Work currently in progress to update an existing transonic circulation control airfoil analysis method is described. Existing methods suffer from two dificiencies: the inability to predict the shock structure of the underexpanded supersonic jets; and the insensitivity of the calculation to small changes in the Coanda surface geometry. A method developed for the analysis of jet exhaust plumes in supersonic flow is being modified for the case of the underexpanded wall jet. In the subsonic case, the same wall jet model was modified to include the calculation of the normal pressure gradient. This model is currently being coupled with the transonic circulation control airfoil analysis

Dash, Sanford M.

Dvorak, Frank A.

English

NASA Technical Reports Server

 88-17593
WALL JET ANALYSIS FOR CIRCULATION CONTROL AERODYNAMICS
PART II: ZONAL MODELING CONCEPTS FOR
WALL JET/POTENTIAL FLOW COUPLING
Frank A. Dvorak
Analytical Methods, Inc.
Redmond, Washington
and
Sanford M. Dash
Science Applications International Corporation
Princeton, New Jersey
SUMMARY
This paper describes work currently in progress to update an existing
transonic circulation control airfoil analysis method. Existing methods
suffer from two deficiencies: -the inability to predict the shock structure
of the underexpanded supersonic Jets; and the insensitivity of the calcula-
tion to small changes in the Coanda surface geometry. A method developed
for the analysis of Jet exhaust plumes in supersonic flow is being modified
for the case of the underexpanded wall Jet. In the subsonic case, the same
wall Jet model has been modified to include the calculation of the normal
pressure gradient. This model is currently being coupled with the transonic
circulation control airfoil analysis.
oReceoe pAG qI NK NOTF,,t zD
_ BLANK NOT FILIV-':_'-
165
https://ntrs.nasa.gov/search.jsp?R=19880008209 2020-03-20T08:18:49+00:00Z
TRACON
T_ORETI CAL APPROACH
• POTENTIAL FLOW
- JAM£SON'S FULL POTENTIAL METHOD
• VISCOUS FLOW
WALL JET _GION
FINITE-DIFFERENCE METHOD USING AN EDDY VIS_ITY MODEL
FOR CLOSURE
- AIRFOIL UPPER SURFACE AHEAD OF SLOT AND ALL OF LOWER SURFACE
INTEGRAL METHODS
LAMINAR -- COHEN AND RESHOTKO
TURBULENT -- GREEN El"AL,
Figure 2. TRACON--Component Analysis Procedures.
168
INPUT AIRFOIL GEOMETRY t
ANGLE-OF-ATTACK t
BLOWI NG MOME NTUM
COEFFICIENT AND
REYNOLDS NUMBER
I,
COMPUTE POTE NTIAL
FLOW SOLUTION
¢,
CALCULATE VISCOUS
LAYER PRO PEP,,.TI E5
AND SEPARATION PRESSURE
Psepu AND Psepl
DETERMINE SOURCE
DISTRIBUTION REPRESENTING
DISPLACEMENT AND
ENTRAINMENT EFFECTS
OF VISCOUS LAYERS
¢,
ESTABLISH NEW ESTIMATE
OF CIRCULATION
AROUND AIRFOIL
¢,
COMPUTE POTENTIAL FLOW
ABOUT CONFIGURATION
INCLUDING VISCOUS EFFECTS
YES NO---'
J PRINTRESULTS ]__J STOP J
Figure.3.. Ca'Iculation Procedure.
169
Having obtained the points of separation and corresponding
static pressures for the upper and lower surfaces, a new value of
circulation is estimated on the basis of separation pressures and
current value of lift. A new potential flow solution can then be
computed using this new estimate of circulation with the viscous
effect, i.e., velocity component normal to the surface taken into
account.
Convergence is checked at this stage. The calculation con-
tinues for another cycle unless Psepu and Psepl are in close
agreement and the variation of the lift coefficient between
successive iterations is in the range of convergence.
As shown in Figures 4 and 5, the basic analysis performed
quite well. A relatively high Mach number case (0.6) at an angle
of attack of -10 ° produces a strong shock wave as shown in Figure
4. The analysis accurately predicts the shock location and
overall pressure distribution. Similarly in Figure 5 for a low
Mach number but with blowing, the analysis again performs well in
comparison with experiment. The strengths and weaknesses of
TRACON are summarized in Figure 6.
3.0 CURRENT DEVELOPMENTS
The two basic objectives of the current work are as follows.
(i) Formulation of the methodology to describe the inviscid flow
of an underexpanded wall jet into a co-flowing stream. The
method must be able to describe the supersonic flow that results
from a nozzle operating choked into a stream having a free-stream
Mach number in the range 0.3 ! M ! 0.8. As part of this objec-
tive, procedures for coupling the wall jet calculation with the
overall circulation control calculation method, TRACON, were
considered. (2) Formulation of methodology to determine the
effect of the Coanda jet on surface pressures. In this approach,
the direct influence of the normal momentum equation is required.
As with the first objective, procedures must be developed for
coupling the normal pressure gradient calculation with solutions
for the streamwise momentum and with the external potential flow
(TRACON).
A literature survey indicated that although several re-
searchers have investigated the flow field of supersonic jet
plumes, including the underexpanded jet, only one group, from
SAIC/Princeton led by Dash and co-workers (5), has considered the
underexpanded wall jet. The shock structure of an underexpanded
wall jet is physically very similar to that of a jet plume;
because of this, Dash and Wolf (6) have recently modified one of
their codes for application to curved wall jets. For the viscous
model the finite difference, two-layer turbulence model of Dash
and Beddini (7) has the required theoretical basis for applica-
tion to circulation control wall jets. This analysis procedure,
called SPLITWJET (hereinafter termed WJET), is completely des-
cribed in (7) and (8). WJET solves a set of curvilinear, higher-
170
-4.0
0 a DATA_ NCCR 1610-8054S
3.0 o& = -I0"
- _. M =0.6
C_ = 0
,_ _A - -- TRACON
-2.0 -
Ce
-I.0[
1.0
(CIRCLE = UPPER SURFACE)
x/c
Figure 4. Comparison between Calculated and Measured
Pressure Distributions; NCCR 1610-8045S.
171
OO
o
6-
I
O
O
I
O
O
QD
I
O
O
I
O
O
!
O
O
O
O
O
Alpha = -0.01; C u = 0.0355; C L = 2.128; CLc = 2.140
EFFECTIVE CHOIID. c'
;,m " 33.ml m.
___/ RIE_IE C_K)RDLJNE _PL[NUM
17e4, THICK S4JI_RCRiTICJU. AJR_ i _ /_,.-,_'- _ / _
WTT_Ir_L_._. CCW T E
INTERCH.ANC,ABLELOWERSURFACJE$
A,NO TRAILINGEDGES
CALCULATION
0 UPPER SURFACE 1[] LOWER SURFACE
[
C
(EXP)
.00
I I I I i
.o2 .o4 .oe .oe 1.oo
X/C
Figure 5. Comparison between Calculated and Measured Pressure
Distributions; Supercritical Airfoil.
172
TRACON
SUMMARY
* ZERO BLOWING -- SHOCK LOCATIONS PREDICTED QUITE
ACCURATELY FOR ROUNDED TRAILING-EDGE AIRFOILS
° LOW BLOWING -- PREDICTED PRESSURES AND CL - C_
IN GOOD AGREEMENT WITH EXPERIMENT
HIGH BLOWING -- PREDICTED BEHAVIOR GOOD AT LOW
MACH NUMBERS BUT AT HIGH MACH NUMBERS A MODEL OF
THE JET SHOCK STRUCTURE IS NEEDED
0 BECAUSE OF EMPIRICAL MODEL TO ACCOUNT FOR COANDA
SUCTION, THE EFFECT OF SMALL CHANGES IN GEOMETRY
CANNOT BE ACCOUNTED FOR IN A CONSISTENT MANNER
DISPLACEMENT THICKNESS COUPLING BETWEEN VISCID AND
INVISCID FLOWS MAY BE INADEQUATE AT HIGHER MACH
NUMBERS
Figure 6. TRACON--Summary of Program Features.
173
order boundary layer equations employing a mapped surface--normal
grid network. A key ingredient of WJET is the inclusion of a
hybrid, two-layer turbulence model which couples a damped Van
Driest inner mixing layer solution to a two-equation, ke outer
solution, matching at the grid point corresponding to y+ - 50(y+
= nT s ½p½ /p£), where n is the distance from the surface, _s is
the wall shear stress, p is the density and p£ is the laminar
viscosity• The turbulence model contains curvature corrections
based on the work of Launder et al. (9) and Hah and
Lakshminarayana (I0) which are required to account for the sig-
nificantly enhanced wall jet mixing rates associated with strong
convex curvature• The combined system of mean flow and turbu-
lence model equations are integrated using an efficient upwind
fully implicit difference algorithm, and the jet growth is con-
trolled by an ordinary differential equation keyed to the edge
vorticity.
The inclusion of normal pressure gradient terms due to
curvature in a boundary layer approach has been addressed by
Mahgoub and Bradshaw (ii). For the wall jet application the
following approach has been developed•
i• Matching between the potential flow and the wall jet occurs
at the wall jet edge.
• The pressure variation across the wall jet is solved using
the viscous normal momentum equation•
Since the inclusion of the normal momentum equation renders
the wall jet equations elliptic, direct spatial marching of the
complete set of wall jet equations is ill posed• The remedy
involves splitting the pressure field such that:
i • the wall jet equations (not including the normal momentum
equation) are solved in a parabolic fashion with the stream-
wise pressure gradient determined from a globally imposed
pressure field, P(s,n); and
• a revised pressure field, P(s,n), is determined in the
course of the parabolic wall jet solution using the con-
tinuity and normal momentum equations; the revised pressure
field is used in local thermodynamic relations and the
normal velocity distribution arrived at from the coupled
continuity/normal momentum equation solution at each step is
used in the convective terms of the parabolic wall jet
equations•
This procedure is summarized in Figure 7.
In the subsonic case the strategy for coupling WJET with
TRACON (Figure 8) is as follows:
174
SUBSONIC WALL JET CALCULATION
n
ue Prescribed from TRACON#
Solution
Surface
TRAShing
C._Aii_i I Surface
PARABOLIC SOLUTION WITH
FLOW SOLUTION
a/as[P( ,Tl)] FROM POTENTIAL
CROSS-FLOW SOLUTION BEGINNING AT OUTER EDGE OF WALL JET
WITH BOUNDARY CONDITIONS FROM TRACON SOLUTION GIVES NEW
P(_,T I)
SECOND ITERATION
PRESSURE FIELD
WITH _/Os [P(_:,TI)] FROM UPDATED
Figure 7. Analysis Procedure for Subsonic Wall Jet.
175
OVERLAP COUPLING FOR A SUBSONIC WALL JET
Viscous Jet Boundary
TRACON Mntchinq SurFace
Airfoil Surface
SOLVE POTENTIAL FLOW OVER TRACON MATCHING SURFACE WITH
_On(S) PRESCRIBED
" SOLVE WALL JET USING PRESSURE SPLIT PNS APPROACH
DETERMINE _°(s) FOR OVERLAP REGION AND GENERATE
FOR NEXT POTENTIAL FLOW SOLUTION
_n(S)
Figure 8. Coupling Procedure for Subsonic Wall Jet.
176
i. the TRACON potential flow calculation is performed utilizing
a trailing-edge geometry which smoothly blends the slot lip
to the airfoil trailing edge (this surface is defined as the
TRACON matching surface in Figure 8; and
. the WJET wall jet calculation is performed over the actual
airfoil surface (Figure 8).
To interactively couple the two solutions, the WJET calculation
requires an inviscid flow map of the TRACON calculation to obtain
outer edge conditions and streamwise pressure gradients, while
the TRACON calculation requires the stipulation of the source
strength distribution, _n(S), along the TRACON matching surface.
The definition of the source strength distribution in a flow with
large normal pressure variations requires careful derivation of
displacement thickness relations. The usual simplifying approxi-
mations employed for standard boundary layer problems cannot be
employed. To date, the wall jet analysis has been coupled with
TRACON and preliminary calculations are being performed to check
out the program logic.
In the supersonic (underexpanded wall jet) case a similar
strategy has been developed. In recent years considerable re-
search has been carried out on the analysis of supersonic plumes.
Dash and co-workers at SAIC/Princeton (12) through (14), and
Wilmoth (15) of NASA Langley Research Center have developed shock
capturing technology which accurately models the multi-cell em-
bedded shock structure of underexpanded jets. Steger (16) and
Diewert (17) of NASA Ames research Center, Birch of Boeing (18),
Perry and Forrester (19), Shang of AFWAL (20) and Cline of Los
Alamos (21) have all in recent years considered the analysis of
supersonic free jets. These analyses have ranged from two-
dimensional parabolized Navier-Stokes solvers to full three-
dimensional time-dependent codes. The shock wave structure of an
underexpanded wall jet is very similar to that of a jet plume,
with one exception: the wall jet does not have the extended
inviscid core region that characterises underexpanded free jets,
and hence, the waves in wall jets would be propagating in a fully
turbulent environment several slot heights downstream of the slot
exit, see Figure 9. To properly treat this viscous problem, a
parabolized Navier-Stokes formulation is required which can be
directly coupled with a potential flow solution.
The basic structure for a supersonic wall jet solver already
exists in WJET. In order to avoid having two separate codes to
analyze subsonic and supersonic wall jets, it is more practical
to develop a supersonic pressure solver for WJET. Thus, WJET
will be used in its present form to solve the entire wall jet
with:
i. pressures in supersonic regions determined by a character-
istic based pressure solver;
177
SUPERSONIC WALL JET CALCULATION
cous Jet Boundary
\ "-."-. "_ TRACON Matching Surface
Sonic Line _ ")_1_ ' "\
Airfoil Surface
SUPERSONIC REGION -- PARABOLIC SOLUTION WITH _P/_s FROM
VISCOUS CHARACTERISTIC METHOD (WAVE SOLVER)
@ SUBSONIC REGION -- PARABOLIC SOLUTION WITH aP/as FROM
POTENTIAL FLOW SOLUTION
" SONIC LINE MATCHING AS IN FREE JET APPROACH OF DASH
CROSS-FLOW SOLUTION IN SUBSONIC REGION WITH BOUNDARY CONDITIONS:
= O) = U(_ = O) TAN _CHARC.V(?_
P(_= i) = Pe
Figure 9. Analysis Procedure for Underexpanded Supersonic Wall Jet.
178
. pressures in subsonic regions split with the streamwise
gradient imposed from TRACON and the normal variation deter-
mined by solving the continuity and normal momentum equa-
tions ; and
• coupling procedures utilized to interface the pressures at
the near wall jet and mixing layer sonic lines.
The same overlap procedure described previously will be
utilized to couple the wall jet and TRACON potential flow solu-
tions. However, the matching surface cannot be arbitrarily
blended from the slot lip to the airfoil surface as if it is for
the subsonic case, since it must remain above the jet mixing
layer sonic line (Figure i0). The extension of the overlap
approach to accommodate this modification is conceptually
straightforward, but the details require significant considera-
tion.
4.0 REFERENCES
i. Dvorak, F.A. and Choi, D.H., "Analysis of Circulation-Con-
trolled Airfoils in Transonic Flow", J- _i_9__, Vol. 20,
No. 4, April 1983.
2. Jameson, A., "Numerical Computation of Transonic Flows with
Shock Waves", International Union of Theoretical and
Mg__, Springer-Verlag, New York, Inc., September 1975,
pp. 384-414•
3. Brune, G.W. and Manke, J.W., "An Improved Version of the NASA
Lockheed Multi-Element Airfoil Analysis Computer Program",
NASA _, March 1978, pp. 69-87.
4. Green, J.E., Weeks, D.J. and Brooman, J.W.F., "Prediction of
Turbulent Boundary Layers and Wakes in Compresible Flow by a
Lag-Entrainment Method", Royal Aircraft Establishment TR-
72231, December 1972.
5. Dash, S.M. and Sinha, N., "Noniterative Cross-Flow Integra-
tion Procedure for the Pressure-Split Analysis of Two-Di-
mensional, Subsonic Mixing Layer Problems", To be Published
in the AIAA Journal.
6. Dash, S.M., Beddini, R.A., Wolf, D.E. and Sinha, N., "Vis-
cous/Inviscid Analysis of Curved Sub- or Supersonic Wall
Jets", AIAA Paper No. 83-1679, Danvers, MA, July 1983.
7. Dash, S.M. and Beddini, R.A., "Viscous/Inviscid Analysis of
Curved Wall Jets: Part 2, Viscous Pressure-Split Model
(SPLITWJET)", Science Applications, Inc., Princeton, N.J.,
TR-7, November 1982.
8. Dash, S.M. and Sinha, N., "Pressure-Split Extensions of
SPLITWJET Model for Wall Jet/Potential Flow Coupling",
179
OVERLAP COUPLING FOR A SUPERSONIC WALL JET
Viscous Jet Boundary
* MATCHING SURFACE CONFIGURED TO RESIDE ABOVE SONIC LINE
POTENTIAL FLOW OVERLAP INCLUDES ONLY SUBSONIC REGION
OF JET
P(s) -- SUPERSONIC
-- SUBSONIC
(T}-0)
(I/-0)
-- WAKE SOLVER
-- PRESSURE SPLIT
6*(s) DETERMINED FOR SUBSONIC PORTION OF JET -- INCLUDES
INFLUENCE OF JET UNDEREXPANSION
Figure i0. Coupling Procedure for Underexpanded Supersonic Wall Jet.
180
Science Applications, Inc., Princeton, N.J., TR-17, February
1984.
9. Launder, B.E., Priddin, C.H. and Sharma, B.I., "The Calcula-
tion of Turbulent Boundary Layers on Spinning and Curved
Surfaces", ASME J. Fluids E/L_K., March 1977, pp. 231-239.
10. Hah, C. and Lakshminarayana, B., "Prediction of Two- and
Three-Dimensional Asymmetrical Turbulent Wakes, Including
Curvature and Rotation Effects", _ I., October 1980, pp.
1196-1204.
ii. Mahgoub, H.E.H. and Bradshaw, P., "Calculation of Turbulent-
Inviscid Flow Interactions with Large Normal Pressure
Gradients", AIAA I-, October 1979, pp. 1025-1029.
12. Dash, S.M. and Pergament, H.S., "A Computational Model for
the Prediction of Jet Entrainment in the Vicinity of Nozzle
Boattails (The BOAT Code)", NASA CR-3075, December 1978.
13. Dash, S.M., Pergament, H.S. and Thorpe, R.D., "Computational
Models for the Viscous/Inviscid Analysis of Jet Aircraft
Plumes", NASA CR-3289, May 1980.
14. Dash, S.M. and Thorpe, R.D., "Shock-Capturing Model for One-
and Two-Phase Supersonic Exhaust Flow", AIAA I-, Vol. 19, No.
7, July 1981.
15. Wilmoth, R.G., "RAXJET: A Computer Program for Predicting
Transonic Axisymmetric Flow over Nozzle Afterbodies with
Supersonic Jet Exhausts", NASA _-83235, February 1982.
16. Steger, J.L., "Numerical Simulation of Steady Supersonic
Viscous Flow", A/_ I., Vol. 18, No. 12, December 1980.
17. Diewert, G.S., "Numerical Simulation of Three-Dimensional
Boattail Afterbody Flows", AIAA Paper No. 80-1347, July 1980.
18. Birch, S.F., Kern, P.R. and Cornette, W.J., "Numerical
Modeling of Three-Dimensional Turbulent Exhaust Streams",
Final Report, Navy Contract N700530-81-0159, 1982.
19. Perry, K.M. and Forrester, C.K., "Numerical Solution of
Navier-Stokes Equations for a Three-Dimensional Cover", _J_
I., Vol. i, No. ii, November 1977.
20. Shang, J.S. and Haney, W.L., "Numerical Solution of Navier-
Stokes Equations for a Three-Dimensional Cover", AIAA J.,
Vol. i, No. ii, November 1977.
21. Cline, M.C., "VNAP2: A Computer Program for Computation of
Two-Dimensional, Time-Dependent Compressible Turbulent Flow",
Report LA8872, Los Alamos National Laboratory, August 1981.
181


Wall jet analysis for circulation control aerodynamics. Part 2: Zonal modeling concepts for wall jet/potential flow coupling

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