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PREDICTION OF HIGH-LIFT FLOWS USING TURBULENT CLOSURE MODELS Christopher L. Rumsey?* Thomas B. Gatski: Susan X. Ying,b**a nd Arild Bertelrudc** aNASA Langley Research Center, Mail Stop 128, Hampton, VA 23681 -0001, bMcDonnell Douglas Corporation, Long Beach, CA, and cAnalytical Services and Materials, lnc., Hampton, VA ABSTRACT The flow over two different multi-element airfoil configurations is computed using linear eddy vis- cosity turbulence models and a nonlinear explicit algebraic stress model. A subset of recently-mea- sured transition locations using hot film on a McDonnell Douglas configuration is presented, and the effect of transition location on the computed solutions is explored. Deficiencies in wake profile compu- tations are found to be attributable in large part to poor boundary layer prediction on the generating element, and not necessarily inadequate turbulence modeling in the wake. Using measured transition locations for the main element improves the prediction of its boundary layer thickness, skin friction, and wake profile shape. However, using measured transition locations on the slat still yields poor slat wake predictions. The computation of the slat flow field represents a key roadblock to successful pre- dictions of multi-element flows. In general, the nonlinear explicit algebraic stress turbulence model gives very similar results to the linear eddy viscosity models. 1. INTRODUCTION include: (1) boundary layer transition, (2) shockhound- ary layer interactions, (3) viscous wake interactions, (4) confluent wakes and boundary layers, and (5) separated 1.1 Overview flows. Some important insights into the physical pro- The prediction of high-lift (multi-element airfoil) cesses that govern high-lift aerodynamics were summa- flow fields currently represents a difficult challenge for rized by A. M. 0. Smith in his landmark 1975 paper? In the computational fluid dynamics (CFD) and turbulence particular, he described several effects that contribute to modeling community. Even in two dimensions, state-of- improved high-lift characteristics of multiple elements the-art CFD codes fail to predict trends with Reynolds over single elements. number or trends with flap/slat rigging changes suffi- A great body of work on high-lift flows, both experi- ciently accurately.' Without the capability to consistent- mental and computational, has built up since that time. ly predict trends using CFD, aircraft designers must rely (See, for example, discussions in thg: papers by Lynch et on heuristic techniques and wind-tunnel experiments, al,' Haines? Wooqward and Lean, Thibert et al? Val- which themselves present additional difficulties when arezo,l0 and Ying. ) Some experiments have been per- attemptin to scale the results up to flight Reynolds formed expressly for the purpose of CFD code numbers3394 validation. For example, an AGARD three-element The flow around a multi-element airfoil or wing is in- take-off configuration, tested in the early 1970's and herently complex. Variations in angle of attack and dif- subseqpently used as a part of a battery of AGARD test ferent slat / flap settings often present very different and cases, was recently used as a code validation distinct challenges. For example, for typical landing challenge12b y the CFD Society of Canada. Experiments configurations, viscous effects can dominate compress- have also been performed in the NASA Langley Low ibility effects near stall, whereas for typical take-off Turbulence Pressure Tunnel (LTPT)'39'4 on McDonnell configurations compressibility can dominate the stall Douglas three-element landing configurations, used as physic^.^ Also, flap separation is often seen at low to test cases in a CFD Challenge Workshop held at NASA moderate angles of attack, whereas stall is often caused Langley in 1993. Several papers have been written that by an unloading of the aft portion of the main element describe various as ects of experimental testing on due to rapidly spreading and merging shear layers and these configurations.5 5-19 wakes over the flap.' Since the CFD Challenge Workshop, there have been Although high-lift devices work essentially because many CFD results reported for the McDonnell Douglas they manipulate the inviscid flow? vi2 c ous effects are three-element configurations, using a variety of numer- crucial as well. According to Meredith, some of the vis- ical schemes for the Navier-Stokes equations. The in- cous features that can affect 2D multi-element systems compressible Navier-Stokes code INS2D, using both point-matched and overset grids, has been used exten- sively to assess the ability of CFD to model trends with configuration changes, as well as to assess the effects of *Senior Member AIAA. tunnel walls, grid density, and turbulence mode1.20-22I t has also been coupled with a transition-prediction meth- Copyright 0 1997 by the American Institute of Aeronautics and od~logy.C~om~ pressible Navier-Stokes codes have Astronautics, Inc. No copyright is asserted in the United States under been used as well. Jones et used the CFL3D code Title 17, U.S. Code. The US.G overnment has a royalty-free license with overset grids to compute flow over both the 2D to exercise all rights under the copyright claimed herein for Govem- McDonnell Douglas three-element configurations as mental purposes. All other rights are reserved by the copyright owner. well as 3D flow over wings with flaps. The structured models are generally smaller than the differences be- grid codes OVERFLOW and TLNS3D and the unstruc- tween computation and experiment. Some further per- tured-mid codes NSU2D and FUN2D have also been spective may be gained on the issue of turbulence applid to the 2D McDonnell Douglas configura- modeling by considering other experimental and com- tions.5,25,26 putational results for differer& configurations. Squire32 and Agoropoulos and Squire compared computed ve- 1.2 Code Validation Issues locity profiles and turbulence quantities with experi- mental results over a two-element model designed to Overall, CFD comparisons with experiment for the explore slat-wake I main-wing-boundary-layer interac- 2D McDonnell Douglas three-element configurations tion. They describe the merging process by three re- have been somewhat ambiguous. Considering the inher- gimes: (1) unmerged, when the wake and boundary ent complexity of the flow field, CFD results are surpris- layer are separated by a potential core, (2) initial merg- ingly good, particularly with regard to surface pressures. ing, when the outer part of the wake and inner part of the Unfortunately, the trends with Reynolds number and boundary layer are unaffected, and (3) full merging re- configuration changes are not accurate enough to meet sulting in a new, thicker boundary layer (although full the needs of wing designers, and the maximum lift coef- merging usually does not occur prior to the main ele- ficient and the anQ l e of attack at which it occurs tend to be overpredicted. However, it is still not clear at this ment trailing edge.) Using the incompressible Navier- Stokes equations with a k - E turbulence model and an time whether the fault is due to (1) inadequate modeling algebraic stress model (ASM), they found good agree- in the CFD (turbulence models, transition models), and/ ment between both models and experiment in the initial or (2) the fact that CFD is not simulating the same con- stages of the merging, with somewhat better results us- figuration as experiment. ing the ASM. Decelerated flows were predicted with the The former possibility may play a role because turbu- same accuracy as those in constant pressure. Squire also lence models vary in the accuracy to which they predict discussed the fact that stress transport models often pre- free shear flow behavior (such as spreading rate), and dict too rapid a relaxation of the flow following distur- most in use today are eddy-viscosity one- and two-equa- bances since model constants are generally weighted tion models that do not account for curvature effects or toward equilibrium flows. This results in a too rapid dis- anisotropy. It is possible that some missing effects such appearance of the velocity defect in the wake, as well as as these may be important in certain regions of multi-el- of the corresponding shear stress peaks. ement flow fields. Additionally, most CFD codes pre- In addition to computing the CFD Challenge Worti scribe rather than predict transition locations; these shop landing configurations, Anderson and Bonhaus locat’on can have a significant effect on the solu- computed the flow over a McDonnell Douglas three-el- Moreover, the transition process itself is usu- ement take-off configuration with the unstructured code ally not modeled. Instead, the eddy viscosity is generally FUN2D. They com ared with the experimental results “switched on” at transition points. More sophisti ated transition models, such as that employed by Cebeci$ 9 (in of Nakayama et aI?’including turbulent shear stress da- ta. Using the one-equation edfj-viscosity turbulence an interactive boundary layer code coupled with an alge- model of Spalart and Allmaras, turbulent shear stress braic turbulence model), are currently not in wide use. profiles were found to be in overall reasonable agree- The presence of laminar separations bubbles, which are ment with the experiment. Peak levels were underpre- usually associated with high peak suctions and steep ad- dicted on the flap, but results in that region may not have verse pressure gradients, are also generally not ac- been sufficiently grid-converged. counted for. - Lien and Lesch~ine2an~d Lien et computed the The latter possibility that CFD may not be simulat- flow over both a separated single-element ONERA air- ing the same configurations as experiment - arises par- foil as well as a two-element (main element and flap) ticularly because of questions regarding deviation from - two-dimensionality in experimental tests and the appli- NLR-7301 airf0il.3~T hey compared results using k E two-equation eddy-viscosity models with full second- cability of 2D CFD simulations to such flows. Addition- moment Reynolds stress closure models on the ONERA ally, the effects of surface roughness, tunnel turbulence, airfoil, and found that the latter models are generally su- external tunnel devices, and structural model deforma- perior. However, all of the turbulence models performed tions need to be considered. Since multi-element airfoil poorly in the far wake, in regions where the turbulence flow appears to be very sensitive to all of these parame- ters, it is often difficult to determine precisely why a production over dissipation is low. The k - E eddy-vis- cosity model performed fairly well on the NLR-7301 CFD simulation is in error from a given experimental re- airfoil, although wake mixing was incorrect and there sult. As an example of the experimental sensitivity, a was insufficient mixing between the wing wake and flap three-element airfoil section representing the section at boundary layer. This was attributed to the inability of 59% span of the A3 10 wing was found to give a negative trend of with Reynolds number between 6 mil- the k - E model to represent curvature-turbulence inter- action. lion and 16 million for an unpolished model, but a posi- Godin et aI4 also computed the flow over the NLR- tive trend when the model was p~lished.~’ 7301 airfoil, using the one- and two-equation eddY iv is - cosity turbulence models of Spalart and Allmaras (S- 1.3 Turbulence Model Studies A) and Menter41 (SST). They found good agreement in Rogers et aI3’ has shown that several different eddy- general with both models, although the SST model tend- viscosity models tend to be consistent in their prediction ed to be more accurate in separated flow regions while of the flow over the McDonnell Douglas three-element the S-A model performed better in attached flows and configuration. The differences between the turbulence wakes, including the merging wake I boundary layer re- 2 gion. Turbulent shear stress profiles appeared to agree codes20p21*22,2o6v er similar configurations. These stud- better in general with experiment than the results of Lien ies indicate that velocity profiles are more sensitive to et a13* using the k - E eddy-viscosity model, but velocity grid density than surface pressures and lift coefficient. - profiles were similar. Cao and Kusunose?’ Jasper et When between 100,000 200,000 grid points are used a1?2 and Fritz43a lso computed this 2D flow, using var- for point-matched grids similar to the grids used in the ious zero-, one-, and two-equation eddy-viscosity mod- current study, further refinement yields on1 minor dif- els. Generally positive agreement with experimental ferences in the computed velocity profiles3 These ear- data was obtained for lift, surface pressures, and veloci- lier studies also indicate the importance of having ty profiles, although the zero-equation (algebraic) mod- sufficient resolution in the wakes and boundary layers. el used in Jasper et al resulted in poorer predictions of The grids used in the current study have over 1 0 0 , ~ boundary layer parameters and stall onset compared grid points with minimum normal wall grid spacings with a one-equation model. No comparisons with Rey- that yield an average y+ of approximately 0.3 - 0.4 for nolds stress data were made in these three references. their respective free stream Reynolds numbers. The The results for the NLR-7301 airfoil seem to support grids are also clustered in the wake regions of each ele- the finding of Rogers et a131 (for the McDonnell-Dou- ment. glas configuration) that, while there are certainly notice- The first case is a three-element configurattpn defined able differences at a detailed level, many eddy-viscosity as case A2 in a battery of AGARD test cases a d used turbulence models overall tend to have only relatively as a test case for the code validation challengel’by the minor effects on global properties for multi-element air- CFD Society of Canada in June 1996. Although tested in foil predictions. (This conclusion is of course dependent a wind tunnel with solid walls, the AGARD ’test case is on particulars of the flow field in question. For example, performed on a “free air” grid with far field extent of for flows with boundary layer separation, models such about 10 chords. (The original model has a stowed chord as S-A and SST have been shown to be superior to the of c = 0.7635 m, and the tunnel height to chord ratio is “standard” Jones-Launder version of k - E !l,*) The H/c = 5.19 .) The slat is positioned at an angle of 25’, question of whether more advanced nonlinear turbu- while the single-slotted flap has a moderate deflection lence models would produce significantly better results angle of 20°, typical of a take-off configuration.A close- for multi-element airfoils remains open. up of the grid used for this case is shown in figure 1. This is a 4-zone grid with 114,908 grid points. The abscissa 1.4 Focus of this Paper of this figure is given in terms of x/c , and the stowed airfoil would have its leading and trailing edges at x/c Because of the complexity and interdependence of of 0 and 1, respectively. This concguration is computed many factors in high-lift computing and experimenta- at M = 0.197 and Re = 3.52 x 10 based on stowed-ge- tion, it seems inappropriate to focus solely on the subject ometry chord. Transition is tripped on the main element of turbulence modeling without regard for other factors. at x/c = 0.125 on both the upper and lower surface, and We therefore take a somewhat broader approach. The is free on the slat and flap. purpose of this paper is to contribute to a greater under- standing of issues surrounding CFD validation against high-lift wind tunnel tests. As a consequence, it focuses both on experimental as well as numerical issues. Spe- cifically, the purpose is threefold: (1) introduce a subset of transition locations for the 2D McDonnell Douglas three-element configuration recently measured in the LTPT with hot film, (2) demonstrate the effect of transi- tion location on CFD solutions, and (3) explore the ef- fect of a nonlinear explicit algebraic Reynolds stress turbulence model45 on the CFD solution for both the AGARD take-off configuration’’ * l2 and the McDonnell Douglas landing configuration.1 5-19 It is hoped that by taking this approach, we can not only determine the im- pact of modeling the nonlinear Reynolds stress terms, but also demonstrate the importance (and difficulty !) of accurately modeling the wind tunnel experiment, partic- ularly with regard to the transition process. 2. DESCRIPTION OF THE AIRFOIL CONFIGURATIONS AND CFD GRIDS 0.0 0.5 1. o Two multi-element configurations are investigated in this paper. Both employ one-to-one point connectivity across grid zones. Grids with one-to-one point connec- Fig. 1. AGARD configuration grid, with every other grid point removed. tivity insure conservation across boundaries and provide improved continuity of grid spacing at zonal interfaces, The second configuration is a three-element McDon- although this type of grid generation is substantially ne11 Douglas config~ration,’~t-e’s~te d in the LTPT and more difficult than for overset grids. used as a test case in a CFD Challenge Workshop held Only fine grids are employed, since extensive grid at NASA Langley in 1993. The model has a stowed sensitivity studies have b en published previously for both the CFL3D cod>4 as well as for other chord of c = 0.5588 m and the tunnel height is 3 H/c = 4.09. The particular slat and flap settings em- the locations of suction peaks and stagnation points to be ployed are: slat deflection of 30°, slat gap of 2.95%, slat displaced in the chord-wise direction. Second, separated overhang of -2.5%, flap deflection of 30°, flap gap of or low-shearregions, as well as brackets, etc., may cause 1.27%, and flap overhang of 0.25%. This rigging desig- spanwise flow that alters the transition data. Assuming nation is referred to as 30P-30N. It is typical of a landing experimental data are available, the upper surface configuration. It is computed using both a “free air” grid chordwise effects may be accounted for in the CFD, at with far field extent of about 15c, as well as a grid that least in part, by relating the transition to the distance models an angle of incidence of 19’ with LTPT walls. downstream of the suction peak as opposed to using an This latter grid extends 15c upstream and 19c down- absolute geometric location. However, for all the Mc- stream of the model to avoid the possibility of inflow I Donne11 Douglas cases in this paper, this is not neces- outflow boundary influence on the solution, although sary because the computed suction peak locations agree the actual LTPT test section does not extend this far. A with those in the experiment to within a distance less close-up of this latter grid is shown in figure 2. This is a than the densest pitch of the hot films. Spanwise effects 5-Zone grid with 138,389 grid points. It is computed at are not easily accounted for. M = 0.2 and Re = 9 x 10 based on stowed-geometry Transition locations are determined based on informa- chord. In the wind tunnel test, transition is free on each tion from 359 surface hot films on the three elements. of the elements. The start and end of transition are extracted from an analysis of a combination of standard deviation, skew- ness, and flatness factors of the hot film signals, plus in most cases an additional examination of the signal traces for auto- or cross-correlations. Note that even though the films are located at 2.54mm pitch (or As/c = 0.0045 ) in the most dense regions, the flows at higher angles of at- tack have fairly short transition regions, so that only one or two films pick up the feature. Table 1 Hot film transition data for 3OP-3ON configuration, M=O.2, Re=9 million lower suct peak n/a n/a lower trans S n/a n/a lower trans E n/a n/a upper suct peak .015 -.084 .006 -.0852 L uppertranss .030 -.077 .010 -.0853 uppertransE .060 -.057 .020 -.082 SIC XIC SIC X/C lower suct peak -.510 ,526 -.620 .635 Fig. 2. McDonnell Douglas 3OP-3ON grid, with every other grid lowertrans S -.405 .422 -.670 .685 point removed. lowertransE - 3 0 S26 n/a uppersuctpeak .OOO A496 .008 .055 3. DESCRIPTION OF THE TRANSITION TEST uppertranss .012 .058 .016 .061 AND DATA uppertransE .025 .068 .025 .068 A subset of transition data recently taken in the LTPT is presented here for the McDonnell Douglas three-ele- PLAP SIC X/C S_IC_ x.-lc - ment configuration. The hot-film sensors are similar to lower suct peak nla nla those used by Nakayama et a14 for a similar configura- lower trans S n/a n/a tion in the same wind tunnel. They are thin nickel films lower trans E nla n/a on a 0.05mm polyimide substrate. The sensors are ar- uppersuctpeak .026 .888 .024 .886 ranged in a straight streamwise array at 73.4% span, whereas most pressure taps are located at 50% span. (mid) Side-wall suction is used to maintain approximate two- uppersuctpeak .020 .882 .016 .878 dimensionality for the flow. However, this is optimized (aux) for 16’ angle of attack. Generally, up through this angle uppertranss .030 .892 .030 .892 the discrepancies in pressure distribution between the 50% span row and an auxiliary pressure tap row near the uppertransE .070 .931 .060 .921 hot films are moderate. Above 16O, three-dimensionality Table 1 lists the starting and ending transition loca- becomes more pronounced; hence it may be a contribut- ing factor in results shown below. Details can be found tions for the 30P-30N configuration at two angles of at- tack, along with locations of the suction peaks. Results in Bertelr~d.~~ Three-dimensionality affects the data in two ways. are given both in terms of the surface coordinate s/c First, span-loading variations, which manifest them- (where s/c = 0 corresponds to the location on the for- ward part of each element in the stowed position where selves as variations in effective angle of attack, cause 4 y/c = 0) as well as the deployed x/c coordinate. De- ative, suggested by P. Spalart in a private communica- pending on location, the data are accurate to between tion (March 1993), that - As/c = f0.002 0.005. Possible film sheet influence on transition has not been taken into account. An “da” for the transition start (S) or end (E) indicates that a de- finitive start or end to transition, respectively, was not detected prior to the cusp on the lower surfaces of the where slat and main elements or prior to the trailing edge on the flap. The “L,” for the upper suction peak at 19’ indicates +q3 that the location is actually on the lower side of the ele- fv2 = (1 ment when the slat is in its rotated position. CVZ Note thediscrepancy present in the location of the flap suction peak between the 50%-span station (mid) and t(haue xa)u axti lbioarthy asntagtlieosn o nf eaatrt atchke. hCoot mfiplumtes da st u7c3ti.o4%n p-sepaakns fv3 = (1 +xfv,X) (l-fvz) (3) agree best with the “mid” data. This table represents only a subset of the transition location measurements and cv2i s taken as 5. The SST model has also been mod- taken. A complete set of more than 50 cases, including ified slightly from its original form. Details are given in different Reynolds numbers, Mach numbers, and flap Menter and R~msey(.N~o~te that there is an error in settings as well as more details of the experimental da- equation 17 in that reference. It should read:‘ tabase, can be found in Bertelr~dan~d~ B ertelrud et 4. DESCRIPTION OF THE COMPUTER CODE The computer code CFL3D49*50,51vs5o2lv es the three- Also, in equation 1 in that reference, the terms o*p, and dimensional time-dependent thin-layer (in each coordi- op, should be replaced by p+o*p, and p++p,, re- nate direction) Reynolds-averaged Navier-Stokes equa- spectively.) tions with an upwind finite-volume formulation. It can The Gatski-Speziale explicit algebraic stress model45 solve flows over multiple-zone grids that are connected (EASM) represents an effective compromise between in a one-to-one, patched, or overset manner, and can em- the full second-moment closure and a two-equation ploy grid sequencing, multigrid, and local time stepping eddy-viscosity model. It extracts an algebraic relation- when accelerating convergence to steady state. Upwind- ship between the turbulent Reynolds stress and the mean biased spatial differencing is used for the inviscid terms, velocity field by assuming equilibrium hypotheses on and flux limiting is used to obtain smooth solutions in both the convective and diffusive terms of the Reynolds the vicinity of shock waves, when present. Viscous stress transport equation. The EASM 5yodel was first terms are centrally differenced. The flux-difference- implemented in CFL3D by Abid et a1 in both k - w splitting (FDS) method of is employed to obtain and k - E form. Further modifications to the model have fluxes at the cell faces. been made since that time.57 For all the results in this pa- The CFL3D code is advanced in time with an implicit per, the model is implemented in k - w formulation as three-factor approximate factorization method. The im- follows. plicit derivatives are written as spatially first-order ac- curate, which results in block tridiagonal inversions for each sweep. However, for solutions that utilize FDS the block tridiagonal inversions are further simplified with a diagonal algorithm (with a spectral radius scaling of the viscous terms). Further details of the CFL3D com- DO puter code are not given here; they can be found in the Dt cited references. CFL3D has been used previously to compute 2D multi-element airfoil flow fields with gen- erally good SUCC~SS.~~*~* where the production terms are: When free-air grids are used, a far-field point vortex correctionW is applied at the outer boundary. This cor- rection has a significant impact, particularly on the com- (7) puted drag for multi-element airfoil flows. l2 When internal flow on a grid with walls is computed, the in- flow total pressure and total temperature are specified according to isentropic flow relations, and the outflow back pressure is set to obtain the desired inflow Mach number. and = 2.2, p = 0.83, (3, ,a nd K = 0.41 . The equilibrium 5. TURBULENCE MODELING in the diffusion terms of The one-equation and SSel two-equation equations (5) and (6) is given by eddy-viscosity turbulence models employed in this study are documented in their respective references. *pk However, the S-A model has a furthgr modification to P,* = cy w (9) improve convergence by preventing S from going neg- 5 . where c,,* = 0.081 The explicit nonlinear constitutive equation that is used to close the Reynolds-averaged Navier-Stokes -4.4 equations is given (after regularization) by --22..84 _-_______ SS-SA T -3.6 _-__ _SS-SA_T _. EASH EASM -2.0 0 SXP p7, = $kS, - 2j.4(Sij- +1 Sjj)- -1.6 -2.8 -1.2 -2.0 a Q 0 -0.8 V -1.2 -0.4 0.0 -0.4 The turbulent viscosity pr is 0.4 0.4 0.8 1.2 I .2 -0.10 -0.05 0.00 0.05 0.10 0.0 0.2 0.4 0.6 0.8 1.0 x/c x/c (a) slat (b) main and + + + c6) 3( 1 q2) 0.2(q6 c,, = (12) 3 + q2+ 6c2q2+ 65’ + q6+ C,6a1 0.8 0.9 1.0 1.1 1.2 1.3 and al = (413 - C2)(g/2), a2 = (2- C3)(g/2), x/c . a3 = (2-C4)(g/2), and g = (C1/2+C,-1)- The (c) flap constants governing the Speziale-Sgkar-Gatski (SSG) pressure-strain correlation model are: CI = 6.8, Fig. 3. AGARD surface pressure coefficient, alpha4.01’. C2 = 0.36, C, = 1.25, C, = 0.4,and C, = 1.88. The :p terms in equation (10) are given by with experimental results at an angle of attack of 4.01’ in figures 3(a) - (c). On the flap and the main element, tpk all three turbulence models predict cp for this case in PI’ = clr w good agreement with experimental levels. On the slat, all three models predict cp in good agreement with ex- where periment over the upper surface, and EASM yields sig- nificantly different pressures from the other two models in the cove region, closer to experiment. A similar comparison of surface gr essure coefficients at a higher angle of attack of 20.18 is shown in figures 4(a) - (c). In this case, all turbulence models yield sim- 6. RESULTS AND DISCUSSION ilar results, in good agreement with the experimental re- sults. Results are computed for both the AGARD and the Boundary layer profiles of total pressure coefficient McDonnell Douglas configurations. Three turbulence models - S-A, SST, and EASM - are used for the are given at x/c = 0.35 on the upper surface of the main element, as well as at three stations on the upper surface former, but only S-A and EASM are used for the latter. of the flap, as shown in figure 5. Results are shown for - the 4.01’ case in figures 6(a) (d), and for the 20.18’ 6.1 AGARD Configuration case in figures 7(a) - (d). The parameter d in the figures For the AGARD configuration, surface pressure coef- represents the normal distance from the airfoil surface. ficients and boundary layer total pressure coefficient At the lower angle of attack, all three models give simi- profiles are compared with experiment’ at two correct- lar results, in good agreement with experiment, with the ed angles of attack of 4.01’ and 20.18’. The effect of exception that EASM predicts more mixing between the transition is not assessed for this configuration. Compu- flap boundary layer and main element wake than exper- tations are performed with transition set at x/c = 0.125 iment or the other models. Also, the computations with on the main element upper and lower surface, and with all three turbulence models show evidence of a slat wake the slat and flap computed “fully turbulent.” The impli- whereas the experiment does not. It is interesting to note cations of these transition settings will be discussed in that even though EASM shows different slat cove cp the context of the McDonnell Douglas configuration in predictions in figure 3(a), its slat wake does not exhibit section 6.2.1. much difference from the other models. Computed surface pressure coefficients are compared At the higher angle of attack, all of the models miss 6 -18.0 r -16.4 - 5-A -8.4 -__ .SS_S-AT __ 0..0. 5. r 0.10 r I ----111 431...826 --56..28 0 EexApS M 0.04 .-. -...o.. . SSeEx-SAATpS M '0 .08 ..- -...o.. .. SSEexAS-ApTS M p 10.0 a 0.03 - 0.06 - -8.4 V -3.6 2- : -6.8 0.02 0.04 -5.2 -2.0 ---320...460 -0.4 0n1.. n01n11 t- - I 00..0020 - " " . " ' 1 ' 1.2 1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 -0.10 -0.05 0.00 0.05 0.10 0.0 0.2 0.4 0.6 0.8 1.0 cPtot Pt. x/c x/c (a) x/c=0.35 (main) (b) x/c=O.91 (hap) (a) slat (b) main 0.10 r v ....... SST ss J 00..00 00..44 00..88 11..22 0.0 0.4 0.8 1.2 C cPt t Ptot (c) x/c=1.069 (flap) (d) x/c=1.214 (flap) 0.8 0.9 1.0 1.1 1.2 1.3 x/c Fig. 6. AGARD total pressure coefficient profiles, alpha = 4.01'. (c) flap Fig. 4. AGARD surface pressure coefficient, alpha=20.18'. the locations of the main and slat wake at the two aft- most stations on the flap. However, as will be shown in section 6.2.2, modeling the wind tunnel walls has a large effect on the velocity profiles over the flap when the multi-element airfoil is at high angle of attack: compu- tations with walls included tend to shift the wake loca- 0 tions upward. This tendency would improve the current \-e 0.04 predictions. There are also small differences in total pressure coefficient levels for the three turbulence mod- els there; in particular, EASM yields a deeper slat wake deficit than the other two models, while SST yields a -0.8 -0.4 0.0 0.4 0.8 1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 deeper main-element wake deficit. cPbt cPtot (a) x/c=0.35 (main) (b) x/c=0.9 1 (flap) d x/c=0.35 1.214 d Fig. 5. AGARD profile locations. 0.0 0.4 0.8 1.2 0.0 0.4 0.8 1.2 Results for this configuration indicate that, while cPtd cPtot there are minor variations between the three turbulence (c) x/c=l.066 (flap) (d) x/c=1.214 (flap) models, all produce very similar surface pressure and boundary layer total pressure predictions in general. Lift, drag, and moment coefficient over the range of an- Fig. 7. AGARD total pressure coefficient profiles, alpha = 20.18'. gle-of-attack through maximum lift are also predicted 7 5 r 0.4 r - - 1 0.0 Fig. 9. 3OP-30N profile locations. 0 10 20 30 0 10 20 30 alpha, deg alpha, deg 6.2.I Effect of Transition Locations (a) lift coefficient (b) drag coefficient The effect of transition locations is explored using the -0.30 r S-A turbulence model on the free-air grid only. It is very -0.34 important to remember that the CFL3D code does not employ any transition modeling. The code merely ze- -0.38 roes out the production terms in the turbulence model c, -0.42 equations in the regions where laminar flow’i s desired. There is no transition state at all; the turbulence produc- -0.46 tion is either “off” or “on.” (Turbulence transport and -0.50 diffusion are always active, however.) This transition procedure is different from the “trip source term” proce- -0.54 0 10 20 30 dure employed by Spalart and Allmara~T.~he~ c urrent alpha, deg method is used to maintain consistency between the dif- (c) moment coefficient ferent turbulence models in CFL3D. It is also important to realize that although “fully tur- Fig. 8. AGARD integrated force coefficients. bulent” solutions are accomplished with the production terms of the turbulence models active everywhere, this similarly by the three turbulence models for this case, as does not necessarily guarantee that a turbulent boundary shown in figures 8(a) - (c). The CFD integrated quanti- layer will exist as far forward as the stagnation point. In- ties compare well with experiment over a large range of stead, in a “fully turbulent” solution, the models essen- angles of attack, but computations overpredict the max- tially transition on their own. In other words, the imum lift coefficient and the angle at which it occurs. solution to the turbulence equations results in eddy vis- The computations also do not exhibit slat separation or cosity levels which may or may not be large enough to the rapid drop-off of lift past QmatyXqic al of take-off create a turbulent boundary layer profile. Generally, at configurations with leading-edge stall. The drag and high Reynolds numbers the “fully turbulent” computa- moment coefficients also do not agree with experiment tions result in transition locations well forward of the lo- at the highest angles of attack past stall. cations seen experimentally. For example, at 19’ the locations where the S-A model transitions on its own are listed in Table 2. (Transition is assumed to occur when 6.2 McDonnell Douglas Configuration the maximum eddy viscosity level nondimensionalized Most of the following results use the McDonnell Dou- by molecular viscosity pt/p.. in the boundary layer first glas 30P-30N landing configuration at an angle of attack exceeds unity.) Stagnation points on the lower surfaces of 19’, although some results are also given for a lower of the slat and main elements are n/c = -0.031 and angle of attack of 8’. It should be stressed that the hot 0.154 , respectively. The “fully turbulent” transition lo- film data and the pressure, velocity, and skin friction cations are all well forward of the experimental regions data were taken in independent wind tunnel tests. 15-17747 from Table 1. Velocity profiles are given at the locations shown in fig- ure 9. When transition locations are set according to the experimental data of Table 1, they are assumed to be at Table 2 “Fully turbulent” transition dc locations for S-A made1 the ending locations from the hot film data. One excep- on 30P-30N configuration, Md.2, Re=9 million, alpha=19’. tion to this is on the slat upper surface at an angle of at- transition x/c, S-A fully turbulent x/c range, tack of 19’. In this case, placing the CFD transition at the ending location results in separation, since the lami- from Table 1 nar boundary layer cannot negotiate the severe adverse SLAT lower -.034 nla - n/a pressure gradient. (Although not shown, this result has SLAT upper -.051 L -.0853 - -.082 also been confirmed with computations using a finer MAIN lower .177 .685 - n/a embedded grid around the slat nose, as well as with computations using an independent boundary layer MAIN upper .125 L .061- .068 code. The result is also the same whether or not tunnel FLAP lower turbulent everywhere n/a - n/a walls are modeled in the CFD.) Therefore, transition is FLAP upper turbulent everywhere .892 - .921 instead placed as far downstream as possible such that the laminar boundary layer on the slat does not separate. 8 shown for the main element fully turbulent versus main element with upper surface transition set close to the -18 r -12 r transition-ending location from Table 1. The slat and -16 - 1 .__f_ully_ t_urb ulent _.___fu_lly. turbulent flap are both fully turbulent in this case. When the main pyition set element is fully turbulent, its boundary layer profile (be- -- --1142 low "slat wake" in figure l l(a)) is too thick compared with experiment.15 When transition is set, the profile be- a low the slat wake agrees better. The part of the wake due I:/ 0 to the main element upper surface boundary layer (upper part of "main wake" in figure 1l (b)) is also better pre- dicted with transition specified. In addition, the comput- -2 0 ed skin friction coefficient on the main element, 0 although still low at the x/c = 0.45 station, is in better agreement with experiment16 when the transition is set, -0.10 -0.06 -0.02 0.02 0.06 0.0 0.2 0.4 0.6 0.8 1.0 as seen in figure 12. x/c x/c (a) slat (b) main -4.8 r c .I_ -4.0 - .-...__ . fturallny stiutiorbnu alecnt t ....... main fully turbulent 0 exp -3.2 - 0.06 - -2.4 : t u" -1.6 - \ 0.04 - -0.8 1 - 0.02 0.0 - 0.8 0.00 0.20 0.24 0.28 0.32 0.36 0.40 1.6 0.8 0.9 1.0 1.1 1.2 s/a, x/c (a) dc4.45 (main) (c) flap 0.12 r1 :r __._m_a_in .f ully turbulent Fig. 10. Effect of transition location on 3OP-3ON surface pres- g!n transition aet sure coefficient, S-A model on free-air grid, alpha=19'. ~ 0.08 Figures 10(a) - (c) show surface pressure coefficients on each of the elements for both the fully turbulent solu- 0.04 tion as well as a solution for which the transition on each of the elements is specified according to the experimen- tal data in Table 1, as discussed above. Both com uted results are in good agreement with e~perirnent,'~~'~with 0.00 0.20 0.24 0.28 0.32 0.36 0.40 only small variations evident on the upper surfaces be- tween the fully-turbulent and transition-specified re- Q/% sults. As pointed out in section 1.1, the multi-element (b) dc4.89817 (flap) interactions largely manipulate the inviscid flow; there- fore it is not surprising that transition location has only Fig. 11. Effect of main element transition location on 3OP-3ON a small effect on the surface pressures. However, these velocity profiles, S-A model on free-air grid, alpha=19'. small variations in pressure translate to a difference in lift coefficient of about 0.12, of the same order of mag- In figures 1l (a) and (b), when the slat is fully turbu- nitude as experimental differences in lift coefficient due lent the slat wake is predicted to be too wide and deep. to flap rigging changes that wing designers would like to Because it is likely that the slat transition location has a predict with CFD.' Also, as will be shown next, the ve- large influence on the slat wake structure over the down- locity field is quite sensitive to transition location. Be- stream elements, we next turn our attention to an inves- cause viscous effects are a contributing factor to skin tigation of its effect. Both the upper and lower surfaces friction forces, possible boundary layer separation, and of the slat contribute to the shape of the slat wake. How- the stall process governed by the unloading of the aft ever, since the lower surface has the added complication end of the main element, it is clearly important to predict of separated flow followed by reattachment in the cove, boundary layer and wake profiles accurately. we focus our attention solely on the effect of upper sur- To compute the boundary layer and wake thickness face transition location. The lower surface transition is correctly over the main element, transition locations set at the cusp for all cases shown here. must be set correctly: This effect is demonstrated for the Unfortunately, the upper surface transition location upper surface in figures 1 l(a) and (b). The velocity pro- on the slat cannot be pushed further downstream than files at the stations x/c = 0.45 and x/c = 0.89817 are approximately x/c = -0.0847, while still maintaining 9 0.03 7 : 0.08 1-_ _____ fu\ll v turbulent slat transition at A slat transition at B 0.06 . slat tra,sition at C 0 exp cf 0.01 - -.- 0.40 0.44 0.48 0.52 0.56 0.60 0.00 I . I , I n I I I daw 0.0 0.2 0.4 0.6 0.8 1.0 [( a) x/c; ;=; 0.1075 (main) I o’08 fully turbulent __._sla.t_ tr ansition at A slat transition at B 0.06 slat transition at C Fig. 12. Effect of main element transition location on 30P-30N upper surface main element skin friction, S-A model on free-air grid, alpha=19’. an attached laminar boundary layer (experimental tran- sition range from Table 1 is x/c = -0.0853 to -0.082 ). To effectively force transition further downstream, we employ suction over a small region on the slat in the computations to prevent the laminar boundary layer 0.20 0.24 0.28 0.32 0.36 0.40 from separating. Computed velocity profiles are shown s/a, - in figures 13(a) (c). In these figures, the locations A, (b) x/c = 0.45 (main) B, and C correspond with x/c = -0.0847, x/c = -0.082, and x/c = -0.073, respectively. Their - slat fully turbulent locations relative to the starting and ending locations ______s lat transition at A from Table 1 are shown in figure 14. Wake velocity pro- ssllaatt ttrraannssiittiioonn aatt CB files that result from transition at location C agree best 0.08 with experimental profiles, although there are still dif- 0 ferences between computation and experiment, particu- \21 larly in the slat wake / main boundary layer m rging 0.04 region at x/c = 0.85. In the notation of Squire,”’ (dis- cussed in section 1.3), this latter station is in the region of initial merging, whereas the first two stations are in the unmerged regime. Note that transition location C is 0.00 0.16 0.20 0.24 0.28 0.32 downstream of the experimentally-measured transition location region. daw Even at the first station x/c = 0.1075 (figure 13(a)), (c) x/c = 0.85 (main) which is on the main element just aft of the slat trailing edge, the wakes predicted using fully turbulent, A, or B Fig. 13. Effect of slat transition location on 30P-30N velocity pro- have deficits and thicknesses that are too large. (The off- files, S-A model on free-air grid, alpha=19’. set velocity difference between computation and exper- iment in this figure is probably a result of improper x/c = 0.45, whereas computations do not. Velocity calibration in the experimental data, as suggested by F. profiles are shown in figures 15(a) and (b) at the first Spaid in a private communication (May 1997)). Using two stations of the main element only (results at location C, the computed slat wake width and deficit x/c = 0.85 are similar). When the slat is fully turbulent, roughly agree with experiment at this first station as well the computed slat wake is too deep and wide at the first as over the entire length of the main element. This indi- station x/c = 0.1075, and remains so further down- cates that (ignoring the wake / boundary layer merging stream. However, even moving the slat transition loca- region at x/c = 0.85 for now) the S-A turbulence model tion to D (x/c = -0.056, which is the approximate can do a fairly good job representing the wake develop- ending location of transition from the experiment) or to ment itselJ given a good initial profile. Therefore, poor E (x/c = 0.015, near the slat trailing edge) still results agreement of the slat wake with experiment may not be in too large a wake deficit. (In this case, boundary layer due to any particular failure of the turbulence model in suction is not necessary to move the transition location modeling the wake, but rather the fact that the computed downstream, since the adverse pressure gradient is not boundary layer leaving the slat is wrong to start with. too severe for the laminar boundary layer to handle.) It At a lower angle of attack of 8O, the experimenti5 in- therefore appears that the computations over the slat dicates an extremely diffuse slat wake at and beyond may again be incorrect by the time they leave the slat 10

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NASA Technical Reports Server (NTRS) 20040105536: Prediction of High-Lift Flows using Turbulent Closure Models PDF

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Preview NASA Technical Reports Server (NTRS) 20040105536: Prediction of High-Lift Flows using Turbulent Closure Models

PREDICTION OF HIGH-LIFT FLOWS USING TURBULENT CLOSURE MODELS Christopher L. Rumsey?* Thomas B. Gatski: Susan X. Ying,b**a nd Arild Bertelrudc** aNASA Langley Research Center, Mail Stop 128, Hampton, VA 23681 -0001, bMcDonnell Douglas Corporation, Long Beach, CA, and cAnalytical Services and Materials, lnc., Hampton, VA ABSTRACT The flow over two different multi-element airfoil configurations is computed using linear eddy vis- cosity turbulence models and a nonlinear explicit algebraic stress model. A subset of recently-mea- sured transition locations using hot film on a McDonnell Douglas configuration is presented, and the effect of transition location on the computed solutions is explored. Deficiencies in wake profile compu- tations are found to be attributable in large part to poor boundary layer prediction on the generating element, and not necessarily inadequate turbulence modeling in the wake. Using measured transition locations for the main element improves the prediction of its boundary layer thickness, skin friction, and wake profile shape. However, using measured transition locations on the slat still yields poor slat wake predictions. The computation of the slat flow field represents a key roadblock to successful pre- dictions of multi-element flows. In general, the nonlinear explicit algebraic stress turbulence model gives very similar results to the linear eddy viscosity models. 1. INTRODUCTION include: (1) boundary layer transition, (2) shockhound- ary layer interactions, (3) viscous wake interactions, (4) confluent wakes and boundary layers, and (5) separated 1.1 Overview flows. Some important insights into the physical pro- The prediction of high-lift (multi-element airfoil) cesses that govern high-lift aerodynamics were summa- flow fields currently represents a difficult challenge for rized by A. M. 0. Smith in his landmark 1975 paper? In the computational fluid dynamics (CFD) and turbulence particular, he described several effects that contribute to modeling community. Even in two dimensions, state-of- improved high-lift characteristics of multiple elements the-art CFD codes fail to predict trends with Reynolds over single elements. number or trends with flap/slat rigging changes suffi- A great body of work on high-lift flows, both experi- ciently accurately.' Without the capability to consistent- mental and computational, has built up since that time. ly predict trends using CFD, aircraft designers must rely (See, for example, discussions in thg: papers by Lynch et on heuristic techniques and wind-tunnel experiments, al,' Haines? Wooqward and Lean, Thibert et al? Val- which themselves present additional difficulties when arezo,l0 and Ying. ) Some experiments have been per- attemptin to scale the results up to flight Reynolds formed expressly for the purpose of CFD code numbers3394 validation. For example, an AGARD three-element The flow around a multi-element airfoil or wing is in- take-off configuration, tested in the early 1970's and herently complex. Variations in angle of attack and dif- subseqpently used as a part of a battery of AGARD test ferent slat / flap settings often present very different and cases, was recently used as a code validation distinct challenges. For example, for typical landing challenge12b y the CFD Society of Canada. Experiments configurations, viscous effects can dominate compress- have also been performed in the NASA Langley Low ibility effects near stall, whereas for typical take-off Turbulence Pressure Tunnel (LTPT)'39'4 on McDonnell configurations compressibility can dominate the stall Douglas three-element landing configurations, used as physic^.^ Also, flap separation is often seen at low to test cases in a CFD Challenge Workshop held at NASA moderate angles of attack, whereas stall is often caused Langley in 1993. Several papers have been written that by an unloading of the aft portion of the main element describe various as ects of experimental testing on due to rapidly spreading and merging shear layers and these configurations.5 5-19 wakes over the flap.' Since the CFD Challenge Workshop, there have been Although high-lift devices work essentially because many CFD results reported for the McDonnell Douglas they manipulate the inviscid flow? vi2 c ous effects are three-element configurations, using a variety of numer- crucial as well. According to Meredith, some of the vis- ical schemes for the Navier-Stokes equations. The in- cous features that can affect 2D multi-element systems compressible Navier-Stokes code INS2D, using both point-matched and overset grids, has been used exten- sively to assess the ability of CFD to model trends with configuration changes, as well as to assess the effects of *Senior Member AIAA. tunnel walls, grid density, and turbulence mode1.20-22I t has also been coupled with a transition-prediction meth- Copyright 0 1997 by the American Institute of Aeronautics and od~logy.C~om~ pressible Navier-Stokes codes have Astronautics, Inc. No copyright is asserted in the United States under been used as well. Jones et used the CFL3D code Title 17, U.S. Code. The US.G overnment has a royalty-free license with overset grids to compute flow over both the 2D to exercise all rights under the copyright claimed herein for Govem- McDonnell Douglas three-element configurations as mental purposes. All other rights are reserved by the copyright owner. well as 3D flow over wings with flaps. The structured models are generally smaller than the differences be- grid codes OVERFLOW and TLNS3D and the unstruc- tween computation and experiment. Some further per- tured-mid codes NSU2D and FUN2D have also been spective may be gained on the issue of turbulence applid to the 2D McDonnell Douglas configura- modeling by considering other experimental and com- tions.5,25,26 putational results for differer& configurations. Squire32 and Agoropoulos and Squire compared computed ve- 1.2 Code Validation Issues locity profiles and turbulence quantities with experi- mental results over a two-element model designed to Overall, CFD comparisons with experiment for the explore slat-wake I main-wing-boundary-layer interac- 2D McDonnell Douglas three-element configurations tion. They describe the merging process by three re- have been somewhat ambiguous. Considering the inher- gimes: (1) unmerged, when the wake and boundary ent complexity of the flow field, CFD results are surpris- layer are separated by a potential core, (2) initial merg- ingly good, particularly with regard to surface pressures. ing, when the outer part of the wake and inner part of the Unfortunately, the trends with Reynolds number and boundary layer are unaffected, and (3) full merging re- configuration changes are not accurate enough to meet sulting in a new, thicker boundary layer (although full the needs of wing designers, and the maximum lift coef- merging usually does not occur prior to the main ele- ficient and the anQ l e of attack at which it occurs tend to be overpredicted. However, it is still not clear at this ment trailing edge.) Using the incompressible Navier- Stokes equations with a k - E turbulence model and an time whether the fault is due to (1) inadequate modeling algebraic stress model (ASM), they found good agree- in the CFD (turbulence models, transition models), and/ ment between both models and experiment in the initial or (2) the fact that CFD is not simulating the same con- stages of the merging, with somewhat better results us- figuration as experiment. ing the ASM. Decelerated flows were predicted with the The former possibility may play a role because turbu- same accuracy as those in constant pressure. Squire also lence models vary in the accuracy to which they predict discussed the fact that stress transport models often pre- free shear flow behavior (such as spreading rate), and dict too rapid a relaxation of the flow following distur- most in use today are eddy-viscosity one- and two-equa- bances since model constants are generally weighted tion models that do not account for curvature effects or toward equilibrium flows. This results in a too rapid dis- anisotropy. It is possible that some missing effects such appearance of the velocity defect in the wake, as well as as these may be important in certain regions of multi-el- of the corresponding shear stress peaks. ement flow fields. Additionally, most CFD codes pre- In addition to computing the CFD Challenge Worti scribe rather than predict transition locations; these shop landing configurations, Anderson and Bonhaus locat’on can have a significant effect on the solu- computed the flow over a McDonnell Douglas three-el- Moreover, the transition process itself is usu- ement take-off configuration with the unstructured code ally not modeled. Instead, the eddy viscosity is generally FUN2D. They com ared with the experimental results “switched on” at transition points. More sophisti ated transition models, such as that employed by Cebeci$ 9 (in of Nakayama et aI?’including turbulent shear stress da- ta. Using the one-equation edfj-viscosity turbulence an interactive boundary layer code coupled with an alge- model of Spalart and Allmaras, turbulent shear stress braic turbulence model), are currently not in wide use. profiles were found to be in overall reasonable agree- The presence of laminar separations bubbles, which are ment with the experiment. Peak levels were underpre- usually associated with high peak suctions and steep ad- dicted on the flap, but results in that region may not have verse pressure gradients, are also generally not ac- been sufficiently grid-converged. counted for. - Lien and Lesch~ine2an~d Lien et computed the The latter possibility that CFD may not be simulat- flow over both a separated single-element ONERA air- ing the same configurations as experiment - arises par- foil as well as a two-element (main element and flap) ticularly because of questions regarding deviation from - two-dimensionality in experimental tests and the appli- NLR-7301 airf0il.3~T hey compared results using k E two-equation eddy-viscosity models with full second- cability of 2D CFD simulations to such flows. Addition- moment Reynolds stress closure models on the ONERA ally, the effects of surface roughness, tunnel turbulence, airfoil, and found that the latter models are generally su- external tunnel devices, and structural model deforma- perior. However, all of the turbulence models performed tions need to be considered. Since multi-element airfoil poorly in the far wake, in regions where the turbulence flow appears to be very sensitive to all of these parame- ters, it is often difficult to determine precisely why a production over dissipation is low. The k - E eddy-vis- cosity model performed fairly well on the NLR-7301 CFD simulation is in error from a given experimental re- airfoil, although wake mixing was incorrect and there sult. As an example of the experimental sensitivity, a was insufficient mixing between the wing wake and flap three-element airfoil section representing the section at boundary layer. This was attributed to the inability of 59% span of the A3 10 wing was found to give a negative trend of with Reynolds number between 6 mil- the k - E model to represent curvature-turbulence inter- action. lion and 16 million for an unpolished model, but a posi- Godin et aI4 also computed the flow over the NLR- tive trend when the model was p~lished.~’ 7301 airfoil, using the one- and two-equation eddY iv is - cosity turbulence models of Spalart and Allmaras (S- 1.3 Turbulence Model Studies A) and Menter41 (SST). They found good agreement in Rogers et aI3’ has shown that several different eddy- general with both models, although the SST model tend- viscosity models tend to be consistent in their prediction ed to be more accurate in separated flow regions while of the flow over the McDonnell Douglas three-element the S-A model performed better in attached flows and configuration. The differences between the turbulence wakes, including the merging wake I boundary layer re- 2 gion. Turbulent shear stress profiles appeared to agree codes20p21*22,2o6v er similar configurations. These stud- better in general with experiment than the results of Lien ies indicate that velocity profiles are more sensitive to et a13* using the k - E eddy-viscosity model, but velocity grid density than surface pressures and lift coefficient. - profiles were similar. Cao and Kusunose?’ Jasper et When between 100,000 200,000 grid points are used a1?2 and Fritz43a lso computed this 2D flow, using var- for point-matched grids similar to the grids used in the ious zero-, one-, and two-equation eddy-viscosity mod- current study, further refinement yields on1 minor dif- els. Generally positive agreement with experimental ferences in the computed velocity profiles3 These ear- data was obtained for lift, surface pressures, and veloci- lier studies also indicate the importance of having ty profiles, although the zero-equation (algebraic) mod- sufficient resolution in the wakes and boundary layers. el used in Jasper et al resulted in poorer predictions of The grids used in the current study have over 1 0 0 , ~ boundary layer parameters and stall onset compared grid points with minimum normal wall grid spacings with a one-equation model. No comparisons with Rey- that yield an average y+ of approximately 0.3 - 0.4 for nolds stress data were made in these three references. their respective free stream Reynolds numbers. The The results for the NLR-7301 airfoil seem to support grids are also clustered in the wake regions of each ele- the finding of Rogers et a131 (for the McDonnell-Dou- ment. glas configuration) that, while there are certainly notice- The first case is a three-element configurattpn defined able differences at a detailed level, many eddy-viscosity as case A2 in a battery of AGARD test cases a d used turbulence models overall tend to have only relatively as a test case for the code validation challengel’by the minor effects on global properties for multi-element air- CFD Society of Canada in June 1996. Although tested in foil predictions. (This conclusion is of course dependent a wind tunnel with solid walls, the AGARD ’test case is on particulars of the flow field in question. For example, performed on a “free air” grid with far field extent of for flows with boundary layer separation, models such about 10 chords. (The original model has a stowed chord as S-A and SST have been shown to be superior to the of c = 0.7635 m, and the tunnel height to chord ratio is “standard” Jones-Launder version of k - E !l,*) The H/c = 5.19 .) The slat is positioned at an angle of 25’, question of whether more advanced nonlinear turbu- while the single-slotted flap has a moderate deflection lence models would produce significantly better results angle of 20°, typical of a take-off configuration.A close- for multi-element airfoils remains open. up of the grid used for this case is shown in figure 1. This is a 4-zone grid with 114,908 grid points. The abscissa 1.4 Focus of this Paper of this figure is given in terms of x/c , and the stowed airfoil would have its leading and trailing edges at x/c Because of the complexity and interdependence of of 0 and 1, respectively. This concguration is computed many factors in high-lift computing and experimenta- at M = 0.197 and Re = 3.52 x 10 based on stowed-ge- tion, it seems inappropriate to focus solely on the subject ometry chord. Transition is tripped on the main element of turbulence modeling without regard for other factors. at x/c = 0.125 on both the upper and lower surface, and We therefore take a somewhat broader approach. The is free on the slat and flap. purpose of this paper is to contribute to a greater under- standing of issues surrounding CFD validation against high-lift wind tunnel tests. As a consequence, it focuses both on experimental as well as numerical issues. Spe- cifically, the purpose is threefold: (1) introduce a subset of transition locations for the 2D McDonnell Douglas three-element configuration recently measured in the LTPT with hot film, (2) demonstrate the effect of transi- tion location on CFD solutions, and (3) explore the ef- fect of a nonlinear explicit algebraic Reynolds stress turbulence model45 on the CFD solution for both the AGARD take-off configuration’’ * l2 and the McDonnell Douglas landing configuration.1 5-19 It is hoped that by taking this approach, we can not only determine the im- pact of modeling the nonlinear Reynolds stress terms, but also demonstrate the importance (and difficulty !) of accurately modeling the wind tunnel experiment, partic- ularly with regard to the transition process. 2. DESCRIPTION OF THE AIRFOIL CONFIGURATIONS AND CFD GRIDS 0.0 0.5 1. o Two multi-element configurations are investigated in this paper. Both employ one-to-one point connectivity across grid zones. Grids with one-to-one point connec- Fig. 1. AGARD configuration grid, with every other grid point removed. tivity insure conservation across boundaries and provide improved continuity of grid spacing at zonal interfaces, The second configuration is a three-element McDon- although this type of grid generation is substantially ne11 Douglas config~ration,’~t-e’s~te d in the LTPT and more difficult than for overset grids. used as a test case in a CFD Challenge Workshop held Only fine grids are employed, since extensive grid at NASA Langley in 1993. The model has a stowed sensitivity studies have b en published previously for both the CFL3D cod>4 as well as for other chord of c = 0.5588 m and the tunnel height is 3 H/c = 4.09. The particular slat and flap settings em- the locations of suction peaks and stagnation points to be ployed are: slat deflection of 30°, slat gap of 2.95%, slat displaced in the chord-wise direction. Second, separated overhang of -2.5%, flap deflection of 30°, flap gap of or low-shearregions, as well as brackets, etc., may cause 1.27%, and flap overhang of 0.25%. This rigging desig- spanwise flow that alters the transition data. Assuming nation is referred to as 30P-30N. It is typical of a landing experimental data are available, the upper surface configuration. It is computed using both a “free air” grid chordwise effects may be accounted for in the CFD, at with far field extent of about 15c, as well as a grid that least in part, by relating the transition to the distance models an angle of incidence of 19’ with LTPT walls. downstream of the suction peak as opposed to using an This latter grid extends 15c upstream and 19c down- absolute geometric location. However, for all the Mc- stream of the model to avoid the possibility of inflow I Donne11 Douglas cases in this paper, this is not neces- outflow boundary influence on the solution, although sary because the computed suction peak locations agree the actual LTPT test section does not extend this far. A with those in the experiment to within a distance less close-up of this latter grid is shown in figure 2. This is a than the densest pitch of the hot films. Spanwise effects 5-Zone grid with 138,389 grid points. It is computed at are not easily accounted for. M = 0.2 and Re = 9 x 10 based on stowed-geometry Transition locations are determined based on informa- chord. In the wind tunnel test, transition is free on each tion from 359 surface hot films on the three elements. of the elements. The start and end of transition are extracted from an analysis of a combination of standard deviation, skew- ness, and flatness factors of the hot film signals, plus in most cases an additional examination of the signal traces for auto- or cross-correlations. Note that even though the films are located at 2.54mm pitch (or As/c = 0.0045 ) in the most dense regions, the flows at higher angles of at- tack have fairly short transition regions, so that only one or two films pick up the feature. Table 1 Hot film transition data for 3OP-3ON configuration, M=O.2, Re=9 million lower suct peak n/a n/a lower trans S n/a n/a lower trans E n/a n/a upper suct peak .015 -.084 .006 -.0852 L uppertranss .030 -.077 .010 -.0853 uppertransE .060 -.057 .020 -.082 SIC XIC SIC X/C lower suct peak -.510 ,526 -.620 .635 Fig. 2. McDonnell Douglas 3OP-3ON grid, with every other grid lowertrans S -.405 .422 -.670 .685 point removed. lowertransE - 3 0 S26 n/a uppersuctpeak .OOO A496 .008 .055 3. DESCRIPTION OF THE TRANSITION TEST uppertranss .012 .058 .016 .061 AND DATA uppertransE .025 .068 .025 .068 A subset of transition data recently taken in the LTPT is presented here for the McDonnell Douglas three-ele- PLAP SIC X/C S_IC_ x.-lc - ment configuration. The hot-film sensors are similar to lower suct peak nla nla those used by Nakayama et a14 for a similar configura- lower trans S n/a n/a tion in the same wind tunnel. They are thin nickel films lower trans E nla n/a on a 0.05mm polyimide substrate. The sensors are ar- uppersuctpeak .026 .888 .024 .886 ranged in a straight streamwise array at 73.4% span, whereas most pressure taps are located at 50% span. (mid) Side-wall suction is used to maintain approximate two- uppersuctpeak .020 .882 .016 .878 dimensionality for the flow. However, this is optimized (aux) for 16’ angle of attack. Generally, up through this angle uppertranss .030 .892 .030 .892 the discrepancies in pressure distribution between the 50% span row and an auxiliary pressure tap row near the uppertransE .070 .931 .060 .921 hot films are moderate. Above 16O, three-dimensionality Table 1 lists the starting and ending transition loca- becomes more pronounced; hence it may be a contribut- ing factor in results shown below. Details can be found tions for the 30P-30N configuration at two angles of at- tack, along with locations of the suction peaks. Results in Bertelr~d.~~ Three-dimensionality affects the data in two ways. are given both in terms of the surface coordinate s/c First, span-loading variations, which manifest them- (where s/c = 0 corresponds to the location on the for- ward part of each element in the stowed position where selves as variations in effective angle of attack, cause 4 y/c = 0) as well as the deployed x/c coordinate. De- ative, suggested by P. Spalart in a private communica- pending on location, the data are accurate to between tion (March 1993), that - As/c = f0.002 0.005. Possible film sheet influence on transition has not been taken into account. An “da” for the transition start (S) or end (E) indicates that a de- finitive start or end to transition, respectively, was not detected prior to the cusp on the lower surfaces of the where slat and main elements or prior to the trailing edge on the flap. The “L,” for the upper suction peak at 19’ indicates +q3 that the location is actually on the lower side of the ele- fv2 = (1 ment when the slat is in its rotated position. CVZ Note thediscrepancy present in the location of the flap suction peak between the 50%-span station (mid) and t(haue xa)u axti lbioarthy asntagtlieosn o nf eaatrt atchke. hCoot mfiplumtes da st u7c3ti.o4%n p-sepaakns fv3 = (1 +xfv,X) (l-fvz) (3) agree best with the “mid” data. This table represents only a subset of the transition location measurements and cv2i s taken as 5. The SST model has also been mod- taken. A complete set of more than 50 cases, including ified slightly from its original form. Details are given in different Reynolds numbers, Mach numbers, and flap Menter and R~msey(.N~o~te that there is an error in settings as well as more details of the experimental da- equation 17 in that reference. It should read:‘ tabase, can be found in Bertelr~dan~d~ B ertelrud et 4. DESCRIPTION OF THE COMPUTER CODE The computer code CFL3D49*50,51vs5o2lv es the three- Also, in equation 1 in that reference, the terms o*p, and dimensional time-dependent thin-layer (in each coordi- op, should be replaced by p+o*p, and p++p,, re- nate direction) Reynolds-averaged Navier-Stokes equa- spectively.) tions with an upwind finite-volume formulation. It can The Gatski-Speziale explicit algebraic stress model45 solve flows over multiple-zone grids that are connected (EASM) represents an effective compromise between in a one-to-one, patched, or overset manner, and can em- the full second-moment closure and a two-equation ploy grid sequencing, multigrid, and local time stepping eddy-viscosity model. It extracts an algebraic relation- when accelerating convergence to steady state. Upwind- ship between the turbulent Reynolds stress and the mean biased spatial differencing is used for the inviscid terms, velocity field by assuming equilibrium hypotheses on and flux limiting is used to obtain smooth solutions in both the convective and diffusive terms of the Reynolds the vicinity of shock waves, when present. Viscous stress transport equation. The EASM 5yodel was first terms are centrally differenced. The flux-difference- implemented in CFL3D by Abid et a1 in both k - w splitting (FDS) method of is employed to obtain and k - E form. Further modifications to the model have fluxes at the cell faces. been made since that time.57 For all the results in this pa- The CFL3D code is advanced in time with an implicit per, the model is implemented in k - w formulation as three-factor approximate factorization method. The im- follows. plicit derivatives are written as spatially first-order ac- curate, which results in block tridiagonal inversions for each sweep. However, for solutions that utilize FDS the block tridiagonal inversions are further simplified with a diagonal algorithm (with a spectral radius scaling of the viscous terms). Further details of the CFL3D com- DO puter code are not given here; they can be found in the Dt cited references. CFL3D has been used previously to compute 2D multi-element airfoil flow fields with gen- erally good SUCC~SS.~~*~* where the production terms are: When free-air grids are used, a far-field point vortex correctionW is applied at the outer boundary. This cor- rection has a significant impact, particularly on the com- (7) puted drag for multi-element airfoil flows. l2 When internal flow on a grid with walls is computed, the in- flow total pressure and total temperature are specified according to isentropic flow relations, and the outflow back pressure is set to obtain the desired inflow Mach number. and = 2.2, p = 0.83, (3, ,a nd K = 0.41 . The equilibrium 5. TURBULENCE MODELING in the diffusion terms of The one-equation and SSel two-equation equations (5) and (6) is given by eddy-viscosity turbulence models employed in this study are documented in their respective references. *pk However, the S-A model has a furthgr modification to P,* = cy w (9) improve convergence by preventing S from going neg- 5 . where c,,* = 0.081 The explicit nonlinear constitutive equation that is used to close the Reynolds-averaged Navier-Stokes -4.4 equations is given (after regularization) by --22..84 _-_______ SS-SA T -3.6 _-__ _SS-SA_T _. EASH EASM -2.0 0 SXP p7, = $kS, - 2j.4(Sij- +1 Sjj)- -1.6 -2.8 -1.2 -2.0 a Q 0 -0.8 V -1.2 -0.4 0.0 -0.4 The turbulent viscosity pr is 0.4 0.4 0.8 1.2 I .2 -0.10 -0.05 0.00 0.05 0.10 0.0 0.2 0.4 0.6 0.8 1.0 x/c x/c (a) slat (b) main and + + + c6) 3( 1 q2) 0.2(q6 c,, = (12) 3 + q2+ 6c2q2+ 65’ + q6+ C,6a1 0.8 0.9 1.0 1.1 1.2 1.3 and al = (413 - C2)(g/2), a2 = (2- C3)(g/2), x/c . a3 = (2-C4)(g/2), and g = (C1/2+C,-1)- The (c) flap constants governing the Speziale-Sgkar-Gatski (SSG) pressure-strain correlation model are: CI = 6.8, Fig. 3. AGARD surface pressure coefficient, alpha4.01’. C2 = 0.36, C, = 1.25, C, = 0.4,and C, = 1.88. The :p terms in equation (10) are given by with experimental results at an angle of attack of 4.01’ in figures 3(a) - (c). On the flap and the main element, tpk all three turbulence models predict cp for this case in PI’ = clr w good agreement with experimental levels. On the slat, all three models predict cp in good agreement with ex- where periment over the upper surface, and EASM yields sig- nificantly different pressures from the other two models in the cove region, closer to experiment. A similar comparison of surface gr essure coefficients at a higher angle of attack of 20.18 is shown in figures 4(a) - (c). In this case, all turbulence models yield sim- 6. RESULTS AND DISCUSSION ilar results, in good agreement with the experimental re- sults. Results are computed for both the AGARD and the Boundary layer profiles of total pressure coefficient McDonnell Douglas configurations. Three turbulence models - S-A, SST, and EASM - are used for the are given at x/c = 0.35 on the upper surface of the main element, as well as at three stations on the upper surface former, but only S-A and EASM are used for the latter. of the flap, as shown in figure 5. Results are shown for - the 4.01’ case in figures 6(a) (d), and for the 20.18’ 6.1 AGARD Configuration case in figures 7(a) - (d). The parameter d in the figures For the AGARD configuration, surface pressure coef- represents the normal distance from the airfoil surface. ficients and boundary layer total pressure coefficient At the lower angle of attack, all three models give simi- profiles are compared with experiment’ at two correct- lar results, in good agreement with experiment, with the ed angles of attack of 4.01’ and 20.18’. The effect of exception that EASM predicts more mixing between the transition is not assessed for this configuration. Compu- flap boundary layer and main element wake than exper- tations are performed with transition set at x/c = 0.125 iment or the other models. Also, the computations with on the main element upper and lower surface, and with all three turbulence models show evidence of a slat wake the slat and flap computed “fully turbulent.” The impli- whereas the experiment does not. It is interesting to note cations of these transition settings will be discussed in that even though EASM shows different slat cove cp the context of the McDonnell Douglas configuration in predictions in figure 3(a), its slat wake does not exhibit section 6.2.1. much difference from the other models. Computed surface pressure coefficients are compared At the higher angle of attack, all of the models miss 6 -18.0 r -16.4 - 5-A -8.4 -__ .SS_S-AT __ 0..0. 5. r 0.10 r I ----111 431...826 --56..28 0 EexApS M 0.04 .-. -...o.. . SSeEx-SAATpS M '0 .08 ..- -...o.. .. SSEexAS-ApTS M p 10.0 a 0.03 - 0.06 - -8.4 V -3.6 2- : -6.8 0.02 0.04 -5.2 -2.0 ---320...460 -0.4 0n1.. n01n11 t- - I 00..0020 - " " . " ' 1 ' 1.2 1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 -0.10 -0.05 0.00 0.05 0.10 0.0 0.2 0.4 0.6 0.8 1.0 cPtot Pt. x/c x/c (a) x/c=0.35 (main) (b) x/c=O.91 (hap) (a) slat (b) main 0.10 r v ....... SST ss J 00..00 00..44 00..88 11..22 0.0 0.4 0.8 1.2 C cPt t Ptot (c) x/c=1.069 (flap) (d) x/c=1.214 (flap) 0.8 0.9 1.0 1.1 1.2 1.3 x/c Fig. 6. AGARD total pressure coefficient profiles, alpha = 4.01'. (c) flap Fig. 4. AGARD surface pressure coefficient, alpha=20.18'. the locations of the main and slat wake at the two aft- most stations on the flap. However, as will be shown in section 6.2.2, modeling the wind tunnel walls has a large effect on the velocity profiles over the flap when the multi-element airfoil is at high angle of attack: compu- tations with walls included tend to shift the wake loca- 0 tions upward. This tendency would improve the current \-e 0.04 predictions. There are also small differences in total pressure coefficient levels for the three turbulence mod- els there; in particular, EASM yields a deeper slat wake deficit than the other two models, while SST yields a -0.8 -0.4 0.0 0.4 0.8 1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 deeper main-element wake deficit. cPbt cPtot (a) x/c=0.35 (main) (b) x/c=0.9 1 (flap) d x/c=0.35 1.214 d Fig. 5. AGARD profile locations. 0.0 0.4 0.8 1.2 0.0 0.4 0.8 1.2 Results for this configuration indicate that, while cPtd cPtot there are minor variations between the three turbulence (c) x/c=l.066 (flap) (d) x/c=1.214 (flap) models, all produce very similar surface pressure and boundary layer total pressure predictions in general. Lift, drag, and moment coefficient over the range of an- Fig. 7. AGARD total pressure coefficient profiles, alpha = 20.18'. gle-of-attack through maximum lift are also predicted 7 5 r 0.4 r - - 1 0.0 Fig. 9. 3OP-30N profile locations. 0 10 20 30 0 10 20 30 alpha, deg alpha, deg 6.2.I Effect of Transition Locations (a) lift coefficient (b) drag coefficient The effect of transition locations is explored using the -0.30 r S-A turbulence model on the free-air grid only. It is very -0.34 important to remember that the CFL3D code does not employ any transition modeling. The code merely ze- -0.38 roes out the production terms in the turbulence model c, -0.42 equations in the regions where laminar flow’i s desired. There is no transition state at all; the turbulence produc- -0.46 tion is either “off” or “on.” (Turbulence transport and -0.50 diffusion are always active, however.) This transition procedure is different from the “trip source term” proce- -0.54 0 10 20 30 dure employed by Spalart and Allmara~T.~he~ c urrent alpha, deg method is used to maintain consistency between the dif- (c) moment coefficient ferent turbulence models in CFL3D. It is also important to realize that although “fully tur- Fig. 8. AGARD integrated force coefficients. bulent” solutions are accomplished with the production terms of the turbulence models active everywhere, this similarly by the three turbulence models for this case, as does not necessarily guarantee that a turbulent boundary shown in figures 8(a) - (c). The CFD integrated quanti- layer will exist as far forward as the stagnation point. In- ties compare well with experiment over a large range of stead, in a “fully turbulent” solution, the models essen- angles of attack, but computations overpredict the max- tially transition on their own. In other words, the imum lift coefficient and the angle at which it occurs. solution to the turbulence equations results in eddy vis- The computations also do not exhibit slat separation or cosity levels which may or may not be large enough to the rapid drop-off of lift past QmatyXqic al of take-off create a turbulent boundary layer profile. Generally, at configurations with leading-edge stall. The drag and high Reynolds numbers the “fully turbulent” computa- moment coefficients also do not agree with experiment tions result in transition locations well forward of the lo- at the highest angles of attack past stall. cations seen experimentally. For example, at 19’ the locations where the S-A model transitions on its own are listed in Table 2. (Transition is assumed to occur when 6.2 McDonnell Douglas Configuration the maximum eddy viscosity level nondimensionalized Most of the following results use the McDonnell Dou- by molecular viscosity pt/p.. in the boundary layer first glas 30P-30N landing configuration at an angle of attack exceeds unity.) Stagnation points on the lower surfaces of 19’, although some results are also given for a lower of the slat and main elements are n/c = -0.031 and angle of attack of 8’. It should be stressed that the hot 0.154 , respectively. The “fully turbulent” transition lo- film data and the pressure, velocity, and skin friction cations are all well forward of the experimental regions data were taken in independent wind tunnel tests. 15-17747 from Table 1. Velocity profiles are given at the locations shown in fig- ure 9. When transition locations are set according to the experimental data of Table 1, they are assumed to be at Table 2 “Fully turbulent” transition dc locations for S-A made1 the ending locations from the hot film data. One excep- on 30P-30N configuration, Md.2, Re=9 million, alpha=19’. tion to this is on the slat upper surface at an angle of at- transition x/c, S-A fully turbulent x/c range, tack of 19’. In this case, placing the CFD transition at the ending location results in separation, since the lami- from Table 1 nar boundary layer cannot negotiate the severe adverse SLAT lower -.034 nla - n/a pressure gradient. (Although not shown, this result has SLAT upper -.051 L -.0853 - -.082 also been confirmed with computations using a finer MAIN lower .177 .685 - n/a embedded grid around the slat nose, as well as with computations using an independent boundary layer MAIN upper .125 L .061- .068 code. The result is also the same whether or not tunnel FLAP lower turbulent everywhere n/a - n/a walls are modeled in the CFD.) Therefore, transition is FLAP upper turbulent everywhere .892 - .921 instead placed as far downstream as possible such that the laminar boundary layer on the slat does not separate. 8 shown for the main element fully turbulent versus main element with upper surface transition set close to the -18 r -12 r transition-ending location from Table 1. The slat and -16 - 1 .__f_ully_ t_urb ulent _.___fu_lly. turbulent flap are both fully turbulent in this case. When the main pyition set element is fully turbulent, its boundary layer profile (be- -- --1142 low "slat wake" in figure l l(a)) is too thick compared with experiment.15 When transition is set, the profile be- a low the slat wake agrees better. The part of the wake due I:/ 0 to the main element upper surface boundary layer (upper part of "main wake" in figure 1l (b)) is also better pre- dicted with transition specified. In addition, the comput- -2 0 ed skin friction coefficient on the main element, 0 although still low at the x/c = 0.45 station, is in better agreement with experiment16 when the transition is set, -0.10 -0.06 -0.02 0.02 0.06 0.0 0.2 0.4 0.6 0.8 1.0 as seen in figure 12. x/c x/c (a) slat (b) main -4.8 r c .I_ -4.0 - .-...__ . fturallny stiutiorbnu alecnt t ....... main fully turbulent 0 exp -3.2 - 0.06 - -2.4 : t u" -1.6 - \ 0.04 - -0.8 1 - 0.02 0.0 - 0.8 0.00 0.20 0.24 0.28 0.32 0.36 0.40 1.6 0.8 0.9 1.0 1.1 1.2 s/a, x/c (a) dc4.45 (main) (c) flap 0.12 r1 :r __._m_a_in .f ully turbulent Fig. 10. Effect of transition location on 3OP-3ON surface pres- g!n transition aet sure coefficient, S-A model on free-air grid, alpha=19'. ~ 0.08 Figures 10(a) - (c) show surface pressure coefficients on each of the elements for both the fully turbulent solu- 0.04 tion as well as a solution for which the transition on each of the elements is specified according to the experimen- tal data in Table 1, as discussed above. Both com uted results are in good agreement with e~perirnent,'~~'~with 0.00 0.20 0.24 0.28 0.32 0.36 0.40 only small variations evident on the upper surfaces be- tween the fully-turbulent and transition-specified re- Q/% sults. As pointed out in section 1.1, the multi-element (b) dc4.89817 (flap) interactions largely manipulate the inviscid flow; there- fore it is not surprising that transition location has only Fig. 11. Effect of main element transition location on 3OP-3ON a small effect on the surface pressures. However, these velocity profiles, S-A model on free-air grid, alpha=19'. small variations in pressure translate to a difference in lift coefficient of about 0.12, of the same order of mag- In figures 1l (a) and (b), when the slat is fully turbu- nitude as experimental differences in lift coefficient due lent the slat wake is predicted to be too wide and deep. to flap rigging changes that wing designers would like to Because it is likely that the slat transition location has a predict with CFD.' Also, as will be shown next, the ve- large influence on the slat wake structure over the down- locity field is quite sensitive to transition location. Be- stream elements, we next turn our attention to an inves- cause viscous effects are a contributing factor to skin tigation of its effect. Both the upper and lower surfaces friction forces, possible boundary layer separation, and of the slat contribute to the shape of the slat wake. How- the stall process governed by the unloading of the aft ever, since the lower surface has the added complication end of the main element, it is clearly important to predict of separated flow followed by reattachment in the cove, boundary layer and wake profiles accurately. we focus our attention solely on the effect of upper sur- To compute the boundary layer and wake thickness face transition location. The lower surface transition is correctly over the main element, transition locations set at the cusp for all cases shown here. must be set correctly: This effect is demonstrated for the Unfortunately, the upper surface transition location upper surface in figures 1 l(a) and (b). The velocity pro- on the slat cannot be pushed further downstream than files at the stations x/c = 0.45 and x/c = 0.89817 are approximately x/c = -0.0847, while still maintaining 9 0.03 7 : 0.08 1-_ _____ fu\ll v turbulent slat transition at A slat transition at B 0.06 . slat tra,sition at C 0 exp cf 0.01 - -.- 0.40 0.44 0.48 0.52 0.56 0.60 0.00 I . I , I n I I I daw 0.0 0.2 0.4 0.6 0.8 1.0 [( a) x/c; ;=; 0.1075 (main) I o’08 fully turbulent __._sla.t_ tr ansition at A slat transition at B 0.06 slat transition at C Fig. 12. Effect of main element transition location on 30P-30N upper surface main element skin friction, S-A model on free-air grid, alpha=19’. an attached laminar boundary layer (experimental tran- sition range from Table 1 is x/c = -0.0853 to -0.082 ). To effectively force transition further downstream, we employ suction over a small region on the slat in the computations to prevent the laminar boundary layer 0.20 0.24 0.28 0.32 0.36 0.40 from separating. Computed velocity profiles are shown s/a, - in figures 13(a) (c). In these figures, the locations A, (b) x/c = 0.45 (main) B, and C correspond with x/c = -0.0847, x/c = -0.082, and x/c = -0.073, respectively. Their - slat fully turbulent locations relative to the starting and ending locations ______s lat transition at A from Table 1 are shown in figure 14. Wake velocity pro- ssllaatt ttrraannssiittiioonn aatt CB files that result from transition at location C agree best 0.08 with experimental profiles, although there are still dif- 0 ferences between computation and experiment, particu- \21 larly in the slat wake / main boundary layer m rging 0.04 region at x/c = 0.85. In the notation of Squire,”’ (dis- cussed in section 1.3), this latter station is in the region of initial merging, whereas the first two stations are in the unmerged regime. Note that transition location C is 0.00 0.16 0.20 0.24 0.28 0.32 downstream of the experimentally-measured transition location region. daw Even at the first station x/c = 0.1075 (figure 13(a)), (c) x/c = 0.85 (main) which is on the main element just aft of the slat trailing edge, the wakes predicted using fully turbulent, A, or B Fig. 13. Effect of slat transition location on 30P-30N velocity pro- have deficits and thicknesses that are too large. (The off- files, S-A model on free-air grid, alpha=19’. set velocity difference between computation and exper- iment in this figure is probably a result of improper x/c = 0.45, whereas computations do not. Velocity calibration in the experimental data, as suggested by F. profiles are shown in figures 15(a) and (b) at the first Spaid in a private communication (May 1997)). Using two stations of the main element only (results at location C, the computed slat wake width and deficit x/c = 0.85 are similar). When the slat is fully turbulent, roughly agree with experiment at this first station as well the computed slat wake is too deep and wide at the first as over the entire length of the main element. This indi- station x/c = 0.1075, and remains so further down- cates that (ignoring the wake / boundary layer merging stream. However, even moving the slat transition loca- region at x/c = 0.85 for now) the S-A turbulence model tion to D (x/c = -0.056, which is the approximate can do a fairly good job representing the wake develop- ending location of transition from the experiment) or to ment itselJ given a good initial profile. Therefore, poor E (x/c = 0.015, near the slat trailing edge) still results agreement of the slat wake with experiment may not be in too large a wake deficit. (In this case, boundary layer due to any particular failure of the turbulence model in suction is not necessary to move the transition location modeling the wake, but rather the fact that the computed downstream, since the adverse pressure gradient is not boundary layer leaving the slat is wrong to start with. too severe for the laminar boundary layer to handle.) It At a lower angle of attack of 8O, the experimenti5 in- therefore appears that the computations over the slat dicates an extremely diffuse slat wake at and beyond may again be incorrect by the time they leave the slat 10

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