NN

I ~CF

EI I

DTIC* ~ ELECTE

*DEPARTMENT OF THE AIR FORCE D ~O19AIR UNIVERSITY

AIR FORCE INSTITUTE OF TECHNOLOGY

Wright- Patterson Air Force Base, Ohio[SA~14

096

AFIT,/GAE/ENY/89D- 10

THSI

AXISMMEN TRST AUMETN

Kenneth 77 R. ag, C p n USAF

AFIT/GAE/ENY/89D-10II

NUMERICAL ANALYSIS OF AN AXISYMMETRIC THRUST

AUGMENTING EJECTOR

ITHESISI

Presented to the Faculty of the School of Engineering

of the Air Force Institute of Technology

Air University

In Partial Fulfillment of the

Requirements for the Degree of

* Master of Science in Aeronautical Engineering

II

Kenneth R. Gage, B.S.

Captain, USAF

I

December 1990

II Approved for public release; distribution unlimited

I

Acknowledgments

This project has been a long time in work and has been

full of ups and downs, more than I care to recall. Through

it all, the support of a few people have kept it, and me,

all going. I would like to take this opportunity to thank

them.

To my advisor, Dr. Franke, for supporting me in taking

on a project which interested me although it was somewhat

out of his field.

U To Dr. Joe Shang, for giving me access to the resources

and personnel to help me along and for the guiding hand when

I needed it most.

To Dr. Don Rizzetta, for helping me iron out the little

technicalities.

Especially to Dr. Kervyn Mach, for setting up and

guiding me through the myriad complexities of working on an

unfamiliar system and for helping me to understand the

program I had to modify!

But mostly to my wife Barbara, who had to put up with

what seemed like an interminable wait. Aocession For

i

D T I C T A BUnannounced

ElIf d ElJustificatio_____'_

By_Distri_bution/

_ vailability Codes

I

NDst

S ec a

Avil ard/or-

ii

s.i

Table of Contents

U Page

I Acknowledgments .. .................... ii

I List of Figures. ...................... v

List of Tables ...................... vii

Notation. ....................... viii

* Abstract .......................... x

I. INTRODUCTION. ..................... 1

Background .................... 1

Purpose and Objectives. ............. 8

Scope. ...................... 9

II. COMPUTATIONAL APPROACH AND PROCEDURES . . . . 11

Ejector Geometry .. .............. 11

Grid. ..................... 12

I Flowfield Initialization .. .......... 13

Flow Solver .. ................. 15

Incorporation of Nozzle Structure . . . . 20

Boundary Conditions. .. ............ 22

* Turbulence Model .. .............. 26

Procedure .. .................. 27

I III. RESULTS AND DISCUSSION. .. ............. 29

I Cases Investigated .. ............. 29

Table of Contents (cont.)

P age

Primary Objectives .. ............. 30IComparison With Experimental Data 30

Data Visualization. .. .......... 35

I Flexibility .................. 40

Secondary Objectives .. ............ 40

Injection Angle .. ............ 41

Nozzle Position .. ............ 45

* Nozzle Area Ratio .. ........... 50

IV. CONCLUSIONS. .................... 53

V. SUGGESTIONS AND RECOMMENDATIONS .. ......... 55

APPENDIX A: GRID GENERATING PROGRAMS AND TABLES A-i

A-i: EJECGRD. ................. A-2

A-2: DEHNEN .. ................. A-8

A-3: EJECVRT .. ............... A-10

3A-4: EJECHRZ .. ............... A-12

APPENDIX B: FLOW SOLVING PROGRAM: JSIAXK . . . . B-i

APPENDIX C: POST-PROCESSING PROGRAM: AUGMENT . C-1

Bibliography

Vita

I iv

II

List of Figures

Figure Page

1. Ejector Concept ....... ............. 2

2. Ideal Thrust Augmentation vs. ...... 2

3. Ejector with Diffuser ............... 4

4. Thrust Augmentation as a Function of a

and )3 ... ............. .8.6

5. Ejector with Coanda Nozzles... ....... 6

6. Control Volume ...... ............. 10

7. Ejector Geometry .. ............ .11

8. Plane of Modeled Flow ............ .12

9. Computational Grid . ........... .14

10. Identification of Nozzle Exit Corners . 21

11. Identification of Nozzle Walls ..... 22

12. Application of Boundary Conditions . . 23

13. Nozzle Locations .. ............ .31

14. Exit Velocity Profile - Numerical . . .. 32

15. Exit Velocity Profile - Experimental . 32

16. Thrust Augmentation vs. Injection Angle

Numerical ............ .. 33

17. Thrust Augmentation vs. Injection Angle

Experimental . ......... .34

18. Total Velocity Contours ......... ... 36

19. Streamlines ... ............... .. 37

20. Velocity Vectors - Nozzle Area ..... 38

21. Inlet Velocity Profiles ......... ... 38

22. Mixing Chamber Velocity Profiles . . .. 39

23. Diffuser Velocity Profiles ....... .40

24. Velocity Contours:.± = 64 degrees 42

25. Exit Velocity Profiles:

o i = 52 and 64 degrees ....... .42

Iv!V

I

List of Figures (cont.)

Figure Page

26. Velocity Contours: i = 36 degrees . . 43

27. Exit Velocity Profiles:

O i = 52 and 36 degrees ....... .44

28. Reference Injection Angles ....... .45

29. Optimum Injection Angle with Relation

to Reference Angles ........ .46

30. Augmentation vs. Position Angle .. ..... 47

31. Nozzle Velocity Profile:

Configuration 3 . .......... .47

32. Nozzle Velocity Profile:

Configuration 0 . .......... .48

33. Pressure Contours: Configuration 3 . 49

34. Pressure Contours: Configuration 0 . 49

35. Augmentation vs. Nozzle Area Ratio (m) 40

36. Augmentation vs. Nozzle Area Ratio (1/G.)

Numerical and Experimental .. ..... 41

v

Iv

I

IList of Tables

* Table Page

I. Nozzle Geometries .. ............ .. 30II. Thrust Augmentation Comparison ..... 34

III. Augmentation with Changing Injection

Angle (X±) .............. .. 41

IV. Augmentation with Changing Nozzle

Area Ratic (oX) ............ ... 50

ii

!I

II

I- vii

III

A Cross-Sectional Area of Mixing Region

AE Cross-Sectional Area of (Diffuser) Exit

Ai Cross-Sectional Area of Jet

A* Critical Area

cv Specific Heat of Constant Volume

D Van Driest Damping Factor

e Energy

F Thrust Force

Fnoz imen Isentropic Thrust of Primary Nozzle

Fwake Wake Function

j Radial Grid Index

k Axial Grid Index

L Scaling Length

Li, L2 Diffuser Section Lengths

Li Nozzle Position

M, N Integers

P Static Pressure

Po nom Nozzle Stagnation Pressure

Pi Static Pressure at Jet Exit Plane

Pa Ambient Pressure

Prat Pressure Ratio

Pr Prandtl Number

Prt Turbulent Prandtl Number

R Gas Constant for Air

r Radial Cylindrical Coordinate

T Static Temperature

Ta Ambient Temperature

Tw Constant Wall Temperature

t Time

u Axial Component of Velocity

Uref Reference Velocity

viii

Notation (cont.)

V Total Velocity

V1 Secondary Flow Velocity at Jet

Exit PlaneVI? Velocity at Exit

Vj Jet Velocity

v Radial Component of Velocity

x Axial Cylindrical Coordinate

y* Critical Distance from Wall

Cj Nozzle Area Ratio Aj / A

O i Flow Injection AngleI / Diffuser Area Ratio AN / A

Ratio of Specific Heats

Turbulent Viscosity

"Axial' Curvilinear Coordinate'Radial' Curvilinear Coordinate

0 Nozzle Position Angle

Viscosity

I Density

Normal StressesI "C Shear Stresses

0 Thrust Augmentation Ratio

Y', Y2 Diffuser Angles

Vorticity

ix

I

Use of an ejector is an effective way to increase the thrust

produced by a jet. In this thesis project an axisymmetric

ejector concept which had been previously explored by

experiment was numerically modeled. An existing

axisymmetric, internal flow code based on the explicit

MacCormack method was modified to incorporate primary nozzle

structure and flow injection within the flowtield. Results

were compared qualitatively and quantitatively with

experimental results to verify the validity of the model.

Internal flow structure, difficult to obtain in experiment,

is easily examined. This code may be used for parametric

analysis of such ejector performance parameters as primary

nozzle location, flow injection angle, diffuser area ratio,

and inlet geometry to optimize future hardware

configurations.

Ix

7

It

IiII

I

NUMERICAL ANALYSIS OF AN AXISYMMETRIC THRUST

AUGMENTING EJECTOR

I Introduction

iI Ejectors provide an attractive solution to a problem

which has plagued designers of jet powered Vertical/Short

Takeoff and Landing (V/STOL) aircraft since they were

conceived. The problem being, that in order to get thrust

greater than the weight of the vehicle such that vertical

takeoff or landing can be achieved, an aircraft must be

equipped with a powerplant which is larger (sometimes

substantially) than that which is needed for its primary

mission. Ejectors, due to their thrust augmenting

characteristics, provide a means for achieving thrust to

weight ratios greater than unity with a more reasonably

sized powerplant.

In an ejector, a jet flow is directed into an open duct

of somewhat larger cross-sectional area. A secondary flow

is induced through the duct by viscous entrainment (Figure

1). A simple analysis de'.3loped by Von Karman (18:461-62)

shows that the thrust theoretically achievable by such a

process is up to twice that of the primary nozzle alone

(Figure 2).

I

I

Fig. 1. Ejector Concept (9:281)

I20

I

)5

I

I 35

I

0 02 04 06 08 '0I =A/A

I Fig. 2. Ideal Thrust Augmentation vs. O (9:281)

2I

The thrust augmentation ratio (0) is defined as the

ratio of the total thrust of the ejector (F) to the

isentropic thrust of the primary nozzle alone (assuming

I incompressible flow):

= (VF/A / V A

U

where O is the ratio of the area of the jet (Aj) to the area

of the mixing chamber (A)

5 a = Aj/A

and VE/Vj is the ratio of the flow velocity following

1 complete mixing (VE) to the flow velocity of the primary

nozzle (Vj) found by applying continuity f-om the jet exit

3 plane to the exit of the ejector:

V, (A-A,)+ VA J = VEA (2)

and applying conservation of momentum:

A (PI-P) = 'A Vp - QA1 V'2 - Q (A-A) V1 (3)

Applying Bernoulli's equation from ahead of the inlet to the

U jet exit plane:

3 P(I = P1 + - V (4)

3 gives three eqLations in three unknowns, Vx, Vi, and Pi.

3U

Eliminating Vi and Pi, the velocity ratio, VE/VJ, is found

to be:

i V - -za ( 1 - 2z_) +( 2 - 6(22 + 6(Z3 -4 ](

I 2a + 2t9) ___ _ _ 51 (7:28)

The thrust augmentation achieved may be further

increased through the use of a diffuser (Figure 3).

I

I 1[_V1

Fig. 3. Ejector with Diffuser (9:283)

IThrough a similar analysis, the modified equation for a

3 diffuser equipped ejector is found to be:

I-IV + 2fi(I -2a) 1 2a -3a(2

/)2+ /) [( - + 2 I - 0-2ia+a2(l+t2 =o (6)SJ 2-1

(9:282)

4U

4U

I!

with 0 now given by (assuming incompressible flow):

QV / V (/rI = ( 1/)2 (A[.,IA) (AIA/)

I=(Vj:/IJ) 2 (fla) (7)

I where:

= AL/A

with VE and AE as defined in Figure 3 (9:282-3).

Plotting the thrust augmentation ratio shows that for

every primary nozzle to mixing chamber area ratio (Aj/A)

there is an optimum diffuser area ratio (AE/A) which

provides the maximum thrust augmentation (Figure 4).

Within the practical limit of area ratios, it can be seen

that thrust augmentations of up to 3 times the primary jet

3 thrust are theoretically achievable.

These theoretical values, however, assume that the

ejector is long enough that complete mixing of the primary

and secondary flows takes place. In practice, the size of

the ejector is limited by aircraft installation constraints

and frictional effects, which lead to separations in long

diffusers. In such short ejectors mixing is incomplete and

coanda nozzles, in which the jet flow is injected along the

wall (Figure 5), hiave proven to be more effective due to the

3 greater mixing surface area of the primary jet. (9:286)

Coanda nozzles provide an additional benefit for

3 ejectors equipped with a diffuser in that the high energy

flow along the wall helps to prevent separation in the

diffuser allowing greater area ratios to be achieved.

55U

a -002

U 30k

2 0 ra=004

0 a=0000 20 3.0 0 .0 60 70 80 0

a=2036 032 028 024 a=0162

IFig. 4. Thrust Augmentation as a Function

of cL andA,. (9:284)

Secondaryf low

P Pr mory

I Fig. 5. Ejector with Coanda Nozzles (9:285)

6

In a previous study, Kedem, (6) experimentally inves-

tigated a two dimensional ejector with center and coanda

nozzles and found that coanda nozzles did provide better

performance (6:51). Reznick (11) and later Unnever (17)

expanded on these results by testing both two dimensional

and circular ejectors with coanda nozzles. The circular

ejectors provided the best performance, achieving a thrust

augmentation ratio of 2.09. This was accomplished through

the use of discrete jets located about the periphery of the

inlet which are referred to as 'hook nozzles' because of

their hook-like shape (11:44). This approach was further

investigated by Lewis (8) and later Uhuad (16). Hardware

3 limitations necessarily constrained the various

configurations which could be tested. It is desirable to

have a computational model of a circular ejector which is

free of such limitations. With this model a full range of

inlet and diffuser geometries, nozzle sizes and positions,

and nozzle plenum pressures can be investigated. The

computational solutions also provide complete data on the

3 behavior of the flow within the ejector, which is difficult,

if not impossible, to obtain experimentally. This model

3 has, however, been constrained to an axisymmetric case to

reduce complexity and required computational power. This

eliminates the possibility of modeling the hook nozzles used

to achieve the high thrust augmentation observed by Reznick.

This model is therefore constrained to the case of an

annular nozzle, which was also one of the configurations

tested by both Reznick and Unnever.

IIII

7

I

Puryos and Objectives

The primary objectives of this study are:

1. Develop a numerical algorithm that models a coanda

flow axisymmetric ejector of the type tested by Reznick and

Unnever.

2. Validate the model by demonstrating agreement with

experimental results.

3. Provide data visualization of internal flow

characteristics.

4. Provide sufficient flexibility to accomplish

secondary objectives.

5. Begin preliminary investigation of secondary

objectives.

*The secondary objectives are:

1. Investigate the geometrical and fluid injection

3 parameters which effect ejector performance. The parameters

which may be investigated include:Ia) Fluid injection angle

b) Nozzle position

c) Nozzle area ratio

d) Diffuser area ratio

e) Diffuser geometry

f) Pressure ratio (Pa nox / Pa)

2. From this parametric analysis, define new ejector3 configurations which may merit further experimental

investigation.

II

8I

A generic axisymmetric, internal, Navier-Stokes flow

solver based on the explicit MacCormack method provided by

WRDC/FIMM was modified to incorporate primary nozzle

structure and flow injection within the flowfield (program

JSIAXK, App B). A diffuser geometry, nozzle pressure ratio,

and nozzle exit area and location were chosen for each run.

The program was then run to a steady-state solution for a

given flow injection angle (Q i). The injection angle was

then varied and the run continued to new steady-state

solutions to collect data on Mi - variation of augmentation.

Additional runs were made with different nozzle locations

holding pressure ratio, nozzie area, and nozzle distance

from the wall constant to provide data on nozzle location

effects on augmentation. Also, runs were made with

different nozzle areas for the same location to provide data

on area ratio effects. Runs with different geometries and

pressure ratios could provide data on variations with these

parameters.

The achieved thrust was calculated by a control volume

analysis (Figure 6). This analysis results in the equation:

F = IAU2dA (8)

where the right side of the equation is the integral of the

x - momentum at the exit (5:12-13). The achieved thrust was

compared to the isentropic thrust of the primary nozzle

alone to calculate the thrust augmentation ratio as in

equation (5). Thrust augmentation ratios were compared

directly with experimental data for similar configurations

and the differences analyzed. Exit plane velocity

distributions and variation of thrust augmentation with C.i

9

and position were compared qualitatively with available

experimental results.

I

Fig. 6. Control Volume

I

IIUII

l 10

II COMPUTATIONAL APPROACH AND PROCEDURESIEjector Geometry

The geometry of the axisymmetric ejector which was

investigated by Reznick and Unnever and was modeled in this

study is portrayed in Figure 7. The mixing chamber was 4.4

inches in diameter and 3 inches in length, the inlet lip had

a 2-inch radius of curvature, and the multi-section diffuser

could be changed to alter the diffuser angles (Y1 , )"2, .... )

and lengths (Li, L2, .... ), up to three sections, and thus

the area ratio AN/A. The annular exit of the nozzle had a

gap of 0.065 inches and a radius of 3.0025 inches and could

be positioned at any distance (Li) from the ejector throat

(constant area mixing chamber). (17:52)

a Y

I :

I Fig. 7. Ejector GeomeLry

11

m1

ii

The computational grid was generated using the program

EJECGRD (Appendix A-1) provided by WRDC/FIMM and modified

for the required geometry. Taking advantage of axial

symmetry, the grid models a single radial/axial plane from

I the centerline to the wall (Figure 8).

I

i. Plane ofinterest

I

I Fig. 8. Plane of Modeled Flow

* The vertical (radial) grid lines are defined as

follows:

i For the inlet, by circular arcs perpendicular to the

wall and centerline.

I12

I

II

For the mixing area and diffuser, by parabolas

perpendicular to the wall and centerline (which

degenerate to straight lines for the mixing area).ISpacing between horizontal grid lines was varied

exponentially to refine the grid near the wall where large

gradients are found due to the jet. The grid was also

refined near the centerline to minimize the effects of the

boundary conditions. Spacing between vertical grid lines

was varied exponentially to refine the grid in the vicinity

of the inlet (and the jet exit) to help offset the tendency

of the gri. to spread out due to the increasing radii of the

circular arcs in the inlet and also to concentrate on the

larger gradients upstream. The exponential spacing was

accomplished using the program DEHNEN (Appendix A-2) also

provided by WRDC/FIMM which was used to produce vertical and

horizontal grid spacing tables, EJECVRT and EJECHRZ

(Appendices A-3,-4). Once a nozzle location was identified,

the grid was refined both vertically and horizontally in the

area of the nozzle exit. An example of the grid is shown in

Figure 9. Note that only every fourth grid line has been

3drawn for the purpose of clarity.

Flowfield Initialization

U The program EJECGRD also calculates an initial

flowfield based on a simple one-dimensional flow area ratio

formula given a value of the critical area (A*), the duct

area through which the flow would theoretically be sonic.

This critical area was chosen to provide a reference Mach

number at the diffuser exit of 0.1 (111.7 ft/sec). This

program was modified to overlay a high-speed jet flow over

the low speed duct flow calculated by this procedure. This

13

IIIIIII ~ 1

-oI0'-4

I -~ K 0"-44-,

4-'I0I K

IIIIIIII 14

was necessary because the formula used assumes a mass flow

balance betwe3n the beginning and end of the duct. If the

jet flow is not accounted for, this provides an extremely

S or initial flowfield which can lead to extended processing

time or even cause the solution to 'blow up', or diverge, as

the flowfield tries to adapt to the increased mass flow

injected by the primary nozzle.

Flow Solver

The flow solving program JSIAXK (Appendix B) solves the

conservative form of the Navier-Stokes equations using the

explicit MacCormack scheme. The conservative Navier-Stokes

equations in axisymmetric coordinates are (3:3):

Equation of Mass

(30o)+ Q(a1) + 0 .~ =t 9

Equation of Axial Motion

(-u ) + (1-A(u2) + (1/r) )r(cUvr) = -(q) + (1/r) r( r TJ ( 1U )(Ir o3r ()X Or ( U

.. Equation of Radial Motion

-(n)v) + ( UV) + (1/r) (ov2r) = (Tr) + (1/r) -- (r, ) - ( 1(3 jiOX or ax or

15

Energy Equation

(3 (33eF

(oue) + (11r) twer)1(i 3x(wr)a P ~4 ("Y +

+c +--- (-u' + -1r )3 -i rE ir,+ v(,

(/ pr P Pr, J (12)

These equations are written in vector form as (4:17):

a~ ± + F (11r) aG (11r)H()

where:

L Pr Pr

( -UV r

(uer - y/ 0-(- + -)-(un. + vUx)L x Pr Pr,

Iy

16

0I01-U H

0

The transformed vector equation for general curvilinear

* coordinates is:

__ + --- + .. . + (1r + Or] = (NI O Ox Ot ,)x a or OrI (14)

Applying the explicit MacCormack scheme to the vector

equation results in the following algorithm (4:27):

0( , 7 . t+ At) = L,(At)0( , q. t) (15)

where L(At) is the two-dimensional numerical operator

representing MacCormack's algorithm acting on the

transformed conservation equations. Through use of time-

splitting, this two-dimensional operator is separated into

two one-dimensional sweep operators in the - and) -

directions. The operator L (at) represents the solution of

the equation:

+ + (1/r)- - 0 (6t O Ox O Or16)

in the ( - direction by a time increment of Lt seconds. In

a like manner, the operator L,(At) represents the solution

of:

OU + O _ + ( 1 /r) q - (l/r)HN t q r Ox Oq Or (17)

3 in the -direction by a time increment of At seconds.

117

I

The dependent variable vector U(C , , t) can then be

advanced in time as:

U(' .q.t + At) = [L /-At/M) L,(At) L' /'(At/M)I U( . i ,) (18)

with At = At, if Atl < At

or as:

C J, ,t + At) = L/2(&/N) L(At) L /2(At/N)j U( 1.7 t) (19)

I with At =At if At, < At

Uwhere M and N are the smallest even integers of the

quotients (At,/itC ) and (AtC/At,) respectively. The

3 timesteps 8t( and At, are the maximum allowable timesteps in

the - and I - directions as determined by stability

3 requirements.

The finite difference form of these sweep operators

consist of a two step predictor - corrector procedure which

uses one-sided differencing in the direction of sweep and

central differencing in the direction perpendicular to the

direction of sweep. When complete, this method is

equivalent to a second order central differencing scheme in

3 two dimensions.

III

18I

The LC(At) sweep operator represents the following

numerical procedure (4:29):

PREDICTOR

1+1. . At ((Uk.1 (uk. 1 0 .- ) - (Fk-_.j)] (y)k.,j

At ,

-(1r) [rk, (Gk.Y' - rk.j (Gk-1jY1 (-r)k.

(20)

I CORRECTOR

(U. 12 { (k]! 4-- + -(/+ J ,) - (Fk.1Y2±/2J+(,A: ax

I(11r) At [rk +l.r+ ,k,1 (kj)r'l V),

- ) ar (21)

Similarly, the L,(Lt) operator represents the following

predictor - corrector steps (4:29,31):

IPREDICTOR

(U .,, +-" = (uk1.,y - [(,k.r - (Fk. 1-1Y'I (---)k.j

1/)At - -

- 11r( -- I ( k.,Y' - rk,j (Gkj-fJ (-)k j + (I/r) At (HkY'

3(22)

19

CORRECTOR

= - {uk. + - . - (E +YI+ (.%.

At, .U-(1/r)- A Irk., (6k.,+I rY' k,, (6k.JY?+±"'I (o -- )k,. + (11r) At (H1 J

(23)

I where n and n-1 designate values at time t and t + At

respectively and n+1/2 indicates a temporary, predicted

value. The values _ and 2 depend only on thevalue.X Th vaue , J.X , 3rgrid geometry and are calculated only once for each grid

i point.Variants of this program for two-dimensional internal

flow and three-dimensional external flow have been used in

studies by Olson, McGowan, and MacCormack (10); Shang,

Hankey and Smith (13); and Shang and MacCormack (14). The

3 internal axisymmetric version of the code was developed for

in-office use by WRDC/FIMM.IIncorporation of Nozzle Structure

In order to model the ejector geometry desired, it was

necessary to identify boundary conditions which accounted

for the nozzle structure and the flow injection at the

3 nozzle exit in addition to the usual wall and centerline

conditions. Once the desired location of the nozzle exit

3 was selected, the grid was refined in that area to better

handle the large gradients which exist at the nozzle exit.

Then, the grid points which best approximated the corners of

I the desired nozzle exit were identified (Figure 10).

20I

Inlet

)\!, \ ,\v \',

• ." \\\ \V ,.\ \ ,

>~4 a

Nozzle.• " .'.Exit ." " ..

Corners-,

Fig. 10. Identification of Nozzle Exit Corners

The outside walls of the nozzle structure were defined

as being three grid lines outside the nozzle exit. The

outside walls and ends of the nozzle structure were defined

as SOLID WALLS for the boundary conditions (Figure 11).The grid points in the gap were defined as the NOZZLE

EXIT for the boundary conditions. The area enclosed within

the nozzle structure did not effect the computation of the

flowfield and was set to zero velocity. Figure 12 shows a

diagram of the grid boundaries with the types of boundary

3 conditions applied identified.

I

211

II

,Wa I I

" •Exit

No lezl

.Wall s.I/ .-. x:

3 Fig. 11. Identification of Nozzle Walls

Boundary Conditions

Boundary conditions were imposed to accommodate the

geometrical restrictions on the flowfield by defining the

solid surfaces, to incorporate primary nozzle flow based on

a constant plenum pressure, and to provide the necessary

upstream and downstream conditions to achieve closure.

I

II

22

Ii

2 3

II

SuI L-[ ..ALL' 4 UPSTkEAM

L EjT-PL i SL ZZLE EX T

3 Ji0,,STREA 6 Set to Zero Velocity

IFig. 12. Application of Boundary ConditionsI

~Solid Walls. For the wall of the ejector and the inner

and outer walls of the primary nozzle, applying the

conditions of no penetration and no slip provides:

3(u). = 0 (24)

3 (ov). = 0 (25)

Allowing no normal pressure gradient ( L = 0 ) leads to:

((e) = [ el - / (u4 + V2) 1 (26)

Applying a constant wall temperature Tw:

= (Qe)w / (cvTw) (27)

where the subscript w indicates the value at the wall and

3 the subscript 1 indicates a value taken one grid point away

from the wail.

I| 23

i

ICenterline. Since the centerline is the axis of

symmetry, there can be no cross velocity. This results in

the equation:

(QV)CL = 0 (28)

i Also, there can be no radial gradients of u, ', or T ( =

/ _ _ 0 ), resulting in the following equations:

(JCL = Q1 (29)I(Qu)cL = (Qu) 1 (30)

S(Qe)CL = (Ce)l - '/2 (Qv) / QCL (31)

-- where the subscript CL indicates the value at the centerline

and the subscript 1 indicates a value taken one grid point

*m away from the centerline.

Downstrea. Enforcing conservation of mass in the -

direction ( - + 1/r = 0 ) by allowing -e" = 0 and-- e( v r aV 30 gives:

(Qu)K = (QU)K-1 (32)

(()V') = (evr)K-1 / rK (33)

where the subscript K indicates the value at the downstream

boundary and the subscript K-I indicates a value taken one

grid point upstream. Since the flow in the ejector modeled

is exclusively subsonic, the exit static pressure must equal

2

i24

I

the ambient pressure Pa. Applying this constraint and

allowing temperature to propagate downstream leads to:

()K = P, / RTKl (34)

(Qe)K = OK I (CJK ) + V_ (UK + vK) J (35)

Upstream. Enforcing conservation of mass in the -3 direction as was done on the downstream boundary leads to:

(Lu)i (QU)2 (36)

(U) = (Qvr)2 / r1 (37)

where the subscr'pt 1 indicates the value at the upstream

boundary an,' -,,e subscript 2 indicates a value taken one

grid poir. ownstream. Additionally, assuming incom-

pressitle, isentropic flow from ambient stagnation

conditions results in the equations:

(Q)I = P. / RT (38)

(e ) , = ( [ (c.FT.) + 1/2 (u{ + vf) (- l)/y 1 (39)

I where Pa and T, are the ambient stagnation pressure and

temperature respectively.

nozze Exit. The nozzle exit was treated the same as

Sthe upstream boundary except that the nozzle total pressure

(Po nom) was based on the defined pressure ratio (Prat):

PO) noz = Prat(Pa) (40)

I and the direction of the flow was constrained to the desired

injection angle (c i).

25I

I

Turbulence model

The turbuleace model used in the original program was a

modified Baldwin-Lomax model based on the upper surface.

This turbulence model uses a two region calculation of the

eddy viscosity (14:4). The inner region calculation e is

* used up to the distance y* from the wall after which the

outer region formulation Eo is used. The distance y* is the

defined as the smallest distance from the wall at which Ei

and 0o are equal.

The inner formulation is given by (14:4):

(i = Q (0.4 L D)2 Ijo I (41)

where the vorticity of the flow, W, the Van Driest damping

factor, D, and the scaling length, L, are given by:

3 = 1AV (42)

1) 1-exp[ ( -C.Iw o. I / u. )I L / 26 (43)

L = [ (_ _ X") 2 + (r - r") 2 f/ ' (44)

and the subscript w represents the value at the wall. The

outer formulation is given by (14:4):

0.0336 p FWk / [1 + 5.5 (0.3 L/Lmax) 6 1 (45)

where the wake function, Fwaka, is the minimum value of the

following at any point in space:

Fwake = Lmax Fmax

or F,,,ke = 0.25 Lmax V2ax / Fmax (46)

1 26

and Lmax is the value of the length scale, L, where F:

F = L D (47)

reaches its maximum value, Fmax, within the turbulent shearlayer.le To simplify this investigation, no attempt was made to

identify better turbulence models for this type of wall jet

flow. The turbulence model already incorporated in JSIAXK

was not changed but was based on the nearest wall to include

nozzle wall effects.

Once the desired location of the nozzle exit was

identified, the vertical and horizontal grid spacing tables,

EJECVRT and EJECHRZ (Appendices A-3,A-4), were modified to

refine the grid in that vicinity. EJECGRD was then run to

produce the grid and establish the initial flowfield.

Setting the flow injection angle (a-i) to approximate the

flow direction established by the simplified initial

flowfield (to minimize extreme gradients) the flow solver

JSIAXK could be started.

Initially, the timestep per iteration was kept small

until the larger gradients could be smoothed out, then was

increased to provide faster convergence to the steady state.

Once the large gradients of the initial flowfield were

Ssmoothed out, it was also possible to change~i until the

desired value was set. The program was then run until

steady state was reached. Steady state was defined for the

purpose of this investigation as a change of less than 0.001

ft/sec in total velocity at each of four critical locations

in 3000 iterations. This process took approximately 90,000

27

iterations to complete at 0.151 CPU seconds per iteration on

the CRAY XMP computer. This solution was then stored on the

Central Datafile System. A new O i was then set to the next

angle of interest. Convergence on a new steady state

solution then took approximately 3600 iterations.

This process was continued until solutions were

achieved for all desired injection angles for the

configuration under investigation. For a new nozzle

location, the process was restarted from the beginning.

Configurations la, lb, and ic were able to be run

consecutively because the changes to the flowfield were

minimal in switching from one to the other.

The post-processing program AUGMENT was then run for

each flowfield solution. This program integrates the x -

momentum across the exit and compares it to the isentropic

thrust of the nozzle alone to calculate the thrust

augmentation per the control volume analysis described in

section I. A sample comparison of mass flows in and out was

also accomplished to ensure that conservation of mass was

being satisfied.

IIIII

28

II

III. Results and Discussion

Cases Investigated

The cases investigated consist of four nozzle location

configurations fc one ejector geometry. The geometry of

the ejector was ,elected to be similar to one investigated

by Unnever to allow for direct comparison. The dimensions

of the ejector studied by Unnever (Figure 7) were (17:60):

Li = 3.5 in Y' = 3-IL2 = 3.5 in 'V2 80

resulting in a diffuser area ratio (j3) of 1.71.

The dimensions of the annular nozzle of Unnever's

experiment and those of the configurations investigated are

tabulated in Table I. The dimensions of Unnever's nozzle

indicate the it was 0.55 inches from the wall. Unnever's

testing was carried out with a pressure ratio of 1.14 which

* was replicated for all configurations investigated.

Configuration la. The location and geometry of the

nozzle for configuration 1 was chosen to approximate as

* closely as possible that of the annular nozzle tested by

Unnever.

I Configurations 0. 2. 3. The locations and geometries

of the nozzles for configurations 0, 2, and 3 were chosen

such that the distance from the wall and the nozzle area

would be approximately the same as configuration la. This

allowed investigation of the thrust augmentation effects of

nozzle position angle, e, only (Figure 13).

i| 29

TABLE I

Nozzle Geometries

Li Radius Gap Aj c).

Unnever 2.25 3.00 0.065 1.226 61.9 0.081

Config la 2.25 2.96 0.072 1.349 61.9 0.089

Config 0 2.40 3.30 0.064 1.325 70.0 0.087

Config 2 1.96 2.51 0.081 1.296 50.0 0.085

Config 3 1.64 2.17 0.094 1.306 40.0 0.086

Config ib 2.26 2.96 0.053 0.989 61.9 0.065

Config Ic 2.25 2.95 0.095 1.774 61.9 0.117

Configurations lb. 1c. The locations of the nozzles

for configurations lb and Ic were chosen to be as close to

that of configuration la as possible. The only change made

was to the size of the gap and therefore the nozzle area.

This was done to investigate nozzle area ratio effects on

thrust augmentation.

Primmrv Objectives

Comparison with Experimental Data. Configuration la

was designed to model as closely as possible the annular

nozzle configuration used in Unnever's experimental

investigation. A qualitative comparison of the exit

velocity profile of configuration la with an experimentally

I measured profile from Reznick (Figs. 14 and 15) shows tit

30

U ~oz~e6 70 deg

Exit

* Configuration 0

I / Exit

Configuration 1

I Configuration 2

I 8=40 deg

Nozzle3 Exi t

Configuration 3

Fig. 13. Nozzle Locations

31

0I

Fi.1. EiIeoit rfl ueia

I1,z3 c

22~32

Ii

the shape of the profile is closely replicated by the model.

This is an indication that the flow structure is indeed

similar to that in the experimental ejector. However, since

the experimental data was produced using the hook nozzles

and is therefore only similar to the ejector modeled, the

comparison cannot be exact.

Similarly, comparison of thrust augmentation vs.

injection angle curves for the numerical model (Figure 16)

with similar curves from Unnever (Figure 17) (17:46) show

that the expected trends are indeed modeled. Again, since

3 the experimental curves are from hook nozzle cases (by

necessity, since the injection angle of the annular nozzle

could not be varied) the comparison can only be qualitative,

not quantitative.

I1 1.70 -

1.60 -3

Z1.50

~1.40Z la

1.30

I 1.20

1.00 I I I I

0 10 20 30 40 50 60 70 80 90INJECTION ANGLE (deg)

Fig. 16. Thrust Augmentation vs. Injection Angle

Numerical

I33

I

II

2

1(

10 20 ii 40 SO 60 /0 30

I luld Injection Argle, (We',rees)

Fig. 17. Thrust Augmentation vs. Injection Angle

Experimental

IHowever, a quantitative comparison of the thrust

augmentation from configuration la with Unnever's annular

nozzle configuration (Table II) (17:60) shows that the

numerical model did not achieve the thrust augmentation

measured experimentally.

I

Table II

Thrust Augmentation Comparison

Ejector

I Numerical Model 1.40

Experimental 1.48

I34I

Possible explanations for this difference include:

1. Turbulence modeling not optimized for a wall jet

flow resulting in poorer mixing in the numerical model.

2. Three dimensional mixing or swirl in the

experimental ejector which is not accounted for in the

numerical model due to the assumption of axial symmetry.

3. Modeling the jet exiting the nozzle as perfectly

parallel flow in the desired direction when there is likely

some divergence in the actual jet experimentally.

Each of these lead to less complete mixing in the

numerical model and would thus account for the lower thrust

augmentation calculated. Additionally, other sources of

error which would account for differences in experimental

versus numerical results include:

4. Insufficient grid resolution.

5. Experimental error.

Using 1.00, or no augmentation, as a baseline, this

results in a 16.7 percent error. This error indicates that

the model, as it is, would not be a good predictor of the

actual thrust augmentation which could be expected from an

experimental setup. However, since trends determined with

this model appear to be consistent with experimental

results, analysis of different parameters should allow

* identification of values which maximize thrust augmentation

which could be used to guide hardware development.

U Data Visualization. One of the benefits of a numerical

simulation is that the solution results in complete

knowledge of the computed flowfield. This knowledge can be

335

used to provide insight into the behavior of the flow within

3 the ejector which would be nearly impossible to determine

experimentally. Plotting velocity contours (Figure 18)

clearly shows the primary characteristics of the flowfield.

I

I- /

V/U ref U ref 111.7 ft/sec0 0.611

1.22I * 1.83

2,44o 3.05

3 Fig. 18. Total Velocity Contours

U First, (noting that the flow is from left to right) one can

see how the jet hugs the wall and negotiates the curvature

in the inlet due to the coanda effect. Second, one can see

how the jet spreads out as it entrains more of the

surrounding flow along with it. The increasing velocity of

the entire flowfield as the cross-sectional area of the duct

3 decreases can also be seen. Lastly, a relatively high

velocity channel flow can be seen between the nozzle

structure (and the jet) and the wall.

A streamline diagram of configuration la at its optimum

injection angle (Figure 19) shows the smooth flow which

characterizes the best performing injection angles.

36I

I

I

IFig. 19. StreamlinesI

I One can also see, however, that a stagnation point

exists on the nozzle structure upstream. Although the

annular nozzle structure, as modeled, is thinner than that

of the experimental apparatus, this diagram shows that

significant flow blockage by the nozzle exists even in the

numerical model just as was suspected in the experimental

work by both Reznick and Unnever. A velocity vector plot of

this region (Figure 20) clarifies the picture.

Finally, a sequence of plots of velocity profiles

(Figures 21-23) shows how the jet mixes with the secondary

flow as it progresses through the ejector. The first plot

(Figure 21) shows the velocity profile at three grid

stations ranging from tLe exit plane of the nozzle (K = 32)

to a cross-section within the constant area mixing chamber,

or throat, of the ejector (K = 75). These plots show

I clearly how the jet begins to mix with the secondary flow

and how the entire flow accelerates as the inlet converges.

I It may further be determined from this plot is that the grid

resolution at the upper surface appears to be barely

sufficient to capture the boundary layer. However, it does

not appear to be sufficient to capture boundary layer

effects on the nozzle walls.

37I

&SII 75

one

onal~ -K 56 32u 117f/

*ref

am on * (17 1 Of I n 4 " ti " S&-- 4 4 4 -tf

Fig.~ 21 ne eoiyPoie

384-

iI

The second plot (Figure 22) shows how the jet continues

to mix with the secondary flow as it progresses from the

beginning (K 75) to the end (K 100) of the mixing

chamber.

01oI al l'

,0, iK 0 0

. oK 75 X { Uref = 111.7 ft/sec

on 0W o n 100 125 15 W 7 n * Z ZS 2 50 2 W I5 300

* Usbkf

Fig. 22. Mixing Chamber Velocity Profiles

IThe last plot (Figure 23) portrays the changing

profiles as the flow proceeds through the diffuser from the

end of the mixing chamber (K = 100) to the exit (K = 130).

* The deceleration of the flow in the diffuser is evident.

Also, the continued spreading of the jet as it mixes with

the secondary flow is clearly visible. These basic flow

features were consistent for all of the configurations

modeled.

39

I

Ri:

I

I o0.00 -

• K = 130o K =110

o K= 100 Uref 111.7 ft/secoo o o s Go Io 12 1. 4 4 0 2o

UIIbI/Tref

Fig. 23. Diffuser Velocity Profiles

Flexibility. This code, as modified for this

investigation, is capable of handling variations of

injection angle, nozzle position, nozzle gap (and therefore

area) and pressure ratio. With some additional effort,

diffuser and inlet geometries could be altered as well.

Secondary Objectives

Several of the secondary objectives were approached in

the course of tnis investigation although all would require

further work to provide the requisite parametrics to use for

hardware design. The parameters studied include injector

angle, nozzle position, and nozzle to throat area ratio.

I40

I

Injection Anole. The effect of injection angle on the

flowfield can be observed by comparing the optimum injecticn

angle for configuration la to two off-nominal cases. For

configuration la, the optimum injection angle was found to

be ± = 52 degrees. This is compared to the off-nominal

cases of 0( = 64 degrees and j = 36 degrees. The thrust

augmentation achieved by each of these cases is tabulated

in Table III.

Table III

Augmentation with Changing Injection Angle (a±)

36 1.264

52 1.398

64 1.308

First, looking at velocity contours for the .± = 64 degreecase (Figure 24) one can see that the jet flow does not

follow the wall closely but instead spreads out into the

main mixing chamber. The improved mixing accomplished by

the increased injection angle would seem to be desirable.

But, as the exit velocity profiles indicate (Figure 25), the

increased centerline flow is accomplished at the expense of

a large drop in flow velocity near the wall. For a circular

ejector, the region near the wall represents a much greater

area in which momentum was sacrificed than the area near the

centerline where momentum was gained. Also, it can be seen

that the flow has begun to separate from the wall resulting

in reversed flow.

I41

I

g0/Uf Uf 111.7 ft/sec

21.832.44I L.~ 3,05

Fig. 24. Velocity Contours mi 64 degrees

I fft'e

Fi.2IEi eoiyPoils:~ 2ad6 ere

*-*--~----*"~ 0 *- 42S

I

The second off-nominal case ( .i = 36 degrees) is one

in which the jet is directed too near the wall. A first

look at the velocity contours (Figure 26) shows the jet

closely hugging the wall which by the above argument would

seem to be desirable. However, a closer look at the area

between the jet and the wall shows that, contrary to the

optimum case (Figure 18), the flow through this channel is

of relatively low velocity. Also, the high speed jet flow

along the wall loses more momentum due to frictional

effects.II j - -i

I V/Ure f Ure f 111.7 ft/secc 0.611

1.22183I2.44

3.05

I Fig. 26. Velocity Contours :c i 36 degrees

IThe effect of the blockage of this high energy flow

source and frictional losses are reflected in the exit

profile (Figure 27). Although the jet is more concentrated

for the o-i = 36 degree case it is no more powerful than the

optimal, o.i = 52 degree, case. The reduced mixing also

results in a decrease in momentum across the majority of the

I43

I

ncenter section of the ejector. Apparently, the optimum case

is one which balances these considerations by achieving

maximum mixing without allowing the jet to separate from the

n wall.

J 1.p-

II

.1:L Ju'. -

J 111.7 ftise /sIJ

oq 2 03 04 0' 5 . O? 07 00 0o : 3

U! t'ref

I Fig. 27. Exit Velocity Profiles 1 = 52 and 36 degrees

I

* Figure 28 defines a pair of angles which the injection

angle of the nozzle can be referenced to. These angles are

those representing injection parallel and tangent to the

wall. Figure 29 shows the relationship of the injection

angle for maximum thrust augmentation to those representing

injection parallel to the wall and tangent to the wall for

each of the four configurations investigated. In all cases,

the optimum injection angle is approximately a quarter of

I44

I

Ithe way between parallel and tangent to the wall. This

conclusion must be caveated by noting that, due to the

circular inlet lip and the fact that all configurations were

limited to be the same distance from the wall, the relative

geometry between the nozzle and the wall is the same for all

configurations. To fully investigate this parameter,

additional data would need to be collected at different

distances from the wall and (if desired) for different inlet

3 geometries.

I

I_

I /

TangentII ParallIel

I Fig. 28. Reference Injection Angles

I3 Nozzle Position. In investigating the influence of

nozzle position on thrust augmentation, it was necessary to

isolate the effect of nozzle movement by constraining the

configurations chosen. In order to eliminate changing wall

effects, all configurations were set to have the nozzle the

same distance from the wall as configuration la (0.55 in.).

I45I

II

I3 - T ',angent to 4all

3- •P arallel to vwall

0) Optimnumn njoction r e

0

©

0

I 3-

I1t1J J ! lTI

0 10 20 30 40 50 60 70 80 90INJECTION ANGLE (deg)

IFig. 29. Optimum Injection Angle with Relation

to Reference Angles

I3 The nozzle gap size was adjusted to achieve similar nozzle

areas for all configurations to eliminate area ratio

effects. This reduces the effect of location changes to

only the effect of nozzle position angle, 9. Plotting the

maximum augmentation achieved at each location vs. the

posi;.ion angle (Figure 30) a definite trend can be detected.

Higher augmentation ratios are achieved with decreasing

position angle, or in other words, placing the nozzle

further into the inlet.

3 The effect of nozzle location can best be seen by

comparing the two extremes studied, configuration 0 and

configuration 3. By looking at velocity profiles of the jet

itself (Figures 31 and 32) we can see that configuration 3

has a higher peak jet velocity than configuration 0.

46

1.75

3Z0

1.50

LiJ 0

1.25

1.00 l i i i30 40 50 60 70 80

POSITION ANGLE (deg)

Fig. 30. Augmentation vs. Position Angle

I

o l

I 1. Ni , , I

I Fig. 31. Nozzle Velocity Profile :Configuration 3

i47

I

II

i uI

*0bot oiu i

3 Fig. 32. ozzle Velocity Profile Configuration 0

In eThis is due to the fact that the plenum pressure of

xboth configuration is nzthe same:

I P, rnom = Prat (P.) (47)

3but, as can be seen in Figures 33 and 34, the exit of

configuration 3"s nozzle is in the lower pressure region

- nearer the throat of the ejector. The pressure near the

-- exit of configuration 3"s nozzle (Figure 33) is about 0.990

P. on the side nearer the wall and about 0.994 P& on the

opposite side. This is compared to configuration O's nozzle

(Figure 34) which is located where the pressures are approx-

imately 0.996 Pa and Pa respectively. Since the exit

48I

II

I--i

mP/PI99 4- 0997

.0980

I Fig. 33. Pressure Contours Configuration 3

900

Fig. 34. Pressure Contours Configuration 0

49

UI

pressure is lower for configuration 3, the exit velocity is

3 necessarily higher. Also, there is less momentum loss due

to friction. This model does not, however, account for

losses within the nozzle which would reduce the effec-

tiveness of the longer nozzle structure of configuration 3.

One would assume that there would be some point at which the

advantages of moving the nozzle toward the throat would be

outweighed by the reduced mixing length allowed. Further

analysis would be necessary to define the optimum location.

One can also see in these plots how a pressure difference is

3 maintained across the jet it which forces the jet to turn.

This is similar to the turning of the flow from a jet flap.

I Nozzle Area Ratio. Configurations lb and ic were

designed to keep all other factors the same as configuration

la except the nozzle gap, and therefore the nozzle area, in

order to investigate the effect of nozzle to throat area

3 ratio changes. Configuration lb had a reduced nozzle area

and configuration ic had an increased nozzle area relative

* to configuration la. The area ratios and achieved thrust

augmentation were as in Table IV. The results are plotted

* in Figure 35.

ITable IV

3 Augmentation with Changing Nozzle Area Ratio (a.)

* Config.l Nozzle Area Ratio

lb 0.0650 1.407

la 0.0887 1.398

Ic 0.1167 1.353

I50

I

1.45

NZ lb0 l

1.40*Z1C

D 1.35<

1.30-0.05 0.07 0.09 0.11 0.13

AREA RATIO

Fig. 35. Augmentation vs. Nozzle Area Ratio (L)

As can be seen from Figure 35, further reduction in

area ratio would appear to be fruitless, contrary to the

theoretical analysis presented earlier which predicted ever

increasing augmentation with decreased area ratio. But, as

Figure 36 shows, these results are in line with experimental

results from Fought's MS Thesis as published in McCormick.

These results suggest that the area ratio used by Reznick

and Unnever (equivalent to configuration la) is near the

optimum for this size ejector (Diameter 112 mm).

I

II

51

I

28k

24 340U 2 15

1 2k5 -m oWG2120F

B 1 8 130- minmodel,B z2.15

1

-, - -3 8 -m m m odel. 13 4 0

4 ~Nurneri ca IConfiguration 1

C2~-112-m-,m ,R= 1.71I 5 10 :5 20 25 30 35 40 45 50

Area ratio - I Ja

Fig. 36. Augmentation vs. Nozzle Area Ratio (1/6L)U Numerical and Experimental (9:285)

I5

I

IV. Conclusions

I All primary objectives of this thesis have been been

met. The numerical model has been shown to provide a

reasonable simulation of the flow characteristics through

the selected ejector configuration. Although the simulation

is not sufficient to permit accurate prediction of actual

thrust augmentation values for experimental hardware, all

trends appear to be adequately modeled. Taking advantage of

the complete knowledge of the flowfield provided by a

numerical solution, the dynamics of the computed internal

flow were able to be analyzed. Data visualization

techniques were able to give us insight into the internal

flow of the ejector which could not be measured

experimentally. Sufficient flexibility has been

incorporated in the code to handle variations of parameters

such as injection angle, nozzle position, nozzle to throat

area ratio, pressure ratio, as well as inlet and diffuser

geometries.

In addition, the secondary objective of exploring the

effect of these parameters on thrust augmentation was

partially investigated allowing some initial conclusions to

be drawn which could affect future experimental hardware

* design.

1) The area ratio used by Reznick and Unnever is near

* the optimum and should be sufficient for future experiments.

However, if it is within manufacturing capability, some

* reduction of nozzle area would be beneficial.

2) Future experiments should concentrate on

configurations which inject the jet at a location closer to

the entrance of the constant area mixing chamber (smaller 0)

if possible.

53I

I3) Initial indications are that an annular nozzle

design should attempt to provide an injection angle

approximately 1/4 of the way between parallel to the wall

and tangent to the wall for the selected nozzle location.

III

IIII

I5i

V. Suggestions and Recommendations

Any continued research in this area should concentrate

on expanding the parametric analysis in the areas of nozzle

location as well as inlet and diffuser geometries. Nozzle

locations further into the inlet and variations in distance

from the wall should be investigated. Larger diffuser

ratios should also provide increased augmentation capability

and different inlet shapes could optimize the incoming flow.

Further analysis of injection angle effects for the new

geometries may also be necessary.

Another primary area of research which would be

beneficial is application of improved turbulence modeling,

better grid refinement, and second-order boundary conditions

to improve the numerical model and try to bring the

predicted thrust augmentation levels in line with

experime.ital results. It may even be desirable to change to

a different solution algorithm to reduce computation time.

Lastly, using the parametric results presented here to

design new experimental hardware should result in improved

performance and would serve to better validate this model.

55

III

Appendix A: Grid Generating Programs and Tables

IIIIII

I-

III

App~riI ix A 1: tllil ~ ~L~CdIiLL

IIIIIIIIIIIIII

A ~

I

IxIu

cr 0

a' -ca

Cr--x u

0, 31

a. .C3 I0;

x r u x-

(4-M 0- M Im 1-. XI=.-, - 0 - 1r - Go - C 4,M

3E x. - Nr.m. 4

Mo. ,, I, (SCAIL)(o-

-, q 0- w 0- xZ=' =) =O 4 ~r -- in (4

* - x Cr 2~ 0-I - ~ 1 ' i 4-

-m =-Cm -c o DC

0- coo x

u , C-.ju UQU 4i04 u u uu

in1CCCO ... .C -IL 0-2 cc a~;i-0 ~ C 41-.--4- 0 4 .

O3 3i4 W~ 0 0 x 4 .

C-CWCC.( in4 t440 .4 CCC 00cUI2

OX 0-

_Z3 X4 .4 Ur 00-0= -j

0 J m .0 0n u 0 o W x .4 >.N 0- M= 0:-

4 (4 M

U4 0, -3 ;i-

m - 0 4

444iNSC (4l- o 4 -u w- 4 w L ~ *4 C

x" mm 44 w 0K c~ -

Cr<<00000000(CA4C( 4 4 4 C-f0.C)(4((4( (4( 0 .4* .40C( (4 (4 OCKV)

A-3

CC

0-V)- a n -am

n ~ -x In . 11Z 1,0 e4

XU=L .X - =-.a

66 o z . ~Z=O= 00= =m -x - _ ).

-: I~ -0

'.0 n ;i~-- 4--7:: <(Cr - 1 n 7LU

I 7-I- -- ,-77x

ox M I 0 0I- 4-

>* m- -. - EA ~~~ oxl) o~f D~ D... - -. LU

Ir xx- ~ - 4<0... x - U*~>LUu >AU X)LU d. - ).

-u u u 0OO 000 -

4 ~ ~~~~ LU xU~ 0 7 07.

3o N w - - -

Ic - - - ' 4 -; o -0

u c,

I A -4

*C

XI ; --< tr

Xm 0 01-

.3 x ~ 1

cc -In0

~0 - .

I~~- IJI x, - .- M4- ----- -=- 0 - 0v 0 >W

- -Z. -

O.O4. It,/i > A -

-. 4 - 4 A -4 I- 3 ~ a3 IA * a c .0 CI-0 U 7 .4 lo * eN *N C. *-w

, 04. :D. .0 -O -4 4 X0- - XQ-. r .- ~ * cra-.. 14 . . 5(4--.4 ) (.4 (3 ,:.n >II 4 4 ~i> ,->( 44 -iII> 0I4I - M "a 411 .

I7

x I.4Z

x I-

Oma a. .4 -->

- I Li i vLia44< < 44I I

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II

Bibliography

1. Anderson, D. A., J. C. Tannehill and R. H. Pletcher.

Computational Fluid Mechanics and Heat Transfer. New

York: Hemisphere Publishing Corporation, 1984.

2. Baldwin, B. S. and H. Lomax. 'Thin Layer Approximation

and Algebraic Model for Separated Turbulent Flows,

AIAA Paper 78-257 (January 1978).

3. Hankey, W. L. and J. S. Shang. 'Natural Transition - A

Self Excited Oscillation,' AIAA Paper 82-1011 (June

1982).

4. Hasen, Capt. Gerald A. 'Navier-Stokes Solutions for an

Axisymmetric Nozzle in a Supersonic External Stream,

AFWAL Technical Report 81-3161 (March 1982).

5. Hill, P. G. and C. R. Peterson. Mechanics and

Thermodynamics of Propulsion. Reading, Massachusetts:

Addison-Wesley Publishing Company, 1965.

6. Kedem, Maj. Eli. Israeli Air Force. An Experimental

Study of Static Thrust Augmentation Using a 2-D

Variable Ejector. MS Thesis AFIT/GAE/AA/79D-7.

School of Engineering, Air Force Institute of

Technology (AU), Wright-Patterson AFB OH, December

1979.

7. Kohlman, D. L. Introduction to V/STOL Airplanes.Ames, Iowa: Iowa State University Press, 1981.

8. Lewis, Capt. William D. US Army. An Experimental Study

of Thrust Augmenting Ejectors. MS Thesis

AFIT/GAE/AA/83D-13. School of Engineering, Air Force

Institute of Technology (AU), Wright-Patterson AFB

OH, December 1983.

II

Bibliography (cont.)

9. McCormick, B. W. Jr. Aerodynamics of V/STOL Flight.

Orlando, Florida: Academic Press, 1967.

10. Olson, L. E., P. R. McGowan and R. W. MacCormack.

'Numerical Solution of the Time-Dependent Compressible

Navier-Stokes Equations in Inlet Regions, N

62338 (March 1974)

11. Reznick, Capt. Steven G. An Exoerimental Study of

Circular and Rectangular Thrust Augmenting Ejectors.

MS Thesis AFIT/GAE/AA/8OD-18. School of Engineering,

Air Force Institute of Technology (AU), Wright-

Patterson AFB OH, December 1980.

12. Roache, P. J. Computational Fluid Dynamics.

Albuquerque, New Mexico: Hermosa Publishers, 1972.

13. Shang, J. S., W. L. Hankey, and R. E. Smith. 'Flow

Oscillations of Spike-Tipped Bodies,' AIAA Paper

80-0062 (January 1980).

14. Shang, J. S. and R. W. MacCormack. 'Flow Over a

Biconic Configuration with an Afterbody Compression

Flap, AFWAL Technical Report 84-3059 (April 1984).

15. Stock, H. W. and W. Haase. 'Determination of Length

Scales in Algebraic Turbulence Models for Navier-Stokes

Methods,' AIAA Journal Vol 27. No 1: 5-14 (January

1989).

Bibliograghv (cont.)

16. Uhuad, Capt. Generoso C. An Exoerimental Investigation

of a Circulagr Thr~ust Augmenting E-jector. MS Thesis

AFIET/GAE/AA/86M-S. School of Engineering, Air Force

Institute of Technology (AU), Wright-Patterson AFB OH,

December 1985.

17. Unnever, Capt. Gregory. An Experimental Study of

Rectangular and Circular Thrust Augmenting Ejectors.

MS Thesis AFIT/GAE/AA/81D-31. School of Engineering,

Air Force Institute of Technology (AU), Wright-

Patterson AFB OH, December 1981.

18. Von K~rmAn, T. "Theoretical Remarks on Thrust Augmen-

tation," Contributions to Applied Mechanics. Reissner

Anniversary Volume, Ann Arbor, Michigan, pp 461-468,

1949.

19. Zucrow, M. J. and J. D. Hoffman. Gas Dynamics Vol1,

New York: John Wiley & Sons, 1976.

Vita _

Captain Kenneth R. Gage

He moved to Branford, Connecticut

in 1965 and graduated from Branford High School in 1980. He

was accepted to and attended the United States Air Force

Academy in Colorado Springs, Colorado, from which he

received the degree of Bachelor of Science in Astronautical

Engineering and a regular commission in the USAF on 30 May

1984. He then went to Headquarters, USAF Space Division

(AFSC) at Los Angeles AFB where he served as a flight

operations manager for the Inertial Upper Stage and as an

advanced launch systems project officer until entering the

School of Engineering, Air Force Institute of Technology, in

May 1988.

Smm u[[Dmff

REPORT DOCUMENTATION PAGE ,. .

I AGENCY USE ONL , 2 REPORT D--:, 3 RE.IORT TYPE AN ) DATES -OvElEDI December 1990 Master's Thesis4 TiTLE AND T9Bi.E S FUND,NG NjMirOBFS

Numerical Analysis of an AxisymmetricThrust Augmenting Ejector

Kenneth R. Gage, Capt, USAF

7 0 1- )0VA, - '. % ',A'~h; S 1 3S N D A DRE S5 E S) 7

Air Force Institute of Technology, WPAFB OH 45433-6583 AFIT/GAE/ENY/89D-1D

9 SPONSORING ,*C.OnR!NG ACENCY NAME(S) AND ADDRESSkES) 10 SPONSCR.NG VC-. , 7AGENCY REPORT .

Flight Dynamics LaboratoryWRDC/F IMMWright Research and Development CenterWright-Patterson AFB OH 45433

11. SUPPLEMENTARY NOTES

12a DSTP!BU"'ON AVAILABIL!TY STATEMENT 12b DIS'RIBu''ON COCE

Approved for public release;distribution unlimited

13. ABSTRACT : V3," m20Owcrds)

Use of an ejector is an effective way to increase the thrust produced by a jet. Inthis thesis project an axisymnietric ejector concept which has been previouslyexplored by experiment was numerically modeled. An existing axisymmetric, internalflow code based on the explicit MacCormack method was modified to incorporateprimary nozzle structure and flow injection within the flowfield. Results werecompared qualitatively and quantitatively with experimental results to verify thevalidity of the model. Internal flow structure, difficult to obtain in experiment,is easily examined. This code may be used for parametric analysis of such ejectorperformance parameters as primary nozzle location, flow injection angle, diffuserarea ratio, nozzle area ratio, arid inlet geometry to optimize future hardwareconfigurations.

14. SUBJECT TERMS 15. NUMBER OF PAGES104Fluid Dynamics Axially Symmetric Flow Air Ejectors 104Fluid Flow Jet Mixing Flow Computational Fluid 6 PRICE CODE

FDvnamirc, (U) _F

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