P
op
= 0.60
Secondary Inj Slot to Primary Throat Area Ratio, A
s
/A* = 0.05
Angle of Injection, α
inj
= 0
Secondary (Injectant) Temperature, T
os
= 490
0
R
Figures 2-9 and 2-10 depicts the geometrical and grid configurations respectively,
employed for the numerical solution of the flow model for onwards comparative study.
Figure 2-9: Geometrical configuration of nozzle studied by Guhse
32
Figure 2-10: Grid configuration of nozzle transformed from the experimental setup of Guhse
As can be observed in figure 2-11, all viscous models under-predict compared to
experimental results. However, realizable k-epsilon (rk-ε) and Spalart Allmaras (SA) are
the closest to the experimental results in the upstream and downstream regions of the
injection slot. Enhanced wall treatment is essential to accurately capture the complex
phenomena occurring upstream and downstream of the injection slot. Also, realizable k-ε
model more accurately predicts the spreading rate of both planer and round jets. It is also
likely to provide superior performance for flow involving rotation, boundary layers under
strong adverse pressure gradients, separation, and recirculation [5]. Figure 2-12 depicts
the flowfield structure in terms of Mach number contours obtained from numerical
solution of Guhse’s experimental configuration using realizable k-ε viscous model with
enhanced wall treatment.
33
rke
34
0
10
20
30
40
50
60
70
12.00
13.20
14.14
14.86
15.42
15.85
16.19
16.45
16.65
16.81
16.93
17.01
17.09
17.19
17.42
17.67
17.95
18.25
18.59
18.96
19.38
Position (in)
Static Pressure (psi)
k-w
sa
lam
inv
Expt
Figure 2-11: Injector upstream & downstream wall static pressure distribution comparison for various
viscous models & Guhse’s experimental data
Figure 2-12: Flowfield structure (Mach number contours) obtained from numerical solution of Guhse’s
experimental configuration (Viscous Model: rk-ε with enhanced wall treatment)
35
Based on the presented analysis, the solver selected and used for all the computations in
this research is given as follows:
- Model Description : 2-D, turbulent, single phase
- Viscous Model : Realizable k-ε model with enhanced wall treatment
- Numerical Strategy : Coupled solver with implicit formulation
- Convergence Criteria : 1e-05
2.5) Flow Characteristics
In the current research, all the numerical test runs were performed for the same fixed
primary flow conditions as given below:
Primary Fluid Calorifically Perfect Air
Primary Stagnation Pressure, P
op
= 3.45 MPa
Primary Stagnation Temperature, T
op
= 3000 K
Primary Nozzle Exit Pressure, P
ep
= 0.1 MPa
The secondary flow characteristics are given as under:
Secondary Fluid Calorifically Perfect Air
Secondary Stagnation Pressure, P
os
Refer to Section 2.7
Secondary Stagnation Temperature, T
os
300 K
2.6) Conical Nozzle Configurations
An important aspect investigated in current research was the flowfield and performance
comparison between contoured (bell shaped) and conical nozzle profiles. Two conical
nozzles having 12 degree and 15 degree divergent half angles were selected for this
study. Table 2-2 provides the geometrical characteristics for all the primary nozzle
profiles investigated.
Comparative Geometrical Configurations of Contoured & Conical Nozzles
Profile 2-D Bell Shaped 2-D Conical 2-D Conical
Contour Slope Angle 30 deg - -
Conical Divergent Half Angle - 12 deg 15 deg
Exit Divergence Angle 6 deg 12 deg 15 deg
Nozzle Throat Height 0.02 m 0.02 m 0.02 m
Throat Area 0.02 m
2
0.02 m
2
0.02 m
2
Area Ratio 10 10 10
Nozzle Length to Throat Height Ratio 17.5 16.8 17.5
Table 2-2: Geometrical properties of bell & conical shaped primary nozzles
Geometrical & grid configurations of bell shaped and conical nozzles are given in figures
2-13 through 2-15. The comparative study for characterization of the flowfield structure
and estimation of performance parameters for above stated primary nozzles profiles was
conducted for similar primary flow and secondary injection conditions as detailed in
section 2.7.
36
37
-0.10
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
-0 .0 5
-0 .0 4
-0 .0 3
-0 .0 2
-0 .0 1
0.01
0.02
0.03
0.05
0.06
0.08
0.09
0.10
0.12
0.13
0.15
0.16
0.18
0.19
0.21
0.22
0.24
0.25
0.27
0.28
0.30
Axial Location (m)
Heig h t (m )
-0.10
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
-0 .0 5
-0 .0 4
-0 .0 3
-0 .0 2
-0 .0 1
0.00
0.01
0.03
0.05
0.07
0.09
0.11
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
0.30
0.31
0.33
0.35
0.37
0.39
0.41
Axial Location (m)
Heig h t (m )
a) Bell Shaped Profile
-0.10
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
-0 .0 5
-0 .0 4
-0 .0 3
-0 .0 2
-0 .0 1
0.00
0.02
0.04
0.05
0.07
0.09
0.10
0.12
0.14
0.15
0.17
0.19
0.20
0.22
0.24
0.25
0.27
0.29
0.30
0.32
0.34
Axial Location (m)
Heig h t (m )
b) Conical 12 Degree Divergent Half Angle Nozzle
c) Conical 15 Degree Divergent Half Angle Nozzle
Figure 2-13: Geometrical configuration of bell & conical shaped nozzles
a) Bell Shaped Profile (Injection Location, M
P
= 2)
b) 12 Degree Divergent Half Angle Conical Profile (Injection Location, M
P
= 2)
c) 15 Degree Divergent Half Angle Conical Profile (Injection Location, M
P
= 2)
Figure 2-14: Two dimensional grid configuration of primary bell and conical shaped nozzles (Showing
relative positions of same injection location at M
P
= 2)
38
a) Bell Shaped Profile (Injection Location, M
P
= 3)
b) 12 Degree Divergent Half Angle Conical Profile (Injection Location, M
P
= 3)
c) 12 Degree Divergent Half Angle Conical Profile (Injection Location, M
P
= 3)
Figure 2-15: Two dimensional grid configuration of primary bell and conical shaped nozzles (Showing
relative positions of same injection location at M
P
= 3)
39
40
2.7) Test Matrices
Identification & relative importance of the parameters influencing the flowfield structure
and, in turn, SITVC performance is of fundamental importance in analyzing the SITVC
systems. A detailed survey of the literature was performed in order to identify and
consolidate these parameters. The following parameters (hereafter called as SITVC
Control Parameters) have been identified from the literature that govern the flowfield
structure and affect SITVC performance.
- Secondary (Injectant) Mass Flow Rate
o Injection Stagnation Pressure
o Injection Slot Area
- Injection Location
- Angle of Injection
- Injector Shape (Geometry)
- Primary (Main) Nozzle Shape
- Physical Properties of Primary & Secondary Fluids
In current research all parameters except injector geometry & physical properties were
investigated. Several test runs were formulated to estimate the SITVC performance &
flowfield structure under the influence of various flow & geometrical parameters as
shown in Tables 2-3 to 2-5.
Batch
Injection Location in terms of
Axial Primary Flow Mach
Number, M
P
@ Injection
Secondary Injector Slot to
Primary Throat Area Ratio
(AR), A
s
/A*
Angle of Injection Comments
A 2 1% 0
B 2 2% 0
C 2 5% 0
E(10) 2 5% 10
E(45) 2 5% 45
41
Table 2-3: Summary of test runs to estimate the influence of injectant pressure, injection slot area, injection location and angle of injection
F 3 1% 0
G 3 2% 0
H 3 5% 0
J(10) 3 5% 10
J(45) 3 5% 45
Every batch contains five cases.
Each case was solved for a
different value of secondary
(injectant) to primary stagnation
pressure ratio (PR),
P
os
/P
op
= 1.25, 1, 0.75, 0.5, 0.25
K 3.75 1% 0
L 3.75 2% 0
M 3.75 5% 0
P 4 5% 0
Q 4.15 5% 0
42
Table 2-4: Summary of test runs to estimate the influence of injectant mass flow rate
Table 2-5: Summary of test runs to estimate the influence of primary nozzle profile
Batch
Injection Location in terms of
Axial Primary Flow Mach
Number, M
P
@ Injection
Secondary Injector Slot
to Primary Throat Area
Ratio (AR), A
s
/A*
Angle of
Injection
Comments
D 2 5% 0
This batch contains five cases. Each
case was solved for a different value of
secondary (injectant) mass flow rate,
m
S
= 1, 1.5, 2, 3, 4, 5 kg/s
I 3 5% 0
This batch contains five cases. Each
case was solved for a different value of
secondary (injectant) mass flow rate,
m
S
= 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 kg/s
Batch
Injection Location in terms of
Axial Primary Flow Mach
Number, M
P
@ Injection
Secondary Injector Slot
to Primary Throat Area
Ratio (AR), A
s
/A*
Angle of
Injection
Comments
Conical Nozzle - Divergent Half Angle = 12 degree
Y(12) 2 5% 0
Conical Nozzle - Divergent Half Angle = 15 degree
Y(15) 2
Every batch contains five cases. Each
case was solved for a different value of
secondary (injectant) to primary
stagnation pressure ratio (PR),
5% 0
P
os
/P
op
= 1.25, 1, 0.75, 0.5, 0.25
43
Chapter 3
Flowfield Structure
3.1) Flowfield Structure Elements
The complex flowfield setup by secondary injection inside primary supersonic flow is
shown in figure 3-1. The flowfield can be characterized by the shock structure composed
of certain elements as explained below. The discussion also reflects the relation between
SITVC performance parameters and flowfield structure.
- The injectant acts as an obstruction (much like a blunt body) and introduces a
strong bow (oblique) shock originating upstream of the injector. The strength of
this bow shock (hereafter referred to as primary bow shock) is characterized by
oblique shock angle. Higher shock angles indicate higher shock strengths. The
primary bow shock angle becomes increasingly important in perspective of shock
impingement on the opposite wall. Primary bow shock also controls the deflection
of the primary flow and, in turn, affects the primary axial thrust.
44
- The primary bow shock–boundary layer interaction causes the flow to separate
introducing a separation shock upstream of the injector. This separation shock, in
turn, results into a higher pressure region upstream of the injector. The strength of
the separation region is characterized by shock angle and pressure level in the
higher pressure region upstream of the injector. Stronger separation shock results
into stronger (relatively higher pressure) injector upstream higher wall pressure
region. Primary bow shock and separation shock originates from the same point
upstream of the injector. Interaction force is dependent on the length (measured
from the origination point of the separation shock upstream of the injector) and
strength (static pressure) of the higher pressure region upstream of the injector.
- Secondary injection also induces a relatively lower pressure region downstream of
the injector. The underlying reason is detachment of the primary flow due to
introduction of the secondary gas (injectant). However, the flow re-attaches
further downstream to the primary nozzle wall. The length and strength of this
region also affects the interaction force to a certain limited extent.
- A secondary bow (oblique) shock may also be present under certain situations,
originating downstream of the injection location. This bow shock (hereafter
referred to as secondary bow shock) is much weaker in strength compared to
primary bow shock. Again, the strength of secondary bow shock is determined by
oblique shock angle. Though secondary bow shock does not contribute towards
45
the side force, however, it may significantly affect the primary axial thrust by
deflecting the primary flow. According to Guhse [6], this shock is apparently
caused by one of the two factors or a combination of both:
a) turning of the supersonic secondary gas stream by the wall, and/or
b) boundary layer separation caused by an adverse pressure gradient. This
adverse pressure gradient is due to a low pressure region immediately
downstream of the injection slot caused by Prandtl-Meyer expansion of
the secondary gas around the downstream edge of the injection slot. The
low pressure region coupled with atmospheric pressure at the exit
produces adverse pressure gradient.
Separation Shock
Upstream Higher
Pressure Region
Primary Nozzle Inlet
Downstream Lower
Pressure Region
Primary Nozzle
Throat
Primary Bow Shock
Impingement
Primary Bow Shock
Secondary Bow Shock
Lower Wall
Boundary Layer
Upper Wall
Boundary Layer
Secondary Inlet
(Injector) Primary Nozzle
Exit
Reflected Primary
Bow Shock
Figure 3-1: Flowfield structure (Mach number contours) setup by secondary injection into primary nozzle flow
46
47
3.2) Flowfield Structure: Observations & Discussion
The qualitative discussion presented herein is intended to provide an insight of the
flowfield structure through its characterization in the perspective of the following SITVC
control parameters.
- secondary mass flow rate
o secondary (injectant) to primary stagnation pressure ratio
o injection slot to primary nozzle throat area ratio
- injection location
- angle of injection
- primary nozzle profile
The range of parameters investigated can be found in Tables 2-2 through 2-4.
3.2.1) Effects of Secondary Stagnation Pressure & Injection Slot Area
(Secondary Mass Flow Rate)
For a given injection location and angle of injection, the effects of secondary mass flow
rate on flowfield structure are described in this section. Figure 3-2 depicts the flowfield
structure in terms of Mach number contours. Figures 3-3 through 3-5 show the injector
upstream, injector downstream and opposite (down) wall static pressure distributions.
48
- The strength (shock angle) of the primary bow shock inside nozzle increases with
the secondary mass flow rate (either by increasing the secondary stagnation
pressure or injection slot area) as shown in figure 3-2.
- The origination point of the primary bow shock moves further upstream of the
injector as the secondary mass flow rate increases (by increasing the secondary
stagnation pressure and/or injection slot area). This, in turn, results into extended
higher pressure region upstream of the injector as depicted in figure 3-3.
- Like primary bow shock, the strength of the separation increases as the secondary
mass flow rate is increased (by increasing the secondary stagnation pressure
and/or injection slot area). Stronger separation shock results into stronger
(relatively high pressure) injector upstream higher wall pressure region as shown
in figure 3-3.
- Higher secondary mass flow rates (resulting from higher secondary stagnation
pressure and/or higher injection slot area) also cause extended lower pressure
regions downstream of the injector. As the injection mass flow rate is lowered, the
reattachment point moves upstream on the primary nozzle wall in the aft section
of the injector as shown in figure 3-4.
- Referring to figure 3-2, secondary bow shock is observed in case of higher
injection mass flow rates only (resulting from higher secondary stagnation
pressure and/or higher injection slot area). At sufficiently lower injection
stagnation pressure, secondary bow shock is essentially non-existent.
49
- For a given injection location, as the secondary mass flow rate increases (by
increasing the secondary stagnation pressure and/or injection slot area), the
chance of primary bow shock impingement on the opposite wall increases. Once
shock impingement limit is achieved for a given configuration, the shock impact
point moves relatively upstream on the opposite wall as the secondary mass flow
rate increases as shown in figures 3-3 and 3-5. Also, relatively higher mass flow
rate results into higher pressure rise on the opposite wall as can be noted in figure
3-5.
a) No Injection Condition
b) PR = 1.25, AR = 5%, α
inj
= 0
o
, M
P
= 3
c) PR = 1.00, AR = 5%, α
inj
= 0
o
, M
P
= 3
Figure 3-2: Effect of injection pressure on flowfield structure (Mach # contours)
50
d) PR = 0.75, AR = 5%, α
inj
= 0
o
, M
P
= 3
e) PR = 0.50, AR = 5%, α
inj
= 0
o
, M
P
= 3
f) PR = 0.25, AR = 5%, α
inj
= 0
o
, M
P
= 3
Figure 3-2 (continued): Effect of injection pressure on flowfield structure (Mach # contours)
51
Injection Location, M
P
= 2
Area Ratio, AR = 2%
Angle of Injection, α
inj
= 0
o
a) AR = 2%, α
inj
= 0
o
, M
P
= 2
Injection Location, M
P
= 3
Area Ratio, AR = 5%
Angle of Injection, α
inj
= 0
o
b) AR = 5%, α
inj
= 0
o
, M
P
= 3
Figure 3-3: Effect of secondary (injection) mass flow rate on injector upstream wall static pressure
distribution
52
Injection Location, M
P
= 2
Area Ratio, AR = 2%
An = 0
o
gle of Injection, α
inj
a) AR = 2%, α
inj
= 0
o
, M
P
= 2 a) AR = 2%, α
b) AR = 5%, α
inj
= 0
o
, M
P
= 3 b) AR = 5%, α
53
inj
= 0
o
, M
P
= 2
inj
= 0
o
, M
P
= 3
Injection Location, M
P
= 3
Area Ratio, AR = 5%
Angle of Injection, α
inj
= 0
o
Figure 3-4: Effect of secondary (injection) mass flow rate on injector downstream wall static pressure
distribution
Figure 3-4: Effect of secondary (injection) mass flow rate on injector downstream wall static pressure
distribution
Injection Location, M
P
= 2
Area Ratio, AR = 2%
Angle of Injection, α
inj
= 0
o
a) AR = 2%, α
inj
= 0
o
, M
P
= 2
Injection Location, M
P
= 3
Area Ratio, AR = 5%
An = 0
o
gle of Injection, α
inj
b) AR = 5%, α
inj
= 0
o
, M
P
= 3
Figure 3-5: Effect of secondary (injection) mass flow rate on down (opposite wall static pressure
distribution
54
55
3.2.2) Effects of Injection Location
For a given secondary mass flow rate (through fixed secondary stagnation pressure and
fixed injection slot area) and angle of injection, the variations in flowfield structure as a
function of injection location are discussed in the following paragraphs. Figures 3-6 and
3-7 depict the flowfield structure in terms of Mach number contours. Figures 3-8 through
3-10 show the injector upstream, injector downstream and opposite (down) wall static
pressure distributions. The observations & comments are as follows:
- For a given secondary mass flow rate (given secondary stagnation pressure and
injection slot area), the strength of the primary bow shock inside primary nozzle
decreases as the injection location is moved farther downstream (in the divergent
part of the nozzle). Thus, in case of downstream injection, both the relatively
smaller primary bow shock angle and relatively shorter wall length available on
the opposite wall for shock interface reduce the chance of shock impingement as
depicted in figures 3-6 and 3-7.
- For a given secondary mass flow rate, the origination point of the primary bow
shock substantially moves further upstream of the injector as injection location is
moved farther downstream. This, in turn, results into relatively much extended
higher pressure region upstream of the injector as shown in figure 3-8.
56
- Strength of the separation notably decreases as the injection location is moved
farther downstream and this, in turn, results into relatively lower pressure in the
injector upstream higher wall pressure region as depicted in figure 3-8.
- Downstream injection (in the divergent part of the nozzle) causes extended lower
pressure regions downstream of the injector as shown in figure 3-9. The
underlying reason is same as in case of higher secondary mass flow rates in
previous section.
- Referring to figures 3-7 and 3-8, in case of upstream injection (in the divergent
part of the nozzle) the strength of the secondary bow shock is higher and it
decreases as the injection location is moved farther downstream.
- For upstream injection, the probability of shock impingement is very high even
for smaller secondary mass flow rates. For a given mass flow rate and angle of
injection, as the injection location is moved farther downstream, the chance of
primary bow shock impingement on the opposite wall decreases. In case of shock
impingement, the shock impact point moves further downstream on the opposite
wall as the injection location is moved further downstream as depicted in figures
3-6, 3-7 and 3-10. Downstream injection also results into relatively lower pressure
rise (due to relatively weaker primary bow shock) on the opposite wall in case of
shock impingement as depicted in figure 3-10. This, in turn, results into less
adverse effect on the positive contribution of interaction force towards the net side
thrust.
a) PR = 1.00, AR = 2%, α
inj
= 0
o
, M
P
= 2
b) PR = 1.00, AR = 2%, α
inj
= 0
o
, M
P
= 3
c) PR = 1.00, AR = 2%, α
inj
= 0
o
, M
P
= 3.75
Figure 3-6: Effect of injection location on flowfield structure (Mach # contours)
57
a) PR = 1.25, AR = 5%, α
inj
= 0
o
, M
P
= 2
b) PR = 1.25, AR = 5%, α
inj
= 0
o
, M
P
= 3
c) PR = 1.25, AR = 5%, α
inj
= 0
o
, M
P
= 3.75
Figure 3-7: Effect of injection location on flowfield structure (Mach # contours)
58
Pressure Ratio, PR = 1.00
Area Ratio, AR = 2%
Angle of Injection, α
inj
= 0
o
a) PR = 1.00, AR = 2%, α
inj
= 0
o
Pressure Ratio, PR = 1.25
Area Ratio, AR = 5%
o
Angle of Injection, = 0 α
inj
b) PR = 1.25, AR = 5%, α
inj
= 0
o
Figure 3-8: Effect of injection location on injector upstream wall static pressure distribution
59
Pressure Ratio, PR = 1.00
Area Ratio, AR = 2%
Angle of Injection, α
inj
= 0
o
a) PR = 1.00, AR = 2%, α
inj
= 0
o
b) PR = 1.25, AR = 5%, α
inj
= 0
o
Pressure Ratio, PR = 1.25
Area Ratio, AR = 5%
An = 0
o
gle of Injection, α
inj
Figure 3-9: Effect of injection location on injector downstream wall static pressure distribution
60
Pressure Ratio, PR = 1.00
Area Ratio, AR = 2%
Angle of Injection, α
inj
= 0
o
a) AR = 1.00, AR = 2%, α
inj
= 0
o
b) AR = 1.25, AR = 5%, α
inj
= 0
o
Pressure Ratio, PR = 1.25
Area Ratio, AR = 5%
An = 0
o
gle of Injection, α
inj
Figure 3-10: Effect of injection location on down (opposite) wall static pressure distribution
61
62
3.2.3) Effects of Angular Injection
For a given secondary mass flow rate (i.e. fixed secondary stagnation pressure and fixed
injection slot area) and injection location, the effects of angle of injection on flowfield
structure are discussed in this section. Figures 3-11 and 3-12 depict the flowfield
structure in terms of Mach number contours. Figures 3-13 through 3-15 show the injector
upstream, injector downstream and opposite (down) wall static pressure distributions.
The observations and comments are as follows:
- Primary bow shock strength decreases as the injection angle is increased. Thus
injection at higher angles reduces the chances of shock impingement. This can be
observed in figures 3-11 & 3-12.
- As the angle of injection is increased the originating point of the primary bow
shock moves towards the injector (i.e. moves downstream in the primary nozzle in
absolute sense). This, in turn, results into shorter higher pressure region upstream
of the injector as shown in figure 3-13.
- The strength of the separation faintly decreases as the injection angle is increased.
Thus, slightly weaker separation shock results into slightly lower pressure in the
injector upstream higher pressure region as shown in figure 3-13.
- As the angle of injection is increased the lower pressure region downstream of the
injector is slightly extended as can be observed in figure 3-14.
- Injection at an angle causes the strength of the secondary bow shock to diminish
as shown in figure 3-11 & 12.
63
- As the angle of injection is increases, the chance of primary bow shock
impingement on the opposite wall decreases and in case of shock impingement,
the shock impact point moves further downstream on the opposite wall with an
increase in injection angle as depicted in figures 3-11, 3-12 and 3-15. Injection at
relatively higher angles also results into relatively weaker shock impact (lower
pressure rise) on the opposite wall as can be noted in figure 3-15.
a) PR = 1.00, AR = 5%, α
inj
= 0
o
, M
P
= 2
b) PR = 1.00, AR = 5%, α
inj
= 10
o
, M
P
= 2
c) PR = 1.00, AR = 5%, α
inj
= 45
o
, M
P
= 2
Figure 3-11: Effect of angle of injection on flowfield structure (Mach # contours)
64
a) PR = 0.75, AR = 5%, α
inj
= 0
o
, M
P
= 3
b) PR = 0.75, AR = 5%, α
inj
= 10
o
, M
P
= 3
c) PR = 0.75, AR = 5%, α
inj
= 45
o
, M
P
= 3
Figure 3-12: Effect of angle of injection on flowfield structure (Mach # contours)
65
Injection Location, M
P
= 2
Pressure Ratio, PR = 1.00
Area Ratio, AR = 5%
a) PR = 1, AR = 5%, M
P
= 2
Injection Location, M
P
= 3
Pressure Ratio, PR = 0.75
Area Ratio, AR = 5%
b) PR = 0.75, AR = 5%, M
P
= 3
Figure 3-13: Effect of angle of injection on injector upstream wall static pressure distribution
66
Injection Location, M
P
= 2
Pressure Ratio, PR = 1.00
Area Ratio, AR = 5%
a) PR = 1, AR = 5%, M
P
= 2
b) PR = 0.75, AR = 5%, M
P
= 3
Injection Location, M
P
= 3
Pressure Ratio, PR = 0.75
Area Ratio, AR = 5%
Figure 3-14: Effect of angle of injection on injector downstream wall static pressure distribution
67
Injection Location, M
P
= 2
Pressure Ratio, PR = 1.00
Area Ratio, AR = 5%
a) PR = 1, AR = 5%, M
P
= 2
Injection Location, M
P
= 3
Pressure Ratio, PR = 0.75
Area Ratio, AR = 5%
b) PR = 0.75, AR = 5%, M
P
= 3
Figure 3-15: Effect of angle of injection on down (opposite) wall static pressure distribution
68
69
3.2.4) Effects of Primary Nozzle Profile
As stated earlier, a comparative study was conducted to investigate the effects of primary
nozzle profile while keeping all the primary flow and secondary injection parameters
constant. As it will be detailed in the following section, while characterizing the flowfield
structure, the injection location was found to be strongly coupled with nozzle profiles
having less rapid diverging expansion rates, for instance the conical shapes with smaller
divergent half angles. That is why the discussion presented below has been systematically
partitioned into flowfield structure comparison among various nozzle profiles for
a) Injection Location, M
P
= 2
b) Injection Location, M
P
= 3
for a given secondary mass flow rate (through fixed secondary stagnation pressure and
fixed injection slot area) and injection angle. Figures 3-16 and 3-17 depict the flowfield
structure in terms of Mach number contours. Figures 3-18 through 3-20 show the injector
upstream, injector downstream and opposite (down) wall static pressure distributions.
The observations and comments recorded are as follows:
70
a) Injection Location, M
P
= 2
- The strength of the primary bow shock inside conical shaped nozzle is higher
compared to bell shaped nozzle. Also, as the conical divergent half angle
increases, shock strength decreases. These effects can be observed in figures 3-16.
- Origination point of primary bow shock upstream of the injector is almost
identical for bell and conical shaped nozzles. That is why, the length of the higher
pressure regions upstream of the injector is nearly same for different profiles, as
depicted in figure 3-18(a).
- For upstream injection locations, conical nozzles result into stronger separation
shocks and, in turn, relatively higher pressure in the injector upstream higher
pressure region. Comparing conical nozzles alone, higher conical divergent half
angles result into stronger shock separation as may be noted in figure 3-18(a).
- The length of the lower pressure region downstream of the injector is almost
identical for all nozzles profiles as can be observed in figure 3-19(a).
- Strength of secondary bow shock is higher in case of bell shaped nozzles as can
be observed in figure 3-16.
- It can be observed in figure 3-16 and 3-20(a) that upstream injection combined
with smaller conical half angles may result into multiple primary bow shock
impingements on both primary nozzle walls. Also, the strength (pressure rise on
the opposite wall) of shock impingement is much higher for upstream injection
locations in conical nozzles compared to bell shaped nozzles as can be observed
in figure 3-20(a).
71
b) Injection Location, M
P
= 3
- The strength of the primary bow shock inside conical shaped nozzle is higher
compared to bell shaped nozzle. Also, as the conical divergent half angle
increases, shock strength decreases. These effects can be observed in figures 3-17.
- For relatively downstream injection, primary bow shock originates relatively
further upstream of the injection location in case of conical shaped nozzle
compared to bell shaped nozzle. Thus in case of conical nozzles extended higher
pressure regions upstream of the injector is observed as depicted in figure 3-18(b).
Also, while comparing conical shaped profiles alone, smaller conical divergent
half angle results into extended higher pressure regions.
- For downstream injection locations, bell shaped nozzle result into stronger
separation shocks (relatively higher pressure in the injector upstream higher
pressure region) compared to conical nozzles as depicted in figure 3-18(b). While
comparing conical nozzles alone, higher conical divergent half angles results into
stronger shock separation.
- For downstream injection locations, the chances of multiple shock impingements
are non-existent for the range of SITVC control parameters investigated in current
study as shown in figure 3-17. Also, the difference in shock impingement strength
is not prominent for either nozzle shape as depicted in figures 3-20(b).
a) PR = 1.25, AR = 5%, α
inj
= 0
o
, M
P
= 2, Bell Shaped Profile
b) PR = 1.25, AR = 5%, α
inj
= 0
o
, M
P
= 2, Conical Divergent Half Angle = 12
o
c) PR = 1.25, AR = 5%, α
inj
= 0
o
, M
P
= 2, Conical Divergent Half Angle = 15
o
Figure 3-16: Effect of primary nozzle profile on flowfield structure (Mach # contours)
72
a) PR = 1, AR = 5%, α
inj
= 0
o
, M
P
= 3, Bell Shaped Profile
b) PR = 1, AR = 5%, α
inj
= 0
o
, M
P
= 3, Conical Divergent Half Angle = 12
o
c) PR = 1, AR = 5%, α
inj
= 0
o
, M
P
= 3, Conical Divergent Half Angle = 15
o
Figure 3-17: Effect of primary nozzle profile on flowfield structure (Mach # contours)
73
Injection Location, M
P
= 2
Pressure Ratio, PR = 1.25
Area Ratio, AR = 5%
o
Angle of Injection, = 0 α
inj
a) PR = 1.25, AR = 5%, α
inj
= 0
o
, M
P
= 2
b) PR = 1, AR = 5%, α
inj
= 0
o
, M
P
= 3
Injection Location, M
P
= 3
Pressure Ratio, PR = 1.00
Area Ratio, AR = 5%
Angle of Injection, α
inj
= 0
o
Figure 3-18: Effect of primary nozzle profile on injector upstream wall static pressure distribution
74
Injection Location, M
P
= 2
Pressure Ratio, PR = 1.25
Area Ratio, AR = 5%
Angle of Injection, α
inj
= 0
o
a) PR = 1.25, AR = 5%, α
inj
= 0
o
, M
P
= 2 a) PR = 1.25, AR = 5%, α
inj
= 0
o
, M
P
= 2
Injection Location, M
P
= 3
Pressure Ratio, PR = 1.00
Area Ratio, AR = 5%
An
o
gle of Injection, = 0 α
inj
b) PR = 1.00 AR = 5%, α
inj
= 0
o
, M
P
= 3 b) PR = 1.00 AR = 5%, α
inj
= 0
o
, M
P
= 3
Figure 3-19: Effect of primary nozzle profile on injector downstream wall static pressure distribution Figure 3-19: Effect of primary nozzle profile on injector downstream wall static pressure distribution
75
Injection Location, M
P
= 2
Pressure Ratio, PR = 1.25
Area Ratio, AR = 5%
o
Angle of Injection, = 0 α
inj
a) PR = 1.25, AR = 5%, α
inj
= 0
o
, M
P
= 2
Injection Location, M
P
= 3
Pressure Ratio, PR = 1.00
Area Ratio, AR = 5%
o
Angle of Injection, = 0 α
inj
b) PR= 1, AR = 5%, α
inj
= 0
o
, M
P
= 3
Figure 3-20: Effect of primary nozzle profile on down (opposite) wall static pressure distribution
76
77
Chapter 4
Performance Analysis
4.1) SITVC Performance Parameters
Secondary injection thrust vector control (SITVC) performance parameters investigated
in present study include:
- Axial Thrust Augmentation
- Side Thrust
o Interaction Force (Side Thrust-Pressure Component)
o Jet Reaction Force (Side Thrust-Momentum Component)
- System Specific Impulse Loss
- Specific Impulse Ratio (Amplification Factor)
Definitions of the performance and other related parameters used in this study are
detailed below.
a) Primary (Axial) Thrust
The primary axial thrust is the force produced by the primary nozzle and is determined by
the rocket thrust equation as given below:
( ) [ ] ( )
ep
i
ap ep px x px p
A P P V A V F
∑
− + Δ = ρ (4-1)
where “i” indicates that the sum is taken over all the grid cell areas of the primary nozzle
exit plane. The first term on the right hand side represents the momentum component of
the primary axial thrust while the second term represents the pressure component of the
primary axial thrust.
b) Primary (Axial) Thrust Augmentation
The introduction of injectant into primary flow results into an increase in the primary
axial thrust as given by
o
p p p
F F F − = Δ (4-2)
In this paper, primary axial thrust augmentation is represented by a dimensionless
parameter given as follows:
o
p
o
p p
o
p
p
F
F F
F
F −
=
Δ
(4-3)
78
c) Primary Specific Impulse
The performance of the primary nozzle is measured through primary specific impulse
which is defined as
e p
p
p
g m
F
Isp
•
= (4-4)
d) Side Thrust
Net side thrust is given as
F
s
= F
n
+ F
j
(4-5)
F
n
, Interaction Force (Side Thrust-Pressure Component) is given as
[ ] [ ]
∑ ∑
− −
Δ − Δ =
i
wall down
y
i
wall upper
y n
A P A P F (4-6)
“i” indicates that sum is taken over all the cells of wall surface. F
j
, Jet Reaction Force
(Side Thrust-Momentum Component) is defined as
() []
inj s as es sy
s
j
A P P V m F β cos − + =
•
(4-7)
79
Pressure component of the side thrust (interaction force) becomes increasingly important
in determining the safe injection configurations i.e. the configurations avoiding the
adverse input from interaction force resulting from primary bow shock impingements.
In this study, the interaction force, jet reaction force and net side thrust are represented in
the form of dimensionless parameters attained through dividing each of the above
parameter by no-injection primary axial thrust, which is a constant in this study.
o
p
F
e) Secondary Specific Impulse
The level of efficient usage of mass supplied through secondary injection is measured by
secondary specific impulse as given by
e
s
s
s
g m
F
Isp
•
= (4-8)
f) Specific Impulse Ratio (Amplification Factor)
Amplification factor is an important parameter employed in the SITVC performance
evaluation. The amplification factor is defined in many different ways in the literature.
The definition used in current study is given as
o
p
s
Isp
Isp
AK = (4-9)
80
g) System Specific Impulse Loss
The total specific impulse of the system is defined as
e s p
s p
sys
g m m
F F
Isp
⎟
⎠
⎞
⎜
⎝
⎛
+
+
=
• •
2 2
(4-10)
Then the system specific impulse loss is given as
o
sys sys sys
Isp Isp Isp − = δ (4-11)
This figure is a measure of the inefficient usage of the mass supplied to the system. This
important performance parameter helps in determining the cost at which SITVC system
provides side thrust and augmentation in primary axial thrust.
81
82
4.2) Performance Calculations
This section contains the systematic progression of the steps used in this study to estimate
the performance parameters.
a) Primary Flow Input Conditions
Primary Stagnation Pressure, P
op
= 3.45 MPa
Primary Stagnation Temperature, T
op
= 3000 K
Primary Nozzle Throat Area, A* = 0.02 m
2
Primary Nozzle Area Ratio, A
e
/ A* = 10
Primary Nozzle Exit Pressure, P
ep
= 0.1 MPa
b) Secondary (Injectant) Flow Input Conditions
Axial Primary Flow Mach # at Injection Location, M
P
= 3
Secondary to Primary Stagnation Pressure Ratio, P
os
/P
op
= 0.75
Injection Slot to Primary Throat Area Ratio, A
s
/A* = 0.05
Secondary Temperature, T
os
= 300 K
Angle of Injection, α
inj
= 0
deg
Wall Angle at Injection Location, β
inj
= 25.56
deg
c) Observations & Performance Calculations
Primary Nozzle Inlet Mass Flow Rate, = 50.7 kg/s
•
p
m
Primary Nozzle Exit Pressure, P
ep
= 0.003585 MPa
Secondary Mass Flow Rate, = 5.968 kg/s
•
s
m
Normal Component of the Injectant Velocity, V
s-y
= 353.912 m/s
Injectant Exit Pressure, P
es
= 1.158 MPa
Freestream Pressure at Injection Location, P
as
= 0.1385 MPa
Primary Axial Thrust,
F
p
= ( ) [ ] ( )
ep
i
ap ep px x px
A P P V A V
∑
− + Δ ρ
= 95140.372 N
Interaction Force, F
n
= [ ] [ ]
∑ ∑
− −
Δ − Δ
i
wall down
y
i
wall upper
y
A P A P
= 195737.60 - 192320.50
= 3417.100 N
Jet Reaction Force, F
j
= () []
inj s as es sy s
A P P V m β cos − +
•
= 3032.148 N
83
Net Side Thrust, F
s
= F
n
+ F
j
= 6449.248 N
System Specific Impulse, Isp
sys
=
e s p
s p
g m m
F F
⎟
⎠
⎞
⎜
⎝
⎛
+
+
• •
2 2
= 171.535 sec
d) Baseline Performance Parameters (No-Injection Condition)
Primary Axial Thrust, =
o
p
F ( ) [ ] ( )
ep
i
ap ep px x px
A P P V A V
∑
− + Δ ρ
= 92477.696 N
System Specific Impulse =
o
sys
Isp
e s p
s p
g m m
F F
⎟
⎠
⎞
⎜
⎝
⎛
+
+
∗ ∗
2 2
=
e s
p
g m
F
•
= 185.817 sec
84
85
4.3) Performance Analysis: Results & Discussion
As stated earlier, SITVC performance trends were investigated for the following factors:
- Secondary Mass Flow Rate
o Secondary (Injectant) To Primary Stagnation Pressure Ratio
o Injection Slot To Primary Nozzle Throat Area Ratio
- Injection Location
- Angle Of Injection
- Primary Nozzle Profile
The range of parameters investigated may be found in Tables 2-2 through 2-4. In the
discussion below, performance parameters are presented as ratios with respected to some
suitable fixed quantity to have non-dimensional figures of merits for comparisons as
explained earlier.
4.3.1) Effects of Secondary Stagnation Pressure & Injection Slot Area
(Secondary Mass Flow Rate)
The effects of injection stagnation pressure & injection slot area on the performance
parameters for a given injection location and angle of injection are shown in the figures
from 4-1 through 4-7. Similarly, the effects of injection mass flow rates for a given
86
injection location and angle of injection on performance parameters have been depicted
in the figures from 4-8 through 4-14 explicitly. The observations are recorded as follows:
- Referring to figure 4-1 and 4-8, secondary mass flow rate is a function of
secondary injection stagnation pressure and injection slot area. In other words,
secondary mass flow rate is directly proportional to injection stagnation pressure
for a given slot area. Same argument goes for injection slot area at a given
injection stagnation pressure.
- As the mass flow rate increases (by increasing the secondary stagnation pressure
and/or injection slot area), the axial thrust augmentation increases as can be
observed in figure 4-2 and 4-9. Primary cause is addition & subsequent adiabatic
expansion of the injectant mass. Thrust augmentation is also a weak function of
strength of the primary & secondary bow shocks that deflect the primary flow
direction in the primary nozzle. More augmentation is resulted in case of stronger
shocks.
- The interaction force increases linearly as the injectant mass flow rate increases
(by increasing the secondary stagnation pressure and/or injection slot area).
However, it should be noted that at a given injection location, angle & fixed
injection slot area, an increase in secondary stagnation pressure, initially causes
an increase in the interaction force owning to pressure rise in the injection vicinity
(on the wall containing the injection slot). As we keep on increasing the
secondary injection pressure, primary bow shock hits the opposite wall and, in
turn, results an un-desirable pressure rise on the opposite wall resulting into
87
negative interaction force. This effect is more severe in case of higher mass flow
rates. This discussion is supported by the data provided in figures 4-3 and 4-10.
- As can be noted in figures 4-4 and 4-11, jet reaction force increases linearly as
injectant mass flow rate increases (by increasing the secondary stagnation
pressure and/or injection slot area).
- Referring to figures 4-5 and 4-12, trend for the net side force is identical to
interaction force. In absence of shock impingement, the interaction force and
hence net side force is a strong function of injectant mass flow rate.
- As the secondary mass flow rate is increased, initially secondary specific impulse
and in turn, amplification factors increases for lower mass flow rates. For
moderate to higher mass flow rates, both the secondary specific impulse and
amplification factor decreases as depicted in figures 4-6 and 4-13. Amplification
factor does not linearly depend on the secondary mass flow rate due to non-
linearities of the governing factors. Amplification factor is a function of
physical/flow properties of primary & secondary fluids, injection location, angle
of injection and primary nozzle geometry. As can be observed, shock
impingement drastically affects the secondary specific impulse & amplification
factors.
- Side thrust & axial thrust augmentation is achieved at the cost of specific impulse.
It can be observed in figures 4-7 and 4-14 that as the secondary mass flow rate
increases (by increasing the secondary stagnation pressure and/or injection slot
area), system specific impulse decreases almost linearly. The reason of this loss is
the inefficient expansion of the injected gas.
88
0
5
10
15
20
25
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
m
s
/ m
p
(%)
AR = 1%
AR = 2%
AR = 5%
AR = 1%
0
5
10
15
20
25
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
m
s
/ m
p
(%)
AR = 2%
AR = 5%
Injection Location, M
P
= 3
An = 0
o
gle of Injection, α
inj
a) α
inj
= 0
o
, M
P
= 3 a) α
inj
= 0
o
, M
P
= 3
Injection Location, M
P
= 3.75
Angle of Injection, α
inj
= 0
o
b) α
inj
= 0
o
, M
P
= 3.75 b) α
inj
= 0
o
, M
P
= 3.75
Figure 4-1: Effect of secondary stagnation pressure & injection slot area on secondary mass flow rate Figure 4-1: Effect of secondary stagnation pressure & injection slot area on secondary mass flow rate
89
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
ΔF
p
/ F
p
o
(%)
AR = 1%
AR = 2%
AR = 5%
Injection Location, M
P
= 3
Angle of Injection, α
inj
= 0
o
a) α
inj
= 0
o
, M
P
= 3
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
ΔF
p
/ F
p
o
(%)
AR = 1%
AR = 2%
AR = 5%
Injection Location, M
P
= 3.75
Angle of Injection, α
inj
= 0
o
b) α
inj
= 0
o
, M
P
= 3.75
Figure 4-2: Effect of secondary stagnation pressure & injection slot area on axial thrust
90
-1
-1
0
1
1
2
2
3
3
4
4
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
F
n
/ F
p
o
(%)
AR = 1%
AR = 1%
AR = 5%
Injection Location, M
P
= 3
Angle of Injection, α
inj
= 0
o
a) α
inj
= 0
o
, M
P
= 3
AR = 1%
0
1
2
3
4
5
6
7
8
9
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
F
n
/ F
p
o
(%)
AR = 1%
AR = 5%
Injection Location, M
P
= 3.75
o
Angle of Injection = 0 α
inj
b) α
inj
= 0
o
, M
P
= 3.75
Figure 4-3: Effect of secondary stagnation pressure & injection slot area on interaction force
91
0
1
2
3
4
5
6
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
F
j
/ F
p
o
(%)
AR = 1%
AR = 2%
AR = 5%
Injection Location, M
P
= 3
Angle of Injection, α
inj
= 0
o
a) α
inj
= 0
o
, M
P
= 3
AR = 1%
0
1
2
3
4
5
6
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
F
j
/ F
p
o
(%)
AR = 2%
AR = 5%
Injection Location, M
P
= 3.75
o
Angle of Injection = 0 α
inj
b) α
inj
= 0
o
, M
P
= 3.75
Figure 4-4: Effect of secondary stagnation pressure & injection slot area on jet reaction force
92
0
2
4
6
8
10
12
14
16
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
F
s
/ F
p
o
(%)
AR = 1%
AR = 2%
AR = 5%
Injection Location, M
P
= 3.75
Angle of Injection, α
inj
= 0
o
0
1
2
3
4
5
6
7
8
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
F
s
/ F
p
o
(%)
AR = 1%
AR = 2%
AR = 5%
Injection Location, M
P
= 3
Angle of Injection, α
inj
= 0
o
a) α
inj
= 0
o
, M
P
= 3
b) α
inj
= 0
o
, M
P
= 3.75
Figure 4-5: Effect of secondary stagnation pressure & injection slot area on net side thrust
93
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
AK
AR = 1%
AR = 2%
AR = 3%
Injection Location, M
P
= 3.75
Angle of Injection, α
inj
= 0
o
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
AK
AR = 1%
AR = 2%
AR = 3%
Injection Location, M
P
= 3
Angle of Injection, α
inj
= 0
o
a) α
inj
= 0
o
, M
P
= 3
b) α
inj
= 0
o
, M
P
= 3
Figure 4-6: Effect of secondary stagnation pressure & injection slot area on amplification factor
AR = 1%
AR = 2%
AR = 5%
-25
-20
-15
-10
-5
0
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
δ Isp
sys
(sec)
Injection Location, M
P
= 3
Angle of Injection, α
inj
= 0
o
a) α
inj
= 0
o
, M
P
= 3
-25
-20
-15
-10
-5
0
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
δ Isp
sys
(sec)
AR = 1%
AR = 2%
AR = 5%
Injection Location, M
P
= 3.75
Angle of Injection, α
inj
= 0
o
b) α
inj
= 0
o
, M
P
= 3.75
Figure 4-7: Effect of secondary stagnation pressure & injection slot area on system specific impulse
94
Injection Location, M
P
= 3
Area Ratio, AR = 5%
An = 0
o
gle of Injection, α
inj
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
2 4 6 8 10 12 14 16 18 20
m
s
/ m
p
(%)
P
os
/ P
op
(%)
Figure 4-8: Dependence of secondary mass flow rate on secondary stagnation pressure
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
2 4 6 8 10 12 14 16 18 20
m
s
/m
p
(%)
ΔF
p
/ F
p
o
(%)
Injection Location, M
P
= 3
Area Ratio, AR = 5%
Angle of Injection, α
inj
= 0
o
Figure 4-9: Effect of secondary mass flow rate on axial thrust augmentation
95
-2
-1
0
1
2
3
4
2468 10 12 14 16 18 20
m
s
/m
p
(%)
F
n
/ F
p
o
(%)
Injection Location, M
P
= 3
Area Ratio, AR = 5%
An = 0
o
gle of Injection, α
inj
Figure 4-10: Effect of secondary mass flow rate on interaction force
0
1
2
3
4
5
6
2 4 6 8 10 12 14 16 18 20
m
s
/m
p
(%)
F
j
/ F
p
o
(%)
Injection Location, M
P
= 3
Area Ratio, AR = 5%
An = 0
o
gle of Injection, α
inj
Figure 4-11: Effect of secondary mass flow rate on jet reaction force
96
0
1
2
3
4
5
6
7
8
2 4 6 8 10 12 14 16 18 20
m
s
/m
p
(%)
F
s
/ F
p
o
(%)
Injection Location, M
P
= 3
Area Ratio, AR = 5%
An = 0
o
gle of Injection, α
inj
Figure 4-12: Effect of secondary mass flow rate on net side thrust
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
2 4 6 8 10 12 14 16 18 20
m
s
/m
p
(%)
AK
Injection Location, M
P
= 3
Area Ratio, AR = 5%
Angle of Injection, α
inj
= 0
o
Figure 4-13: Effect of secondary mass flow rate on amplification factor
97
-25
-20
-15
-10
-5
0
2 4 6 8 10 12 14 16 18 20
m
s
/m
p
(%)
δ Isp
sys
(sec)
Injection Location, M
P
= 3
Area Ratio, AR = 5%
An = 0
o
gle of Injection, α
inj
Figure 4-14: Effect of secondary mass flow rate on system specific impulse
98
99
4.3.2) Effects of Injection Location
For a given secondary mass flow rate (i.e. given secondary stagnation pressure and
injection slot area) and angle of injection, the effects of injection location on the
performance parameters for given are shown in the figures from 4-15 through 4-21. The
observations and conclusions are as follows:
- It can be observed in figure 4-15 that the secondary mass flow rate is essentially
independent of the injection location & depends solely on the secondary
stagnation pressure and injection slot area. The reason being the fact that the ratio
of the secondary stagnation pressure to freestream primary nozzle pressure at the
point of injection is greater than critical pressure ratio in most of the cases test
runs.
However, departure from this behavior is noted in case of upstream injection (in
the divergent section of the primary nozzle) when secondary stagnation pressure
is sufficiently lower (Pos < 0.25 Pop). This is due to the fact the ratio of the
secondary stagnation pressure to freestream pressure at the point of injection is
less than critical pressure ratio.
- In general, for a given injectant mass flow rate, upstream injection (in the
divergent part of the nozzle) results into higher axial thrust augmentation. This
augmentation reduces as the injection location moves farther downstream. The
100
underlying reason is the efficient adiabatic expansion of the injectant gas in case
of upstream injection.
However, in case of relatively lower secondary mass flow rates (due to lower
injection stagnation pressure and/or lower injection slot area) departure from this
behavior is noted. A possible explanation to this is the fact that the deflection
(from the axial direction) of the primary fluid is not severe in this case due to
smaller angles of primary bow shock and absence of shock reflection. Also,
relatively lower injection stagnation pressures result into negative pressure
component of primary axial thrust due to overexpansion. The discussion is
supported by the data provided in figures 4-16.
- Interaction force is a strong function of the injection location. For a given mass
flow rate, the contribution of the interaction force towards the net side force
increases as the injection location is moved farther downstream (in the divergent
part of the nozzle) as depicted in figure 4-17. This is due to extended high
pressure regions up- and down-stream of the injection location.
- As we know, secondary injection causes a strong primary bow shock in the flow.
Strength of this shock (measured by shock angle) depends on the injectant mass
flow rate and injection location (injector downstream flow conditions). Thus, for a
given mass flow rate, as the injection location is moved further downstream (in
the divergent section of the primary nozzle), the chances of reflection decreases
and beyond a certain injection location no-reflection condition is achieved. This is
101
a direct indication that there is safe injection configuration (in terms of injection
location and secondary mass flow rate) for which no impingement condition will
occur thus eliminating the chances for un-desirable effects from side injection.
- Jet reaction force is a very weak function of injection location. However, as we
move farther downstream, the jet reaction force increases as shown in figure 4-18.
This is due to slightly decreased freestream pressure at the injection exit plane
that, in turn, results into higher pressure component of the jet reaction force.
- Trend for the net side force is identical to interaction force as can be observed in
figure 4-19. In absence of shock impingement, the interaction force and hence net
side force increases as the injection location is moved farther downstream for a
given secondary mass flow rate.
- Referring to figure 4-20, for a given secondary mass flow rate, secondary specific
impulse and hence amplification factor increases as the injection location is
moved farther downstream in the divergent section of the primary nozzle. Shock
impingement causes both the performance parameters to drop drastically.
- As the injection location is moved farther downstream, the loss in system specific
impulse increases as shown in figure 4-21. This is due to relatively less efficient
adiabatic expansion in case of downstream injection. However, this loss is
relatively a weak function of the injection location compared to secondary mass
flow rate.
0
1
2
3
4
5
6
7
8
9
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
m
s
/ m
p
(%)
Injection Location Mp = 2
Injection Location Mp = 3
Injection Location Mp = 3.75
Area Ratio, AR = 2%
Angle of Injection, α
inj
= 0
o
a) AR = 2%, α
inj
= 0
o
102
0
5
10
15
20
25
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
m
s
/ m
p
(%)
Injection Location Mp = 2
Injection Location Mp = 3
Injection Location Mp = 3.75
Area Ratio, AR = 5%
Angle of Injection, α
inj
= 0
o
b) AR = 5%, α
inj
= 0
o
Figure 4-15: Effect of injection location on secondary mass flow rate
103
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
ΔF
p
/ F
p
o
(%)
Injection Location Mp = 2
Injection Location Mp = 3
Injection Location Mp = 3.75
Area Ratio, AR = 2%
o
Angle of Injection = 0 α
inj
a) AR = 2%, α
inj
= 0
o
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
ΔF
p
/ F
p
o
(%)
Injection Location Mp = 2
Injection Location Mp = 3
Injection Location Mp = 3.75
Area Ratio, AR = 5%
Angle of Injection, α
inj
= 0
o
b) AR = 5%, α
inj
= 0
o
Figure 4-16: Effect of injection location on axial thrust augmentation
-2
-1
0
1
2
3
4
5
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
F
n
/ F
p
o
(%)
Injection Location Mp = 2
Injection Location Mp = 3
Injection Location Mp = 3.75
Area Ratio, AR = 2%
Angle of Injection α
inj
= 0
o
a) AR = 2%, α
inj
= 0
o
104
-8
-6
-4
-2
0
2
4
6
8
10
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
F
n
/ F
p
o
(%)
Injection Location Mp = 2
Injection Location Mp = 3
Injection Location Mp = 3.75
Area Ratio, AR = 5%
Angle of Injection, α
inj
= 0
o
b) AR = 5%, α
inj
= 0
o
Figure 4-17: Effect of injection location on interaction force
105
0
1
1
2
2
3
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
F
j
/ F
p
o
(%)
Injection Location Mp = 2
Injection Location Mp = 3
Injection Location Mp = 3.75
Area Ratio, AR = 2%
o
Angle of Injection = 0 α
inj
a) AR = 2%, α
inj
= 0
o
0
1
2
3
4
5
6
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
F
j
/ F
p
o
(%)
Injection Location Mp = 2
Injection Location Mp = 3
Injection Location Mp = 3.75
Area Ratio, AR = 5%
Angle of Injection, α
inj
= 0
o
b) AR = 5%, α
inj
= 0
o
Figure 4-18: Effect of injection location on jet reaction force
106
0
1
2
3
4
5
6
7
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
F
s
/ F
p
o
(%)
Injection Location Mp = 2
Injection Location Mp = 3
Injection Location Mp = 3.75
Area Ratio, AR = 2%
o
Angle of Injection = 0 α
inj
a) AR = 2%, α
inj
= 0
o
-4
-2
0
2
4
6
8
10
12
14
16
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
F
s
/ F
p
o
(%)
Injection Location Mp = 2
Injection Location Mp = 3
Injection Location Mp = 3.75
Area Ratio, AR = 5%
Angle of Injection, α
inj
= 0
o
b) AR = 5%, α
inj
= 0
o
Figure 4-19: Effect of injection location on net side thrust
Injection Location Mp = 2
107
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
AK
Injection Location Mp = 3
Injection Location Mp = 3.75
Area Ratio, AR = 2%
o
Angle of Injection = 0 α
inj
a) AR = 2%, α
inj
= 0
o
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
AK
Injection Location Mp = 2
Injection Location Mp = 3
Injection Location Mp = 3.75
Area Ratio, AR = 5%
Angle of Injection, α
inj
= 0
o
b) AR = 5%, α
inj
= 0
o
Figure 4-20: Effect of injection location on amplification factor
Injection Location Mp = 2
108
-12
-10
-8
-6
-4
-2
0
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
δ Isp
sys
(sec)
Injection Location Mp = 3
Injection Location Mp = 3.75
Area Ratio, AR = 2%
o
Angle of Injection = 0 α
inj
a) AR = 2%, α
inj
= 0
o
-25
-20
-15
-10
-5
0
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
δ Isp
sys
(sec)
Injection Location Mp = 2
Injection Location Mp = 3
Injection Location Mp = 3.75
Area Ratio, AR = 5%
Angle of Injection, α
inj
= 0
o
b) AR = 5%, α
inj
= 0
o
Figure 4-21: Effect of injection location on system specific impulse
109
4.3.3) Effects of Angular Injection
To identify the effects of angular injection on performance parameters, several numerical
models were solved for secondary injection at angles 0, 10 and 45 degrees. For a given
injection location and secondary mass flow rate (i.e. given secondary stagnation pressure
and injection slot area), the effects of angle of injection on the performance parameters
are shown in the figures from 4-22 through 4-28. The observations and conclusions are as
follows:
- Secondary mass flow rate is essentially independent of injection angle. However,
in case of higher injection angles the mass flow rate is slightly higher as shown in
figure 4-22. The possible reason might be the slightly lower “effective”
downstream pressure at the point of injection due to reduced resistance from the
primary nozzle flow as the secondary injection is not strictly cross-flow jet in case
of angular injection.
- For a given secondary mass flow rate, axial thrust augmentation is slightly higher
for higher injection angles as can be seen in figure 4-23. The underlying reason is
relatively higher parallel (to the primary nozzle axis) velocity component of the
injectant.
- For moderate to higher secondary mass flow rates, interaction force is slightly
lower for higher injection angles in the absence of shock impingement. The
110
reason is shorter higher pressure regions upstream of the injector along with
extended lower pressure regions downstream of the injector.
However, substantially small secondary mass flow rates (i.e. injection at reduced
secondary stagnation pressure or smaller injection slot areas or both), higher
injection angles result into slightly higher interaction force. The underlying reason
is relatively weaker lower pressure region downstream of the injection location. In
case of shock impingement, higher injection angles always provide higher values
of interaction force due to weaker or no shock impingement. The conclusions are
based on the data provided in figure 4-24.
- Jet reaction force is lesser for the higher injection angles as depicted in figure 4-
25. The reason is the lower normal (to the primary nozzle axis) velocity
component of the injectant.
- Referring to figure 4-26, it can be observed that the trend for the net side thrust is
identical to the interaction force. For moderate to higher secondary mass flow
rates, in absence of shock impingement, net side thrust is slightly lower for higher
injection angles owing to lower interaction & jet reaction force components of the
side thrust as described earlier. Departure from this trend is noted in case of very
small secondary mass flow rates, the reason of which is explained in detail while
discussing interaction force above. In case of shock impingement, net side thrust
for the higher injection angles is always larger for higher injection angles due to
smaller primary bow shock angle resulting into less severe impingement.
111
- In the absence of shock impingement, higher injection angles result into smaller
secondary specific impulse and amplification factors for moderate to higher
secondary mass flow rates. For very low secondary mass flow rates, higher
injection angles are advantageous. However, in case of shock impingement, both
the performance parameters are always larger for higher injection angles. The
quantitative data is provided in figure 4-27.
- In general, system specific impulse loss is negligibly slightly lesser for higher
injection angles as can be seen in figure 4-28. However, departure from the trend
may be observed if primary axial thrust augmentation is sufficiently higher.
112
0
5
10
15
20
25
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
m
s
/ m
p
(%)
Angle of Injection = 0 deg
Angle of Injection = 10 deg
Angle of Injection = 45 deg
Injection Location, M
P
= 2
Area Ratio, AR = 5%
a) AR = 5%, M
P
= 2
0
5
10
15
20
25
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
m
s
/ m
p
(%)
Angle of Injection = 0 deg
Angle of Injection = 10 deg
Angle of Injection = 45 deg
Injection Location, M
P
= 3
Area Ratio, AR = 5%
b) AR = 5%, M
P
= 3
Figure 4-22: Effect of angle of injection on secondary mass flow rate
113
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
ΔF
p
/ F
p
o
(%)
Angle of Injection = 0 deg
Angle of Injection = 10 deg
Angle of Injection = 45 deg
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
ΔF
p
/ F
p
o
(%)
Angle of Injection = 0 deg
Angle of Injection = 10 deg
Angle of Injection = 45 deg
Injection Location, M
P
= 2
Area Ratio, AR = 5%
a) AR = 5%, M
P
= 2
Injection Location, M
P
= 3
Area Ratio, AR = 5%
b) AR = 5%, M
P
= 3
Figure 4-23: Effect of angle of injection on axial thrust augmentation
114
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
F
n
/ F
p
o
(%)
Angle of Injection = 0 deg
Angle of Injection = 10 deg
Angle of Injection = 45 deg
Injection Location, M
P
= 2
Area Ratio, AR = 5%
a) AR = 5%, M
P
= 2
-1
0
1
2
3
4
5
6
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
F
n
/ F
p
o
(%)
Angle of Injection = 0 deg
Angle of Injection = 10 deg
Angle of Injection = 45 deg
Injection Location, M
P
= 3
Area Ratio, AR = 5%
b) AR = 5%, M
P
= 3
Figure 4-24: Effect of angle of injection on interaction force
115
0
1
2
3
4
5
6
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
F
j
/ F
p
o
(%)
Angle of Injection = 0 deg
Angle of Injection = 10 deg
Angle of Injection = 45 deg
Injection Location, M
P
= 2
Area Ratio, AR = 5%
a) AR = 5%, M
P
= 2
0
1
2
3
4
5
6
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
F
j
/ F
p
o
(%)
Angle of Injection = 0 deg
Angle of Injection = 10 deg
Angle of Injection = 45 deg
Injection Location, M
P
= 3
Area Ratio, AR = 5%
b) AR = 5%, M
P
= 3
Figure 4-25: Effect of angle of injection on jet reaction force
116
0
1
2
3
4
5
6
7
8
9
10
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
F
s
/ F
p
o
(%)
Angle of Injection = 0 deg
Angle of Injection = 10 deg
Angle of Injection = 45 deg
Injection Location, M
P
= 3
Area Ratio, AR = 5%
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
F
s
/ F
p
o
(%)
Angle of Injection = 0 deg
Angle of Injection = 10 deg
Angle of Injection = 45 deg
Injection Location, M
P
= 2
Area Ratio, AR = 5%
a) AR = 5%, M
P
= 2
b) AR = 5%, M
P
= 3
Figure 4-26: Effect of angle of injection on net side thrust
117
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
AK
Angle of Injection = 0 deg
Angle of Injection = 10 deg
Angle of Injection = 45 deg
Injection Location, M
P
= 2
Area Ratio, AR = 5%
a) AR = 5%, M
P
= 2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
AK
Angle of Injection = 0 deg
Angle of Injection = 10 deg
Angle of Injection = 45 deg
Injection Location, M
P
= 3
Area Ratio, AR = 5%
b) AR = 5%, M
P
= 3
Figure 4-27: Effect of angle of injection on amplification factor
118
-25
-20
-15
-10
-5
0
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
δ Isp
sys
(sec)
Angle of Injection = 0 deg
Angle of Injection = 10 deg
Angle of Injection = 45 deg
Injection Location, M
P
= 2
Area Ratio, AR = 5%
a) AR = 5%, M
P
= 2
-25
-20
-15
-10
-5
0
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
δ Isp
sys
(sec)
Angle of Injection = 0 deg
Angle of Injection = 10 deg
Angle of Injection = 45 deg
Injection Location, M
P
= 3
Area Ratio, AR = 5%
b) AR = 5%, M
P
= 3
Figure 4-28: Effect of angle of injection on system specific impulse
119
4.3.4) Effects of Primary Nozzle Profile
As stated earlier, the flowfield structure characteristics of nozzle profiles were found to
be strongly coupled with injection location and thus, in turn, some of the SITVC
performance parameters are deeply influenced by this coupling. That is why the
performance parameters, for which this coupling becomes increasingly important, have
been explicitly identified in the following discussion. For a given injection location, angle
of injection and secondary mass flow rate (i.e. given secondary stagnation pressure and
injection slot area), the effects of nozzle profile on the performance parameters are shown
in the figures from 4-29 through 4-35. The observations and conclusions are as follows:
- Referring to figure 4-29, it can be observed that secondary mass flow rate is
essentially independent of nozzle profile. Strictly speaking secondary mass flow
rate is slightly higher in case of bell shaped nozzle compared to conical nozzles.
The possible reason is slightly lower effective downstream pressure owing to
higher wall angle at the point of injection for bell shaped nozzles.
- For a given secondary mass flow rate, axial thrust augmentation is always higher
for conical nozzles compared to bell shaped nozzle. Primarily this is due to
stronger primary bow shock in case of conical nozzles that turns the primary flow
more towards axial direction. The existence of multiple shock impingements
results into even higher primary thrust augmentation. Smaller conical divergent
half angle is another important factor resulting into higher axial thrust
augmentation. Figure 4-30 aids the discussion quantitatively.
120
- Interaction Force
a) In case of upstream injection location, M
P
= 2
For a given mass flow rate (i.e. fixed secondary stagnation pressure and injection
slot area), in case of single shock impingement, interaction force is relatively
lower for conical profiles owing to the extended & stronger higher pressure region
upstream of the injector and greater wall length of the divergent section of the
nozzle. However, the presence of multiple shock impingements may result into
better performance for conical nozzles as shown in figure 4-31(a).
b) In case of downstream injection location, M
P
= 3
For smaller mass flow rates (resulting in the absence of shock impingement) and
for relatively downstream injection, the interaction force is higher for conical
profile owing to the extended higher pressure region upstream of the injector and
greater wall length of the conical nozzle. However, it should be kept in mind that
the greater length of the conical nozzle for the same expansion ratio, makes it
more likely for the primary bow shock to impinge on the opposite wall and thus in
case of shock impingement, conical nozzle with 12 deg divergent half angles is
less efficient compared to bell shaped nozzle. Conversely, conical nozzle with 15
deg divergent half angle is more efficient in case of shock impingement compared
to bell shaped nozzle. This is owing to the extended higher pressure region
upstream of the injector and relatively less severe shock impingement. The
quantitative results may be observed in figure 4-31(b).
- As expected, jet reaction force solely depends on the secondary mass flow rate
(secondary stagnation pressure & injection slot area) as shown in figure 4-32.
121
- Referring to figures 4-33 and 4-34, net side thrust, amplification factors & thus
secondary specific impulse have the identical trends as that of interaction force.
Thus, all the reasoning given above for respective injection location, also applies
to the trend of these performance parameters.
- Specific System Loss
a) In case of upstream injection location, M
P
= 2
In general, for a given mass flow rate (i.e. fixed secondary stagnation pressure and
injection slot area) system specific impulse loss is lower for conical shaped nozzle
compared to bell shaped nozzles. Comparing conical nozzles alone, loss increases
as the divergent half angle is increased as can be observed in figure 4-35(a).
b) In case of downstream injection location, M
P
= 3
For smaller mass flow rates (in absence of shock impingement) and for
downstream injection, the system specific impulse loss is lower for conical shaped
nozzle compared to bell shaped nozzles. However, departure from this behavior is
noted for higher secondary mass flow rates where conical nozzle with 12 deg
divergent half angles is slightly more efficient compared to bell shaped nozzle.
Conversely, conical nozzle with 15 deg divergent half angle is slightly less
efficient in case of shock impingement compared to bell shaped nozzle. This is
owing to sufficiently higher primary axial thrust augmentation in case of smaller
conical divergent angles. The quantitative results may be observed in figure 4-
35(b).
122
0
5
10
15
20
25
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
m
s
/ m
p
(%)
Bell Shaped
Conical Half Divergent Angle = 12 deg
Conical Half Divergent Angle = 15 deg
0
5
10
15
20
25
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
m
s
/ m
p
(%)
Bell Shaped
Conical Half Divergent Angle = 12 deg
Conical Half Divergent Angle = 15 deg
a) AR = 5%, α
inj
= 0
o
, M
P
= 2
Injection Location, M
P
= 3
Area Ratio, AR = 5%
Angle of Injection, α
inj
= 0
o
b) AR = 5%, α
inj
= 0
o
, M
P
= 3
Figure 4-29: Effect of primary nozzle shape on secondary mass flow rate
123
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
ΔF
p
/ F
p
o
(%)
Bell Shaped
Conical Half Divergent Angle = 12 deg
Conical Half Divergent Angle = 15 deg
Injection Location, M
P
= 2
Area Ratio, AR = 5%
Angle of Injection, α
inj
= 0
o
a) AR = 5%, α
inj
= 0
o
, M
P
= 2
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
ΔF
p
/ F
p
o
(%)
Bell Shaped
Conical Half Divergent Angle = 12 deg
Conical Half Divergent Angle = 15 deg
Injection Location, M
P
= 3
Area Ratio, AR = 5%
o
Angle of Injection = 0 α
inj
b) AR = 5%, α
inj
= 0
o
, M
P
= 3
Figure 4-30: Effect of primary nozzle shape on axial thrust augmentation
Bell Shaped
Conical Half Divergent Angle = 12 deg
Conical Half Divergent Angle = 15 deg
-8
-7
-6
-5
-4
-3
-2
-1
0
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
F
n
/ F
p
o
(%)
Injection Location, M
P
= 2
Area Ratio, AR = 5%
Angle of Injection, α
inj
= 0
o
124
-4
-3
-2
-1
0
1
2
3
4
5
6
7
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
F
n
/ F
p
o
(%)
Bell Shaped
Conical Half Divergent Angle = 12 deg
Conical Half Divergent Angle = 15 deg
a) AR = 5%, α
inj
= 0
o
, M
P
= 2
b) AR = 5%, α
inj
= 0
o
, M
P
= 3
Injection Location, M
P
= 3
Area Ratio, AR = 5%
o
Angle of Injection = 0 α
inj
Figure 4-31: Effect of primary nozzle shape on interaction force
125
0
1
2
3
4
5
6
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
F
j
/ F
p
o
(%)
Bell Shaped
Conical Half Divergent Angle = 12 deg
Conical Half Divergent Angle = 15 deg
Injection Location, M
P
= 3
Area Ratio, AR = 5%
Angle of Injection, α
inj
= 0
o
0
1
2
3
4
5
6
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
F
j
/ F
p
o
(%)
Bell Shaped
Conical Half Divergent Angle = 12 deg
Conical Half Divergent Angle = 15 deg
Injection Location, M
P
= 2
Area Ratio, AR = 5%
Angle of Injection, α
inj
= 0
o
a) AR = 5%, α
inj
= 0
o
, M
P
= 2
b) AR = 5%, α
inj
= 0
o
, M
P
= 3
Figure 4-32: Effect of primary nozzle shape on jet reaction force
126
0
1
2
3
4
5
6
7
8
9
10
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
F
s
/ F
p
o
(%)
Bell Shaped
Conical Half Divergent Angle = 12 deg
Conical Half Divergent Angle = 15 deg
Injection Location, M
P
= 3
Area Ratio, AR = 5%
Angle of Injection α
inj
= 0
o
-2
-1
0
1
2
3
4
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
F
s
/ F
p
o
(%)
Bell Shaped
Conical Half Divergent Angle = 12 deg
Conical Half Divergent Angle = 15 deg
Injection Location, M
P
= 2
Area Ratio, AR = 5%
Angle of Injection, α
inj
= 0
o
a) AR = 5%, α
inj
= 0
o
, M
P
= 2
b) AR = 5%, α
inj
= 0
o
, M
P
= 3
Figure 4-33: Effect of primary nozzle shape on net side thrust
127
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
AK
Bell Shaped
Conical Half Divergent Angle = 12 deg
Conical Half Divergent Angle = 15 deg
Injection Location, M
P
= 3
Area Ratio, AR = 5%
Angle of Injection α
inj
= 0
o
-1.4
-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
AK
Bell Shaped
Conical Half Divergent Angle = 12 deg
Conical Half Divergent Angle = 15 deg
Injection Location, M
P
= 2
Area Ratio, AR = 5%
Angle of Injection, α
inj
= 0
o
a) AR = 5%, α
inj
= 0
o
, M
P
= 2
b) AR = 5%, α
inj
= 0
o
, M
P
= 3
Figure 4-34: Effect of primary nozzle shape on amplification factor
128
-25
-20
-15
-10
-5
0
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
δ Isp
sys
(sec)
Bell Shaped
Conical Half Divergent Angle = 12 deg
Conical Half Divergent Angle = 15 deg
Injection Location, M
P
= 3
Area Ratio, AR = 5%
Angle of Injection, α
inj
= 0
o
-25
-20
-15
-10
-5
0
5
0.25 0.50 0.75 1.00 1.25
P
os
/P
op
δ Isp
sys
(sec)
Bell Shaped
Conical Half Divergent Angle = 12 deg
Conical Half Divergent Angle = 15 deg
Injection Location, M
P
= 2
Area Ratio, AR = 5%
Angle of Injection, α
inj
= 0
o
a) AR = 5%, α
inj
= 0
o
, M
P
= 2
b) AR = 5%, α
inj
= 0
o
, M
P
= 3 b) AR = 5%, α
Figure 4-35: Effect of primary nozzle shape on system specific impulse Figure 4-35: Effect of primary nozzle shape on system specific impulse
inj
= 0
o
, M
P
= 3
129
4.4) Safe Injection Limits
As we know, secondary injection induces a strong bow shock in the primary flow.
Strength of this shock (measured by shock angle) depends primarily on the secondary
(injectant) mass flow rate, injection location (injector downstream flow conditions). We
have discussed earlier that for a given primary nozzle profile as the secondary mass flow
rate is increased, the strength of the primary bow shock increases. We also noted that for
a given secondary mass flow rate (i.e. given stagnation pressure ratio and injection slot
area), as the injection location is moved farther downstream in the divergent section of
the primary nozzle, the strength of the primary bow shock decreases. Under certain
conditions, the primary bow shock may impinge on the opposite nozzle wall. This
impingement of primary bow shock on the opposite wall results into an un-desirable
pressure rise on the opposite wall. This, in turn, appears as reduced side force because the
interaction force (pressure component of the side thrust) might be negative in this case.
This effect is more evident in case of higher mass flow rates or in case of relatively
upstream injection locations (in the divergent part of the nozzle).
The shock impingement on the opposite wall is a function of bow shock strength (shock
angle) and profile of the divergent section of the nozzle. A successful SITVC design
should ensure that bow shock lies on the exit section of the nozzle without impinging the
opposite wall. Thus, for a specific injection location shock impingement may be avoided
by keeping the secondary mass flow rate below a certain limit. Or, for a given secondary
mass flow rate, as the injection location is moved farther downstream, the chances of
reflection decreases and beyond a certain injection location no-reflection condition is
achieved.
This is a direct indication that there is a safe injection configuration (in terms of injection
location and secondary mass flow rate) for which no impingement condition of primary
bow shock with the opposite wall will occur, thus, eliminating the chances for un-
desirable effects of side injection. Several test runs were conducted to determine the safe
injection limits (in terms of injection and mass flow rates) for fixed primary flow
conditions and bell shaped profile as detailed in chapter 2. The findings are depicted in
figure 4-36 below.
0
5
10
15
20
25
30
35
40
45
1.5 2 2.5 3 3.5 3.75
Injection Location (in terms of Primary Flow Mach #)
Maximum Secondary Mass Flow Rate to Primary Mass
Flow Rate Ratio without Shock Impingement (%)
Figure 4-36: Safe injection limits for bell shaped nozzle
130
4.5) Results Verification
In current research, analytical model by James Broadwell [2] has been employed for the
verification of the numerical results. A brief introduction to the Broadwell’s
investigations has already been presented earlier in this report. Broadwell’s analytical
model predicts net side force accounting for both the pressure and momentum
components of the side force. Analytical relations provided by Broadwell are
exceptionally simple and elegant.
According to Broadwell, interaction force is a function of freestream Mach number,
freestream velocity and injectant mass flow rate at the point of injection and can be
estimated with the following relation
{ }
{}
inj
op s p
os p p
p p s n
T MW M
T MW M
V M m F β
γ
γ
γ σ cos
) 1 ( 2
) 1 ( 2
1 ) ( 2 . 1
2
2
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
− +
− +
+ = (4-12)
where σ(γ) is a parameter determined in blast wave theory. γ represents the specific heat
ratio for the secondary gas. For air, σ(γ) = σ(1.4) = 0.17 as provided by Broadwell [2].
Momentum component of side force is estimated as jet reaction force and can be
calculated using well-known thrust equation
() []
inj s as es sy
s
j
A P P V m F β cos − + =
•
(4-13)
131
132
The net side thrust is given as
F
s
= F
n
+ F
j
(4-14)
Observations & Comments
- In general, the analytical predictions have fairly close agreement with
computational results. However, rigorously speaking analytical predictions are
slightly under-predicted compared to computational results. The underlying
reason is the fact that the Broadwell’s analytical model does not account for the
viscous effects at all. These viscous effects are responsible for higher pressure
walls and thus, in turn, higher interaction force.
- Analyzing the dependence of net side force on the secondary (injection)
stagnation pressure for a given injection slot area, angle of injection and fixed
injection location, it can be observed in figure 4-37 that the difference between
analytical prediction and numerical results increases as injection stagnation
pressure increases.
- For a given secondary stagnation pressure, fixed injection location and angle of
injection, as the injection area is increased the mismatch between analytical
predictions and numerical results increases as depicted in figure 4-37. However,
departure from this trend was noted for sufficiently larger injection slot area (AR
≥ 5%).
133
- For a given mass flow rate (i.e. given injection stagnation pressure and injection
location), as the injection location is moved farther downstream, the difference
between analytical and predicted increases as shown in figure 4-38. Again, this
difference is very obvious for higher mass flow rates. This suggests that the
analytical relation provides good estimation of the side thrust for relatively
downstream injections.
- For a given mass flow rate and injection location, as the angle at which injectant
enters the primary nozzle is increases, the difference between predicted and
numerical values increases as depicted in figure 4-39.
- The predicted values of Broadwell’s analytical model differ for bell and conical
shaped nozzles for a given mass flow rate as shown in figure 4-40. Comparatively
the predictions are better for bell shaped nozzles. It is interesting to note at the
divergent half angle increases, the difference between predicted and numerical
value increases. The underlying reason is the different mach line structures within
conical and bell shaped nozzles.
- Since the theory was developed using the flat plate, it has no mechanism to
determine shock impingement and thus fails to predict net side force in case of
primary shock impingement from the opposite wall.
134
0
2
4
6
8
10
12
14
0.25 0.50 0.75 1.00 1.25
P
os
/ P
op
F
s
/ F
p
o
(%)
AR = 1% (Computational)
AR = 1% (Analytical)
AR = 2% (Computational)
AR = 2% (Analytical)
AR = 5% (Computational)
AR = 5% (Analytical)
Injection Location, M
p
= 3
Angle of Injection, α
inj
= 0
o
0
2
4
6
8
10
12
14
16
0.25 0.50 0.75 1.00 1.25
P
os
/ P
op
F
s
/ F
p
o
(%)
AR = 1% (Computational)
AR = 1% (Analytical)
AR = 2% (Computational)
AR = 2% (Analytical)
AR = 5% (Computational)
AR = 5% (Analytical)
Injection Location, M
p
= 3.75
Angle of Injection, α
inj
= 0
o
d) α
inj
= 0
o
, M
P
= 3
e) α
inj
= 0
o
, M
P
= 3.75
Figure 4-37: Effect of injection pressure & injection slot area (Comparison b/w Analytical &
Computational Results)
135
0
1
2
3
4
5
6
7
0.25 0.50 0.75 1.00 1.25
P
os
/ P
op
F
s
/ F
p
o
(%)
Mp = 2 (Computational)
Mp = 2 (Analytical)
Mp = 3 (Computational)
MP = 3 (Analytical)
Mp = 3.75 (Computational)
Mp = 3.75 (Analytical)
Area Ratio, AR = 2%
Angle of Injection, α
inj
= 0
o
-4
-2
0
2
4
6
8
10
12
14
16
0.25 0.50 0.75 1.00 1.25
F
s
/ F
p
o
(%)
P
os
/ P
op
Mp = 2 (Computational)
Mp = 2 (Analytical)
Mp = 3 (Computational)
MP = 3 (Analytical)
Mp = 3.75 (Computational)
Mp = 3.75 (Analytical)
Area Ratio, AR = 5%
Angle of Injection, α
inj
= 0
o
a) AR = 2%, α
inj
= 0
o
b) AR = 5%, α
inj
= 0
o
Figure 4-38: Effect of injection location (Comparison b/w Analytical & Computational Results)
136
0
2
4
6
8
10
12
14
16
0.25 0.50 0.75 1.00 1.25
P
os
/ P
op
F
s
/ F
p
o
(%)
Bell Shaped (Computational)
Bell Shaped (Analytical)
Con. Div. Half Angle = 12 deg (Computational)
Con. Div. Half Angle = 12 deg (Analytical)
Con. Div. Half Angle = 15 deg (Computational)
Con. Div. Half Angle = 15 deg (Analytical)
Injection Location, M
P
= 3
Area Ratio, AR = 5%
Angle of Injection, α
inj
= 0
o
0
2
4
6
8
10
12
14
0.25 0.50 0.75 1.00 1.25
P
os
/ P
op
F
s
/ F
p
o
(%)
alpha = 0 deg (Computational)
alpha = 0 deg (Analytical)
alpha = 10 deg (Computational)
alpha = 10 deg (Analytical)
alpha = 45 deg (Computational)
alpha = 45 deg (Analytical)
Injection Location, M
P
= 3
Area Ratio, AR = 5%
Figure 4-39: Effect of angle of injection (Comparison b/w Analytical & Computational Results)
Figure 4-40: Effect of primary nozzle profile (Comparison b/w Analytical & Computational Results)
137
Chapter 5
Summary and Conclusions
The objective of present numerical study was to characterize the flowfield structure and
performance parameters of a secondary injection thrust vector (SITVC) system for a two
dimensional convergent divergent (2DCD) nozzle under the influence of various
parameters such as secondary stagnation pressure, injection slot area, injection location,
angle of injection and primary nozzle profile. The influence of all the parameters on
SITVC system was investigated in a systematic manner. In particular, the effects of
primary bow shock impingement on overall flowfield structure and performance
parameters were investigated. An important aspect of the investigation was to identify
the safe injection limits for a specific configuration. The summary and conclusions are
presented in the following sections.
5.1) Research Summary
A) For a given injection location and angle of injection, higher injectant mass flow rates
results into
138
Flowfield Structure:
o stronger primary bow shocks
o stronger secondary bow shocks
o stronger separation shocks
o extended injector upstream higher wall pressure regions
o extended injector downstream lower wall pressure regions
o higher probability of shock impingement from opposite wall
o stronger shock impingement (higher pressure rise on opposite wall)
Performance:
o higher side thrust
o lower amplification factor
o higher thrust augmentation
o lower system specific impulse
B) For a given mass flow rate & angle of injection, downstream injection (in the
diverging section of the nozzle) compared to upstream injection results into
Flowfield Structure:
o weaker primary bow shocks
o weaker secondary bow shocks
o weaker separation shocks
o very extended injector upstream higher pressure regions
139
o extended injector downstream lower wall pressure regions
o lower probability of shock impingement from opposite
o weaker shock impingement (lower pressure rise on opposite wall)
Performance:
o higher side thrust
o higher amplification factor
o higher thrust augmentation
o lower system specific impulse
C) For a given mass flow rate & injection location, injection at an angle results into
Flowfield Structure:
o slightly weaker primary bow shocks
o slightly weaker secondary bow shocks
o slightly weaker separation shocks
o slightly shorter injector upstream higher pressure regions
o extended injector downstream lower wall pressure regions
o lower probability of shock impingement from opposite wall
o weaker shock impingement (lower pressure rise on opposite wall)
Performance:
o lower side thrust
140
o lower amplification factor
o higher thrust augmentation
o higher system specific impulse
D) For a given mass flow rate & injection location, bell shaped nozzle (compared to
conical nozzle) results into
Flowfield Structure:
o slightly weaker primary bow shocks
o weaker secondary bow shocks
o comparable or stronger separation shocks depending on injection location
o shorter injector upstream higher pressure regions
o shorter injector downstream lower wall pressure regions
o very low probability of multiple shock impingements
o lower probability of shock impingement from opposite wall
o comparable or weaker shock impingement (lower pressure rise on
opposite wall) depending on the injection location
Performance:
It was observed that nozzle profile is strongly coupled with injection location. In
other words, while studying nozzle profiles, injection location and shock
impingement becomes increasingly important. Systematically speaking
141
a) Comparing bell shaped nozzle performance to that of conical nozzle with smaller
conical divergent half angles (~ 12 degree), we observe
i) in the absence of shock impingement (observed in case of relatively
downstream and/or lower secondary mass flow rates) bell shaped nozzle
compared to conical nozzle results into
o lower side thrust
o lower amplification factor
o lower thrust augmentation
o higher system specific impulse
ii) in case of single shock impingement (observed for downstream injections)
bell shaped nozzle compared to conical nozzle results into
o higher side thrust
o higher amplification factor
o lower thrust augmentation
o lower system specific impulse
iii) in case of multiple shock impingement (observed for upstream injections
and/or higher secondary mass flow rates) bell shaped nozzle compared to
conical nozzle results into
142
o lower side thrust
o lower amplification factor
o lower thrust augmentation
o lower system specific impulse
b) For a given mass flow rate & injection location, bell shaped nozzle compared to
conical nozzle with larger conical divergent half angle (~ 15 deg) , results into
i) in the absence or single shock impingement case (observed for downstream
injections)
o lower side thrust
o lower amplification factor
o lower thrust augmentation
o higher system specific impulse
ii) in case of multiple shock impingement (observed for downstream injections)
o higher side thrust
o higher amplification factor
o lower thrust augmentation
o lower system specific impulse
143
5.2) Conclusions & Recommendations
- In general, flowfield structure & performance parameters are strong functions of
secondary (injectant) mass flow rate and injection location, and primary nozzle
profile while these are relatively weak functions of injection angle.
- The injection location is strongly coupled with such nozzle profiles with less rapid
diverging rates, for instance in case of the conical nozzles with smaller divergent
half angles.
- Injectant mass flow rate is the only viable parameter that can provide a wide range
of operational flexibility & controllability in SITVC systems.
- For a given injection & geometrical configuration, downstream injection is much
more efficient from overall SITVC performance viewpoint.
- For a given injection & geometrical configuration, higher injection angles are
slightly favorable from thrust vectoring viewpoint.
- Conical nozzles with smaller divergent half angles are not favorable from SITVC
viewpoint.
- As detailed in the report, shock impingement can have notable adverse effects on
the overall SITVC performance & thus it should be taken into consideration while
designing SITVC systems.
- The prime objective of the secondary injection is to have net side thrust in desired
direction which is always attained at the cost of system specific impulse.
144
5.3) Proposed Future Studies
Though current research helped in better understanding of the performance trend and
flowfield structure of the SITVC systems, however, for building more realistic
performance & flowfield models, following aspects should be further investigated.
- Liquid injection thrust vector control (LITVC)
- Unlike previous studies, this report particularly investigated the qualitative and
quantitative effects of shock impingement phenomenon on both the flowfield
structure and SITVC performance. However, more rigorous investigation of the
shock impingement as a function of primary & secondary physical/flow properties
and nozzle profile is essential. This would help in determining the safe injection
limits for given configurations. In perspective of practical applications, three
dimensional analyses would provide more accurate & applicable models.
- During literature survey it was observed that all the existing models estimate the
performance for the steady state operational modes only. In practical systems,
however, instabilities may also be present due to various factors for instance due
to shear layer instabilities. That is why unsteady state behavior should be
explicitly studied for identification and characterization of instabilities from TVC
viewpoint.
145
Bibliography
1 Balu, R., “Analysis of Performance of a Hot Gas Injection Thrust Vector Control
System,” Journal of Propulsion and Power, Vol. 7, No. 4, 1991, pp. 580–585.
2 Broadwell, J. E., “Analysis of Fluid Mechanics of Secondary Injection for Thrust
Vector Control”, AIAA Journal, Vol. 1, No. 10, 1963, pp. 580–585.
3 Erdem, E., Albayrak K., and Tinaztepe h. T., “Parametric Study of Secondary Gas
Injection into a Conical Rocket Nozzle for Thrust Vectoring”, Presented at 42
nd
Joint
Propulsion Conference, July 09-12, 2006.
4 Fluent Inc., URL:http://www.fluent.com, [cited 15 May, 2007]
5 Fluent Inc., Fluent 6.2 Handbook, 2006.
6 Guhse, R. D., “An Experimental Investigation of Thrust Vector Control by Secondary
Injection” NASA CR-297 (1965).
7 Ko, Hyun and Yoon, Woong-Sup, “Performance Analysis of Secondary Gas Injection
into a Conical Rocket Nozzle”, Journal of Propulsion and Power, Vol. 18 No. 3, May-
June 2002.
8 Walker R.E., Stone A.R., and Shandor M., “Influence of Injectant Properties for Fluid
Injection Thrust Vector Control” Journal of Spacecraft and Rockets Vol. 1 No. 4 pp
409-413 (July-August 1964).
9 Wu, J. M., Chapkis, R. L., and Mager, A., “Approximate Analysis of Thrust Vector
Control by Fluid Injection,” ARS Journal, Vol. 31, No. 6, Dec. 1961, pp. 1677–1685.
10 Zukoski, E. E., and Spaid, F.W., “Secondary Injection of Gases into a Supersonic
Flow”, NASA CR-53817 (1963).
Abstract (if available)
Abstract
A numerical study was conducted to investigate the effects of secondary gaseous injection into primary supersonic gas stream by characterizing the resulting flowfield and estimating the thrust vector control performance for a 2DCD nozzle. Flowfield structure and performance parameters were systematically investigated for several variables such as secondary (injectant) stagnation pressure, injection slot area, angle of injection, and primary nozzle profile. FLUENT, a commercial CFD software was employed for current numerical investigation. 2D coupled-implicit solver with realizable k-epsilon viscous model was used throughout the research. The results showed that flowfield structure and performance parameters were primarily influenced by injectant mass flow rate, injection location, and primary nozzle profile whereas injection angle was less influential for the range of parameters investigated. An important aspect of the research was the identification of the safe injection limits for a specific configuration. Numerical estimations were found to have fairly close agreement with analytical results.
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Asset Metadata
Creator
Sadiq, Muhammad Usman
(author)
Core Title
Performance analysis and flowfield characterization of secondary injection thrust vector control (SITVC) for a 2DCD nozzle
School
Viterbi School of Engineering
Degree
Master of Science
Degree Program
Astronautical Engineering
Publication Date
07/27/2007
Defense Date
06/01/2007
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
LITVC,OAI-PMH Harvest,secondary injection,secondary injection thrust vector control,SITVC,thrust vector control
Language
English
Advisor
Erwin, Daniel A. (
committee chair
), Goodfellow, Keith (
committee member
), Gruntman, Michael A. (
committee member
), Ronney, Paul D. (
committee member
)
Creator Email
sadiq@usc.edu
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-m710
Unique identifier
UC1336313
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Legacy Identifier
etd-Sadiq-20070727.pdf
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Sadiq, Muhammad Usman
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
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Repository Name
Libraries, University of Southern California
Repository Location
Los Angeles, California
Repository Email
cisadmin@lib.usc.edu
Tags
LITVC
secondary injection
secondary injection thrust vector control
SITVC
thrust vector control