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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 -->
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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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