Computational Modeling for the Flow Over a Multi-Element Airfoil

9 Pages·1999·0.4 MB·English

by  Liou, William W.

/l/_i &-.-l- / ? 7 _'
(AIAA 99-3177, AIAA 17th Applied Aerodynamics Conference, Norfolk, VA, June 1999)
COMPUTATIONAL MODELING FOR THE FLOW OVER __I,__ _ _ )7 "7
AMULTI-ELEMENTAIRFOIL
William W. Liou" and Fengjun Liu"°
Department of Mechanical and Aeronautical Engineering
Western Michigan University
Kalamazoo, MI 49008
Abstract As the slat wake convects downstream, it may fur-
ther interact with the transitional flow over the suc-
ceeding elements, such as the flow over the main el-
The flow over a multi-element airfoil is computed
ement and the flap. As a result, an accurate predic-
using two two-equation turbulence models. The com-
tion of the flow transition represents a major challenge
putations are performed using the INS2D Navier-
for the computation of the flow over multi-element air-
Stokes code for two angles of attack. Overset grids
foils and the use of a transition model often becomes a
are used for the three-element airfoil. The computed
discriminating factor in the outcomes of a prediction.
results are compared with experimental data for the
Turbulence models are frequently used in the high-lift
surface pressure, skin friction coefficient, and velocity
flow calculations. In this practice, turbulence models
magnitude. The computed surface quantities generally
are "turned-on" at a designated location on the air-
agree well with the measurement. The computed re-
foils. The designated locations are usually correlated
suits reveal the possible existence of a mixing-layer-like
with the measured location of transition onset and the
region of flow next to the suction surface of the slat for
computational results can vary significantly with the
both angles of attack.
assigned transition location.
I. Introduction In this paper, the flow fields over a multi-element
airfoil are calculated numerically using two two-
equation turbulence models.
Flows past multi-element airfoils have been sub-
These computational exercises are necessary in an
jected to intensive experimental and computational
effort to identify the limitation of turbulence models in
studies 1,2,3 for the past two decades. An accurate pre-
the prediction of transitional flows. The computational
diction of such flows can enhance the performance and
results may also help to investigate areas of the flow
the safety factor of aircrafts in high-lift operations.
where experimental data are difficult to obtain.
Even with the advances of computational fluid dynam-
The Navier-Stokes solver used in the study is de-
ics (CFD), the prediction of high-lift flow fields remains scribed in the next section. The Chimera composite
a challenge. The flow fields around multi-element air-
grids used are also presented.
foils are complex and are known to be dominated by
different flow mechanisms at different operating condi-
tions. lI. Flow Solver
A significant portion of tile flow around multi-
element airfoils is transitional over a wide range of op-
The flow calculations presented here were performed
erating condition. The onset location of the transition with the INS2D code 4'5'6. The code solves the two-
process varies with, for example, angles of attack and
dimensional, incompressible form of the Reynolds-
Reynolds numbers. In addition to boundary layer tran-
averaged Navier Stokes equations using an artificial
sition, free shear flow transition is also likely to occur
compressibility approach. The INSgD code is a fi-
in, for example, the flow over the slat.
nite difference solver, using Roe's third order upwind-
biased, flux-difference splitting for the convective terms
" Associate Professor, Senior Member AIAA. and a second order central differencing for the viscous
**Graduate Student. terms. The code is capable of solving both steady and
Copyright©1999 by tile authors. Published by the unsteady problems with point-to-point matched grids
American Institute of Aeronautics and Astronautics, or Chimera overset grids. The details of the INS2D
code can be found in the references cited above. The
Inc. with permission.
1
INS2Dcodehasbeenappliedextensiveltyotheflow
C. k (3)
overvarious single- and multi_element airfoils 4'5'6 and Ao + A,U(') 7
has been shown to be a very reliable tool for such where
purposes. Generating the necessary grids for multi- U(*)
element airfoil flow calculations can be very time- --_ V SijSij "at-
consuming regardless of the grid topology one chooses (_i3 = (_ij - 2eijkWk
to use. In this study, overset grids were used and the
(_ij "_ _ij -- (ijkt_)k
grids were generated using the OVERMAGG 7software.
OVERMAGG is an automated script system specifi- f2ij is the mean rotation rate viewed in a rotating ref-
cally designed to perform overset grid generation for erence frame with the angular velocity wk. The param-
multi-element airfoils. The use of OVERMAGG has eter A_ is determined by
resulted in a significant amount of saving in time dur-
1
ing this study.
A, = v_cos@, ¢ = 5arccos(v/-6W)
III. Turbulence Models W = S_Sjk&_ (4)
Sa
The SST model s and a k- _¢9,10,11 model were used
to study the flow field. The SST model is available as a
The damping function is defined by
model option in the INS2D code. The k - e model was
recently implemented as a separate module to the code.
fu ---[-I.- exp(--(a,Rk+ a3R 3 + asR_))]½ (5)
There are two other one-equation model options in the
INS2D code. The SST and the two one-equation mod-
where
els have been applied to the flow over the 30P30N ge-
ometry and the results have been reported previously 3.
The SST model was designed to take advantange of ax = 1.7 x 10-3, aa = 10-9, a5 = 5 x 10-1a
both the robustness of the k - _ type of models in the
v_y
near wall region and the free-stream independence of Rk--
the k- e type of models in the outer part of boundary bt
layers and for free shear layers. The eddy-viscosity was The near-wall boundary conditions for the turbulent
formulated to account for the transport of the principal
quantities are
turbulent shear stress in boundary layers. The SST
model has been shown to perform very well for many U4
different flows. k = 0.25u_ and e = 0.251-_" (6)
//
The k - e model used here represents a variant of
the model developed by Shih and Lumley 9, with the where u_ denotes the surface friction velocity.
constant Co(=0.09 ) replaced by a variable Cu formula-
tion. Tile new formulation of Cu, with an explicit de- IV. Geometry
pendence on the mean strain rate, was developed based
on the realizability constraints of the Reynolds stresses.
The McDonnell Douglas 30P-30N landing config-
The model has been shown to work well for a wide range uration was used in this study. Figure 1 shows the
of flows l°'ll .
geometry and the stations where profile data will be
The model equations for k and _are,
presented. Both the leading-edge slat and the trailing-
k t + Uiki --- [(u + ut)ki],i - u---_Ui.j - e (1) edge flap have a deflection angle of 30°. The airfoil
has been tested extensively at NASA Langley Low
t:t
Turbulence Pressure Tunnel (LTPT) 1,t2. The geometry
' O-E has been used as a test case in a CFD Challenge Work-
;_ (2)
shop held at NASA Langley in 1993 and many compu-
-- (f2f2 5_. + l]l]tS,iX, i tational results obtained by using different solvers and
where models have been reported 2'3'6.
Cl = 1.44, C2 = 1.92, a_ = 1.3 The computational grid consists of seven zones and
a total of about 103,000 grid points. Figure 2 shows
f2 = I -0.22exp[- (__)]2 , Rt = k--s the C grids around the slat, the main element, and the
flap,whichconsisot f 175x453,81x 133, and 221x85 1.1125), there seems to be a better overall agreement
points, respectively. Two H grids were used for the between the k- _ model and the measurement in terms
main-element cove and for the wake region of the flap. of the development of the slat and the main-element
A background H grid extends to the top and the bot- wakes. None of the models gives a good prediction for
tom walls of the wind tunnel. When the grid for one the deficit of the main-element wake.
element overlaps another element(s), holes and outer Figure 6 shows the velocity profiles on the main el-
boundaries are determined by using the PEGSUS code. ement for AOA--8 °. The slat wake is predicted well
The communicaiton between the overset grids are also at x/c -- 0.1075. The predicted main element surface
handled by the PEGSUS code. boundary layer is more developed than what the data
Comprehensive grid-independence studies have has shown. At the later stations, x/c = 0.45 and 0.85,
been performed and reported previously using similar the predicted velocity profiles agree well the measure-
overset grids for the same geometry 3'6. These and other ment.
calculations for the same geometry indicate that the Figure 7 shows the surface skin friction coeificient
grid point distributions in the wake regions can have distributions on the main element for AOA=19 °. The
certain effects on the velocity profiles in those regions computed results agree very well with the available
and the wall pressure is not sensitive to the grid den- measured data.
sity. These results also show that further refinement It should be noted that correction terms for transi-
of the grid from the current level does not change the tion modeling have been proposed for both models 2'3' 13.
results appreciably. These corrections have not been included in the calcu-
It should be noted that the turbulence models were lations presented here.
applied without including any explicit account for the It is apparent that, based on the results shown here
flow transition.
and those published in the previous studies, the two
Results will be presented for a Reynolds number of turbulence models used in this study can give a fairly
nine million and two angles of attack (AOA) of 8° and accurate account of the outer inviscid flow field around
19°. the multi-element airfoil. The near wall viscous flow
regions have not been predicted well. A measure com-
V. Results and Discussions monly adpoted to improve the prediction of the near
wall viscous flow was to include some type of correction
terms for the boundary layer transition, as the measure-
Figure 3 shows the comparison of the surface pres-
sure coefficient distributions for the 19° case. Both ment did show a fairly large region of boundary layer
transition on all three elements for a range of flow con-
models predict the surface pressure well with a slightly
ditions. Various approaches have been proposed 2'3 and
faster external flow predicted by the k - e model over
the suction surface of tile slat. have shown a significant improvement. These results
indicate that the slat flow prediciton plays a critical
For AOA--8 °, the surface pressure coefficient distri-
role in the overall flow computation.
butions are shown in Figure 4. The overall agreement
with the measurement is good for the main element and The flow field around the slat is complicated and
difficult to measure due to the small sizes of the slat.
the flap. On the suction surface of the slat, the k - c
model is predicting a faster external flow. The laminar/turbulent separation and reattchment in
the lower pressure surface and the boundary layer tran-
Figure 5 shows the velocity profiles on the main el-
ement and on the flap for AOA-=19 °. At x/c = 0.1075, sition on the upper suction surface have been proposed
there is almost an uniform offset between the data and as among the phenomena that need to be modeled cor-
the predictions. This may have been caused by possible rectly to obtain reasonable predictions, indeed, Rum-
improper data calibration 2. The predicted slat wake is sey et al. 2have shown that the velocity on the main el-
located slightly further away from the main element ement can be predicted well if the calculated slat wake
surface at all three stations (x/c=0.1075, 0.45, and agrees with the measured wake to begin with.
0.85). As a result, the merging of the slat wake and the Since the Reynolds number is large, tile initial slat
boundary layer is apparently yet tooccur at x/c _- 0.85. wake development depends largely upon the boundary
The boundary layer velocity profiles were predicted well layer at the point of separation.
by tile k - e model, which resulted in a better predic- in the following, we examine the boundary layer on
tion of the main wake immediatedly behind the main the suction side of the slat By using the /¢- E model
element trailing edge (Figure 5.d, x/c = 0.89817). results, hopeing to gain a better understanding of the
On the flap (Figures 5.e and 5.f, x/c = 1.0321 and possible physical mechanisms at play in the slat flow.
Figures8and9showthedistributionsoftheveloc- 2 C.L. Rumsey, T.B. Gatski, S.X. Ying, and A.
itymangitudaendtheturbulentkineticenergyprofiles Bertelrud, "Prediction of high-lift flows using tur-
in thedirectionnormaltothesurfaceat threeloca-
bulent closure models," AIAA paper 97-2260.
tionsonthesuctionsideoftheslatforAOA=8° and
3 S.E. Rogers, F.R. Menter, P.A. Durbin, N.N. Man-
190. Notethatthevelocitymagnitudaendtheturbu-
sour, "A comparison of turbulence models in com-
lentkineticenergyhavebeennormalizebdythelocal
puting multi_element airfoil flows," AIAA paper 94-
skinfrictionvelocity.Astheboundarylayeronthe
0291.
slatsurfacedevelopsit,interactswiththeouter"invis-
cid"flow.ForAOA=19°, Figure8.bshowsthat,asa 4 S.E. Rogers and D. Kwak, "An upwind differencing
resultofthisinteractiono,rmixing,ofthelowspeed scheme for the steady-state incompressible Navier-
flownearthesurfaceandthehighspeedflowinthe Stokes equation", Journal of Applied Numerical
outerstream,aregionofflowwithinflectionavleloc- Mathematics, 8, 43-64, (1991).
itydistributionappearsT.hismixingphenomanmaay s S.E. Rogers, S.E., D. Kwak, and C. Kiris, "Numer-
besimilarto thatin thefreeshearlayer.Themix- ical solution of the incompressible Navier-Stokes
ingregionisalsodetectibleforAOA=8° inFigure8.a, equations for steaAy-state and time-dependent
butbecomemsoreapparenfturtherdownstreamonthe problems," AIAA Journal, 29, 603-610 (1991).
slat.
6 S.E. Rogers, "A comparison of implicit schemes for
the incompressible Navier-Sotkes equations with ar-
Figure9showsthattheseinflectionavlelocitydis-
tributionshaveproducedlocalpeaksofturbulentki- tificial compressibility," AIAA paper 95-0567.
neticenergyin the"mixing"zoneoftheflow(x/c=- 7 S.E. Rogers, H.V. Cao, and T.Y. Su, "Grid gener-
0.071and0.0053)F.orAOA=8°,thelocalpeaksseem ation for complex high-lift configurations," AIAA
tobedevelopinagnd,forAOA=1°9, theirvalueshave paper 98-3011.
exceedetdhoseinthebufferlayer.Thereforet,hevis-
s F.R. Menter, "Zonal two equation k-w turbulence
couslayerontheslatsuctionsurfaceexhibitsadouble-
models for aerodynamic flows," AIAA paper 93-
deckstructurew, ithaboundarylayernearthewalland 2906.
mixing-layer-likebehavioirntheouterregion.
9 T.-H Shih and J.L. Lumley, "Kolmogorov behav-
Aswasmentioneedarlier,thereisnodetailedflow ior of near-wall turbulence and its application in
profilemeasuremeanvtailablefortheslatregion.The turbulence modeling," Comp. FluM Dyn., 1, 43-56
observatiomnadeherehasbeenbasedentirelyupon
(1993).
the
computed results. However, to the extend that the 10 W.W. Liou and T.-lt. Shih, "Transonic turbulent
observation is valid, it is evident that the transition in flow predictions with new two equation turbulence
the shear layer and in the boundary layer are among models", AIAA paper 95 1805.
the essential features of the flow around the slat.
11 Z. Yang, N. Georgiadis, ,l. Zhu, and T.-H. Shih,
"Calculations of inlet/nozzle flows using a new k - e
Acknowledgment model," AIAA paper 95-2761.
12 P.C. Stainback, R.J. McGhee, W.D. Beas[ey, and
This work has been supported by NASA Langley Re- H.L. Jr. Morgan, "Tile Langley Research Center's
search Center under a grant NAG 1-1979. The technical Low Turbulence Pressure Tunnel," AIAA paper 86-
monitor is Dr. Ronald D. Joslin. The authors would 0762.
like to thank Dr. Stuart E. Rogers at NASA Ames Re- t3 W.W.Liou and T.-tl. Shill, "Bypass transitional
search Center for assistance and advices in using the flow calculations using a Navier-Stokes solver
INS2D and OVERMAGG codes. Dr. Christopher L. and two-equation models," AIAA paper 97-2738.
Rumsey at NASA Langley Research Center kindly pro-
vides tile experimental data.
References
a A. Bertelrud, "Transition on a three-element high
lift configuration at high Reynolds numbers," AIAA
paper 98--0703.
0.45
0.1075 I
0.85
0.89817
J
X/C=-0.087_
_1.1125
Figure l. 30P30N geometry and survey stations.
Figure '2 (:ompulalJ¢_Hal gri¢ls
(a) slat
(a) slat !_
-2
-16 ..-0.I 30 "0"050 X/c
-%.io i -0I.06 t -o'.o2 0.02 0.06
)dc
(b) main
0
a.
" " gJC
-12 0.40 0.60
o.oo 020 xlc
(c) flap
1 --_ - - 0
-4 -.._ hog 1.00 1.05 1.10 ,.85 090 0.95 X./c
,.85 0.90 u._o _C
Figure 4. Walt pressure coefficient. 80
Figure 3. Wall pressure coefficient. 19°
(a) x]_---O. 1075(maia)
Co) xJ_-O.45(main)
0.08 t 0.08
1 _v_ I ' ' I ' ' 1 ' ' ] ' 1 ' 1 ' '0(I
\\ oEXP
\ \ -- -- SST
0.06 0.06
0.04 ;_ 0.04
0.02 0.02
0.00 '-
0.40 0.44 0.48 0.52 0.56 0.00 ,
0.2O 0.24 0.28 0.32 0.36 O,4(3
q/ao
q/ao
(C) x/c:_.85(main) (d) X./C.=0.89817(flap)
0.12
i
I ' I ' 1 ' It
0.10 I o,o
0.08 - ----SST I _i i1 0.=L
. -- k--E: I./ )_ I" ,'/ o
t
o-I
0.02
0.00
0.16 0.20 024 0.28 0.3; 0..20 024 0.28 0.32 0.36 0.40
q/ao
q/%
(e) x./c= 1.0321 (flap) (0 x/c=1.1125(flap)
0.16
I ' I ' 1 t II _ 024 ' _ I ' I ' I ' 1
0.14
0.20 - t_
0.12
oDCP oEXP .e_ _ .
0.10 - - SST 0.16 - -- SST _% _
O.08
0.04
0.02
0.00 0.00 I , I , ___
0.0_ 0.08 0.12 0.16 0.20 0.00 0.04 0.08 0.12 0.16 02t
q/ao q/%
Figure 5. Velocity profiles. 190
(a)x/c=O.I075(main) (b)x/c=0.45(main)
t
0.08
i i I v i i
, I _ I i e , I if'
0.06
oEXP
0.06 I
k--£ oEXP
0.04 0.04
0.02
0.02 f J I ___i
0.00 i i i 0.00
0.30 0.34 0.38 0.42 0.46 _.50 0.16 0.20 0.24 0.28 0.32
q/ao q/ao
(c)x/c=0.85(main)
0,08
i ! ! I , _ I
0.06
L 0.04
0.02
0.00 1 I
0.16 020 024 028 0.:12
q/%
Figure 6. Velocity profiles. 80
0.060
i i i i
I
0.050 l
0.040 OEXP
0.030 - SST
- Ic-_
o- 0.020
0.010
0.000 t
--0.010
-0.020 0I.2 I o14i o16i o16a
0.0 1.0
x/c
Figure 7.Skin friction coefficient. 190
(a) (b)
40.0
40.0
30.0
30.0 .....
4' 20.0 +:_ 20.0
10.0
10.0
/ j t::" tI-';- o_1I i f- I I"""" I
0.0
0.01.0 10.0 100..0 1000.0 10000.0 1.0 I0.0 IY00#0 1000.0 10000.0
Y
Figure 8. Sla.t Velocity profiles. (a.)80; (b) 19°.
i
(a) (b)
7.0 7.0
6.0 6.0 ---.:,,_-,.O_J0=7l,, J
04_63 ,
5.0 .5.0
4.0 4.0
3.0 3.0
.. :_
2.0 2.0
1.0 1.0
" \\ I
0.01.0 10.0 10_.0 1000.0 10000.0 0.01.0 1o.o to_.o lOOO,O 10000.0
Y Y
Figure 9. Slat turbulent kinetic energy.(a) 8°; (b) 19°.