Numerical investigation of an airfoil with a Gurney ßap

Aircraft Design 1 (1998) 75—88 Numerical investigation of an airfoil with a Gurney flap Cory S. Jangº, James C. Ross', Russell M. Cummingsº* º California Polytechnic State University, San Luis Obispo, CA 93407, USA ' NASA Ames Research Center, Moffett Field, CA 94035, USA Abstract A two-dimensional numerical investigation was performed to determine the effect of a Gurney flap on a NACA4412 airfoil. A Gurney flap is a flat plate on the order of 1—3% of the airfoil chord in length, orien

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  Aircraft Design 1 (1998) 75 —  88 Numerical investigation of an airfoil with a Gurney flap Cory S. Jang  , James C. Ross  , Russell M. Cummings   *  California Polytechnic State Uni v ersity, San Luis Obispo, CA 93407, USA   NASA Ames Research Center, Mo  ff  ett Field, CA 94035, USA Abstract A two-dimensional numerical investigation was performed to determine the effect of a Gurney flap ona NACA4412 airfoil.A Gurneyflap is a flat plate on the order of 1 —  3% of the airfoil chordin length, orientedperpendicular to the chord line and located on the airfoil windward side at the trailing edge. The flowfieldaround the airfoil was numerically predicted using INS2D, an incompressible Navier —  Stokes solver, and theone-equation turbulence model of Baldwin and Barth. Gurney flap sizes of 0.5%, 1.0%, 1.25%, 1.5%, 2.0%,and 3.0% of the airfoil chord were studied. Computational results were compared with available experi-mental results. The numerical solutions show that some Gurney flaps increase the airfoil lift coefficient withonly a slight increase in drag coefficient. Use of a 1.5% chord length Gurney flap increases the airfoil liftcoefficient by  C J + 0.3 and decreases the angle of attack required to obtain a given lift coefficient by  *  '! 3 ° .The numericalsolutions show the details of the flow structureat the trailing edge and providea possible explanation for the increased aerodynamic performance.  1998 Elsevier Science Ltd. All rightsreserved. Nomenclature c airfoil reference chord C  sectional drag coefficient ( d / q  c ) C  total skin friction coefficient C  sectional lift coefficient ( l / q  c ) C  sectional pitching moment coefficient (takenabout c /4) ( m / q  c  ) d sectional drag e , f  inviscid flux terms in x , y directions, respectively e  , f   viscous flux terms in x , y directions, respectively ¸ geometric length scale l sectional lift m sectional pitching moment coefficient p pressure q  freestream dynamic pressure (   º  ) * Corresponding author. Tel.: 0018057561359; fax: 0018057562376; e-mail: rcumming @$ —  see front matter  1998 Elsevier Science Ltd. All rights reserved.PII: S1369-8869(98)00010-X  Re Reynolds number ( º  c /   ) t physical time u , v velocity components in x , y directions, respec-tively º  friction velocity, º  (  C  /2 º  freestream velocity x , y spatial dimensions in physical plane y > wall dimension, y º  /    angle of attack  artificial compressibility factor   kinematic viscosity  density  pseudo-time parameter  GH stress tensor R freestream conditions 1. Introduction The high-lift performanceof a commercialaircraft has a large influence on the economicviabilityof that aircraft. An effective high-lift system allows greater payload capacity for a given wing, aswell as a longer range for a given gross weight. The generation of increased lift also allows fora steeper takeoff ascent,which can reduce the amount of noise impartedto the areasurrounding anairport. An increase in the climb lift-to-drag ratio makes it possible for the aircraft to attain cruisealtitude faster, resulting in a more fuel-efficient flight. Finally, mechanicallysimple high-lift systemswould minimize manufacturing and maintenance costs, and therefore increase an aircraft’s profit-ability.One mechanically simple way to increase the lift coefficient of an airfoil is by using the Gurneyflap. Liebeck stated that race car testing by Dan Gurney showed that the vehicle had increasedcornering and straight-away speeds when the flap was installed on the rear wing [1]. The increasedcornering speeds were attributed to the increased downforce (i.e. lift) applied by the inverted wing.It was also noticed, however, that increasing the flap size above 2% of the wing chord lengthnoticeably increased the drag, even though there was a continuing increase in downward force.Liebeck tested a 1.25% chord Gurney flap on a Newman airfoil and found that the lift coefficientwas increased with a small decrease in the drag coefficient. Liebeck hypothesized that the Gurneyflap effectively changed the flowfield in the region of the trailing edge by introducing twocontrarotating vortices aft of the flap, which altered the Kutta condition and circulation in theregion (seeFig. 1). He basedhis assumption on the trailingedge flowfield for a clean airfoil reportedby Kuchemann [2]. When Liebeckused a tufted probe in the vicinity of the trailing edge he noticedconsiderable turning of the flow over the back side of the flap.A wind tunnel investigation of the Gurney flap was also conducted on a multi-element race carwing by Katz and Largman [3], and on a four element car wing by Katz and Dykstra [4]. In bothinvestigationsthe wings tested used end plates to structurally fix the elements in place, as well as toincrease the lift-curve slope by reducing three-dimensional affects. The Gurney flaps were locatedon the trailing edge of the most aft wing element in both studies. Katz and Largman reported thatusing a 5% chord Gurney flap increased the lift coefficient of the wing above the baseline wing byabout 50% [3]. However, the drag increased to such an extent that the lift-to-drag ratio wasdecreased in the design angle of attack range of the wing (2 ° 4  4 12 ° ). Katz and Dykstra foundthat adding a 2% chord Gurneyflap increased the winglift coefficientas well as the drag coefficient[4]. Wing lift-to-drag ratio with the Gurney flap was also lower than the baseline wing in thisstudy. 76 C.S. Jang et al. / Aircraft Design 1 (1998) 75 —  88  Fig. 1. Hypothesized trailing edge flow structure for an airfoil with a Gurney flap (from description in [1]). Roesch and Vuillet reported on an Aerospatiale wind tunnel test involving the use of theGurney flap on the horizontal tails and vertical fins of various helicopter models [5]. Gurneyflap sizes of 1.25% and 5% chord length were examined on the horizontal stabilizer, whichused a NACA 5414 airfoil section. The results showed that the 5% chord Gurney flap in-creased the lift coefficient by 40%, raised the lift curve slope by 6%, and shifted the angle of attack for zero lift by  *  ! 6 ° . The drag polars, however, indicated that larger Gurneyflap sizes caused an increase in drag coefficient at moderate and low values of lift coefficient.For the case of the 5% chord flap, the drag coefficient was almost doubled at moderatelift coefficients. However, while the lift improvement was less with the 1.25% chord flap, there wasno significant drag penalty. While the drag reduction benefits hypothesized by Liebeck were notseen in the Aerospatiale tests, Roesch and Vuillet reported general agreement between the twostudies.A water tunnel study of several Gurney flap configurations was performed on a NACA0012 wing by Neuhart and Pendergraft [6]. Flow visualization results showed thatLiebeck’s hypothesized flowfield caused by the Gurney flap was generally correct, and thatthe effect of the Gurney flap was to increase the local camber of the trailing edge. Thishypothesis was strengthened by the results of Sewall et al., whose wind tunnel tests studiedthe effects of increasing the local trailing edge camber of the EA-6B wing [7]. The lift curvewas shifted upwards from the baseline geometry, which gave higher maximum lift as well asa more negative  *  . Just as with the 1.25% chord Gurney flap, there was no appreciabledrag penalty associated with the trailing edge modifications at low and moderate lift co-efficients.The computed effects of the Gurney flap in the current study (as well as in [5]) are very similar tothe pressure, lift, and drag changes that occurredwith the use of the DivergentTrailing Edge(DTE)device reported by Hemme [8]. The modified trailing edges used in that study were very much likea Gurney flap, with the high pressure side filled in with a concave ramp. Hemme stated that theDTE acted like a Gurney flap on a high-speed airfoil.The objective of the present study is to provide quantitative and qualitative computational dataon the performance of the Gurney flap. Computations of a baseline NACA 4412 airfoil arecompared with experimental results obtained in a two-dimensional wind tunnel test performed atthe NASA Ames 7- by 10-foot Wind Tunnel by Wadcock [9]. Subsequent computations wereperformed to determine the effect of various sizes of Gurney flaps on the lift and the drag of thesame airfoil. C.S. Jang et al. / Aircraft Design 1 (1998) 75 —  88 77  2. Theoretical background Governing Equations . The non-dimensional Reynolds-averaged Navier —  Stokes equations forincompressible viscous flow written in two dimensions may be expressed as j u   J  j x   J  # j v   J  j y   J  0 , (1) j u   J  j t   J  # jj x   J  ( e ! e  ) # jj y   J  ( f  !  f   ) 0 , (2)where x   J  G x G / ¸ , t   I  t º  / ¸ , u   J  G u G / º  , p   J  p /  º  ,        / ¸º  Re \ , and   GH  GH /  º  .Details about the non-dimensionalization and the flux vectors, e , e  , f  , f   , can be found in [10, 11].To enhance convergence of numerical solutions of these equations, the concept of artificialcompressibility can be applied by adding a time derivative of pressure to the continuityequation (1): j p   J  j  !  ) u   J  , (3)where  is the artificial compressibility parameter and  a pseudo-time parameter [10]. Together,the momentum and modified continuity equations form a hyperbolic system of partial differentialequations which can be solved with various compressible flow algorithms. As these equations aremarched through pseudo-time, j p   J  / j  P 0, and the artificial compressibility term drops out. ¹ urbulence model . The present study assumes that the flow over the airfoil surface is completelyturbulent. This matches the wind tunnel test conditions, which used a grit boundary-layer trip nearthe leading edge of the airfoil. Turbulence viscosity is determined using the Baldwin —  Barthturbulence model, an eddy-viscosity model that combines the transport equations of turbulentkinetic energy and turbulence dissipation into one equation [12]. Flows over various airfoils havebeen computed using the model without the need to calculate a turbulence length scale, whichmakes it more desirable for flows with confluent shear/boundary layers and wakes [12]. Numerical algorithm . The implicit numerical scheme employed is the INS2D algorithm asreported by Rogers and Kwak in [10] and Rogers in [12]. The algorithm uses flux-differencesplitting to allow upwind differencing of the convective terms. The upwind differencing yieldsa natural numerical dissipation without the need for added artificial dissipation. The equations aresolved using an implicit line-relaxation scheme, which provides a stable way for iterating with largepseudo-time step values, and allows for faster convergence. 3. Geometry modeling and grid generation Geometry modeling . The geometry used for the Gurney flap study is a NACA 4412 airfoil.Computations were performed for Gurney flap sizes ranging from 0.5% to 3% chord length, withthe flaps located on the windward side of the airfoil at the trailing edge. For simplicity, the windtunnel walls used for the experimentwerenot modeled.INS2D has the capabilityto selectpoints inthe computationalgrid where solutions will be obtained. Any interior surface can be created within 78 C.S. Jang et al. / Aircraft Design 1 (1998) 75 —  88
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