strugle between CFD & MFG! omg

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 masters 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.

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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

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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

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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

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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 & Guhses experimental data 34

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Figure 2-12: Flowfield structure (Mach number contours) obtained from numerical solution of Guhses experimental configuration (Viscous Model: rk- 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 MP = 2) 38 Figure 2-15: Two dimensional grid configuration of primary bell and conical shaped nozzles (Showing relative positions of same injection location at MP = 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

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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

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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

Fp Primary Axial Thrust [N] Fs Net Side Thrust [N] Fn Interaction Force (Side Thrust-Pressure Component) [N] Fj Jet Reaction Force (Side Thrust-Momentum Component) [N]

opF Primary (Axial) Thrust No Injection Condition [N]

Ispp Primary Specific Impulse [sec] Ispp Secondary Specific Impulse [sec] Ispsys System Specific Impulse [sec] Ispsys System Specific Impulse Loss [sec] AK Amplification Factor

opIsp Primary Specific Impulse No Injection Condition [sec]

Pop Primary Stagnation Pressure (Primary Nozzle Inlet Pressure) [Pa] Pep Primary Exit Pressure at Primary Nozzle Exit [Pa] Pap Primary Ambient Pressure (Atmospheric Pressure) [Pa] Pos Secondary Stagnation Pressure (Injection Slot Inlet Pressure) [Pa] Pes Secondary Exit Pressure at Injection Slot Exit [Pa] Pas Secondary Ambient Pressure at Injection Slot Exit [Pa] PR Secondary to Primary Stagnation Pressure Ratio Top Primary Stagnation Temperature [K] Tos Secondary Stagnation Temperature [K] xi

Vp Primary Flow Exit Velocity at Primary Nozzle Exit [m/s] Vpx Primary Flow Exit Velocity Axial Component at Primary Nozzle Exit [m/s] Vpy Primary Flow Exit Velocity Normal Component at Primary Nozzle Exit [m/s] Vs Secondary Flow (Injectant) Exit Velocity at Injection Slot Exit [m/s] Vsx Secondary Flow Exit Velocity Axial Component at Injection Slot Exit [m/s] Vsy Secondary Flow Exit Velocity Normal Component at Injection Slot Exit [m/s] Ae Primary Nozzle Exit Area [m2] As Injection Slot Area [m2] Ax X-Face Area of Grid Cell [m2] Ay Y-Face Area of Grid Cell [m2] H* Height of Primary Nozzle Throat [m] A* Primary Nozzle Throat Area [m2] AR Injection Slot to Primary Nozzle Throat Areas Ratio

pm

Primary Mass Flow Rate [kg/s]

sm

Secondary (Injectant) Mass Flow Rate [kg/s] MWp Molecular Weight of Primary Gas MWs Molecular Weight of Secondary Gas (Injectant) inj Angle of Injection [deg]

(Angle between injection slot axis and normal to the primary nozzle axis) 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)

MP Injection Location (in terms of Primary Flow Axial Mach # corresponding to Injection Point located on Primary Nozzle Wall)

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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

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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- 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

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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

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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

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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.

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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 MacCormacks

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-

) model with low Reynolds number treatment. Parameters investigated by the

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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- 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.

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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.

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- 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.

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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

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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

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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 m2Area 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

-0.0

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)

Hei

ght (

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, MP = 2, Injection Angle = 0o, AR = 5%

b) Injection Location, MP = 3, Injection Angle = 45o, AR = 5%

Figure 2-5: Two dimensional 250x75 grid configurations for different injection configurations

24

c) Injection Location, MP = 3.75, Injection Angle = 0o, 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, Pop = 3.45 MPa

Primary Stagnation Temperature, Top = 3000 K

Primary Nozzle Throat Area, A* = 0.02 m2

Primary Nozzle Area Ratio, Ae/A* = 10

Primary Nozzle Exit Pressure, Pep = 0.1 MPa

Axial Primary Flow Mach # @ Injection Location, MP = 3

Secondary to Primary Stagnation Pressure Ratio, Pos/Pop = 0.75

Secondary Inj Slot to Primary Throat Area Ratio, As/A* = 0.01

Angle of Injection, inj = 0 Secondary (Injectant) Temperature, Tos = 300 K

2-D, coupled implicit solver with realizable k- 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- with Enhanced Wall Treatment - Realizable k- 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, Pop = 100 psig

Primary Stagnation Temperature, Top = 465 0R

Primary Nozzle Throat Height, H* = 3.556 in

Primary Nozzle Throat Area, A* = 7.112 in2

Primary Nozzle Area Ratio, Ae/A* = 1.687

Primary Nozzle Exit Pressure, Pep = 12.7 psi

Secondary Fluid Air

Axial Primary Flow Mach # @ Injection Location, MP = 1.904

Secondary to Primary Stagnation Pressure Ratio, Pos/Pop = 0.60

Secondary Inj Slot to Primary Throat Area Ratio, As/A* = 0.05

Angle of Injection, inj = 0 Secondary (Injectant) Temperature, Tos = 490 0R

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-) 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- 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 Guhses experimental configuration using realizable k- viscous model with enhanced wall treatment.

33

rke

34

0

10

20

30

40

50

60

70

12.0

0

13.2

0

14.1

4

14.8

6

15.4

2

15.8

5

16.1

9

16.4

5

16.6

5

16.8

1

16.9

3

17.0

1

17.0

9

17.1

9

17.4

2

17.6

7

17.9

5

18.2

5

18.5

9

18.9

6

19.3

8

Position (in)

Stat

ic P

ress

ure

(psi

)

k-wsalaminvExpt

Figure 2-11: Injector upstream & downstream wall static pressure distribution comparison for various viscous models & Guhses experimental data

Figure 2-12: Flowfield structure (Mach number contours) obtained from numerical solution of Guhses

experimental configuration (Viscous Model: rk- 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- 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, Pop = 3.45 MPa

Primary Stagnation Temperature, Top = 3000 K

Primary Nozzle Exit Pressure, Pep = 0.1 MPa

The secondary flow characteristics are given as under:

Secondary Fluid Calorifically Perfect Air

Secondary Stagnation Pressure, Pos Refer to Section 2.7

Secondary Stagnation Temperature, Tos 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 m2 0.02 m2 0.02 m2

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

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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)

Hei

ght (

m)

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

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5

-0.0

4

-0.0

3

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2

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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)

Hei

ght (

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

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5

-0.0

4

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3

-0.0

2

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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)

Hei

ght (

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, MP = 2)

b) 12 Degree Divergent Half Angle Conical Profile (Injection Location, MP = 2)

c) 15 Degree Divergent Half Angle Conical Profile (Injection Location, MP = 2)

Figure 2-14: Two dimensional grid configuration of primary bell and conical shaped nozzles (Showing relative positions of same injection location at MP = 2)

38

a) Bell Shaped Profile (Injection Location, MP = 3)

b) 12 Degree Divergent Half Angle Conical Profile (Injection Location, MP = 3)

c) 12 Degree Divergent Half Angle Conical Profile (Injection Location, MP = 3)

Figure 2-15: Two dimensional grid configuration of primary bell and conical shaped nozzles (Showing relative positions of same injection location at MP = 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, MP @ Injection

Secondary Injector Slot to Primary Throat Area Ratio

(AR), As/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), Pos/Pop = 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



Secondary Injector Slot to Primary Throat Area

Ratio (AR), As/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, mS = 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, mS = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 kg/s



Secondary Injector Slot to Primary Throat Area

Ratio (AR), As/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

Pos/Pop = 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 shockboundary 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%, inj = 0o, MP = 3

c) PR = 1.00, AR = 5%, inj = 0o, MP = 3

Figure 3-2: Effect of injection pressure on flowfield structure (Mach # contours)

50

d) PR = 0.75, AR = 5%, inj = 0o, MP = 3

e) PR = 0.50, AR = 5%, inj = 0o, MP = 3

f) PR = 0.25, AR = 5%, inj = 0o, MP = 3

Figure 3-2 (continued): Effect of injection pressure on flowfield structure (Mach # contours)

51

Injection Location, MP = 2 Area Ratio, AR = 2%

Angle of Injection, inj = 0o

a) AR = 2%, inj = 0o, MP = 2



b) AR = 5%, inj = 0o, MP = 3 Figure 3-3: Effect of secondary (injection) mass flow rate on injector upstream wall static pressure

distribution

52


An = 0ogle of Injection, inj

a) AR = 2%, inj = 0o, MP = 2 a) AR = 2%,

b) AR = 5%, inj = 0o, MP = 3 b) AR = 5%,

53

inj = 0o, MP = 2

inj = 0o, MP = 3



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



a) AR = 2%, inj = 0o, MP = 2



b) AR = 5%, inj = 0o, MP = 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%, inj = 0o, MP = 2

b) PR = 1.00, AR = 2%, inj = 0o, MP = 3

c) PR = 1.00, AR = 2%, inj = 0o, MP = 3.75

Figure 3-6: Effect of injection location on flowfield structure (Mach # contours)

57

a) PR = 1.25, AR = 5%, inj = 0o, MP = 2

b) PR = 1.25, AR = 5%, inj = 0o, MP = 3

c) PR = 1.25, AR = 5%, inj = 0o, MP = 3.75

Figure 3-7: Effect of injection location on flowfield structure (Mach # contours)

58

Pressure Ratio, PR = 1.00 Area Ratio, AR = 2%


a) PR = 1.00, AR = 2%, inj = 0o


oAngle of Injection, = 0inj

b) PR = 1.25, AR = 5%, inj = 0o

Figure 3-8: Effect of injection location on injector upstream wall static pressure distribution

59



a) PR = 1.00, AR = 2%, inj = 0o

b) PR = 1.25, AR = 5%, inj = 0o



Figure 3-9: Effect of injection location on injector downstream wall static pressure distribution

60



a) AR = 1.00, AR = 2%, inj = 0o

b) AR = 1.25, AR = 5%, inj = 0o



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



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%, inj = 0o, MP = 2

b) PR = 1.00, AR = 5%, inj = 10o, MP = 2

c) PR = 1.00, AR = 5%, inj = 45o, MP = 2

Figure 3-11: Effect of angle of injection on flowfield structure (Mach # contours)

64

a) PR = 0.75, AR = 5%, inj = 0o, MP = 3

b) PR = 0.75, AR = 5%, inj = 10o, MP = 3

c) PR = 0.75, AR = 5%, inj = 45o, MP = 3

Figure 3-12: Effect of angle of injection on flowfield structure (Mach # contours)

65

Injection Location, MP = 2 Pressure Ratio, PR = 1.00

Area Ratio, AR = 5%

a) PR = 1, AR = 5%, MP = 2


Area Ratio, AR = 5%

b) PR = 0.75, AR = 5%, MP = 3

Figure 3-13: Effect of angle of injection on injector upstream wall static pressure distribution

66


Area Ratio, AR = 5%

a) PR = 1, AR = 5%, MP = 2

b) PR = 0.75, AR = 5%, MP = 3


Area Ratio, AR = 5%

Figure 3-14: Effect of angle of injection on injector downstream wall static pressure distribution

67


Area Ratio, AR = 5%

a) PR = 1, AR = 5%, MP = 2


Area Ratio, AR = 5%

b) PR = 0.75, AR = 5%, MP = 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, MP = 2

b) Injection Location, MP = 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



The observations and comments recorded are as follows:

70

a) Injection Location, MP = 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, MP = 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%, inj = 0o, MP = 2, Bell Shaped Profile

b) PR = 1.25, AR = 5%, inj = 0o, MP = 2, Conical Divergent Half Angle = 12o

c) PR = 1.25, AR = 5%, inj = 0o, MP = 2, Conical Divergent Half Angle = 15o

Figure 3-16: Effect of primary nozzle profile on flowfield structure (Mach # contours)

72

a) PR = 1, AR = 5%, inj = 0o, MP = 3, Bell Shaped Profile

b) PR = 1, AR = 5%, inj = 0o, MP = 3, Conical Divergent Half Angle = 12o

c) PR = 1, AR = 5%, inj = 0o, MP = 3, Conical Divergent Half Angle = 15o

Figure 3-17: Effect of primary nozzle profile on flowfield structure (Mach # contours)

73


Area Ratio, AR = 5% oAngle of Injection, = 0inj

a) PR = 1.25, AR = 5%, inj = 0o, MP = 2

b) PR = 1, AR = 5%, inj = 0o, MP = 3


Area Ratio, AR = 5% Angle of Injection, inj = 0o

Figure 3-18: Effect of primary nozzle profile on injector upstream wall static pressure distribution

74


Area Ratio, AR = 5% Angle of Injection, inj = 0o

a) PR = 1.25, AR = 5%, inj = 0o, MP = 2 a) PR = 1.25, AR = 5%,

inj = 0o, MP = 2


Area Ratio, AR = 5% An ogle of Injection, = 0inj

b) PR = 1.00 AR = 5%, inj = 0o, MP = 3 b) PR = 1.00 AR = 5%, inj = 0o, MP = 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



a) PR = 1.25, AR = 5%, inj = 0o, MP = 2



b) PR= 1, AR = 5%, inj = 0o, MP = 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:

( )[ ] ( ) epi

apeppxxpxp APPVAVF += (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

oppp FFF = (4-2)

In this paper, primary axial thrust augmentation is represented by a dimensionless

parameter given as follows:

op

opp

op

p

FFF

FF = (4-3)

78

c) Primary Specific Impulse

The performance of the primary nozzle is measured through primary specific impulse

which is defined as

ep

pp

gm

FIsp

= (4-4)

d) Side Thrust

Net side thrust is given as

Fs = Fn + Fj (4-5)

Fn, Interaction Force (Side Thrust-Pressure Component) is given as

[ ] [ ] =i

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