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This is to certify that the
dissertation entitled

Free Stream Surface Methods for Stabilizing Mixed-
Compression Inlets

presented by

David Benjamin Benson

has been accepted towards fulfillment
of the requirements for the

PhD. degree in Mechanical Engineering

 

 

 

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Date

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Free Stream-Surface Methods for Stabilizing Mixed-Compression lnlets
By

David Benjamin Benson

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
DEPARTMENT OF MECHANICAL ENGINEERING

2004

ABSTRACT

FREE-STREAM SURFACE METHODS FOR STABILIZING MIXED-
COMPRESSION INLETS

By

David Benjamin Benson

Mixed-compression inlets are needed by turbojet engines powering
aircraft intended to cruise at Mach numbers exceeding about 2.5 for efficient
conversion of inlet air’s dynamic pressure to static pressure. Unfortunately,
mixed-compression inlets are not very stable because of flow separation from
shock-wave / boundary-layer interactions, which changes the effective inlet
surface geometry. In this study, two methods for controlling the effective inlet
geometry for stable fluid flow in a mixed-compression inlet are proposed and
investigated by using computational fluid dynamics (CF D). CFD simulations
were performed to (1) characterize the near-throat flow of the mixed-compression
inlet under critical flow conditions with bleed and (2) examine free-stream
surfaces formed by two proposed control methods.

In the first set of simulations, critical flow through an axisymmetric, mixed-
compression inlet was examined using two different bleed boundary conditions to
model the flow through the cowl and centerbody bleed holes. In one bleed

boundary condition, the locations of the bleed holes were discerned. In the

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other, each row of bleed holes was modeled as a porous surface, where the
number of bleed holes in each row was accounted for to give the correct bleed
rate. These simulations characterized the shock structure in the throat region of
the inlet and indicated that the bleed-hole configuration, in addition to the overall
bleed rate, is a central element in determining the shock structure and strength in
this region. The second set of simulations uses combined supersonic injection
and suction in a turbulent, supersonic crossflow to generate a desired free-
stream surface that behaves like a wall of the inlet except with a slip surface.
Key properties of the jet structure were well-captured and results for the height of
the surface generated indicate that there is little impact as the Mach number of
the injected fluid is increased. The third set of simulations uses subsonic
injection into a recessed cavity placed in a turbulent, supersonic crossflow. The
driven fluid is used to control the deflection of the crossflow by the cavity and to
modify the boundary layer downstream of the cavity. For the range of
parameters investigated, results indicate that the deflection of the separated
crossflow is only modestly influenced by either the Mach number or the mass
flow rate of the injected fluid and that the shape of the cavity is the most
important parameter in determining the downstream profile of the boundary layer.

The CFD simulations were generated by using the CFLSD code, which
solves the Reynolds-averaged continuity, compressible Navier-Stokes (using a
modified form the thin-shear layer approximation), and total energy equations for
a thermally perfect gas. The turbulent stresses were modeled by the one-

equation Spalart-Allmaras model and the shear-stress transport (SST) model.

To my wife, Tamara, and t0 the Laughter which we share.

iv

ACKNOWLEDGEMENTS

I would like to extend my special thanks to my thesis advisor, Dr. Tom l-P.
Shih, for his guidance and assistance during my graduate studies. I would also
like to thank the members of my committee for their guidance and their
willingness to commit their time to this process: Dr. Manoocher Koochesfahani,
Dr. Farhad Jaberi, Dr. Mei Zhuang, and Dr. Guowei Wei.

In addition, I would like to thank Fred Hall for his patience and assistance
with all of the computer and network glitches that occupied my time in graduate
school and Dr. Robert Stein for his advice and for his assistance in helping me
turn CFL3Dv6.1 into CFLSDv6.2. I would also like to thank Dr. Charles Petty for
his interest and approach to students and education.

I would like to thank my spouse, Tamara, for her support and my son,
Isaac, for his patience. He grew up with this research and was an excellent
assistant. A note of thanks also goes to C&J Editing of Chevy Chase, MD for
they’re excellent work.

Finally, I would like to thank David 0. Davis and Brian Wills from NASA
Glenn for their funding of the mixed-compression inlet simulations. The inlet
research was supported by grant NAG 3-2234 from NASA Glenn Research

Center and I am grateful for this support.

 

 

LIST OF
LIST OF
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TABLE OF CONTENTS

LIST OF FIGURES .............................. viii
LIST OF TABLES ............................... xv
KEY TO SYMBOLS AND ABBREVIATIONS ................. xvi
Chapter

1. Introduction

1.1 Objectives ......................... 1
1.2 Theory and Background .................. 10
1.3 Dissertation Outline ..................... 25

2. CFD Simulations of Critical Flow Through an Axisymmetric Mixed-
Compression Inlet with Bleed Through Discrete Holes

2.1 Summary .......................... 27
2.2 Introduction ......................... 29
2.3 Description of Problem Studied and Methods Employed
2.3.1 Problem Description ............ 34
2.3.2 Problem Formulation ............ 42
2.3.3 Boundary Conditions ........... 42
2.3.4 Numerical Method of Solution ....... 49
2.3.5 Grid Structure ............... 49
2.4 Method for Initialization of Flow within an Inlet ....... 52
2.5 Results ........................... 58
2.6 Conclusions ........................ 81

3. CFD Simulations of a Free Stream-Surface Control Method Using a
Transverse Jet-in-Crossflow and Bleed Through Discrete Holes

3.1 Summary .......................... 83
3.2 Introduction ......................... 84
3.3 Description of Problem Studied and Methods Employed
3.3.1 Problem Description ............ 86
3.3.2 Problem Formulation ........... 89
3.3.3 Boundary Conditions ........... 89
3.3.4 Numerical Method of Solution ....... 90
3.3.5 Grid Structure ............... 91
3.4 Results ........................... 93
vi

3.5 Conclusions ........................ 102

4. CFD Simulations of a Free Stream-Surface Control Method Using a
Driven Cavity Flow Field

4.1 Summary .......................... 105
4.2 Introduction ......................... 106
4.3 Description of Problem Studied and Methods Employed
4.3.1 Problem Description ............ 112
4.3.2 Problem Formulation ........... 115
4.3.3 Boundary Conditions ............ 115
4.3.4 Numerical Method of Solution ....... 117
4.3.5 Grid Structure ............... 118
4.4 Results ........................... 121
4.5 Conclusions ......................... 137

5. Conclusions and Recommendations

5.1 Conclusions ........................ 140

5.2 Recommendations ..................... 145

LIST OF REFERENCES ........................... 148
vii

 

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LIST OF FIGURES

Images in this dissertation are presented in color.

Figure 1.1

Figure 1.2

Figure 1.3

Figure 1.4

Figure 1.5

Figure 1.6

Figure 1.7

Figure 1.8

General flow pattem observed in the mixed-compression

inlet operating at design conditions.

Illustration of one of the proposed free stream-surface
control methods as implemented in the throat region of

a mixed-compression inlet.

Diagram of a suction spit flap on an airfoil indicating the
trapped (standing) vortex and the diverted flow pattern
(Chang, 1976).

A potential flow model for the generation of a free
streamline for use in altering the shape of an airfoil
(Hurley, 1961).

Mach Number contours for CFD simulation of flow
through a mixed-compression inlet (Benson et al.,
2003)

Schematic and pressure profile of the interaction of a
transverse jet (slot) with a supersonic main flow (Spaid
and Zukoski, 1968).

Schematic and pressure profile of the interaction of a
transverse jet (slot) with a supersonic main flow (Schetz
and Billig, 1966).

Three-dimensional flowfield due to transverse injection

into a supersonic crossflow (VanLerberghe et al., 2000).

viii

12

14

16

19

21

22

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Figure 1.9

Figure 2.1

Figure 2.2

Figure 2.3

Figure 2.4

Figure 2.5

Figure 2.6

Figure 2.7

Figure 2.8

Figure 2.9

Schematic for helium injection into an annular cavity
placed in a conic re-entry vehicle (Nicholl, as referenced
in Chang, 1976).

Schematic of the mixed-compression inlet.

General flow pattern observed in the mixed-compression

inlet operating at design conditions.

Model schematic for the mixed-compression inlet

(Smeltzer and Sorensen, 1973).

Bleed hole configuration (configuration C) on cowl and

centerbody (Smeltzer and Sorensen, 1973).

Details of the bleed hole configuration (configuration C)
and measurement locations for (a) the cowl surface and
(b) the centerbody surface of the axisymmetric, mixed-

compression inlet.

Boundary condition schematic for the mixed-

compression inlet simulations.

The four block, multigrid system employed in

simulations of the mixed-compression inlet.

Mach number contours along centerline for the bleed
boundary condition that resolves individual bleed holes

(bleed-hole boundary condition).

Pressure contours along centerline and solid surfaces
for the bleed boundary condition that resolves individual

bleed holes (bleed-hole boundary condition).

ix

24

35

37

39

40

43

44

5O

59

60

 

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Figure 2.10

Figure 2.1 1

Figure 2.1 2

Figure 2.13

Figure 2.14

Figure 2.1 5

Mach number contours along the centerline for the bleed
boundary condition that treats each row of bleed holes

as a slot (bleed-slot boundary condition).

Pressure contours along the centerline and solid
surfaces for the bleed boundary condition that treats
each row of bleed holes as a slot (bleed-slot boundary

condition).

Average total pressure within a cross-section of
constant x/R. Normalization is with respect to the
average total pressure within a cross-section of the

freestream capture-area of the inlet.

Surface pressure, predictions versus measurements.

Mach number profile on cowl surface along centerline
(A-A’, Fig. 8) at (a) 10d upstream of bleed, (b) mid-way
between 2 bleed patches (point a’, Fig. 7), (0) 5d
downstream of last row of bleed holes (D-D’), and (d)

15d downstream of last row of bleed holes.

Mach number profiles on centerbody surface along
centerline (A-A’, Fig. 8) at (a) 10d upstream of bleed, (b)
mid-way between 2 bleed patches (point a, Fig. 7), (c)
5d downstream of last row of bleed holes (C-C’), and (d)
15d downstream of last row of bleed holes.

62

63

64

66

68

70

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Figure 2.16

Figure 2.17

Figure 2.18

Figure 2.19

Figure 3.1

Figure 3.2

Mach number profile on centerbody surface along B-B’
(Fig. 8) at (a) 10d upstream of bleed, (b) mid-way
between 2 bleed patches (point b, Fig. 7), (0) 5d
downstream of last row of bleed holes (C-C’), and (d)

15d downstream of last row of bleed holes.

Mach number profiles on centerbody surface for the
hole-disceming bleed BC along A-A’ and B-B’ (Fig. 8)
at (a) mid-way between the two sets of bleed patches
(point c, Fig. 7), (b) mid-way between 2 bleed patches
(point b, Fig. 8), (0) 5d downstream of last row of bleed
holes (C-C’).

Pressure profile on centerbody surface along centerline
(A-A’, Fig. 7) at (a) 10d upstream of bleed, (b) mid-way
between 2 bleed patches (point a, Fig. 7), (0) 5d
downstream of last row of bleed holes (C-C’), and (d)
15d downstream of last row of bleed holes.

Pressure profile on cowl surface along centerline (A-A’,
Fig. 8) at (a) 10d upstream of bleed, (b) mid-way
between 2 bleed patches (point a, Fig. 7), (0) 5d
downstream of last row of bleed holes (C-C’), and (d)

15d downstream of last row of bleed holes.

Schematic of computational domain for the free stream-
surface simulations: top-down view of flat plate surface

(dashed lines indicate periodic boundary planes).

Boundary condition schematic for the free stream-

surface simulations.

xi

72

74

77

79

87

87

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Figure 3.3

Figure 3.4

Figure 3.5

Figure 3.6

Figure 3.7

Figure 3.8

Figure 3.9

Figure 4.1

Figure 4.2

Figure 4.3

Single block grid system used in the free stream-surface

simulations.

Mach number contours and selected streamlines for the
two-dimensional simulations of the free stream-surface

control structure.

Mach number contours and selected streamlines along
the centerline for a three-dimensional simulation of the

free stream-surface control structure.

Pressure contours along the flat plate and selected

streamlines from the crossflow and the injected jet.

Pressure contours along the flat plate and selected

streamlines from the crossflow.

Mach number contours around the injection port and
bleed region on the flat plate surface and along the
centerline.

Relationship between injection Mach number and the
forward and normal penetration of the jet for a typical

case.

Description of the different types of cavity flow: (a) open
cavity flow, (b) closed cavity flow, (0) transitional cavity
flow (Plentovich et al, 1993 and Stallings et al, 1987).

Schematic of computational domain for the driven cavity

simulations.

Boundary condition schematic for the driven cavity

problem.

xii

92

94

96

97

99

100

101

110

114

116

 

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Figure 4.4

Figure 4.5

Figure 4.6

Figure 4.7

Figure 4.8

Figure 4.9

Figure 4.10

Figure 4.11

Figure 4.12

Figure 4.13

The four block, wrap-around grid system used for driven

cavity flow problem.

Mach number contours for case 1: baseline cavity
(L/h = 5.0).

Pressure contours and selected streamlines for case 1:
baseline cavity (L/h=5.0).

Mach number contours for case 2: Min): 0.6, 0: 45
degrees (L/h=5.0).

Pressure contours and selected streamlines for case 2:
Mini: 0.6, 6: 45 degrees (L/h=5.0).

Mach number profiles normal to the plate surface at
X/L = 1.5 and at X/L=1.0 for case 2: Mini: 0.6, 0: 45
degrees (L/h=5.0).

Mach number profiles normal to the plate surface at
X/L = 1.5 for case 1, case 2 and case 3: Mini: 0,
Mini: 0.26 and Mini: 06, respectively (L/h=5.0).

Pressure profiles (normalized) across the length of the
cavity floor (streamwise direction) for case 5, case 6
and case 7: Mini: 0, Mini: 0.26 and Mini: 06,
respectively (L/h=5.0).

Pressure profiles (normalized) across the length of the
cavity floor (streamwise direction) for case 8 and case 9:
Mini: 0, Mini: 0.8, respectively (L/h=15.0).

Pressure profiles (normalized) along cavity floor in the
streamwise direction for delta/h = 0.8 and delta/h = 0.4:

case 3 and case 4, respectively (L/h = 5.0).

xiii

119

122

123

124

125

127

128

129

131

132

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Figure 4.14 Pressure profiles (normalized) along flat plate surface in 133

Figure 4.15

Figure 4.16

the streamwise direction for delta/h = 0.8 and delta/h =

0.4: case 3 and case 4, respectively (L/h = 5.0).

Patched-grid system used for comparison with the 134

wrap-around grid system case (L/h = 5.0).

Normalized pressure profiles(a) ahead of the cavity, (b) 135
along the cavity floor, and (0) just downstream of the
cavity for the wrap-around grid and the patched grid in

the L/h :50 case (case 1: no injection).

xiv

 

Tabil

 

 

LIST OF TABLES

Table 4.1 Table listing relevant parameters of cases presented for 113

the driven cavity simulations.

XV

KEY TO SYMBOLS AND ABBREVIATIONS

inf

CD

ST

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N

Zwall

spanwise spacing between bleed holes
crossflow property

discharge coefficient

injection/bleed hole diameter

inlet capture diameter

freestream property

freestream property

jet property

jet-to-crossflow momentum ratio
turbulent kinetic energy

Mach number

pressure

inlet capture radius

shear-stress transport

velocity

normal velocity

x-coordinate

streamwise distance as measured from cowl lip
y-coordinate

wall coordinate

z-coordinate

local wall coordinate as measured from centerbody
sunace

local wall coordinate as measured from cowl surface

xvi

Greek Symbols
density
flap angle
angle of injection measured relative to x-coordinate
normal distance from first grid point to wall
dissipation rate per unit turbulent kinetic energy

ratio of specific heats

xvii

 

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CHA PTER 1

Introduction

1.1 Objectives

The performance and efficiency of a turbojet engine depends strongly
upon the design and performance of the engine’s inlet (of. Seddon and
Goldsmith, 1985). The inlet determines the amount of air entering each engine
as well as the velocity and pressure of the air when it reaches the engine's
compressor face. Since the compressor requires air at low subsonic speeds,
supersonic air entering the inlet must be decelerated to the conditions required
by the compressor with a maximum of pressure recovery and a minimum of flow
distortion.

To accomplish these objectives during supersonic flight, there are two
types of inlets available for turbojet engines: external compression inlets and
mixed-compression inlets. In an external compression inlet, the fluid undergoes
a strong shock at the entrance or just outside the entrance to the inlet. From the
entrance of the inlet to the compressor face, therefore, the fluid is subsonic and
is further decelerated by the shape of the inlet to the conditions required by the
compressor. When the flight Mach number exceeds about 2.5, however, mixed-

compression inlets are the preferred approach because they can effectively

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convert dynamic pressure of the high Mach number flow to static pressure over
relatively compact space. In a mixed-compression inlet, the flow is first
decelerated through a series of oblique shocks. Just downstream of the throat,
these oblique shocks culminate in a weak terminal shock. From this point, the
remainder of the inlet is a subsonic diffuser and the flow is further decelerated to
the conditions required by the compressor (Figure 1.1). In this way, the
objectives of the inlet can be obtained with a minimum of internal drag and a
large pressure recovery.

The ideal flow through a mixed-compression inlet is one in which the inlet
captures all of the air approaching the inlet’s cross-section and the normal
(terminal) shock is stabilized just downstream of the inlet’s throat. At this
location, the Mach number is only slightly above unity and the loss across the
terminal shock is minimized. This flow, referred to as critical flow, is preferred,
but is difficult to maintain because small perturbations in the flow field can move
the terminal shock upstream of the throat.

If the terminal shock should move upstream of the throat for any reason,
the shock will continue to move upstream until the flow is subsonic throughout
the inlet and a bow shock is formed outside of the inlet. For a mixed-
compression inlet, this situation causes most of the flow approaching the inlet to
be diverted away from the inlet and is known as the unstart condition since the
engine will shut down from an insufficient amount of air. When this occurs, the
engine is shut down and the inlet needs to be reconfigured so as to re-initialize

the flow in the inlet.

 

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Figure 1.1 General flow pattern observed in the mixed-compression inlet

operating at design conditions.

 

 

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In order to maintain critical flow with the terminal shock stabilized just
downstream of the throat, it is necessary to bleed (i.e., suction away) some of the
air in the boundary layer about all locations on the inlet where shock waves
impinge on the boundary layer (Figure 1.1). Bleeding makes the velocity profile
in the boundary layer “fuller" so that the flow can overcome the adverse pressure
gradient created by the incident and terminal shock waves without separating.

An additional issue associated with the operation of a mixed-compression
inlet is the method by which the flow through the inlet is initialized. Since the
mixed-compression inlet is designed to operate at supersonic speeds, special
measures must be taken to bring the aircraft and the inlet up to the design
speeds. During the initialization of flow through the inlet, the geometry of the
inlet is changed to maintain operating conditions at the engine face as the speed
of the aircraft increases. In a mixed-compression inlet, this is accomplished by
moving the cowl to change the geometric profile of the inlet. As a result,
designing a mixed-compression inlet requires that certain trade-offs be made in
the profiles that are generated as the cowl is translated: the inlet profile
requirements for high-speed flight are quite different for those at low-speed flight.
This inherently means that, to achieve efficient flight at the design speed,
sacrifices are made during flight at lower speeds.

As a result of the need to restructure the inlet profile by physically
changing the geometry of the inlet, both inlet unstart and the flow initialization
procedure are awkward aspects of mixed-compression inlet operation. This

research into the operation and improvement of mixed-compression inlets,

 

 

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therefore, has two objectives. The first objective is to improve the current state of
the art in the numerical simulation of flow through mixed-compression inlets by
implementing a set of bleed boundary conditions to model the bleed process that
is central to inlet operation. Currently, much of the computational investigation
into the flow within mixed-compression inlets has resorted to simulating the bleed
holes, used to control the boundary-layer growth within the inlet, as slots or
porous walls. This simplification omits many of the three-dimensional aspects
that are present in the inlet flow. By modeling the bleed regions as discrete
holes, the three-dimensional nature of the flow within the mixed-compression
inlet can be more accurately captured, thereby improving our understanding of
the nature of the shock structure within the inlet and its relationship with the
boundary layer. Improving the numerical simulation of the mixed-compression
inlet will also permit the development of alternative control methods for these
types of inlets.

This work also presents a method for initializing the flow through a mixed-
compression inlet in CFD simulations. The nature of critical flow with in the inlet,
with its subsonic and supersonic domains, as well as the complicated boundary-
layer/shock wave interactions, presents exceptional difficulties when initializing
the flow through the inlet. The methods that are available to the experimentalist
in starting the flow though the inlet, involving the translation of the cowl or
centerbody to change the shape of the inlet, are not reasonable for use in CFD
simulations. In addition, this problem is also complicated by issues associated

with the positioning of the terminal shock just downstream of the throat and inlet

unstart. As a result, a general method is needed to initialize the flow through the
inlet for computations.

The second objective of this research is to examine the feasibility of
implementing a free stream-surface control method in flow conditions that are
similar to the near-throat region of a mixed-compression inlet. In the first
approach, the free stream-surface control method is implemented as a
supersonic jet injected into a supersonic flow over the inlet centerbody or cowl
surface with the addition of downstream bleed. The injected plume forms a free
stream-surface that penetrates some distance into the freestream flow and then
reconnects to the flat plate at the downstream bleed location. This captured free
stream-surface traps a region of the fluid beneath it and causes the exterior flow
to be diverted past the reconnected structure. In several respects, this system is
similar to the aeroshaping work that has been done in aerodynamics for
changing wing shapes. In the previous work, however, the injected plume is
used to change the shape of the wing to affect its lift and drag characteristics or
to prevent flow separation. In the current situation, however, it is suggested that
the Injected plume would be used for internal control to change the effective-area
ratio of an inlet.

The second approach taken in generating a free stream-surface in a
mixed-compression inlet uses injection within a recessed cavity that is placed in
the centerbody or cowl surface of the inlet. In this approach, the injected fluid
serves to drive the recirculating flow that is already present in the cavity. In this

manner, either the thickness of the boundary layer as the freestream flow

 

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reconnects to the surface or the height of the recirculation region within the cavity
can be altered to control the effective-area ratio of the inlet. The advantage of
this approach, however, is that the injection process is shielded from the high
momentum fluid present in the crossflow. To complete the circuit, downstream
bleed is provided by the bleed holes that would ordinarily be used within the inlet
to control boundary layer separation.

In conducting this research, it is proposed that a free stream-surface
control method can be used to address both of the main issues facing the
operation of a mixed-compression inlet: inlet unstart and the flow initialization
procedure. For example, a free stream-surface control method, implemented in
the converging portion of a mixed-compression inlet, could be used to replace or
reduce the amount of cowl translation needed to bring the aircraft to its
operational speed. By methodically changing the amount and/or angle of
injection or by modifying the number of active bleed holes, the free stream-
surface can be controlled in such a way as to replicate the necessary changing
geometry of the inlet, mimicking the effect of the translating cowl (Figure 1.2). A
free stream-surface control method could also be implemented to respond to the
initial stages of unstart so as to change the effective area ratio of the inlet
upstream of the shock and to re-establish favorable operating conditions. The
simulations conducted here seek to establish the relevant parameters of the free
stream-surface control method and to set the stage for future research into

implementing the concept.

Location of throat before
application of free stream-
surface control

 

 

 

 

 

 

 

 

Shapes formed by injection New location of inlet
and suction on cowl and throat
centerbody surfaces

Figure 1.2 Illustration of one of the proposed free stream-surface control method
as implemented in the throat region of a mixed-compression inlet. Top: Before

the addition of control mechanism. Bottom: After addition of control mechanism.

 

 

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In the first set of simulations conducted, the free stream-surface is
generated by a transverse supersonic jet injected into a supersonic turbulent flow
over a flat plate coupled with a series of bleed holes located at some distance
downstream of the injection port. The injected plume forms the free stream-
surface that enters into the crossflow and then reconnects to the flat plate at the
downstream bleed location. In these simulations, the downstream bleed region
is modeled, using a bleed boundary condition suitable for choked bleed, as a
configuration of discrete bleed holes and the injected jet is modeled as simple
square injection port using a supersonic patch boundary condition. The shape of
the injected plume is controlled by varying the Mach number and total pressure
of the injected fluid or by varying the size, location and pattem of the bleed holes.

In the second set of simulations, the driven cavity portion of a free stream-
surface control mechanism is generated by injecting a high-subsonic fluid into a
recessed cavity that is placed in a supersonic, turbulent crossflow. In these
simulations, the injection occurs on the leading face of the cavity (streamwise
face). The Mach number of the injected fluid, the amount of injected fluid and the
angle of injection are used to control both the deflection of the crossflow as it
separates off the leading edge of the cavity and the boundary layer profile
downstream of the cavity. The influence of these parameters on the flow are
examined for several cavity length-to-depth ratios (L/h) and for several ratios of
the approaching boundary layer height to the cavity depth (5/L). An additional
study was conducted investigating the influence of grid stmcture on the

simulation results.

 

viaw:

"if.

tree 2

 

 

1.2

Taken as a whole, these three studies form the beginnings of a much
larger research project. Central to any future research on the development of a
viable free stream-surface control mechanism are: (1) the characterization of the
free stream-surface profile as a function of the injection and bleed rates; (2) the
generation the system’s response to an incident, oblique shock; and (3) the
response of the core flow within the inlet to changes in the effective area. These
research areas are the logical next steps in the process. Additional future
research directions indicated are as follows: a characterization of the response of
the system in the presence of a normal shock; an investigation of the drag and
mixing effects of the free stream-surface system; an exploration into the possible
uses of a localized high Mach region that has been observed; and the insertion of

the control structure into an inlet.

1.2 Theory and Background

Active flow control is a broad term that describes many different methods
used to achieve responsive control of a fluid environment beyond its static
design. For example, boundary-layer suction is often used on airfoils to delay the
onset of the airfoil’s natural separation point. Some of the active flow control
methods currently in development include variable geometry techniques, such as
MEMs-based active flow manipulators (AFM) and flexible surfaces; the use of
combined injection and suction to generate appropriate free stream surfaces; and
piezoelectric actuators used to drive oscillations within a flow. In some circles,

the term pseudo-active flow control (Joslin et al., 1999) is applied to methods

10

such as constant boundary-layer bleed and vortex generators, where the control
method is not continually evolving to respond to inputs from the flow field. While
the control method included in this study could be realized in either category, it is
here presented as a pseudo—active control mechanism.

Free stream-surface control methods have been employed in many
circumstances where a main flow needs to negotiate a complex geometry.
Classical engineering examples include cusp-surface configurations for diffusers
and split flaps for airfoils (Chang, 1976). In the suction split flap example, shown
in Figure 1.3, a hinged portion of an airfoil is detached from the surface on the
suction side of an airfoil. As the flow over the upper surface of the airfoil
reattaches to the split flap, a standing vortex is trapped in the wedge between the
airfoil and the flap. The effect of the split flap, in this case, is to change the
shape of the airfoil, thereby changing its lift and drag properties.

Free stream-surface control can also be found in nature. Two examples of
this are flow over snow comices and silt deposits past dams (Chang, 1976). In
snow comices, blown snow piles up on the leading edge of a surface and a
trapped vortex is generated as the wind blows across the structure. As a result,
any additional blown snow is diverted past the region where the vortex is trapped
and builds up on the downwind side of the cornice. This process is self-
reinforcing and ends up exaggerating the pointed structure of the snow cornice.
In each of these situations, the shape of a trapped (standing) vortex serves to
change the main flow in such a way as to improve its passage over an obstacle

(Chang, 1976).

ll

 

I? _

.lN. . :Ilr I L].

 

 

 

 

 

 

 

 

Figure 1.3 Diagram of a suction spit flap on an airfoil indicating the trapped

(standing) vortex and the diverted flow pattern (Chang, 1976).

12

In 1961, Hurley developed a potential flow analysis for the generation of a
free streamline flap (two-dimensional analysis) that, in practice, could be used to
change the effective profile of a thin airfoil. By utilizing injection on the leading
edge of the airfoil and suction on the trailing edge, the free streamline generates
a “thick pseudo-body shape” (Figure 1.4) and can, therefore, alter the lift
characteristics of the thin airfoil. In Hurley’s analysis, the line CD, is initially
closed and resting on line 302. At some later time, the two are separated by an
angle 1: and fluid is injected tangentially from point B. Suction applied at point C
serves to generate a streamline that begins and ends on the two physical
surfaces. Within the two lines, a trapped vortex region exists, and the net effect
is that the system now has a thick wing shape. This system was designed for
use in improving the take-off (low-speed) characteristics of thin airfoils such as
those used in supersonic aircraft. Subsequent experiments utilizing injection
slots served to confirm the two-dimensional analysis.

One potential application for the free stream-surface, generated by either
the direct action of combined injection and suction or by injection within a cavity,
is in the near throat region of a mixed-compression inlet. Control methods
implemented in this environment could be used to initiate flow through the inlet
without having to physically move or change the cowl or centerbody shape and to
aid in the prevention of unstart by influencing the effective-area ratio of the inlet.
In either circumstance, these control methods would have direct application to

supersonic flight projects such as the high-speed civil transport (HSCT).

l3

 

f ___‘ . ~‘fl _
I"; '
‘ .

 

Ur

FREE STREAM LINE ON WHICH FLUID SPEED IS qm

 

 

 

z-—PLANE

Figure 1.4 A potential flow model for the generation of a free streamline for use
in altering the shape of an airfoil (Hurley, 1961).

 

 

V..-.~ a.

 

 

 

 

In high-speed flight, at speeds greater than Mach 2.5, mixed-compression
inlets are the preferred method for bringing the supersonic air entering the inlet to
the low subsonic speeds required by the compressor (of. Seddon and Goldsmith,
1985). These Inlets are very effective at converting the dynamic pressure of the
high Mach number flow into the static pressure needed by the compressor. They
are also capable of achieving this goal over a relatively short length, thereby
decreasing the internal drag of the inlet. However, numerous complications arise
when using mixed—compression inlets.

The ideal flow through a mixed-compression inlet is one in which the inlet
captures all of the air approaching the inlet cross-section and where the normal
(terminal) shock is stabilized just downstream of the inlet’s throat. Within the
inlet, the flow is decelerated through a series of oblique shocks until it reaches
the throat region where it terminates in a strong shock (Figure 1.5).

At the terminal shock location, the local Mach number is only slightly
above unity so that the loss across the terminal shock is minimized. This flow,
referred to as critical flow, is preferred, but it is difficult to maintain because small
perturbations in the flow field can move the terminal shock upstream of the
throat. Once the terminal shock moves upstream of the throat, it will continue to
move upstream until the flow is subsonic throughout the inlet and a bow shock
forms outside the inlet. This causes most of the flow approaching the inlet to be
diverted away and is known as the unstart condition since the engine will shut

down from an insufficient amount of air.

15

41/: i ,r/;:.\/// i/ ‘
Reflected Shocks ’ / \f / /

    
    
    

Cowl

Centerbody

2.7

1-8 Mach
0.9 Number
0.0

Primary Oblique

Shock Terminal Shock / Throat

Figure 1.5 Mach Number contours for CFD simulation of flow through a mixed-

compresslon inlet (Benson et al., 2003). Inset: Perspective view of a 180 degree
slice of the inlet.

1m-

J
' ‘U “WI-I,

 

downs
air in II
on the
1wa

the inc

inlet. tl
bound
mued
BSpec’
contro
the pm

the efl

iI‘Il‘eeti
dFlier
iSabc
Some
Comp
”Mach
Inlet.

HarjO

In order to maintain critical flow with the terminal shock stabilized just
downstream of the throat, it is necessary to bleed (i.e., suction away) some of the
air in the boundary layer at all locations on the inlet where shock waves impinge
on the boundary layer. Bleeding makes the velocity profile in the boundary layer
“fuller” so that the flow can overcome the adverse pressure gradient created by
the incident and terminal shock waves without separating.

In a mixed-compression inlet, the flow responds to the geometry of the
inlet, the imposed back-pressure at the engine face, and the effect of the
boundary-layer growth on top of the geometry. Since the terminal shock in a
mixed-compression inlet is held (ideally) very close to the throat, the inlet is
especially sensitive to disturbances and area changes. A free stream-surface
control structure acting in the near-throat region of the inlet needs to be stable in
the presence of incident oblique shock waves and capable of appreciably altering
the effective-area ratio of the inlet.

Active/Pseudo-Active flow control with free stream-surfaces utilizing
injection and bleed through discrete holes is highly dependent on the three-
dimensional behavior of the flow. This three-dimensional behavior of the system
is also of interest to this study since the injection and suction regions are to be, in
some cases, modeled by boundary conditions. This is necessary from a
computational efficiency standpoint, especially if, in future research, the control
mechanism is to be implemented within a simulation of a mixed-compression
inlet. For the modeling of bleed through discrete holes, various authors (cf.

Harloff and Smith, 1985; Paynter et al., 1994; Benson et al., 2000) have already

17

‘ if 'i'\"”l.‘|1‘

 

done:

captur

iterai
adetr
Ifigur
comps
jetcar
alrap
shock
Dafier
Expar
rechc

flOWr:

Denel
anhc

deVei
ifiach

DOW]

imDc

done extensive work developing the bleed boundary conditions to accurately
capture the physics of the bleed process.

In 1968, Spaid and Zukoski developed an analytical model for the
interaction of a supersonic transverse jet with a supersonic cross-flow and were
able to develop relationships for, among other things, the jet penetration height
(Figure 1.6). This analytical model, developed for two-dimensional flow,
compared well with slot injection experiments. In these experiments, the injected
jet caused the boundary-layer flow upstream of the jet to separate and generated
a trapped region of recirculating flow in front of the jet. Within the jet, a series of
shocks were observed as the flow turned and was swept downstream. The
pattern of shocks was also observed to be dependent on the degree of under-
expansion of the jet. Downstream of the jet, another trapped region of
recirculating flow was observed and a compression shock was generated as the
flow reattached.

In 1970, Povinelli etal. and Billig et al. (Chang, 1976) investigated the
penetration of a single, normal gas jet injected into a supersonic crossflow. The
authors classified the shape of the resulting shock structure within the jet and
developed methods for ascertaining the penetration height as a function of the
Mach number ratio, momentum ratio, nozzle diameter, and downstream distance
from the injection point.

The study identified the momentum flux ratio was identified as the most

important parameter in determining the penetration of the jet into the crossflow.

18

 

STATII
mess

{Slot}

BOW SHOCK

      
  

SEPARATION SHOCK

I
'0
’0’.
o

    
  

I
a

._..,:-;{i‘.-"’suocr<s m JET

. ,. T necomnessron SHOCK

JET FLOW

 

SLOT LOCATION
STATIC /

PRESSURE

P 1 ' if

x, DISTANCE FROM SLOT

 

 

 

 

Figure 1.6 Schematic and pressure profile of the interaction of a transverse jet

(slot) with a supersonic main flow (Spaid and Zukoski, 1968).

19

 

The mc

where.

Schetz
exp-ant
IEFmIFII
idenUh
aso al

CFOSS-

GI al.,
Sifigie
exper
di‘v’C-rl

nEarl

The momentum flux ratio, J, is determined as

,0 1'ij

J __
AVE

where j and 0 refer to the transverse jet and crossflow properties, respectively.

Figure 1.7 displays the details the internal jet structure as described by
Schetz and Billig (1966). In these experiments, they observed that the jet
expanded as it entered the crossflow and this structure had a barrel shape that
terminated in a disk-shaped shock referred to as the barrel shock. In addition to
identifying qualitative features of the jet structure, Schetz and Billig (1966) were
also able to develop models for the width and location of the Mach disk and the
cross-sectional area distribution of the jet.

Other jet-in-crossflow research (of. VanLerberghe et al., 2000 and Huang
et al., 1990) has focused on the mixing aspects associated with injection by a
single transverse jet at various angles of injection. In these simulations and
experiments, the jet causes a bow shock to form that allows the crossflow to
divert around the jet. A horseshoe vortex is also seen to develop as the flow
near the surface is diverted around the jet (Figure 1 .8).

The jet plume is also observed to consist of a counter-rotating vortex pair
that forms in response to the deflection of flow around the jet and the separation
at the rear of the jet. The flow is clearly three-dimensional, and this plays a large

role in the mixing behavior of the jet. Much of the previous referenced research

20

 

Figur

{slot}

CONTROL BOUNDARY

 

 

 

I 1
I / MACH orsx "76:5
, M A
, ARREL M, 2

SHOCK
Mi

 

I 1 III/14.; 1’. /I/7/1’£r////'/.’ 1. //

Ar
, ,/.1'. 1C/ I PI ’
// 5
// // I

 

Figure 1.7 Schematic and pressure profile of the interaction of a transverse jet
(slot) with a supersonic main flow (Schetz and Billig, 1966).

21

F “TI

 

Su
On

7

Fig

SUDE

, Bow
Supersonic

   
  

Shock Jet Internal Shock Structure
crOSSflOW J (Barrel Shock and Mach Disk)
' Jet
~ Boundary
hr
\\

Horseshoe . . I .
Vortex Jet Wake \\ Counter-Rotating

Region \ Vortex Pair

Figure 1.8 Three-dimensional flowfield due to transverse injection into a
supersonic crossflow (VanLerberghe et al., 2000).

22

 

invol
horse
While
regio
featu
fealu

inIIuE

involved two-dimensional simulations and experiments; as a result, this
horseshoe vortex and the counter-rotating vortex pair in the jet were not present.
While these jet-in-crossflow experiments have not employed an associated bleed
region, they have done extensive work in identifying the three-dimensional
features of the injected flow. Their results are of use in identifying salient
features of the free stream-surface control mechanism and in assessing the
influence of the bleed region on the main flow.

Early work on cavity insertion in supersonic flow focused primarily on
reducing the heat transfer rate for protection of hypersonic vehicles. Chang
(1976) reports that experimenters were able to reduce the heat transfer rate by a
factor of two when a laminar cavity flow replaced a laminar boundary layer flow.
However, Chang also that these same studies showed that the Changes in the
downstream heat transfer rates tended to nullify the positive effects of the
injection into the cavity. In 1965, Nicholl (Chang, 1976) conducted experimental
studies with helium injection in an annular cavity on a conic re-entry vehicle at
Mach 11 (Figure 1.9). Nicholl found that by increasing the height of the
separation shoulder above the line of the conic surface, the injected fluid was
able to pass into the downstream boundary layer flow and dramatically reduce
the downstream heat transfer rates.

Current interest in cavity flow fields at supersonic speeds has focused on
the issues associated with stores separation from high-speed aircraft. Recent
developments in stealth technologies and the desire to reduce radar cross-

section from the external store carriages in military aircraft are the motivating

23

 

COnir

0.005" DIA.

 

NOSE
L. 2 ,

 

“—-—-. 1' /16 0.0. ——’-i

 

3
ALL MODEL AXISYMMETRIC\’/

EACH CORNER
RAD. o

6: CAV'TY a POSITIVE
i DEPTH D

\‘ _ f - “’7 WAMETEH
\‘T s ;

CAVITY LENGTH L

I

L) = 1%.!

L a 5,8"

D = 1/8"

6 = 10°

6, = 0, 0.01
0.02 AND
0.03 INCHES

Figure 1.9 Schematic for helium injection into an annular cavity placed in a

conic re-entry vehicle (Nicholl, as referenced in Chang, 1976).

24

I? .
N !

—.— -— -—- - J .u

.f’

 

1.3

factors in the examination of internal store carriages for supersonic aircraft.
Research by various authors (of. Wilcox, 1990; Stallings etal., 1991; Plentovich
et al., 1993) has focused on quantifying the flow field in the cavity by measuring
the pressure, force and moment distributions on a generic store separating from
within a box cavity. Various researchers have also proposed different methods to
control of the moments and drag experienced by the stores. For example,
Wilcox (1990) presented an approach using a cavity with a porous-floor to modify
the cavity flow field. By venting the high-pressure fluid in the rear of the cavity to
the low-pressure fluid in the front, the objective was to reduce the overall drag
characteristics of the cavity. Each of these approaches, however, has involved
the passive control of the fluid within the cavity for the purpose of drag reduction

or the prevention of flow oscillation.

1.3 Dissertation Outline

This study is an investigation into the three-dimensional aspects of a
mixed-compression inlet and of a free stream-surface control method for use in
these types of inlets. Chapter 2 focuses on the implementation of bleed
boundary conditions within a mixed-compression inlet to examine the three-
dimensional aspects of the flow and to provide a background for the control
method described. Simulations where the bleed holes are modeled as slots are
used for comparison. In Chapter 3, three-dimensional simulations are conducted
to assess the structure and form of the proposed free stream-surface control

method generated by combined injection and suction directly into the crossflow.

25

 

In this

In this study, various features of the free stream-surface control mechanism are
qualitatively characterized and the degree of penetration and shape of the
structure is examined as a function of jet speed and pressure. Chapter 4
presents the results of several three-dimensional simulations of driven cavity
placed in a crossflow. The influence of the driven cavity on the deflection of the
crossflow and on the downstream boundary layer profile is examined as a
function of jet speed and mass flow rate for several cavity length-to-height ratios.
An additional aspect of this study is that it is the examination of the importance of

grid structure on the simulation results.

26

2.1

 

6

LI'I m.

at ir

H...

.U

CHAPTER 2

CFD Simulations of Critical Flow Through an
Axisymmetric Mixed-Compression Inlet with

Bleed Through Discrete Holes

2.1 Summag

CFD simulations were performed to investigate boundary-layer control
through bleed patches in an axisymmetric mixed-compression inlet in which the
bleed patches are modeled by two global bleed boundary conditions. In one
bleed boundary condition, the locations of the bleed holes are discerned. In the
other bleed boundary condition, each row of bleed holes is modeled as a porous
surface where the number of bleed holes in each row is accounted for by an
adjusted discharge coefficient that gives the correct bleed rate. Experimental
data for the mixed-compression inlet is used as a basis for comparison between
the two boundary conditions.

In this study of critical flow through mixed-compression inlets, there are
three main objectives. The first objective is to describe a method or procedure
for initializing critical flow through mixed-compression inlets and to develop
guidelines on the type of grid system needed to capture the flow physics in this

type of inlet. This explicit detailing of the method for initializing the flow through

27

 

80C

FIUI'

Cor

the inlet will be of use in any future experimentation. The second objective of this
research is to present results for two bleed boundary conditions and to compare
the results from modeling discrete bleed holes with the more conventional
approach using bleed slots. Finally, this research serves as an introduction to
the problem of controlling effective-area through the use of combined suction and
bleed that will be presented in later sections.

Results are presented for the predicted bleed rates, pressure on the cowl
and centerbody surfaces, and Mach number profiles at several key points. Mach
number and pressure contours are also presented for the entire flow field.
Comparisons were made with available experimental data. Also presented is a
method based on one-dimensional isentropic and normal shock solutions to get
the flow “started” in CFD simulations of critical flow in mixed-compression inlets.

This computational study is based on the Reynolds-averaged
conservation equations of mass (continuity); momentum, using a modified form
of the thin-shear layer, compressible Navier-Stokes equations (Biedron et al.,
1986); and total energy. These equations are closed by the shear-stress
transport (SST) turbulence model of Menter, where integration is to the wall.
Solutions were generated by a cell-centered, finite-volume method that uses
third-order accurate flux-difference splitting of Roe with limiters, multigrid
acceleration of a diagonalized ADI scheme with local time stepping, and

patched/overlapped structured grids.

28

2.2

C0l

 

ref.

inle

dis

2.2 Introduction

The performance and efficiency of a turbojet engine depends strongly
upon the engine’s inlet (of. Seddon and Goldsmith, 1985). The inlet determines
the amount of air entering each engine as well as the velocity and pressure of the
air at the engine's compressor face. Because the compressor requires air at low
subsonic speeds, supersonic air entering the inlet must be decelerated with a
maximum of pressure recovery and a minimum of flow distortion.

To accomplish this, turbojets utilize two main types of inlets: external
compression inlets and mixed-compression inlets. At flight Mach numbers above
Mach 2.5, mixed-compression inlets are preferred because they can effectively
convert the dynamic pressure of a high Mach number flow to static pressure over
relatively compact space. In addition, with proper design, mixed-compression
inlets can achieve a very high pressure recovery with a minimum of flow
distortion.

The ideal flow through a mixed-compression inlet occurs when the inlet
captures all the air approaching the inlet cross-section and the normal (terminal)
shock is stabilized just downstream of the inlet’s throat. At this location, the
Mach number is only slightly above unity and the loss across the terminal shock
is minimized.

This ideal flow, referred to as critical flow, is preferred, but it is difficult to
maintain because small perturbations in the flow field can move the terminal
shock upstream of the throat. Once this happens, the terminal shock will

continue to move upstream until the flow is subsonic throughout the inlet and a

29

 

of
co
inl

Iirr

bow shock is formed outside of the entrance to the inlet. This causes most of the
flow approaching the inlet to be diverted and is known as the ‘unstart condition’
because the engine will shut down from an insufficient amount of air. In order to
maintain critical flow with the terminal shock stabilized just downstream of the
throat, some of the air in the boundary layer must be bled (i.e., suctioned away)
at all of the locations on the inlet where shock waves impinge on the boundary
layer. Bleeding “thickens” the velocity profile in the boundary layer so that the
flow can overcome, and not be separated by, the adverse pressure gradient
created by the incident and terminal shock waves.

Although many investigators have performed numerical studies of inlet
flows (of. Presley, 1975; Knight, 1977; Chen and Caughey, 1980; Buggeln, etal.,
1980; Paynter and Chen, 1983; Vaydak eta/., 1984; Chyu et al., 1986), relatively
few investigators (Kawamura etal., 1987; Vaydak et al., 1987; Chyu et al., 1992)
have reported simulations of critical flow through mixed-compression inlets. One
of these studies, by Chyu et al. (1992), investigated numerous bleed boundary
conditions for a two-dimensional, axisymmetric slice of a mixed compression
inlet. However, because their study was two-dimensional, their results were
limited to modeling the bleed holes as slots.

In simulating mixed-compression inlets, a researcher using numerical
methods to study the flow encounters two areas of difficulty. The first area of
difficulty is associated with the initialization of flow within the inlet and the method
by which the position of the terminal shock is controlled. A physical inlet begins

from rest, and the flow through the inlet is gradually increased to the operating

30

 

0W1
Char
trar.
uns
rap

ace

I
I”-
I
I

conditions. In this process, the physical inlet is brought through all of the stages
of development in the flight. The flow begins as subsonic in the freestream and
throughout the inlet. Gradually, the flow is transitioned to a state where the
freestream flow is supersonic and the flow throughout the inlet is both supersonic
and subsonic.

In addition, with a physical inlet the terminal shock is positioned
downstream of the throat by translating either the centerbody or the cowl to
Change the inlet profile to match the flight conditions. At first glance, the
translation of the cowl or centerbody may appear be a suitable control for the
unstart condition; however, when the inlet unstarts, the process occurs at such a
rapid rate that there would be no way for a mechanical system to respond. To
accommodate the changing position of the shock within the inlet and the various
possible operational speeds of the aircraft, the final design of a mixed-
compression inlet is, therefore, a compromise based on several optimized
designs for static inlets.

In summary, the methods employed to initialize the flow in the physical
inlet case require that both the inflow boundary conditions and the inlet geometry
are functions of time. The flight conditions change as the inlet is brought from
rest to operating speeds and the shape of the inlet is changed to hold the
terminal shock just downstream of the throat. To an investigator conducting
numerical simulations of the flow through a mixed-compression inlet, neither of
the methods that are available to the experimentalist for initializing the flow within

the inlet are feasible. Even if these methods were available to the CFD

31

 

 

 

 

researcher, the time costs in damping out transients that occur after each change
in either the freestream conditions or the geometry of the inlet would be
prohibitive.

The second main difficulty in simulating mixed-compression inlets is in
modeling the bleed patches where the boundary layer flow is suctioned away.
With different patterns of circular holes, each bleed hole and its associated
plenum would have to be numerically modeled and the flow through them
simulated. The level of complexity introduced by this is considerable. Rimlinger
et al. (1996) conducted simulations that studied supersonic boundary layer bleed
through discrete bleed holes in a variety of configurations and environments. In
these simulatiOns, the surface of the bleed hole, or bleed half-hole because of
symmetry considerations, typically required 32 grid points to appropriately
capture the physics of the bleed process. To model the flow past and through a
region consisting of six rows of holes, over 1.5 million grid points were used.
Extending this level of grid refinement to a full mixed-compression inlet with four
or five distinct bleed regions would require a prohibitively large number of grid
points. An additional complication to the explicit modeling of the flow through the
holes and plenum involves the configuration of the bleed holes being studied. If
the patterns of bleed holes is modified in any way, a major reconstruction of the
grid as well as the grid patching and overlapping information would be required,
especially if multigrid methods are used.

A standard practice in the simulation of mixed-compression inlets, as well

as in other devices that use bleed through discrete holes, is to replace the bleed

32

r... .-- _?

 

trough
isbou
1990 S
hrough
Inlonu
ileed If
:onfigu

low. ar

 

 

through discrete holes with a bleed-slot or porous-wall boundary condition. With
this boundary condition, the effect of the bleed is distributed along a patch of the
bleed surface. In a typical bleed-slot boundary condition, the mass flow rate
through the boundary (as a percentage of the freestream) is a free parameter.
Unfortunately, when the bleed-slot boundary condition is used to approximate
bleed through discrete holes, much of the physics associated with the shape and
configuration of the bleed holes, as well as the three-dimensional aspects of the
flow, are lost.

To accurately capture the dynamics of the bleed process, Benson et al.
(2000 and 2001) presented results for a bleed boundary condition that could be
used to replace the simulation of flow through choked bleed holes. This
boundary condition, applied only at the locations where the bleed is known to
occur, treats the flow in the normal direction through the boundary as a function
of the local sound speed above the hole. In this research, replacing the hole and
its associated plenum with a bleed boundary condition was determined to be
acceptable even in the most extreme cases where a single grid point was used to
model a bleed hole. In doing so, Benson et al. (2000 and 2001) were able to
model the flow turning that occurs in the bleed process and to capture the barrier
shocks that form on the downstream edge of each bleed hole.

In this current research, the bleed process within the mixed-compression
inlet will be simulated using two bleed boundary conditions. The first method

uses the bleed boundary condition developed by Benson et al. (2000 and 2001)

33

 

where E;
commo"

j.
compreI
method .
and to c‘
physics
the flora-
second
compar
convent
researc

OI comt

 

 

where each of the bleed holes is discretely modeled. The second approach,
common in practice, models each row of bleed holes as a porous surface or slot.
With these two approaches, this study of critical flow through a mixed-
compression inlet has three main objectives. The first objective is to describe a
method or procedure for initializing critical flow through mixed-compression inlets
and to develop guidelines on the type of grid system needed to capture the flow
physics in this type of inlet. This explicit detailing of the method for initializing
the flow through the inlet will be of use in any future experimentation. The
second objective is to present results for two bleed boundary conditions and to
compare the results from modeling discrete bleed holes with the more
conventional approach using bleed slots. The third and final objective of this
research is to introduce the problem of controlling the effective-area through use

of combined suction and bleed; this will be presented in later sections.

2.3 Descrigtion of Problem Studied and Methods Employed

2.3.1 Problem Description

The flow simulation studied involves a uniform, supersonic freestream flow
incident upon and passing through an axisymmetric mixed-compression inlet.
The main features of the inlet (Figure 2.1) consist of a centerbody, a cowl with
both interior and exterior surfaces, bleed holes on both the centerbody and
interior cowl surfaces, and an engine compressor face that is downstream of the
throat. Other features of the inlet, such as the bypass valves and the bleed hole

plenums, are not utilized in this study.

34

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ocean. em
82m .38

mean. oEmcm
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ED 335

no. D. So
32m C Fr .: o

35

 

I
i
3
i
l
I
s. ..

CE

0t
thr
SU
is i
SI):

sul

Within the inlet, the approaching supersonic flow is first decelerated and
turned by an oblique shock that forms from the centerbody tip (Figure 2.2). At
the inlet’s designed operating conditions, the primary oblique shock terminates
on the lip of the cowl, thereby preventing any of the turned flow from being
diverted past the inlet. This defines a capture diameter (D) for the inlet because
all of the freestream flow within this capture diameter is passed through the inlet.
If, for some configuration, the primary oblique shock does not terminate on the
cowl lip, some of the flow that would have been available for use by the engine is
diverted over the cowl; this is referred to as “spillage.” When “spillage” is
present, the inlet is less efficient.

The flow that was turned by the primary oblique shock travels up the
centerbody ramp and enters the supersonic diffuser section of the inlet.
Upstream of the throat, in the converging section of the inlet, a series of weak
oblique shocks are formed and the flow is decelerated as it approaches the
throat. Just past the throat, a normal shock forms and the flow transitions from
supersonic flow to subsonic flow. In the configuration studied, the terminal shock
is intentionally held close to the throat and the terminal shock is a weak normal
shock. The remainder of the diverging section of the inlet now functions as a
subsonic diffuser and the flow is further decelerated as it approaches the engine
face.

To maintain the flow through the inlet, the low-momentum fluid near the
wall is suctioned (bled) through a series of discrete bleed holes. Without this

boundary layer bleed, shock waves interacting with the boundary layer will cause

36

Vr
d COWI
Cowl Translation

Primary
Oblique Shock ‘ F

 

 

 

 

 

 

 

Centerbody

Terminal Shock

Bleed Hole Locations

Figure 2.2 General flow pattern observed in the mixed-compression inlet

operating at design conditions.

37

1h

F6

9 i

j |

a;
l

 

“flit!!! 4H 1

‘i

the flow to separate and the inlet will unstart. For the configuration studied in this
research, no spillage is indicated, and the experimental bleed rate was given as
8.2 percent of the mass flow rate for the captured flow.

The prototype inlet simulated in this study was acquired from wind tunnel
studies done by Smeltzer and Sorensen (1973). The prototype inlet is
approximately one-quarter scale and has a capture diameter of D = 38.8 cm (R =
19.4 cm). The supersonic diffuser was designed for operation at a Mach number
of 2.65. It was also designed with the objective of achieving optimal efficiency at
the design conditions while permitting a large mass flow rate at a low Mach
number flight and minimizing the length of the inlet to address internal drag
issues. With this prototype inlet, the cowl was translated to change the inlet
profile during the initialization of the flow within the inlet.

For this research, the properties of the inlet were examined at the design
condition (Mach 2.65) and for a single configuration of the bleed holes
(configuration C). At the design condition, the cowl lip is positioned downstream
of the centerbody tip at x/R=2.325 (Figure 2.3), where x is the distance as
measured from the centerbody tip. The engine face, fixed for all configurations,
is located at x/R = 6.800 as measured relative to the centerbody tip.

The location of the bleed holes on the inlet cowl and centerbody walls, for
the configuration studied (bleed hole configuration C), are shown in Figure 2.4.
Each bleed hole has a diameter of d = 0.0125R, where R = D/2. For the inlet’s
design Mach number, this hole diameter is anticipated to be of the same order as

the momentum thickness at the throat and is typical for this type of problem.

38

A;

 

Sore

Struts
(three equally spaced)

Cowl
translation I

2.2l9 4.582

 

   
 

 

 

D:- 388 cm ([525 in I

\ ,_
Xc/R=O

 

 

 

 

 

 

 

 

 

 

 

 

74°C.
885°

 

Figure 2.3 Model schematic for the mixed-compression inlet (Smeltzer and
Sorensen, 1973).

39

d

_:0.0125
F?
(all holes) .2 = 0.0322
R b
_=0.0186
O 000 R
O 0
000
X ID at 3 ID Cowl
—=:a E "28
x n .. ~ — as
R: 8 8 8. '2 “I“!
T :0 ¢ V V?

Centerbody

Bleed Divider

Figure 2.4 Bleed hole configuration (configuration C) on cowl and centerbody
(Smeltzer and Sorensen, 1973).

40

For the bleed configuration studied, there are four discrete bleed zones.
Zones 1 and 2 are upstream of the throat region and are located on the cowl and
the centerbody, respectively. On the centerbody, the bleed has been divided in
to two clusters. The first is placed significantly upstream of the throat to minimize
the boundary layer growth. The second Cluster of bleed holes is placed just
upstream of the throat and is intended to prevent separation that will arise from
the dynamics of the shock-wave/boundary-layer interaction because of the
persistent reflecting oblique shocks. Bleed zones 3 and 4 are placed at the
throat region and are intended to control the boundary layer thickening that will

occur both before and after the terminal shock. In Figure 2.4, the measurements
of XJ R for the cowl surface reference the distance from the cowl lip, whereas

those measurements on the centerbody surface are referenced from the
centerbody tip. Additional details regarding the geometry of the inlet, the bleed
configuration, and the design of the inlet can be found in Smeltzer and Sorensen
(1973)

For the simulations described in this paper, the inlet described in the
previous paragraphs is taken to be stationary and a uniform flow approaches at
zero angle of attack. The freestream static temperature, pressure, and Mach
number are 129.8 K, 4,700 Pa, and 2.65, respectively. This leads to a total
pressure of approximately 1 atmosphere (1 atm). The Reynolds number per

meter, based on the freestream conditions, is 8.53 x 106.

41

2.3.2 Problem Formulation

The problem described in the previous section is modeled by the
Reynolds—averaged conservation equations of mass (continuitY); momentum ( a
modified form of the thin-shear layer, compressible Navier—Stokes equations),
and total energy for a thermally and calorically perfect gas with Sutherland's
model for themal conductivity. Turbulence is modeled by the shear-stress
transport (SST) model of Menter (Menter, 1992 and Menter, 1993). Additional
details of the governing equations are available in the C_F|_3i User’s Manu_al

(Version 5.0) by Biedron et al. (1996).

2.3.3 Boundary Conditions

Although the mixed-compression inlet studied is geometrically
axisymmetric and the angle of attack is zero, the inclusion of the discrete bleed
hole configuration in the simulation makes the problem three-dimensional. In
these simulations, a 2.5 degree wedge of the inlet is modeled; this angle of the
wedge is just large enough for the bleed hole patterns to repeat in the azimuthal
direction for bleed configuration C. Figure 2.5 details the bleed hole patterns on
both the cowl and the centerbody and indicates several key measurement
locations. At the two boundary planes in the azimuthal direction (solid lines in
Figure 2.5), periodic boundary conditions were imposed.

The boundary conditions applied at the other boundaries of the flow
domain (shaded area in Figure 2.6) are as follows. At the inflow boundary, all

flow variables were specified at the freestream conditions. At the freestream

42

periodic boundary

 

 

 

 

V V V \7 , V O V
A IIILIZIIIZZIZZQ.LILII.ILLI.1)I.Q_ii.......l.llj.Q.llifflj.....{21...},a;.l.ILIIII..I.I.I.ZIZ’"I...ILZ....A:
(x-x,)/R=1 .556 (x-X.)/R=1 -797 D
(a)
x/IR=3.905 x/R=4.033 x/R=4.161 C’
\J V I \J i O U
A ................... Q ................................. x9 .................. 0 ..................... *3 ................... ....... A'
B ........ h ................... A ....................................................... m ........... b' ....... G ....... m ....... B’
(b) C

Figure 2.5 Details of the bleed hole configuration (configuration C) and
measurement locations for (a) the cowl surface and (b) the centerbody surface of
the axisymmetric, mixed-compression inlet. Freestream flow is from left to right.

R = capture radius, xc = location of cowl lip.

43

 

 

int)
he

Fig-

Sim

 

Figure 2.6 Boundary condition schematic for the mixed-compression inlet
simulations.

 

Mule

lmedr

 

wihn
melt
dose

Imemi

mmm:

denst

 

 

{95681:
comp'
subsc;

lssue

 

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adu

boundary, exterior to the cowl, all of the flow variables were also specified at the
freestream conditions. At the outflow boundary, the flow is supersonic, except
within the very thin boundary layer that forms on the exterior surface, and all of
the flow variables were extrapolated. The location for the outflow boundary was
chosen to be far enough from the region of interest so that any effects due to the
interaction of the boundary layer with the boundary condition would be
minimized.

At the compressor face, a back-pressure (Pb) was imposed, and the
density and velocity were extrapolated. In the simulations conducted in this
research, a converging section was appended to the engine face of the mixed-
compression inlet. This was done to address an issue that developed in the
subsonic diffuser section of the inlet downstream of the terminal shock. This
issue and the reasons for appending a converging section are addressed in the
Results section (Section 2.5). The effect of adding this converging section is
equivalent to simply shifting the compressor face boundary downstream from its
actual location; the flow is still subsonic as it exits the domain. At all solid
surfaces, the no-slip condition was imposed. These surfaces were treated as
adiabatic walls and a zero normal-pressure gradient was also imposed.

The boundary conditions used for the turbulence model are as follows.
On the wall, the turbulent kinetic energy (k) is set to zero, and o) (the dissipation
rate per unit k) is set equal to 60v/(B Ayz). In that boundary condition, [3 equals to
3/40, and Ay is the normal distance of the first grid point from the wall. The first

grid point from the wall must be within a y+ of unity. At the inflow, k is set to zero

45

 

andcr

wWGC

wwla
numer
Need
Hahn

l

The a1

Rlnhr

9nnfl%
ltgel
edes

”Owiq

 

bounc
Abtat
iQQ:

“UV-

and

and a) is set so that the flow is effectively laminar. At all other boundaries, k and
(n were extrapolated.

To address the bleed through the discrete holes that occur on both the
cowl and centerbody surfaces, two approaches are available when conducting
numerical simulations. The first approach is to simulate the flow in the entire
bleed system, including the flow through each bleed hole and the plenum (cf.
Hahn etal., 1993; Shih eta/., 1993; Chyu etal., 1995; Hamed etal., 1995;
Rimlinger etal., 1996; Rimlinger etal., 1996; Lin etal., 1997; Flores etal., 1999).
The advantage of this approach is that the physics of the bleed process is
simulated by using first principles. The disadvantage, however, is that a very
large number of grid points or cells would be needed to resolve the flow in the
holes and the plenum. The second approach is to model instead of simulate the
flow in the bleed holes and the plenum by using what are referred to as bleed
boundary conditions, which are applied on surfaces where bleed is to occur (cf.
Abrahamson etal., 1988; Paynter etal., 1994; Lee eta/., 1994; Harloff etal.,
1995; Benson et al., 2000; Shih et al., 1997). By not resolving the bleed holes
and the plenum, fewer grid points are needed and this leads to greatly reduced
memory and CPU-time requirements. From a computational efficiency point of
view, the second approach based on bleed boundary conditions is preferred;
however, its usefulness hinges on the accuracy of the bleed boundary conditions
in modeling the relevant physics (Shih et al., 1997).

Until only just recently, most bleed boundary conditions have treated each

bleed patch (i.e., a region with bleed holes) as a porous surface. With these

46

I_ ‘:I

types *
repres
Abram

bounc

cons»:

disreg

 

been:

 

bleed ‘

 

accoe
J

imprei

 

differe

the re

 

2001 )

 

 

One g:
W68 8

new

types of models, the information on hole geometry and arrangement is not
represented (cf. Chyu etal., 1986; Kawamura et al., 1987; Chyu eta/., 1992;
Abrahamson etal., 1988; Benhachmi etal.,1989). The focus of these bleed
boundary conditions has been on acquiring the correct bleed rate, which is
considered to be the most important part of the bleed process. However, by
disregarding the bleed hole geometry some aspects of bleeding a supersonic
boundary layer are lost. In particular, the “barrier” shocks that occur inside the
bleed holes and the influence of those shocks on boundary-layer control are not
accounted for in these models. Paynter et al. (1994) and Lee et al. (1994)
improved the porous-wall type bleed boundary conditions by adding a partial
differential equation that resembles a one-equation turbulence model to model
the roughness effects induced by the bleed process. Benson et al. (2000 and
2001) presented a non-porous-wall bleed boundary condition in which at least
one grid point is within each bleed hole. With such a bleed boundary condition, it
was shown that it is possible to get the bleed rate correct and to account for
many of the effects of the “barrier” shock.

In this current study, the bleed boundary condition developed by Benson
et al. (2000 and 2001 ) is employed to model the effect of bleed through the
discrete holes without having to simulate the flow through the bleed hole and its
associated plenum. The investigators developed this bleed boundary condition
using simulations of choked bleed that resolve the holes and the plenum as a
guide and they demonstrated that the bleed boundary condition was effective at

capturing the relevant physics of the bleed process and its effects on the flow,

47

even in a coarse grid simulation where the bleed is modeled with only one point
per hole.
In this bleed boundary condition, the normal velocity, W, is calculated as a

function of the local sound speed at one grid point above the bleed hole by using

a discharge coefficient, that is, W = - CD (HP/p , where CD, the discharge

coefficient, is a constant over the entire hole, and y is the ratio of the specific
heats. Its value is chosen to ensure the correct average normal velocity over the
bleed hole on the basis of simulations that resolved the flow through each bleed
hole and plenum. The density (p), pressure (P), and the other two velocity
components in each hole are extrapolated by assuming zero normal derivatives.
The total energy is then computed by using the equation of state.

In these simulations, the above bleed boundary condition was
implemented in two ways. In the first method, the locations of the bleed holes
are discerned (i.e., at least one grid point represents the location of each bleed
hole with the CD distributed over a cell face about that grid point). In the other
bleed boundary condition employed, each row of bleed holes is modeled as a
porous surface (bleed slot) with a width equal to the hole diameter and where the
number of bleed holes in each row is accounted for by adjusting the discharge
coefficient to give the correct bleed rate. For the porous-surface bleed boundary
condition, the problem becomes two-dimensional axisymmetric with a
corresponding reduction in the number of grid points in the azimuthal direction

from 13 to 2.

48

2.3.4 Numerical Method of Solution

Solutions to the governing equations described in the previous section
were obtained by using a cell-centered, finite-volume code called CFLBD
(Thomas et al., 1990 and Rumsey et al., 1993). All inviscid terms were
approximated by the flux-difference splitting of Roe (1981 and 1983) (third-order
accurate) with the slope limiter of Chakravarthy and Osher (1983). All of the
diffusion terms were approximated conservatively by differencing derivatives at
cell faces. Since only steady-state solutions were of interest, time derivatives
were approximated by the Euler implicit formula. The system of nonlinear
equations that resulted from the aforementioned approximations to the space-
and time-derivatives were analyzed by using a diagonalized altemating-direction
scheme (Pulliam et al., 1981) with local time-stepping (local Courant number
always set to unity) and a three-level V-cycle multigrid (Ni, 1981 and Ramsey et

al., 1988).

2.3.5 Grid Structure

The multi-block structured grid system used is shown in Figure 2.7. It has
1,391,676 grid points and is made up of four blocks that are connected through
both grid patching and overlapping. In addition, all dimensions are designed so
that multigrid methods can be used and accommodations have been made so
that each patch and overlapping region, as well as bleed hole, can be fully

included in the multigrid.

49

 

:igl
lile

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

_ _: _
z : _
V Z _
H :
_ I
H 2
H :
H H
_ I
B: Z
:_ B:
dHZ: 2:
E _
ICZj. _:
.4

I u

I _
a
I. m

I x a m.
WIVU _ ..
“lei. ,I_.f, f
t ii .I. is
i ,ildlwil

,fi. .

 

       

TLII r: Ea”
14+ T, L . ,
Lulu»? .32.?
I use,
til-Isl. , .
. . III-.5. ,

Figure 2.7 The four block, multigrid system employed in simulations of the

mixed-compression inlet.

 

Block 1 fills the region between the centerbody and the cowl from the
inflow boundary to the compressor face/inlet exit. This grid with dimensions 861
x 13 x 41 (13 grid points in the azimuthal direction) provides a fairly uniform
distribution of grid points. Within Block 1, the aspect ratio is near unity
everywhere so that shook reflections and interactions can be accurately resolved.

To capture the flow exterior to the cowl surface in the event of spillage, a
second grid, Block 2, was patched to Block 1 and continues along the exterior
surface of the cowl until such a point where the shock from the cowl lip would
pass out of the downstream, outflow boundary. Block 2 has dimensions 333 x 13
x 33 and is similar to Block 1 in that it has a fairly uniform distribution of grid
points with near unity aspect ratio near the patched surface. Because of its
limited use in the analysis of the simulation, the grid for Block 2 is intentionally
not of sufficient grid spacing to resolve any of the boundary layer development on
the exterior cowl surface.

The third grid, Block 3, has dimensions 621 x 13 x 41 and overlaps Block
1 near the centerbody surface. Block 3 is included to provide the fine grid
resolution needed to resolve the boundary layer that develops next to the
centerbody. Near the surface, large aspect ratios exist because of the difference
between the normal spacing required to capture the boundary layer and the
coarser streamwise grid spacing. With this grid, it was determined that the
streamwise spacing should be as close as possible to the main interior grid,
Block 1. One reason for this restriction is that the length scales for these two

directions are so disparate that any attempt to satisfy one of them would lead to

51

large aspect ratios in either the middle of the inlet or near the walls. This
restriction on the streamwise spacing was also necessary to prevent interpolation
errors that might result as the oblique shocks pass from one grid to the other.
Another feature of Block 3 is that it was extended forward of the centerbody tip to
the inflow boundary so as to properly capture the oblique shock forming off of the
centerbody tip.

To resolve the boundary layer that forms adjacent to the interior cowl
surface, a fourth grid, Block 4, is overlapped to the first grid, Block 1. Block 4,
with dimensions 145 x 13 x 41, also overlaps Block 1 and provides the fine grid
resolution needed to resolve the boundary layer next to the cowl. Block 4,
however, cannot be extended forward to the inflow boundary in the same manner
that Block 3 was extended.

For both Block 3 and Block 4, the first grid points away from the
centerbody and cowl all have a y+ value less than unity. In addition, the first five
grid points away from these walls all have y+ values less than 10. For these
simulations, an initial value for y+ was determined by treating the inlet as a flat
plate. As the simulations progressed, the value of y+ was re-assessed and

corrections were made to the grids to provide appropriate adjustments.

2.4 Method for lnitiali_za_tion of Flow “fihin the Inlet

One of the more difficult aspects of simulating flow through mixed-
compression inlets is the method used to initialize the flow field within the inlet.

Although the problem appears to be amenable to a solution using one-

52

dimensional isentropic theory, the presence of oblique shocks in the flow
complicates matters to such a degree that special considerations need to be
developed and implemented to initialize the flow throughout the inlet.

Simulating critical flow in a mixed-compression inlet is difficult for several
reasons. The first problem involves the transients that may develop during the
initialization of the flow. In the converging section of the mixed-compression
inlet, the flow rate through the inlet is a constant, but the flow is supersonic and
the cross-sectional area changes along the flow direction. If the initial conditions
are inappropriate, then complicated transients may create disturbances that
either cause the flow to unstart or require the need for an exorbitantly large
number of iterations to damp or remove the disturbances. A second difficulty
arises from the fact that, for a given area ratio between the capture area and the
throat area, only a range of flow rates and Mach number distributions are
possible. The problem here is that any deviations from this distribution that arise
during the flow initialization procedure may be unrecoverable.

In addition to the above difficulties, several other problems arise from the
dynamics of the flow through the inlet. For example, once the flow has been
established, the shock-wave/boundary—Iayer interactions and the boundary-layer
bleed cause the displacement thickness within the inlet to change. This change
in the displacement thickness will affect the effective-area ratio of the inlet and, in
turn, cause all the flow properties of the inlet to adjust to the new configuration.
As the flow is developing, the interaction of the boundary layer with the effective-

area ratio of the inlet becomes a critical and difficult parameter for control.

53

In addition to the problem associated with the displacement thickness, the
location of the terminal shock is another complicating factor. The location of the
terminal shock depends strongly on the back-pressure imposed at the
compressor face; however, it also depends on several other factors such as the
bleed rate, bleed hole configuration and the geometry of the inlet. In addition, if
the terminal shock is moving, the effects of any compensatory changes in the
back-pressure will not arrive at the terminal shock location in time to arrest its
motion because the compressor face boundary is so far away from the throat.
Finally, although the mass flow rate for the boundary-layer suction is known for
this problem, the physics of the flow field above the bleed holes is not. Changing
bleed locally to stabilize the shock location can, therefore, cause transient
disturbances that end up destabilizing the location of the terminal shock.

The method described below outlines the best of the approaches that
were used in initializing the flow through the mixed-compression inlet. Care has
been taken to illuminate the special problems that occur at each junction in the
solution process and to explain the reason for the proposed steps. Since each
problem and the geometry associated with it is unique, knowledge of the general
issues faced will allow future users to anticipate and prepare for all eventual
problems. The method proposed takes special advantage of a slow start
boundary condition to move from CFL3D’s default initial condition, where all
values set to freestream conditions everywhere, to a situation where the flow
upstream of the throat region is converged. The slow-start boundary condition is

a solid-wall boundary condition where the effects of the wall are gradually faded

54

into the simulation. In other words, with the slow-start boundary condition, the

fluid can initially pass through the surface as if it were not present in the flow. As

the number of iterations increases, the normal velocity of the fluid passing

through the surface is reduced until the wall is completely “faded in” and

impenetrable.

1.

The method for initializing the flow proceeds as follows:

Beginning with a coarse and uniform grid, the freestream conditions are
used as the initial condition for entire flow field. Supersonic inflow
boundary conditions are applied at the inflow boundary (all variables are
specified), and supersonic outflow boundary conditions are applied at the
outflow boundary and compressor face (all variables extrapolated).
Before initiating the code, it should be decided where the terminal shock
should be located downstream of the throat. We suggest choosing a
location substantially downstream of the desired final position. The
reasons for this are explained in step 10.

Slow-start, inviscid wall boundary conditions are applied on the inlet walls
and the code is run until the flow upstream of the intended terminal shock
location has converged. It should be noted that it is unnecessary for the
entire flow field to be converged because the geometry and the grid
employed in the diffuser section of the mixed-compression inlet is not
intended to resolve supersonic flows with embedded shocks. At the
conclusion of this step, a solution that involves supersonic flow throughout

the mixed-compression inlet is obtained. This is referred to as

55

supercritical flow. The slow-start, inviscid wall boundary condition initially
treats all solid walls as completely porous so that flow can penetrate the
walls and then, over a finite number of time steps, the walls are made less
and less porous until they are impermeable.

. From this intermediate solution, the average static pressure, Mach
number, and temperature are calculated just upstream of the intended
terminal shock location. These values will be used in one-dimensional
normal shock relations to determine the flow conditions on the
downstream side of the terminal shock.

. One-dimensional isentropic relations are applied to determine the solution
from the downstream side of the shock wave to the compressor face,
taking into consideration changes in inlet’s cross-sectional area. Since the
geometry in the subsonic diffuser may not meet the slowly varying
requirements of the one-dimensional isentropic relations, some leeway
should be accounted for when imposing the theoretical solution.

. The solution obtained under step (3) for the region upstream of the
terminal shock is combined with the solution obtained under step (5) for
the solution downstream of the terminal shock. The combined solution is
used as the new initial condition for the inlet.

. Slow-start inviscid wall boundary conditions are applied from the location
of the terminal shock to the compressor face and the code is run again. At
the conclusion of this step, a converged, inviscid critical-flow through a

mixed-compression inlet is obtained.

56

8. To speed up steps (1) through (7), a coarse grid could be used. If a
coarse grid is used in these steps, the solution must now be interpolated
to a fine mesh to account for viscous effects and bleeding next to the
centerbody and cowl. In this study, Blocks 1 and 2 were used to carry out
steps (1) to (7). Blocks 3 and 4 were then added to account for viscous
effects and bleeding. To make the code more robust, first-order upwind
could be used in the beginning and then later transitioned to higher-order
accurate differencing formulas.

9. Using the converged, inviscid critical-flow solutions as initial conditions,
the code is run with viscous wall boundary conditions and bleed initiated
simultaneously. This will allow for the development of the boundary layer
and prevent separation that may arise from the interaction between the
oblique shock waves and the boundary layer.

10.The terminal shock location is then adjusted by fine-tuning the imposed
back-pressure and the amount of bleed. Unfortunately, there is a
difference in the response delay between the bleed and the back-
pressure. Because bleed is a local phenomenon, changing the amount of
bleed causes the terminal shock to move almost instantaneously.
However, when the back-pressure is changed at the compressor face or
inlet outflow boundary, the changes in back-pressure take time to be felt at
the terminal shock location. Since the final terminal shock location

depends on the combination of imposed back-pressure and bleed, the

57

7. “h

 

 

In... .. .I Lilli). LI. 4!! Ir
r _

 

process of moving the shock should be accomplished incrementally. This

difficulty can be accentuated if large pressure waves are present.

2.5 Results

The computed Mach number and pressure distributions for an
axisymmetric mixed-compression inlet at zero angle of attack with boundary-
layer bleed are shown in Figure 2.8 and Figure 2.9. Figure 2.9 also displays
pressure contours along the cowl and centerbody surfaces in the bleed region.
Both of these figures represent the results of the simulations where the bleed
regions were modeled as discrete holes. These figures show that the expected
shock-wave structure involving oblique shock waves, their reflections, and the
terminal shock are well resolved. For example, the oblique shock generated by
the centerbody tip terminates on the cowl lip with near zero spillage; the reflected
shocks within the supersonic diffuser are well defined; and the terminal shock is
held by the bleed just downstream of the throat. The shock exterior to the cowl
surface is not as well resolved as the interior shocks; however, as was noted
previously, the exterior features were only included to allow for spillage to exist, if
present at all, and not for measuring surface drag or for any other analysis.

Although not obvious in Figure 2.8, a large separated region exists in the
subsonic diffuser section next to the centerbody. This separated region extends
all the way to the compressor face and was unaccounted for in the prototype
experiments: there was no experimental evidence to suggest that it did or did not

exist. Several methods were employed to test the legitimacy of the separated

58

2.7

148 Mach
()9 Number

9.0

 

 

 

Figure 2.8 Mach number contours along centerline for the bleed boundary
condition that resolves individual bleed holes (bleed-hole boundary condition).

59

 

 

 

. 4' : ‘ . , ,7-, ’f
TF’I’ESSLIFB 096 227 357 4187 1317 748 878 1008 1139 1269 J

  

/‘

Figure 2.9 Pressure contours along centerline and solid surfaces for the bleed
boundary condition that resolves individual bleed holes (bleed-hole boundary
condition).

60

region, and the results from all of these tests were inconclusive. It is supposed
that the separation could be a result of (1) a coarse database for constructing the
geometry or (2) an artifact of the start-up procedure when the shock was moved
to the throat region.

Re-circulating flows at the outflow boundary can be problematic because
flow both enters and exits at the boundary. To solve this problem, a converging
section was added to the end of the inlet at the compressor-face location. With
this converging section attached, the flow re-attaches downstream of the
compressor face before exiting the computational domain. Although the
pressure at the outflow boundary is no longer comparable with the back-pressure
referenced in the experimental literature, all of the flow will be moving outwards
at the outflow boundary.

When a comparison is made between the hole-disceming bleed boundary
condition results and the row-slot bleed boundary condition results that shown in
Figure 2.10 and Figure 2.11, it is clear that the hole-disceming bleed boundary
condition predicts a more complicated shock structure in the bleed region than
does the slot-row bleed boundary condition. With both bleed boundary
conditions generating the same bleed rate, this more complicated shock structure
in the bleed region is most likely the result of the bleed variation in the azimuthal
direction that is produced when the holes are discretely modeled.

Figure 2.12 compares the average total pressure within a cross-section of
constant x/R between the hole-disceming bleed boundary condition and the row-

slot bleed boundary condition. The data, normalized to the average total

61

 

 

 

Figure 2.10 Mach number contours along the centerline for the bleed boundary
condition that treats each row of bleed holes as a slot (bleed-slot boundary
condition).

62

 

 

unhalizedPressure 096 227 357 48.7 617 748 878 100811391269 ]

   

J /

Figure 2.11 Pressure contours along the centerline and solid surfaces for the
bleed boundary condition that treats each row of bleed holes as a slot (bleed-slot
boundary condition).

63

3.5

 

 

3-0 w ——+— holes
[3 ~ slots
C.
:5
33 25
2 ' ‘
a.
7.3
O
E-‘ ,
Q) ,
OD .
8 2.0 .- '
a) .
> ,.
< e
,9
1.5 l '
,3
3"" Mar-“51
10j+-_fl_,_,_—T — ' T I r
-o.5 0.5 1.5 ”R 2.5 3.5

Figure 2.12 Average total pressure within a cross-section of constant x/R.

 

 

 

 

 

 

 

4.5

Normalization is with respect to the average total pressure within a cross-section

of the freestream capture-area of the inlet. The cowl lip is located at x/R = 1.

64

pressure in a cross-section of the freestream capture area, indicates that the flow
upstream of the bleed region (x/R = 3.87 — 4.23) is identical for each of the bleed
boundary conditions studied. The differences in the average total pressure
observed in the bleed region of Figure 2.12 are due to the differences that exist
in the shock-wave structure formed by these two bleed boundary conditions.
Downstream of the bleed region, the hole-disceming bleed boundary condition
yields a slightly higher average total pressure than the row-slot bleed boundary
condition.

Figure 2.13 compares the predicted surface pressure on the centerbody
and cowl with experimentally measured values. The comparison is reasonable
considering that the CFD study bled 10.2 percent of the captured flow, whereas
the experimental study bled 8.2 percent. However, the CFD study predicts
oscillations in the surface pressure created by the bleed process. that were not
evident in the experimental measurement. The two bleed boundary conditions
yielded similar results, although the row-slot bleed boundary condition yielded a
slightly higher pressure downstream of the bleed region.

Regarding the oscillations in pressure about the bleed region that were
predicted by the CFD study but not observed in the experimental results (Figure
2.13), it should be noted that CFD simulations that resolve the flow through each
bleed in detail (Shih etal., 1993; Chyu etal., 1995; and Rimlinger etal., 1996)
show that the bleed process creates a “barrier" shock in each bleed hole. This
process is a source of pressure oscillations and it is therefore possible that the

measurements in the experiment were not made over the bleed holes.

65

PIP_inf

20~

 

 

   
 

 

~—A— experimental (8.6% bleed rate)
+simulation - holes (10.2% bleed rate)
+simulation - slots (10.2% bleed rate)

 

 

T fl

4.1 4.3 4.5

 

 

4.1 4.3 4.5

(b) cowl

Figure 2.13 Surface pressure, predictions versus measurements.

66

 

Figure 2.5 details the bleed configuration for the hole-disceming bleed
boundary condition and indicates the locations selected for comparing the Mach
number and pressure profiles of the two simulations. Figure 2.14 and Figure
2.15 compare the Mach number profiles on the cowl and centerbody predicted by
the two different methods of implementing the bleed boundary condition. From
these figures, it can be seen that at 10d upstream of the bleed region (d = bleed-
hole diameter), the Mach number profiles are identical for the hole-disceming
and the row-slot bleed boundary conditions. At a point midway between the two
bleed patches, a significant difference can be seen. In this region, the row-slot
bleed boundary condition and the hole-disceming bleed boundary condition
produce nearly identical profiles near the surface; however, the row-slot bleed
boundary condition generates significantly higher Mach number flow near the
centerline. At 5d and 15d downstream of the bleed region, the hole-disceming
bleed boundary condition produces a fuller Mach number profile than predicted
by the row-slot bleed boundary condition. This result indicates that the bleed
rate, on its own, does not determine the velocity profile downstream of the bleed
region. It also demonstrates that concentrated bleed at selected locations, such
as bleed holes, is more effective in creating a fuller profile than the same bleed
spread out over a slot.

Figure 2.16 and Figure 2.17 illustrate the variation of the Mach number
profiles in the azimuthal direction on the centerbody. The data in Figure 2.16,
comparing the hole-disceming and the row-slot bleed boundary conditions, were

acquired at the same streamwise locations as in Figure 2.15, but on a different

67

 

 

 

 

 

 

 

 

 

 

 

CI: 0.12 'e e
\ t
N I“
I ;_
é a
N 0.06 j~
E
0.1141191121w1‘4‘LA‘ 1 11111111 111
0 0.5 1 1.5
Mach Number
(60
:_ x
0.12 :-
0: L
\ .
N ' 3
I Z .
1:1. 9 -’
: 4
T r’
L
000 ‘r 1 ;1 1 21 'se‘ 31”}: J 1
0 0.5 1.5
Mach Number

(b)

Figure 2.14 Mach number profile on cowl surface along centerline (A-A’, Fig. 8)
at (a) 10d upstream of bleed, (b) mid-way between 2 bleed patches (point a’, Fig.
7), (c) 5d downstream of last row of bleed holes (D-D’), and (d) 15d downstream

of last row of bleed holes.

2 = radial coordinate, Zwall = local wall coordinate, d = bleed-hole diameter

68

Figure 2.14 (cont’d)

 

 

 

 

 

 

 

0.12 :

 

Mach Number

(C)

 

_
4
0.
0

m \ AN 1 =98

0.12 -
0.08 _—

00711

 

 

0.

0.6

0.4

0.2

Mach Number

(d)

69

 

 

 

 

 

 

    

 

 

 

 

 

0.15 - \
----~--- Slots <1
9 Hobs j
\
’23 1’
N In
1
El 005 - ..
04 4 1 1 1 1 1A
0 0.5 1 1.5 2 2.5
Mach Number
(8)
0.15 7
Ir
m 0.1 -
\ :
’8 ;
N .
I
[xi 0.05_e
0: 11111l|ll11LL111111144
0 0.25 0.5 0.75 1 1.25

Mach Number
(b)

Figure 2.15 Mach number profiles on centerbody surface along centerline (A-A’,
Fig. 8) at (a) 10d upstream of bleed, (b) mid-way between 2 bleed patches (point
a, Fig. 7), (0) 5d downstream of last row of bleed holes (GO), and (d) 15d

downstream of last row of bleed holes.

2 = radial coordinate, 20 = local wall coordinate, d = bleed—hole diameter.

70

Figure 2.15 (cont’d)

 

 

 

 

 

 

 

 

0.15
0: 0.1
\
’8
N
I
N
v 0.05
0 4
0
0.15 '
CE
\ 0.1 ’
’8
N
l
N 1
0 4

 

 

 

 

0.25 0.5 0.75
Mach Number
(0)
.1
f
;
'1 <1
’1 Cl
0.25 0.5 0.75
Mach Number
(d)

71

 

0.15 f

. --n+- She
0-12 T 0 Holes ,,

 

 

 

 

0.09 - 41

0.06 l

(z—zm/R

 

0.03

    

I l L J

 

0 0.5 1 1.5 2 2.5
Mach Number
(3)

0.15 r
0.12 -

0.09 }

a—zm/R

0.06 -

0.03 _-

 

 

 

ofigfw‘" 11.11.11.11111111111
0 0.25 0.5 0.75 1 1.25

Mach Number
(b)

Figure 2.16 Mach number profile on centerbody surface along B-B’ (Fig. 8) at
(a) 10d upstream of bleed, (b) mid-way between 2 bleed patches (point b, Fig. 7),
(c) 5d downstream of last row of bleed holes (C-C’), and (d) 15d downstream of

last row of bleed holes.

2 = radial coordinate, 20 = local wall coordinate, d = bleed-hole diameter.

72

Figure 2.16 (cont’d)

l
0.75

 

0.5

 

0.25

 

 

 

 

 

 

Mach Number

(0)

 

 

 

 

0.75

0.5

0.25

Mach Number

(d)

73

 

0.15 -

 

 

 

 

 

 

 

 

 

L

- __.__ Holes (A-A') ..

~——-«-—-—- Holes (B-B') .j
E 0.1 -

\ 11

”'5 1

N <1
I .

u 0.05 '- 4)

0F1L91151¢13-AIA/11
0 0.5 1 1.5 2 2.5
Mach Number
(a)
0.15 _-
m 0.1 E
\ C
’8 _
N .
I I
N 0.05 f
0b "111411111111111111111
0 0.25 0.5 0.75 1 1.25

Mach Number
(b)

Figure 2.17 Mach number profiles on centerbody surface for the hole-disceming
bleed BC along A-A’ and B-B’ (Fig. 8) at (a) mid-way between the two sets of
bleed patches (point c, Fig. 7), (b) mid-way between 2 bleed patches (point b,
Fig. 8), (0) 5d downstream of last row of bleed holes (C-C’).

Z = radial coordinate, 20 = local wall coordinate, d = bleed-hole diameter.

74

(Z—Zo)/R

Figure 2.17 (cont’d)

 

 

 

 

 

 

 

 

 

 

0.15 -
-—-e— Holes(A-A')
Holes(B-B')
0.1 -
0.05 r
0 ‘ 1 l 1 1 l 1 1 1 1 I
0 0.25 0.5 0.75
Mach Number
(C)
0.15 —
0.1 — J.
0
0.05 "' 41

 

 

 

0 0.25 0.5 0.75
Mach Number

(d)

75

azimuthal plane. The results in this alternate azimuthal plane, Figure 2.16, are
similar to the centerline results with only a slight difference in the near-wall
behavior around the bleed holes. This difference is anticipated and explained by
the presence of the discrete bleed holes. Figure 2.17 displays the variation in
the azimuthal direction for the hole-discerning bleed boundary condition. The
results for the hole-disceming bleed boundary condition show significant
differences existing in the azimuthal direction only in the region near the bleed
holes and confined to near the surface. The data for the row-slot bleed
boundary condition, however, displays no variation in the azimuthal direction and
is not shown.

Figure 2.18 and Figure 2.19 compare the pressure distributions predicted
by the two different methods of implementing the bleed boundary condition on
the cowl and centerbody. From these figures, it can be seen that at 10d
upstream of the bleed region, the pressure distributions are identical for the hole-
discerning and row-slot bleed boundary conditions. At a point midway between
the two bleed patches, a considerable difference can be seen in the two profiles.
At 5d and 15d downstream of the bleed region, both bleed boundary conditions
gave similarly shaped distributions. At these locations, the row-slot bleed
boundary condition yielded higher pressures than the hole-disceming bleed
boundary condition, indicating that the row-slot bleed boundary condition created

a stronger terminal shock than the hole-disceming bleed boundary condition.

76

0.18 -

 

 

 

 

 

 

 

 

 

 

Ct .
2 127
o F
N .
I L
\N/ P
0.06 :—
0 :1 '
1.5
P/Pinf
0.18 .
1
t
a: _ i
; 0.12_ I
O » r
N f
I 1
E 1'
0.06 : f
' /
ft,
x.
n’
0 ljgjlllllllplpll
12 14

 

P/Pw
(b)

Figure 2.18 Pressure profile on centerbody surface along centerline (A-A’, Fig.
7) at (a) 10d upstream of bleed, (b) mid-way between 2 bleed patches (point a,
Fig. 7), (0) 5d downstream of last row of bleed holes (C-C'), and (d) 15d
downstream of last row of bleed holes.

2 = radial coordinate, 20 = local wall coordinate, d = bleed-hole diameter.

77

(Z—Zo)/R

 

Figure 2.18 (cont’d)

 

 

 

 

 

 

 

 

 

0.18 [- f
. P
: i
T 1‘
I ; f ------- Slots
\ 0.12 _- 1 0 Holes
’8 i 1
'1 '- 1
'3', L \
0.06 _ \\
i X
'_ ‘1
X
0'111111111111..|.. 11.141111111139111
15.25 15.75 16.25 16.75 17.25
P/PW
(C)
0.18 f 4
: 31
g 1
' ‘1
i 1
0.12 :- L‘
: Q
»_ 1
;
: 1
0.06 _- 1,
C 4
~_ 1
. L
. L
. A
0 i 1 1 1 g 1 1 1 1 LL. 1
16 16.5 17

78

 

 

 

 

 

 

 

 

 

 

 

[I 0.12 f
\ I
s F
l L
5 :
3 1
1:11 0.06 f
.—
000'
4.25 4.75 5.25
P/Pinf
(a)
[I 0.12 _'
\
KI
I _ .
3 ~ 1.”
13 0.06; 1’
:_ x
: ‘1
; i
1 I
0.00 L41111111111‘111
6 7
P/Pinf
(b)

Figure 2.19 Pressure profile on cowl surface along centerline (A-A’, Fig. 8) at
(a) 10d upstream of bleed, (b) mid-way between 2 bleed patches (point a, Fig. 7),
(c) 5d downstream of last row of bleed holes (C-C'), and (d) 15d downstream of

last row of bleed holes.

Z = radial coordinate, Zwa" = local wall coordinate, d = bleed-hole diameter.

79

(Zwan - Z) / R

 

 

Figure 2.19 (cont’d)

 

 

 

 

 

 

 

 

 

80

,
,'
.’
1 ----~--- Slots
1 e Hobs
.
‘.
‘4
‘4
\a
‘4
‘4.
1.
0.0 1.11111111114111111.111.1111‘111
15.25 15.75 16.25 16.75
(C)
. .'
0.12: ,'
.1'
1‘
.1
; f
0.06, ,1
' 1'
,'
,1
,
0.00” 11" "‘1'
16.5 17
P/Pinf
(d)

2.6 Qonclusions

Computations were performed for an axisymmetric mixed-compression
inlet at zero angle of attack in which a bleed boundary condition involving a
discharge coefficient is implemented in two different ways. In one
implementation, the locations of the bleed holes are discerned. In the other
implementation, each row of bleed holes is modeled as a porous surface or slot,
where the number of bleed holes in each row is accounted for by adjusting the
discharge coefficient to give the correct bleed rate.

During these simulations, it was noted that the initialization of the flow
through the mixed-compression inlet was complicated by several factors. To
assist future CFD research into these types of inlets, a set of guidelines was
generated for this type of flow. These guidelines outline and detail the major
difficulties and propose methods for initializing the flow through the inlet. One
key outcome of this method is the inclusion of a buffer in the placement of the
terminal shock during the construction of the inviscid, critical flow solution. This
buffer is intended to account for the effective-area changes that will occur when
the viscous solution is initiated.

For critical flow through the mixed-compression inlet, stable solutions with
no spillage were achieved for both the bleed hole (row-hole) and bleed-slot (row-
slot) boundary conditions. Results from the simulations obtained show that
although both implementations of the bleed boundary conditions gave the same
overall bleed rate in approximately the same locations. The predicted Mach

number profiles and pressure distributions downstream of the bleed region,

81

however, differed considerably between the row-hole and row-slot boundary
conditions. These results indicate that the boundary layer development, the
Mach number profile, the shock-wave/boundary-layer interaction, and the
terminal shock strength are all affected by both the bleed rate and the bleed hole
pattern.

The observations made regarding the role of the boundary layer growth
during the initialization of the flow within the inlet have led to the proposal of a
method of control that is especially suited for a mixed-compression inlet. This
proposed method takes advantage of the fact that small changes in the boundary
layer can result in significant changes to the properties of an inlet. This approach
uses combined suction and bleed to create closed surfaces within the flow,

thereby changing the effective-area ratio of an inlet.

82

CHAPTER 3

CFD Simulations of a Free Stream-Surface
Control Method Using a Transverse Jet-in-

Crossflow and Bleed Through Discrete Holes

3.1 Summag

CFD simulations were performed to demonstrate and investigate the
general properties of a free stream-surface control method using jets injected
transversally into a supersonic crossflow. In these simulations, a slightly
underexpanded, supersonic jet is injected into a supersonic crossflow and, with
the addition of bleed downstream of the injection port, closed surfaces are
created in the crossflow. It is proposed that these surfaces, termed free stream-
surfaces, can be used to control various aspects of the crossflow. For example,
in a mixed-compression inlet these surfaces could be used to change the
effective-area of the supersonic diffuser, thereby changing the location of the
terminal shock in the inlet.

Results are presented for several cases to determine the general
characteristics of the flow and the free stream-surface control mechanism.
Estimates of the jet shape and penetration, as well as a description of the free

stream-surface control mechanism are also provided. For these simulations, the

83

injection port is modeled as a simple square injection port in a periodic
environment. The downstream bleed region is modeled using a bleed boundary
condition that has been designed specifically to capture the physics of choked
bleed through discrete holes: for example, barrier shock formation and the flow
turning that occurs between holes.

This computational study is based on the Reynolds-averaged, thin-shear
layer, compressible Navier-Stokes equations and the conservation equations of
mass (continuity) and total energy closed by the one-equation model of Spalart-
Allmaras. Solutions were generated by a cell-centered, finite-volume method
that uses third-order accurate, flux-difference splitting of Roe with limiters and
multigrid acceleration of a diagonalized ADI scheme with local time stepping on

structured grids.

3.2 Introduction

In the simulation of mixed-compression inlet (Chapter 2), the interplay
between the boundary layer height, the applied back pressure, the bleed rate,
and the translation of the cowl proved to be difficult to model. During these
simulations it was observed that slight changes in the area ratio of the inlet could
very easily change the properties of the inlet so that the terminal shock would
move fonlvard of the throat and be expelled. These slight changes were often
caused by the growth of the boundary layer in the supersonic diffuser section. In
a physical inlet, the influence of the boundary layer on the effective-area in

supersonic diffuser is addressed by placing one set of bleed holes far upstream

84

of the throat. In the simulations of the mixed-compression inlet (Chapter 2), the
changes in the boundary layer height occurred during the initialization process,
when the solid surfaces were transitioned to viscous walls, or when the upstream
bleed rate was insufficient for the flow conditions. While these are both issues
that are unique to the simulation process, in a physical inlet these changes could
also be induced by a change in the angle of attack, an inappropriate placement
of the upstream bleed holes, or by an insufficient amount of upstream bleed.

It is proposed that a free stream surface control method, implemented in
this manner, can be used to address both of the main issues facing the operation
of a mixed-compression inlet. For example, a free stream surface control
method implemented in the converging portion of a mixed-compression inlet
could be used to replace or reduce the amount of translation needed to bring the
aircraft to its operational speed. By methodically changing the amount and/or
angle of injection or by modifying the number of active bleed holes, the free
stream-surface could be controlled in such a way as to replicate the necessary
changing geometry of the inlet, mimicking the effect of the translating cowl. A
free stream-surface control method could also be implemented in such a way as
to respond to the initial stages of unstart by changing the effective-area ratio of
the inlet upstream of the shock and re-establishing favorable operating
conditions.

Since critical flow in an inlet occurs when the shock is held at or near the
throat, the system is operating very close to a marginally stable state and would

benefit from any additional control. The advantage of using the free stream-

85

surface control method is that only small changes in the boundary layer height
are needed to effect large changes in the properties of the inlet. The current
approach is to model the injection as an individual hole in a periodic environment
and to model the downstream bleed using a bleed boundary condition that
permits the simulation of bleed through discrete holes. In this manner, the free
stream-surface control mechanism can be quickly studied and the overall

features can be examined.

3.3 Description of the Problem Studied and the Methods Employed

3.3.1 Problem Description

The flow simulation studied involves a supersonic, underexpanded,
square jet injected into a turbulent, supersonic crossflow. Depending on the
simulation, the Mach number was within 1.2 to 2.0 and the jet was slightly
underexpanded. For these simulations, the jet momentum ratio was typically
between 1.1 and 1.4 and, as a result, the penetration of the jet into the crossflow
was minimal. The angle of injection (0) for these simulations was 135 degrees.

A schematic diagram of the three-dimensional system studied is shown in
Figure 3.1. The system consists of a flat plate, a square injection port, and
circular bleed openings with a diameter (d) of 2.5 mm. The location and pattern
of the bleed holes and the injection port are shown in Figure 3.2. The injection
port has a width equal to the bleed hole diameter and is located in the center of a

computational domain that is two hole diameters in width (spanwise direction).

86

 

I~D-o-—-.-.- .............

Figure 3.1 Schematic of computational domain for the free stream-surface
simulations: top-down view of flat plate surface (dashed lines indicate periodic

boundary planes).

 

 

’7' “7“?“ 7" 7“" 1
mv1301d wall
freestream

I Vf extrapolation

inviscid wall
Viscous wall

)1

\
\
\
0

1'” viscous wall \ e ,1':\\ “a

-__ ‘Q X
injection be bleed bc

 

Figure 3.2 Boundary condition schematic for the free stream-surface

simulations.

87

The flat plate is 2.32 m long and the approach length, the distance from
the beginning of the viscous flat plate to the injection port, is 2.14 meters. This
leads to a momentum thickness at the injection port, without injection, that is
comparable to the width of the injection port. This thickness is also comparable
to the actual momentum thickness in the near-throat region of a mixed-
compression inlet that was used in a previous study. The bleed hole and
injection port dimensions were also chosen so as to be comparable to the
dimensions of the bleed holes used in an experimental study of a mixed-
compression inlet.

Bleed is applied downstream of the injection port at several locations and,
depending on the simulation, the number and location of the bleed holes could
be varied. The center of the first row of holes was located at a distance of 11d
downstream of the center of the injection port and the center of the last row of
holes that could be used, the seventh row, was located 17d downstream of the
injection port (Figure 3.2). Each hole is 1d in diameter and is modeled as a
rough circle. The holes are arranged in a staggered fashion with no overlap
between rows.

The boundary condition used is a discharge-coefficient, bleed boundary
condition which permits the modeling of choked bleed through individual bleed
holes. Since generating a zero net-mass flux is a difficult matter with this
boundary condition, the bleed rate was permitted to float. For these simulations,
the discharge coefficient for the bleed holes was fixed, based on previous

research, at 0.75.

88

In the simulations described in this paper, the freestream static
temperature, pressure, and Mach number are 173 K, 10.930 kPa, and 1.2
respectively. The Reynold’s number-per-meter, based on the freestream
conditions, is 3.495 x 107 m". Flow conditions were designed to replicate the
near-throat conditions of a mixed-compression inlet that was used in a previous
study. The mixed-compression inlet problem described above was selected
because experimental and computational data exists which can be used in future

research to implement the results of this study.

3.3.2 Problem Formulation

The problem described in the previous section is modeled by the
Reynolds-averaged, thin-shear layer, compressible Navier-Stokes equations and
the conservation equations of mass (continuity) and total energy closed by the
single equation model of Spalart-Allmaras. Additional details of the governing
equations are available in the $.30 User’s Manual (Version 5.0) by Biedron et

al. (1996).

3.3.3 Boundary Conditions

The boundary conditions applied at the boundaries of the flow domain
(Figure 3.2) are as follows. At the inflow boundary, all flow variables are fixed at
the supersonic freestream conditions. At the outflow boundary, a supersonic-
outflow boundary condition is applied and all of the flow variables are

extrapolated. The supersonic outflow boundary is situated far away from the

89

dynamic regions so that any influences resulting from incompatibility of the
boundary condition with the outgoing boundary layer will not propagate into
regions of interest. On the upper surface, the wall is set as an inviscid wall
boundary. This was considered appropriate because the dynamics of the
interaction of the upper wall boundary and the bow shock were not considered a
part of this study. In the spanwise direction, periodic boundary conditions were
imposed at the two boundaries to simulate a single element in a series of
structures in an axisymmetric environment.

The solid surfaces in the simulations were treated as viscous, adiabatic
walls and, at these surfaces, the no-slip condition and a zero nonnal-pressure
gradient were imposed. At the injection inflow boundary, the flow was either
sonic or supersonic, depending on the simulation, and all of the variables were
specified. The bleed holes were modeled using a non-porous-wall bleed
boundary condition (discharge coefficient boundary condition) as a model for
bleed through discrete holes in which at least one grid point is located within
each bleed hole. This is the same bleed boundary condition described in detail

in Chapter 2.

3.3.4 Numerical Method of Solution

Solutions to the governing equations described in the previous section
were obtained by using a cell-centered, finite-volume code called CFL3D. All
inviscid terms were approximated by the flux-difference splitting of Roe (third-

order accurate) with the slope limiter of Chakravarthy and Osher. All of the

90

diffusion terms were approximated conservatively by differencing derivatives at
cell faces. In the steady-state solutions, time derivatives were approximated by
the Euler implicit formula. The system of nonlinear equations that resulted from
the aforementioned approximations to the space- and time-derivatives local time-
stepping (local Courant number always set to unity) and three-level V-cycle

multigrid.

3.3.5 Grid Structure

The single block, structured grid system used is shown in Figure 3.3. It
has 1,225,105 grid points with the majority of the grid points clustered near the
expected location of the bow shock and the injection and bleed holes. All of the
grid dimensions were designed so that multigrid methods could be employed.

This grid, with dimensions 497 x 17 x 145, has 17 grid points in the
spanwise direction. Depending on the simulation, the streamwise direction
spans a distance between 10 and 40 injection hole diameters (10d - 40d)
upstream of the injection region to 13d downstream of the injection port. Within
the regions of interest, the aspect ratio is kept near unity so that the various
shock structures could be reasonably captured. In the normal direction, the grid
spacing was designed for use in a future simulation that would implement a k-co
turbulence model with the shear stress transport model of Menter. To resolve
the boundary layer that forms adjacent to the flat plate surface, the grid is very

densely clustered in the normal direction. With this structuring, the first grid point

91

 

 

IIIII
“1111

||

           

   

oomo

ooo‘

  

 

 

surface

3 Single block grid system used in the free stream

Figure 3.

simulations. The scale in the spanwise direction (y) has been expanded by a

Region around injection and

factor of 200. Top: Overall grid system. Bottom

= 0).

suction (x

92

has a y+ value of less than unity. In addition, there were 5 grid points within a y+
of 10 and 25 grid points within a y+ of 100.

The injection port is modeled as a square measuring 8 cells on a side and
the bleed holes are modeled as rough holes with 64 cells per hole. There are 4

cells between the injection port and each periodic boundary.

3.4 Results

Figure 3.4 shows the results from a two-dimensional simulation of the free
stream-surface control mechanism. In this case, the two-dimensional grid was
taken as the centerline plane of the three-dimensional problem. The injection jet
is set at a Mach number of 1.6 and is only slightly underexpanded. In addition,
the angle of injection is fixed at 135 degrees relative to the freestream flow
direction. In this figure, the Mach number contours and several illustrative
streamlines that emanate from both the freestream and the injection port are
shown to illustrate the free stream-surface control mechanism. The jet, injected
in to the crossflow, rises to a height of approximately 2.5d and then turns
downstream. The majority of the injected fluid is recaptured by the bleed region,
however, because the bleed rate was difficult to control with a discharge
coefficient, there is a net injection of mass into the crossflow.

Downstream of the injection port a trapped recirculation region is clearly
visible beneath the injection plume and, at the bleed location, the barrier shocks
from the flow entering the holes (slots) coalesce into a single shock. Also visible

on the downstream end of the control mechanism is a region of high Mach

93

 

 

Figure 3.4 Mach number contours and selected streamlines for the two-
dimensional simulations of the free stream-surface control structure. The

freestream flow is from right to left.

94

number fluid. This is generated when the main flow expands as the injected jet is
drawn back down towards the flat plate surface by the bleed. Within the jet itself,
the expected expansion of the jet as it enters the crossflow is not apparent: this is
a result of both the angle of injection and the slight underexpansion of the jet.

Figure 3.5 displays the Mach number contours along the centerline for
one of the three-dimensional cases studied. In this case, the slightly-
underexpanded injected jet has a Mach number of 1.4. In many respects, this
profile is similar to the results of the two-dimensional study. The injected jet is
seen to penetrate some distance into the fluid before it is turned by both the
crossflow and the presence of the suction region. The main difference between
this and the two-dimensional simulation is in the lack of a recirculation region
downstream of the jet.

Figure 3.6 provides a perspective view of the injection port section of the
free stream-surface control mechanism. Pressure contours are displayed along
the flat plate and several selected streamlines for both the jet and crossflow are
presented. The pressure contours on the plate surface show the pressure rise
ahead of the jet and a low-pressure region forming the downstream side of the
jet. Figure 3.6 also shows how streamlines from the approaching flow are
diverted past the injection plume. Some of the approaching flow is clearly
entrained by the leading edge of the plume while the majority of the flow seems
to be diverted around the injected fluid. Downstream of the injection port, the

diverted flow is captured by the bleed process and removed from the crossflow.

95

 

 

 

 

”a“: 31! I1... lll} ll. 1

 

 

 

Figure 3.5 Mach number contours and selected streamlines along the centerline

for a three-dimensional simulation of the free stream-surface control structure.
The freestream flow is from right to left.

96

              

PrBSSlJre 0280724 0438428 0596132 0753836 091154 106924 1.22695 1.38465

 

Figure 3.6 Pressure contours along the flat plate and selected streamlines from
the crossflow and the injected jet. Freestream flow is from left to right.

97

Some of the diverted flow, however, reverses and is entrained by the
downstream edge of the plume.

Figure 3.7 shows a series of streamlines from two heights within the
approaching flow for the same case as described in Figure 3.6. These
streamlines, especially the upper set, show the deformation of the freestream
flow in response to the injected fluid. Also visible in this figure is the spanwise
shape of the control surface: the injection of fluid from a square injection port
yields a wavy control surface.

Figure 3.8 provides a perspective view of the injection-suction system.
Mach number contours along the centerline plane and on the plate surface
provide an overview of the free stream-surface control structure in three
dimensions. On the left of the figure, the injection port is clearly seen, as is the
stagnation of the fluid ahead of the injection port. Downstream of the injection
port, the influence of the bleed holes can be seen as the flow turns to reconnect
with the surface. Just past the last row of bleed holes, the barrier shocks from
the bleed holes are seen to coalesce and the flow changes direction to follow the
flat plate again. One of the interesting features of this plot is the region of high
Mach number that is generated as the freestream flow turns to follow the suction.

Figure 3.9 shows the relationships between the injection Mach number
and both the injected plume height and toward penetration of the jet for the
three-dimensional cases studied. In this plot it is observed that there is a linear
relationship between the injection Mach number and the maximum height

achieved by the jet with a slope of 2.66.

98

 

 

 

Pressure 0 281 U 438 [1,596 0754 [I 912 1069 1.227 1.385

 

 

 

Figure 3.7 Pressure contours along the flat plate and selected streamlines from
the crossflow.

99

 

  
    

II-i’a-HW

MaChNumtJEr 011021032 043 053 0.64 0.750 85 0961.061171281381491,60

 

Figure 3.8 Mach number contours around the injection port and bleed region on

the flat plate surface and along the centerline.

10 1.

 

    

 

 

 

 

 

 

 

 

: :

e: a 11

E 1.

.2 ~

“U

.1.» l

6 e 1

U

U

r: 4 .
.1

g ,,

8

s > a

E 2 1» -0- Forward Penetration

3!

g + Normal Penetration

0 fik—_L___.J._ l.___ _1_- § 1 J_ l l + l .L. #

1.2 1.45 1 .7 1 .95

Injection Mach Number

Figure 3.9 Relationship between injection Mach number and the fonNard and

normal penetration of the jet for a typical case.

101

3.6 Conclusions

A number of simulations were conducted to investigate a proposed free
stream-surface control structure using paired injection and suction to control the
diversion of a crossflow. Simulations were conducted with a square, variable-
Mach number, slightly-underexpanded jet exhausting into a supersonic
crossflow. Downstream bleed was applied to alter the trajectory of the injected
jet and to generate closed surfaces whose height and length are controllable.
Initial results from a three-dimensional, turbulent case were presented which
illustrate the three-dimensional properties of this flow and demonstrate the
potential for use as a flow control mechanism.

The results from these simulations illustrate the main features of the free
stream-surface control structure and provide information for the development of
future studies. Items such as the location of the bow shock, the maximum
penetration of the jet into the crossflow, and fonlvard penetration of the jet were
identified as important factors to be examined and addressed in future
simulations.

In the simulations, it was observed that the injected plume clearly forms a
free stream-surface whose reconnection can be improved by the proper choice of
location for the suction. The injected jet was observed to penetrate into the
crossflow before being turned by both the crossflow and the downstream suction
and the jet’s maximum height and forward penetration were acquired as a
function of the Mach number of injection. From this, it was determined that the

energy input required to effect meaningful control was significant and, potentially,

102

prohibitive. At the downstream bleed location, the jet reconnected to the flat
plate surface and the flow realigned with the plate surface.

The main issue associated with the shape of the free stream-surface
involves the manner by which the injected fluid is forced into the crossflow. Since
the injection was conducted through a discrete hole, instead of a slot, much of
the fluid that would be diverted by the jet in a slot configuration is, instead, either
entrained into the jet or ends up being drawn out by the bleed holes. In other
words, the injected plume fans out and is not completely recaptured by the bleed
region, even if the discharge coefficient were set for a zero net-mass inflow.
While this may be a disadvantage in controlling the shape of the free stream-
surface, because of the flow turning at reconnection, this should act on the region
downstream of the bleed as if there were tangential slot injection. One aspect of
this, therefore, is that the boundary layer is energized by the expanding flow as
the plume turns in response to the bleed.

During this research, two additional issues were identified as crucial for
future investigation. The first issue deals with the control of the net bleed rate
with the bleed boundary condition used in the simulations. Since the bleed
boundary condition used models the bleed through each hole as a function of the
local speed of sound, modifying the discharge coefficient to affect a given bleed
rate is awkward. It is recommended that the bleed boundary condition
subroutine be modified so that the mass flow rate through each hole can be

tracked and adjusted.

103

The second issue involves the shape of the control structure when
individual holes are used for injection. With the injection being accomplished by
individual holes, the shape of the free stream-surface in the streamwise direction
is highly distorted. In a mixed-compression inlet, this distortion will lead to local
expansion and contraction of the flow and would be undesirable in practice.

Future work in this area should focus on further characterizing the profile
of the jet as a function of the location of the bleed holes, the bleed hole
configuration, and the Mach number and pressure of the injected fluid. Additional
directions should also focus on alternative methods for shielding the injection
from the high momentum crossflow. To this end, approaches such as injection
behind a rearward facing step, tangential slot injection, or the injection of fluid
into a recessed cavity would function starting points for alternative methods for

generating free stream-surface control.

104

CHAPTER 4

CFD Simulations of a Free Stream-Surface

Control Method Using 3 Driven Cavity

4.1 Summag

CFD simulations were performed to demonstrate and investigate the
general properties of a free stream-surface control method using driven cavity
flow. In these simulations, a subsonic jet is injected into cavity that is recessed
within a turbulent, supersonic crossflow. By injecting fluid into the cavity, it is
proposed that both the deflection of the separated crossflow and the downstream
boundary layer profile can be controlled while, at the same time, shielding the
injection process from the high-momentum crossflow fluid. With the addition of
bleed downstream of the cavity, closed surfaces can be created which can be
used to control various aspects of the crossflow. For example, in a mixed-
compression inlet these surfaces could be used to change the effective area of
the supersonic diffuser, thereby changing the location of the terminal shock in the
inlet.

Results are presented for length-to-depth ratios (5.0, 8.0, 15.0, and 17.5)
that cover both open and closed cavity flow. Mach number contours and profiles

downstream of the cavity are presented to assess the impact of the driven cavity

105

I1 my,

on the crossflow. In addition, pressure profiles along the cavity floor are provided
to assess the impact of the injection on the pressure gradient that would be
experienced by stores enclosed in the cavity. Additional studies are conducted
to examine the impact of the approaching boundary layer height on the dynamics
of the driven cavity flow for L/h = 5.0 and to address the grid structure influences
on the driven cavity flow.

This computational study is based on the Reynolds-averaged, thin-shear
layer, compressible Navier—Stokes equations and the conservation equations of
mass (continuity) and total energy closed by shear-stress transport (SST)
turbulence model of Menter. Solutions were generated by a cell-centered, finite-
volume method that uses third-order accurate, flux-difference splitting of Roe with
limiters and multigrid acceleration of a diagonalized ADI scheme with local time

stepping on structured grids.

4.2 Introduction

In the simulation of the mixed-compression inlet (Chapter 2), it was
observed that the interplay between the boundary layer height, the applied back-
pressure, the bleed rate, and the translation of the cowl was responsible for
much of the instability that is experienced by mixed-compression inlets. When
these influences are properly balanced within the inlet, efficient and effective
operation is achieved. However, when any one of these items is out of balance,
the natural response of the inlet is either inefficient operation, where the terminal

shock is placed far downstream of the throat, or inlet unstart.

106

I'I

One potential method of control for a mixed-compression inlet involves
modifying the properties of the inlet through the effective-area ratio profile
upstream of the throat. During simulations of the mixed-compression inlet
(Chapter 2), it was observed that slight changes in the boundary layer thickness
in the supersonic diffuser section of the inlet, often caused by an improper pairing
of the bleed rate and back-pressure, could change the properties of the inlet so
that the terminal shock would move forward of the throat and be expelled. As a
result, it was proposed that the insertion of a free stream-surface control
mechanism, applied in the supersonic diffuser section or near the throat, could
effectively control the thickness of the boundary layer and, therefore, provide a
measure of control for the entire inlet.

In Chapter 3, it was observed that the generation of free stream-surfaces
by combined injection and suction was very effective at generating controllable
shapes and that, with some modification, true free stream-surfaces could be
generated to control the diversion of the crossflow. The downside to this
approach was that the injection of fluid directly into a supersonic crossflow is very
expensive. In addition, the bow shock resulting from direct injection into a
supersonic crossflow is a potential problem for flow control in a mixed-
compression inlet environment. From these simulations, it was apparent that this
type of control affects not only the boundary layer height of the fluid, but also the
core flow.

The approach taken in this chapter is to generate the free stream-surface

control using a driven-cavity flow field. In this iteration, a cavity would be placed

107

in the supersonic diffuser section of the inlet and the flow within the cavity would
be driven by subsonic injection on the upstream face of the cavity. To close the
surface, the bleed system used for normal inlet operation could be incorporated.
By methodically changing the amount and/or angle of injection or selecting the
geometry of the cavity, the free stream-surface can be used to control the
effective-area ratio in such a way as to replicate the changing geometry of the
inlet, thereby mimicking the effect of the translating cowl.

Early work on cavity insertion as a control device in supersonic flows
focused primarily on reducing the heat transfer rate for protection of hypersonic
vehicles. Chang (1976) reports that experimenters were able to reduce the heat
transfer rate by a factor of two when a laminar cavity flow replaced a laminar
boundary layer flow. However, Chang also that these same studies showed that
the changes in the downstream heat transfer rates tended to nullify the positive
effects of the injection into the cavity. In 1965, Nicholl (Chang, 1976) conducted
experimental studies with helium injection in an annular cavity on a conic re-entry
vehicle at Mach 11. Nicholl found that by increasing the height of the separation
shoulder above the line of the conic surface, the injected fluid was able to pass
into the downstream boundary layer flow and dramatically reduce the
downstream heat transfer rates.

Current interest in cavity flow fields at supersonic speeds has focused on
the issues associated with stores separation from high-speed aircraft. Recent
developments in stealth technologies and the desire to reduce radar cross-

section from the external store carriages in military aircraft are the motivating

108

factors in the examination of internal store carriages for supersonic aircraft.
Simply modeled, these internal store carriages are cavities set into the airframe.
Research by various authors (cf. Wilcox, 1990; Stallings et al., 1991; Plentovich
et al., 1993) has focused on quantifying the flow field in the cavity by measuring
the pressure, force and moment distributions on a generic store separating from
within a box cavity. Various researchers have also proposed different methods to
control of the moments and drag experienced by the stores. For example,
Wilcox (1990) presented an approach using a cavity with a porous-floor to modify
the cavity flow field. By venting the high-pressure fluid in the rear of the cavity to
the low-pressure fluid in the front, the objective was to reduce the overall drag
characteristics of the cavity. Each of these approaches, however, has involved
the passive control of the fluid within the cavity for the purpose of drag reduction
or the control of moments experienced by stores within the cavity.

For flow over cavities at supersonic speeds, there are two general types of
cavity flow fields observed. In these flows, the type of flow field observed is
determined primarily by the length-to-height ratio (L/h) of the cavity. For L/h
greater than 13, the flow field is referred to as closed-cavity flow. In closed-cavity
flow, the separating shear layer expands over the leading edge of the cavity and
then, because of the length of the cavity, the shear layer impinges on the floor of
the cavity before exiting the cavity ahead of the downstream face (Figure 4.1).

In this case, the pressure distribution along the floor of the cavity contains a low-
pressure region in the upstream portion of the cavity, in the area under the

separated shear layer before it impinges on the floor of the cavity. The pressure

109

 

‘F——"-_‘:l

'I 1"”?!

 

 

 

(“I
I I

Impingement shock
Exit shock

 

//
(C)

Figure 4.1 Description of the different types of cavity flow: (a) open cavity flow,
(b) closed cavity flow, (0) transitional cavity flow (Plentovich et al, 1993 and
Stallings et al, 1987).

110

then rises as the impingement location is reached and then it is observed to level
off. As the downstream face of the cavity is approached, the pressure levels on
the floor of the cavity rise again and reach a maximum value just ahead of the
downstream face of the cavity.

An open cavity, on the other hand, is classified as a cavity with a length-
to-height ratio (L/h) less than 10. In this case, the shear layer is able to bridge
the cavity and does not impinge on the cavity floor. Across the floor of the
cavity, the pressure recovery coefficient (Cp) is positive, however, it is very small
for the majority of the cavity’s length. In the supersonic crossflow cases studied
by Stallings, et al (1987), the pressure recovery coefficient for the open cavities
was below 0.05 in the leading edge of the cavity and jumped to only 0.2 at the
downstream face of the cavity.

Between these two general cases for cavity flow is a region that has often
been referred to as transitional cavity flow. In transitional cavity flow, the angle
through which the shear layer turns to exit is such that the impingement shock
and the exit shock coincide. Often, this range is further sub-divided into
transitional-open cavity flow and transitional-closed cavity flow, depending on the
degree to which the separated shear layer penetrates into the cavity. For this
study, both open and closed-cavity type flows are investigated, however the

transitional regimes are avoided because of their difficulty in classification.

11]

4.3 Description of the Problem Studied and the Methods Employed

4.3.1 Problem Description

The flow simulation studied involves a subsonic jet injected into a cavity
that is placed in a flat plate within a turbulent, supersonic crossflow. The
freestream conditions are set so as to be representative of the flow within a
mixed-compression inlet: the freestream Mach number, total pressure and static
temperature are, respectively, 2.65, 1 atm and 129.772K. The boundary layer
thickness at the leading edge of the cavity was fixed at 0.005 m. For the
configurations studied, the depth of the cavity was fixed at 0.0127 m and the
length-to-depth ratio of the cavity (L/h) was 5.0, 8.0, 15.0 and 17.5. Depending
on the simulation, the Mach number for the injected jet either 0.4, 0.6 or 0.8. The
angle of injection (9), for each case, was either normal to the wall or at 45
degrees to the horizontal (streamwise direction). The amount of injected fluid
was modified by changing the area of injection along the upstream wall. The
different cases presented in this paper are summarized in Table 4.1 and a
schematic diagram of the system studied is shown in Figure 4.2. The system
consists of a long flat plate on which the boundary layer is allowed to develop
and a cavity recessed in the flat plate where the boundary layer was the desired
thickness. In these simulations, the cavity is modeled as a two-dimensional
structure and the injection occurs on the upstream sidewall of the cavity.

The momentum thickness at the leading edge of the cavity that is fixed at
0.005 m. This thickness is comparable to the actual momentum thickness in the

near-throat region of a mixed-compression inlet that was used in a previous

112

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Case Injection Injection Mach Injection Area

Label L/h Angle Number (fraction of waIQ 6/h Name
#1 5 - 0 0.8 0.4 5 - baseline
#2 5 45 0.26 0.8 0.4 5 - 45 - 0.26 - 8
#3 5 45 0.6 0.8 0.4 5 - 45 - 0.6 - 8
#4 5 45 0.6 0.8 0.8
#5 5 45 0.26 0.4 0.4 5 - 45 - 0.26 — 4
#6 5 45 0.4 0.4 0.4 5 - 45 - 0.4 - 4
#7 5 45 0.6 0.4 0.4 5 - 45 - 0.6 - 4
#8 15 - 0 0.8 0.4 15 - baseline
#9 15 45 0.8 0.8 0.4 15 - 45 - 0.8 - 8

 

Table 4.1 Table listing relevant parameters of cases presented for the driven

cavity simulations.

113

 

 

V
_f_}

flat plate

 

 

V

 

V

 

V

 

 

 

517/

 

 

Figure 4.2 Schematic of computational domain for the driven cavity simulations.

injection port

114

 

 

 

 

 

/\

V

 

part
i

“ ”‘II

 

study. The bleed hole and injection port dimensions were also chosen to be
comparable to the dimensions of the bleed holes used in an experimental study

of a mixed-compression inlet.

4.3.2 Problem Formulation

The problem described in the previous section is modeled by the
Reynolds-averaged, thin-shear layer, compressible Navier—Stokes equations and
the conservation equations of mass (continuity) and total energy closed by shear-
stress transport (SST) turbulence model of Menter. Additional details of the
governing equations are available in the CFL3D User’s Manual (Version 5.0) by

Biedron et al. (1996).

4.3.3 Boundary Conditions

The boundary conditions applied at the boundaries of the flow domain
(Figure 4.3) are as follows. At the inflow boundary, all flow variables are fixed at
the supersonic freestream conditions. By allowing the boundary layer to develop
in the simulation, the environment into which the fluid is injected can be easily
modified with minimal changes to the grid. At the outflow boundary, a
supersonic-outflow boundary condition is applied and all of the flow variables are
extrapolated. The supersonic outflow boundary is situated far away from the
dynamic regions so that any influences of the incompatibility of the boundary
conditions with the boundary layer will not propagate far into the domain and

influence any measurements.

115

inviscid wall

 

freestream outflow boundary

p viscous wall

mwscrd wall injection bc tax I\ I
\~\\ "\

 

 

 

 

 

 

 

‘\
\.
\\‘
x \ \

\ \\\

\\

viscous wall

Figure 4.3 Boundary condition schematic for the driven cavity problem.

116

On the upper surface, the wall is set as an inviscid wall boundary. In the
spanwise direction, symmetry boundary conditions were imposed at the two
boundaries. The solid surfaces in the simulations were treated as viscous,
adiabatic walls and, at these surfaces, the no-slip condition and a zero normal-
pressure gradient were imposed. At the injection inflow boundary, the flow was
subsonic. At this boundary, the velocity of the flow was fixed at the desired value
and angle as was the mass flow rate. From this information, the pressure is
extrapolated.

The boundary condition used for the bleed region is a discharge-
coefficient, bleed boundary condition which permits the modeling of individual
bleed holes. Since generating a zero-net mass-flux is a difficult matter with this
boundary condition, the bleed rate was permitted to float. For these simulations,
the discharge coefficient for the bleed holes was fixed, based on previous

research, at 0.75.

4.3.4 Numerical Method of Solution

Solutions to the governing equations described in the previous section
were obtained by using a cell-centered, finite-volume code called CFL3D. All
inviscid terms were approximated by the flux-difference splitting of Roe (third-
order accurate) with the slope limiter of Chakravarthy and Osher. All of the
diffusion terms were approximated conservatively by differencing derivatives at

cell faces. In the steady-state solutions, time derivatives were approximated by

117

the Euler implicit formula. The system of nonlinear equations that resulted from
the aforementioned approximations to the space- and time-derivatives local time-
stepping (local Courant number always set to unity) and three-level V-cycle

multigrid.

4.3.5 Grid Structure

For each of the configurations studied, a four block, structured grid
system is used to model the recessed cavity. The grid system used for L/h=5 is
shown in Figure 4.4. The grid system used to model the cavity is a wrap-around
grid system. It has 183,624 grid points and is made up of four blocks that are
connected through one-to-one blocking. In addition, all dimensions are designed
so that multigrid methods can be used and accommodations have been made so
that each block can be fully included in the multigrid. Although the grid for these
simulations is three-dimensional, the problem studied is two-dimensional: the
extra grid point in the spanwise direction is required because the version of the
code being used was unable to run two-dimensional simulations.

Block 1 is a wrap-around grid that conforms to the surface of the flat plate
and the cavity. This grid has dimensions 675 x 3 x 57 (3 grid points in the
spanwise direction) and, except in the comer regions, provides a fairly uniform
distribution of grid points. While the aspect ratio and grid distortion of Block 1 is
unavoidable at the comers of the cavity, the use of a wrap-around grid does
reduce the issues associated with high aspect ratios or the need for grid patching

at these points.

118

 

Figure 4.4 The four block, wrap-around grid system used for driven cavity flow
problem.

119

i'nl

Block 2 fills the region above the wrap-around grid (Block 1) upstream of
the recessed cavity. Block 2 has dimensions 121 x 3 x 49 and has a fairly
uniform distribution of grid points. The third grid, Block 3, has dimensions 119 x
3 x 57 and fills the region directly above the cavity. This grid is included because
a wrap-around grid would have to stretch considerably within the cavity to
encompass the majority of the cavity. One-to-one blocking is used along each
interface with the wrap-around grid to permit efficient transfer of information
across the interfaces.

The fourth grid, Block 4, fills the region above the wrap-around grid (Block
1) downstream of the recessed cavity. Block 4, with dimensions 233 x 3 x 49
and is included to permit the growth of the boundary layer downstream of the
cavity beyond the height of Block 1. Block 4 is also included to permit the
compression shock, expected from where the separated shear layer reconnects
with the downstream edge of the cavity, to properly exit the flow domain.

For Block 1, the first grid point away from the surface has a y+ value less
than unity and the first five grid points away from this wall are within a y+ value of
ten. This grid spacing is required for the turbulence model of Menter’s SST,
where integration is to the wall. For these simulations, an initial value for y+ was
determined by treating the inlet as a flat plate. As the simulations progressed,
the value of y+ was re-assessed and corrections were made to the grid to

provide appropriate adjustments.

120

 

 

4.4 Results

Figure 4.5 shows the Mach contours of the baseline case, no injection, for
the open cavity flow where Uh: 5.0. This figure shows the boundary layer of the

approaching flow and the separation of the crossflow at the cavity lip.

 

Downstream of the cavity, the crossflow reconnects with the flat plate with the
result that the boundary layer is thicker. A slight compression shock results
where the flow reconnects to the plate and the boundary layer thickens. Figure
4.6 shows pressure contours and several streamlines for the same case. Within
the cavity, the flow is subsonic and it can be seen, from the deformation of the
streamlines, that the separated flow penetrates the cavity only slightly for this
configuration.

Figure 4.7 shows the Mach number contours for the L/h = 5.0 case where
the injected fluid is at 45 degrees to the horizontal at Mach 0.8. In this case, the
area of injection was the maximum studied (case #4). Figure 4.8 shows the
pressure contours and selected streamlines for the case. Although the
differences between this case and the baseline for this geometry are minor,
several differences do stand out. First, the injected fluid, seen clearly at the
leading face of the cavity, appears to deflect the crossflow and prevents it from
penetrating into the cavity. The deflection of the crossflow can also be seen in
the presence of a weak compression shock above the leading edge of the cavity.
In Figure 4.8, the injected fluid is also seen to deform the shape of the

recirculating region within the cavity as it passes into the crossflow. Also visible

[

IJS'

 

 

   

  
     

MaEI’ItIf 01702341051 068085 02119136153170187 203 220237 254

 

 

Figure 4.5 Mach number contours for case 1: baseline cavity (Uh = 5.0).

122

 

 

 

PIP."f 071078 085 093100107114122129136144151158166173

 

 

Figure 4.6 Pressure contours and selected streamlines for case 1: baseline
cavity (L/h=5.0).

123

('1

 

Mach# 01'034051068086102I19136153170187703270237254

 

Figure 4.7 Mach number contours for case 2: Min]: 0.6, 6: 45 degrees
(L/h=5.0).

I24

 

 

 

 

jjIIp-

PIP” 0710 78085 093100107114122129136144151158166173

 

 

 

Figure 4.8 Pressure contours and selected streamlines for case 2: Mini: 0.6, 9:
45 degrees (L/h=5.0).

125

 

w-l

in this figure is the pressure rise that occurs where the crossflow/injected fluid
reconnects to the plate surface.

Figure 4.9 displays the Mach number profile at 1.0L and 1.5L downstream
of the rear face of the cavity for the L/h=5.0 case with an injection Mach number
of 0.60 (case #2). The Mach number profile at the just ahead of the leading edge
of the cavity is also included for comparison. In this figure it can be seen that the
height of the boundary layer downstream is significantly larger, however, the
profile is also significantly shallower.

Figure 4.10 displays the Mach number profiles at a distance of 1.0L
downstream of the injection port, for the baseline case in the L/h= 5.0 geometry
and for two injection Mach numbers. In this figure, it is observed that the
differences between the baseline and the two injection Mach number cases are
minimal. All three produce shallow profiles with similar inflection points, however
it is clear that the effect of the injected fluid was to primarily influence the profile
in the region above the inflection point, in upper half of the boundary layer.
Similar results are observed for the L/h = 8.0 case, however the effects are
significantly damped out for the higher L/h ratio cases.

Figure 4.11 shows the relationship between the injection Mach number
and the pressure across the cavity floor for the case where L/h = 5.0. The
streamwise component, X/L, is zero at the leading edge of the cavity and one at
the downstream face. In the baseline case there is no injection into the cavity
and there exists a low-pressure region in the leading half of the cavity and a high-

pressure region in the downstream half. When the injection is applied on the

126

 

 

0.01

 

0.009

 

1.0 L Downstream ,1

.1

— ------ 1.5 L DownstIeam
_ _ —— —- Upstream

0.008

 

 

 

0.007

0.006

N 0005

0.004

0.003

0.002

0.001

 

ATfiIIT1TIIIIITIIIIIIIlll'lllllIIIIIIIIIIITWTIIIIII

 

Mach Number

Figure 4.9 Mach number profiles normal to the plate surface at X/L = 1.5 and at
X/L=1.0 for case 2: Mini: 0.6, 9: 45 degrees (L/h=5.0).

127

‘ a,

0.015

 

 

 

 

 

 

 

 

 

 

 

 

[-
I-
- ------ 5-baseline
- 5-45-0.26-8 '
F - ----------- 5-45-0.60-8 ,
0.01- '
N :
0005*
I
0|Lll lllllllllLlllLlll
0 0.5 1 1.5 2 2.5 3

 

Mach N umber

Figure 4.10 Mach number profiles normal to the plate surface at X/L = 1.5 for
case 1, case 2 and case 3: Mini: 0, Mini: 0.26 and Mini: 06, respectively
(L/h=5.0).

128

 

1.5

 

 

 

 

 

 

 

 

3 —A— 5-45-0.26-4 '
1_4 ; —0— 5—45-0.40—4 .
: ——v—— 5-45-0.60-4 ___
- ——Cl— 5—baseline ’ l
1-3 r '1 ..
E :
e. I
n_ 1.2 r
1.1 :-
1‘
” 1 l l I 1 a l l l l l l
0 0.5 1
X/L

Figure 4.11 Pressure profiles (normalized) across the length of the cavity floor
(streamwise direction) for case 5, case 6 and case 7: Mini: 0, Mini: 0.26 and
Mini: 06, respectively (L/h=5.0).

129 r

u?

upstream face of the cavity, the effect is to even out the pressure distribution on
the floor of the cavity. This trend is repeated for the L/h=8.0 case, however, the
injection produced little to no effect on the floor pressure profiles in the L/h = 15.0
and L/h=17.5 cases (Figure 4.12).

Figure 4.13 shows a comparison when the height of the boundary layer is
modified with respect to the cavity. In this figure, pressure profiles along the
cavity floor are plotted for two ratios of the incoming boundary layer height to the
depth of the cavity (delta/h) for a case where there is no injection. Figure 4.14
shows the profile along the entire flat plate surface, including the cavity floor.
Both cases yield the same pressure rise ahead of the cavity where the flow
separates, but differ both along the cavity floor and downstream of the cavity. At
most, they differ by approximately 10 percent, however, at distances far
downstream of the cavity, they tend to even out.

Figure 4.15 details the grid system used to compare with the results from
the wrap-around grid system. The grid system shown in Figure 4.15 is a three
block, patched grid system. The grid has a high aspect ratio across the entrance
to the cavity due to the level of grid refinement needed to capture the boundary
layer ahead of the cavity. Figure 4.16 details the pressure profiles at three key
points within the flow field: just ahead of the cavity, along the cavity floor, and just
downstream of the cavity where the separated shear layer reconnects to the flat
plate. In this figure, differences are observed to exist between the two grid

methods.

130

ml

Pfi‘

my

 

 

. ——D-— 15 - baseline
——0— 15— 45- 0.80- 8

 

 

 

 

 

 

 

Figure 4.12 Pressure profiles (normalized) across the length of the cavity floor
(streamwise direction) for case 8 and case 9: Mini: 0, Mini: 0.8, respectively
(L/h=15.0).

131

1.6 '-

 

——-I:I-— delta/h= 0.4
_ ——.— deltalh=0.8

 

 

 

PIPlrlf

 

 

 

l I l l l 1 l l l I
0.8 L

Figure 4.13 Pressure profiles (normalized) along cavity floor in the streamwise
direction for delta/h = 0.8 and delta/h = 0.4: case 3 and case 4, respectively
(Uh = 5.0).

132

 

“7':

 

 

—D— delta/h= 0.4

1,5 —0— delta/h=0.8

 

 

 

 

1.4

 

1.2

IllTllljllTIrI1

 

 

P/Pim.

0.8

 

 
 

l l l l l l r T l

 

 

0.6 ""‘l

I
_x
D

Figure 4.14 Pressure profiles (normalized) along flat plate surface in the
streamwise direction for delta/h = 0.8 and delta/h = 0.4: case 3 and case 4,

respectively (L/h = 5.0).

n

 

 

Figure 4.15 Patched-grid system used for comparison with the wrap-around grid
system case (Uh = 5.0).

134 .

1.05 -

 

 

 

 

 

 

 

    

 

 

—o— patched grid
-—O-— wrap—around grid 1'
’2
“a I‘ f
.1- f
o. ,4 ff
1
1 l I
-02 -0.1 0
X I L
(a)
1.5 _—
I— .7.
: ,/
1.4 F
: I‘
i J/ 1'"
o. - . ,9' 1
1 2 "' c
O. "a 11"
11"
1:
1.1 :’ '1’-
1 '_ ‘I‘-'.-...rl"'"
t 1 1 1 l 1 1 1 L l 1 1 1 1 l 1 J
0 0.25 0.5 0.75 1
X I L
(b)

Figure 4.16 Normalized pressure profiles(a) ahead of the cavity, (b) along the
cavity floor, and (c) just downstream of the cavity for the wrap-around grid and

the patched grid in the Uh :50 case (case 1: no injection).

13S

 

I

 

P / Pinf

 

 

Figure 4.16 (cont’d)

 

 

 

 

 

 

 

1 .—
m.;:;:+:;;;4—¥W*H
I
0.8 r
a patched grid
0.64 1.:11“‘Ll.
1.5 2 2.5
XIL
(C)

136

 

 

 

 

4.5 Conclusions

A number of simulations were conducted to investigate a proposed free
stream-surface control structure generated by driving the flow within a cavity that
is placed in a supersonic crossflow. Simulations were conducted to assess the

dependence of the driven cavity flow field on the Mach number of the injected

 

fluid and the mass flow rate of the injected fluid for length-to-depth (Uh) ratios

that covered both open and closed cavity flow. In these simulations, the injection

 

was implemented as a patch boundary condition and the total mass flow rate was
controlled by the size of the injection boundary.

The results from the simulations on the closed cavity flows indicate that,
for the situations examined, the injection on the upstream face of the cavity has
little to no impact on the Mach number profiles downstream of the cavity. In this
situation, the impingement of the separated shear layer on the floor of the cavity

appears to wipe out any influences of the injected flow. In addition, the injected

 

fluid has very little impact on the pressure profiles observed on the floor of the
cavity and, therefore, is of little interest for the control of stores in aircraft. For the
influence of the flow on the stores, however, bleed through the floor of the cavity
combined with injection may result in the ability to tailor the location of the
impingement and to change the character of the pressure profile in the leading
edge of the cavity.

The results from the open cavity simulations provided a more direct
assessment of the capabilities and potential for the driven cavity form of control.

Without injection, an open-type cavity produces a dramatic jump in the boundary

137

;:I

layer thickness as the separated shear flow reconnects to the crossflow plate. In

 

this case, although the pressure recovery coefficient on the cavity floor is positive
and small, a pressure gradient does exist across the cavity floor. When fluid is
injected on the leading edge of the cavity, the effect was to reduce the
penetration of the separated crossflow into the cavity and to level the pressure

profile along the cavity floor ahead of the jump that occurs at reconnection.

3

Downstream of the cavity, the influence of the injected jets is difficult to
ascertain. In each case, the boundary layer profile was shallower than the
upstream boundary layer profile and the boundary layer profile was observed to
undergo an inflection near the halfway point. In these open geometry cases, the
injection had the greatest impact on energizing the upper half of the boundary
layer and not on the thickness of the boundary layer. The influence of the
injected jet on the boundary layer profile can be further examined by increasing
the total mass flow rate of the injected fluid. Since the depth of the cavity for the
main cases studied was only slightly larger than the boundary layer height of the
approaching fluid (often used as a bleed hole diameter measure), the injection
port could conceivably take up the majority of the leading edge surface. This
may result in a much larger boundary layer and a much fuller profile than was
observed.

An additional assessment of the influence of the boundary layer height on
the flow was conducted for the baseline case where Uh = 5.0. In these

simulations, the height of the boundary layer in relation to the depth of the cavity

7‘11

138

was shown to have a minor influence on the flow patterns that resulted. The
largest impact seemed to occur on the reconnection face of the cavity.

Finally, a comparison the grid system (wrap-around vs. conventionally-
structured grid) is presented. The results from this comparison indicate that the
grid is a sensitive issue in the study of driven flow fields. With the patched grid,
large aspect ratios exist directly in the region of the cavity where the separated
shear flow undergoes its greatest amount of turning. In addition, patched grid

boundaries exist at both the leading edge and reconnection lips of the cavities

and both of these regions are where much of the dynamics of the flow take place.

The wrap-around grid eliminates both of these issues, but instead introduces grid

elements that are skewed and distorted.

139

 

 

 

CHAPTER 5

Conclusions and Recommendations

5.1 Conclusions

CF D simulations of a mixed-compression inlet and two methods for
generating free stream-surfaces in a crossflow were conducted to motivate and
initiate the development of a free stream-surface control method for use in the
control of mixed-compression inlets. Where available, the results of these
simulations were compared with experimental data to validate the methods
employed and the conclusions reached. This research is presented to introduce
a method of inlet control using free stream-surface structures and to address
issues for future study. This includes items such as the location of bleed regions,
methods for shielding the injection process from the high momentum of the
crossflow, and areas for grid refinement.

During the simulation of flow through a mixed-compression inlet, several
objectives were achieved. First, a method was developed for initiating critical
flow in a simulation. Early on in this research one of the most difficult problems
encountered was transitioning the flow from the initial conditions to the critical
flow state. The flow initialization process was observed to be complicated by the

interdependence of the shock location, applied back-pressure, bleed rate, and

140

 

I ‘11

bleed location. To assist with future simulations of these types of inlets, a method
for initiating critical flow in a simulation of a mixed-compression inlet was
developed. The key elements of this process are (1) the use of “slow-start”
boundary conditions on the walls and (2) a method for positioning the terminal
shock that anticipates the reduction in the effective-area that will occur when the
solid surfaces are switched from inviscid walls to viscous walls.

A second outcome of these simulations was that a bleed boundary
condition, designed to discern the flow through individual bleed holes, was
implemented in the mixed-compression inlet. By modeling, instead of simulating,
the flow through the bleed holes, the number of grid points needed to simulate
critical flow was greatly reduced. In addition, this bleed boundary condition was
designed to better capture the physics of the bleed process such as the barrier
shocks and the flow turning that is characteristic of a bleed configuration.

In the simulations, this bleed boundary condition produced very different
results from the bleed-slot boundary condition that is commonly used in practice.
While both simulation of the bleed boundary condition and the slots led to
separation, the bleed slots simulations led to steeper boundary layer profile and a
stronger terminal shock. These differences highlight the influence of the bleed
hole configuration and the effects of removing the azimuthal variation in the flow
that is produced by bleed through discrete holes.

Finally, the simulations of the mixed-compression inlet have led to the
proposal of a method of internal flow control that has been termed “free stream-

surface control”. In this approach, small changes in the effective-area of the inlet

141

 

 

 

‘Tt/

‘i.

are generated by the combination of injection and suction in the inlet. This
process echoes the observations made during the development of the boundary
layer of the mixed-compression inlet simulations. This free stream-surface
control method could be used in mixed-compression inlets to mitigate the amount
of cowl translation that is needed in initializing the flow or, possibly, to assist in
the prevention of unstart.

After the simulations of the mixed—compression inlet were concluded, two
different approaches to generating a free stream-surface control process were
implemented to examine their potential for the control of a mixed-compression
inlet. The objective of these simulations was to determine the relevant
parameters of each method and to identify any issues associated with their use
or implementation.

The first free stream-surface control mechanism that was examined used
combined injection and suction to generate closed surfaces within the crossflow.
In these simulations, the injection was modeled as a simple square injection port
with a supersonic inflow boundary condition and the suction region was modeled
with a boundary condition that permits bleed through discrete holes. Using this
approach, it was observed that the combined injection and suction produced
significant and easily recognizable free stream-surface control surfaces whose
height could be adjusted by modifying the injection Mach number. The injected
jet was observed to penetrate some distance into the crossflow and then turn and

reconnect with the flat plate surface downstream of the bleed region.

142

 

 

 

i “Til

Two issues associated with the method were identified. The first involves
the degree to which the penetration of the crossflow was achieved with changes
in Mach number. In these simulations it was observed that the maximum height
achieved by the free stream-surface was linearly related to the injection Mach
number. To affect meaningful control of the inlet profile with jets injected directly
into the crossflow, this method would therefore require a significant energy input
to achieve even modest results.

The second issue involves the generation of a zero net-mass flow and the
bleed process used in the simulation. The discharge coefficient boundary
condition for choked bleed through discrete holes does not permit the
determination of the bleed rate as a part of the boundary condition. In addition, it
was observed that the majority of the flow that was bled through the plate surface
was from the fluid that was diverted by the jet rather than from the jet itself. The
injected jet still responds to the bleed region, but it is not completely bled away
by the suction region. This, however, may not be a negative issue for the
system in that the boundary layer downstream of the bleed region is much fuller
than it would have been without the free stream-surface control mechanism.

One other observation arising from these simulations is that the use of
individual injection holes would lead to a distorted control shape and that a slot
approach would be preferred even though the slot can only be implemented
within an axisymmetric mixed-compression inlet in a modified form. To satisfy

this issue, it was proposed that the slots could be replaced with closely packed,

143

‘1‘!

elongated ellipses. While this system will have a distorted shape around the
gaps in between the slots, it will, for the most part, behave as a uniform slot.

The second method for generating a free stream-surface involved the
injection of fluid into a cavity that is recessed within the crossflow. In this
approach, fluid injected through the sidewall of a cavity would drive the cavity
flow and cause the separated of the crossflow to be diverted. In this manner, the
injected fluid would be shielded from the high momentum of the supersonic
crossflow and still be capable of altering the boundary layer profile downstream
of the cavity. With a driven cavity, the downstream bleed needed to close the
free stream-surface would be provided by the bleed holes that are normally used
in the operation of the mixed-compression inlet.

Two different cavity geometry configurations were examined in this part of
the research: open-cavity flow and closed-cavity flow. In the open-cavity flow,
the length-to-depth ratio of the cavity was less than ten and the separated shear
layer does not impinge of the floor of the cavity. In these simulations, the
injected fluid was observed to affect the penetration of the crossflow into the
cavity and to level out the pressure profile on the floor of the cavity, however, the
impact of the injection on the downstream Mach number profiles and the
boundary layer height was insignificant when compared with the action of an un-
driven slot on the crossflow.

In the closed-cavity flow simulations, the injected jet had almost no impact
on any of the examined parameters: pressure profile along the cavity floor,

downstream Mach number profiles, boundary layer height. The strong effects of

144

 

 

 

1”"!

the crossflow impinging on the floor of the cavity were too much for the injections
studied. In this configuration, the injection on the leading edge of the cavity

would most likely affect the location of the impingement.

5.2 Recommendations

This study is a first step in understanding the use of combined injection

and suction to control flow throughout a mixed-compression inlet. The motivation

 

for this study has been to identify and develop methods for controlling the
location of the terminal shock within an inlet and preventing unstart. Continuing
toward this goal, the next phase in this study should include several simulations
involving the transverse injection of a jet into a supersonic crossflow to further
identify the characteristics of the jet and this control method. In addition, further
lines of investigation should address the shielding of the injection process and
develop methods to achieve a boundary layer profile that is both thicker and fuller
so that it will provide the desired level of control and resistance to separation.
Future research would also involve implementing this control structure in a
simulation of a mixed-compression inlet.

The first simulations conducted after this work should replace the coarse
model of the injection port, presented in the third chapter, with a contoured
nozzle for which experimental data exists as a basis for comparison. Although
changing the method of injecting the fluid into the crossflow from a straight
injection port to a nozzle would require significant additional grid generation, this

would be necessary for a thorough examination of the jet-in-crossflow problem

145

”-51

and for generating injection boundary condition patches so that the free stream-
surface control system can be implemented in a mixed-compression inlet
simulation

Once these simulations are completed, the bleed through discrete holes can
be implemented, and the general characteristics of the free stream-surface
control structure can be examined in further detail for a round-hole injection.
These simulations will benefit from the development of the discharge-coefficient
bleed boundary condition and can utilize the same grid and solution from the
previous studies. From these simulations, information about the shape and size
of the control structure, as well as a functional relationship between the shape
and the relevant parameters, can be acquired. As a additional study, if the
turbulence characteristics of the jet-in-crossflow can be adequately modeled in
simulations, it would be interesting to examine the effect that the addition of
suction has on the mixing properties of the jet.

For the driven cavity method for controlling the flow through an inlet, future
research should focus on examining the effect of increasing of the mass flow rate
for the injection and on inserting injection within the driven cavity flow to control
the reconnection of the separated shear layer. Methods also need to be
established to generate a fuller velocity profile downstream of the cavity. To
achieve this, experiments with supersonic injection into the subsonic cavity flow
may lead to improvements in the boundary layer profiles.

For both of the approaches examined, an additional consideration that

needs to be addressed in this research is the response of the system to oblique

146

 

 

 

{”1

and normal shocks. The environment where this system is envisioned to
operate is complex in structure and rich in oblique shocks. When an oblique
shock impinges on the structure, it is anticipated that the boundary layer would
thicken appreciably, but the response of the system is unclear. As the boundary
layer thickens, however, the profile above the downstream suction holes would
be affected as well and it is important to characterize this response.

Finally, the stability of the suction-injection system in response to changes
in the freestream conditions needs to be examined. This can be accomplished
by imposing perturbations on the freestream boundary conditions in time-
accurate simulations of a zero-net-mass flow system. Because of the grid
spacing requirements near the solid surfaces, the time steps for these
simulations will be very small. Although the perturbations will be in the
streamwise direction, the variation and dynamics in the normal direction are

significant and need to be addressed.

147

 

my

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