AIAA-56094-309

Numerical Simulation of Gurney Flap on RAE-2822 Supercritical Airfoil T. Yu,∗ J. J. Wang,† and P. F. Zhang‡ Beijing University of Aeronautics and Astronautics, 100191 Beijing, People’s Republic of China DOI: 10.2514/1.C031285 A two-dimensional steady Reynolds-averaged Navier–Stokes equation was solved to investigate the effects of a Gurney flap on RAE-2822 (Royal Aeronautical Establishment) supercritical airfoil aerodynamic performance. The heights ofGurneyflaps range from0.25 to 3%airfoil chord lengths. The incompressible/compressibleNavier–Stokes equations were used to simulate the flow structure around the airfoils in subsonic/transonic flows, respectively, with the Spalart–Allmaras turbulence model. In comparison with the clean airfoil, the Gurney flap can significantly increase the prestall lift and lift-to-drag ratio of an RAE-2822 airfoil at a small angle of attack. Nosedown pitching moment also increased with the Gurney flap height. At both takeoff-and-landing status and cruise phase, the aerodynamic performance of the airfoil was significantly improved byGurney flaps with the height below 1%airfoil chord length. In addition, the surface pressure distribution, wake flow velocity profile, and trailing-edge flow structure of the airfoil were illustrated, which helps to understand the mechanisms of the Gurney flap to improve RAE-2822 airfoil aerodynamic performance. Nomenclature C = chord length CD = drag coefficient Cf = skin friction coefficient CL = lift coefficient CM = quarter-chord pitching moment coefficient CP = pressure coefficient h = height of Gurney flap L=D = lift-to-drag ratio M = Mach number P1 = freestream static pressure Re = Reynolds number T1 = freestream static temperature u=U = measured/freestream velocity x, y = streamwise and normal directions �CL = increment of lift coefficient �L=D = increment of lift-to-drag ratio 1. Introduction I N THE last several decades, rapid development of the globalaviation industry has brought tremendous contribution to the world economics. However, the globalmain airports are gettingmore andmore crowded by the sustained growth of passenger quantity and scheduled flight. To solve this problem, the short-distance takeoff- and-landing (STOL) concept was proposed by NASA to reduce the takeoff-and-landing distance of airplanes and then enhance runway efficiency [1]. The key problem to STOL lies in increasing the lift of aircraft when taking off and landing, namely, lift-enhancement devices design. Studies [2] of the past 20 years indicate that the Gurney flap (GF) is a simple and effective high-lift device consisting of a small flat tab fitted perpendicular to the pressure surface of the airfoil in the vicinity of the trailing edge. Typical GF configuration is illustrated in Fig. 1. The original application of the GF, used by race car driver Dan Gurney, was a small piece of steel rigidlyfixed to the top trailing edge of the rearwing of his cars. This devicewas installed pointing upward to increase downforce generated by the wing, providing efficient sideway-friction forcewhen cornering. Previouswind-tunnel experi- mental studies by Liebeck [3] indicated that the GF increased the lift of the Newman symmetry airfoil and its aerodynamic characteristics as well. Neuhart and Pendergraft [4] performed a visual investigation of the NACA-0012 on a water tunnel, and it was suggested that the GF increased the effective camber of the airfoil, resulting in lift enhancement. Similar experimental/numerical studies by Storms and Jang [5] and Jang et al. [6] showed that the lift coefficient was substantially increased by using a GF with a height of 1% chord length under a highCL circumstance. More attention was attracted in recent years to the GF lift enhancement for airfoils [7–12], wings [13–15], and aircraft models [16–18] for subsonic flow, and it is concluded that the GF significantly increased the prestall lift and lift- to-drag ratio at small angles of attack (AOAs). For more exhaustive application, as well as parameter influence of the GF on lift enhancement, please refer to the review paper by Wang et al. [2]. Nowadays, most large-scale civil airplanes, which adopt super- critical airfoil for their wings, generally have a cruising speed of aboutMach number 0.8. As a result, it becomes an importantmission to design effective high-lift devices for such airfoils. Most recently, wind-tunnel investigation of a supercritical (S-C) airfoil with aGF by Li et al. [19] showed that, under cruise Mach number, the position of shock wave on the upper surface of the airfoil was greatly shifted downstream, which led to an increase in CL and L=D, as well as a postponed stall angle, and it obviously improved the aerodynamic characteristics of the airfoil. The RAE-2822 S-C airfoil was selected by 16 EUROVAL§ European cooperation projects and AGARD as a typical numerical validation case of a two-dimensional transitional turbulence flow model; the tested data were sufficient for compar- ison. Therefore, in the present study, numerical simulations under subsonic/transonic flow conditions are carried out for this S-C airfoil. By comparing the lift, drag, moment, pressure distribution, wake flow, and trailing-edge flowfield of the airfoil with and without the GF, the present work, which concentrates on lift enhancement, thoroughly analyzes the influence of the GF on the S-C airfoil. Received 27 October 2010; revision received 26 April 2011; accepted for publication 10May 2011. Copyright © 2011 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to theCopyright Clearance Center, Inc., 222RosewoodDrive, Danvers,MA01923; include the code 0021-8669/ 11 and $10.00 in correspondence with the CCC. ∗Graduate Student, Key Laboratory for Fluid Mechanics of Ministry of Education, Institute of Fluid Mechanics; yutu1987@gmail.com. †Professor, Key Laboratory for Fluid Mechanics of Ministry of Education, Institute of Fluid Mechanics; jjwang@buaa.edu.cn. Member AIAA (Corresponding Author). ‡Associate Professor, Key Laboratory for Fluid Mechanics of Ministry of Education, Institute of Fluid Mechanics; pfzhang@buaa.edu.cn. §A European initiative on validation of computational fluid dynamics (CFD) codes, 1990–1992. JOURNAL OF AIRCRAFT Vol. 48, No. 5, September–October 2011 1565 Takeoff-and-landing characteristics are shown in Sec. II, and cruising performances are presented in Sec. III. II. Aerodynamic Characteristics During Takeoff and Landing A. Governing Equation and Numerical Method The flowfield is governed by a Reynolds-averaged Navier–Stokes (RANS) equation, and for two-dimensional steady incompressible flow, the conservation of mass and moment equations can be written as @ui @xi � 0 (1) � @�uiuj� @xj � @p @xi � @�jj @xj �Gi (2) All the numerical investigations presented in this part were carried out with a separated solver in the engineering simulation software Fluent to solve RANS equations under a rectangular coordinate system. The PISO (pressure-implicit with splitting of operators) algorithmwas used to do steady simulation. The pressure termswere discretized using the second-order upwind scheme, the moment terms used a third-order central MUSCL scheme, and the viscosity term adopted a first-order upwind scheme. For this separation process, the converge criteria were to require a normalized residual less than 10�6 for the continuity terms and less than 10�5 for all other equations. The turbulence model adopted in all conditions of this study was the Spalart–Allmaras (S–A) one-equation model [20]. It was widely verified that the S–A turbulence model had robust and efficient characteristics in a variety of flowfields, and it can be applied in general aerodynamic flows consisting of flow separation and reattachment and circumfluence around high-lift wings. In this model, the vortex viscosity coefficient can be directly obtained by solving a single transport equation. There is no longer a need to estimate any ambiguous length scale about shear layer thickness, as is the case with many former algebraic and one-equation models. For high-lift flow, compared with previous algebraic and other one-equation models, the S–A model [21] performed as well as high-order turbulence models. B. Geometry Modeling and Mesh Generation In the present simulation, the chord length of the RAE-2822 airfoil is 1 m, freestream velocity is 85 m=s, and the Reynolds number based on chord length is Re� 5:8 � 106. The grid-generation code Gridgen is used to construct a C-type structured grid, and the total number of grid points is 380 � 140, with 240 points distributing on the surface of the airfoil (Fig. 2a). Upper and lower boundaries of the simulation domain are 10 chord lengths away from the airfoil chord, which is defined as the velocity-inlet boundary condition, and the downstream outflow boundary is 20 chord lengths away. The surface boundaries of the airfoil and theGFare set as a no-slipwall condition. The algebraic stretching function of hyperbolic tangent (TANH) is used to determine the circumferential and normal point distributions of the airfoil surface. To obtain reasonable resolution of the flowfield in the boundary layer and vortex structure around the GF, we cluster surface grids of the airfoil as well as grids near the trailing edge. The first grid point above the surface, which locates at y� � 1, is 5 � 10�6 times of chord length away. A zoom-in view of the numerical grids in the vicinity of the RAE-2822 S-C airfoil can be seen in Fig. 2b. C. Result and Discussion To examine the effect of the grids and the algorithm adopted in this paper on the predication of aerodynamic forces, numerical validation for an airfoil without a GF, compared with the numerical/ experimental data in [22],¶ was simulated beforehand. The comparison of CL is shown in Fig. 3a. It can be conclude that the linear slope of theCL curve in this study is substantially parallel with that obtained by Xfoil simulation. Because the Re in this study is 5:8 � 106, compared with the Xfoil simulation condition of Re� 105, the predicted stall angles vary from each other. The present test case has a larger stall angle than theXfoil simulation result, which fits well with general trends of Re influence. Moreover, CL and the pressure distribution at 0 AOA in the present simulation match well withHanet al.’s [22] numerical simulation results. Besides, compared with the experiment results by Cook et al. [23], the surface pressure distribution by the numerical results of the present work is illustrated in Fig. 3b. It is obvious that they match well. Therefore, the reliability of the present numerical study is verified. Figure 4 presents the aerodynamic force coefficient as well as the pitching moment results of an RAE-2822 airfoil with and without a GF. In the present simulation, the Mach number is Ma� 0:25 and the Reynolds number based on the airfoil chord length is Re� 5:8 � 106. The data marked with “No GF” show the lift curve of the clean airfoil, and the curves marked with “h� x%” indicate the lift curves of the RAE-2822 airfoil with GF height x%. The GF clearly increases the lift coefficient of the airfoil, as shown in Fig. 4a. The maximum CL is increased by 6, 10, 15, 19, 23, and 28% for GF heights of 0.25, 0.5, 1.0, 1.5, 2.0, and 3.0% airfoil chord length, respectively. At the same time, the stall angle is decreased from 16 to 14�, as the GFs are higher than 1%C, due to the increased effective camber of the airfoil. So, from the perspective of stall angle, GFs with heights less than 1%C should be selected so that the stall angle of the airfoil will not change, and the lift-enhancement benefit will be obtained at the same time. The results are in good accordance with other investigators [3–5,7] for subsonic flow over airfoils. Figure 4b shows the drag curve for the same configuration; it is obvious that the drag coefficient also increases along with the ascendant CL with a larger height of GF. The difference is that the drag augmentation is slight under medium or small AOAs, while it becomes obvious at high AOAs. In the region before the stall angle, due to the significant lift augmentation and tiny drag increment induced by the GF, it seems profitable in improving the lift-to-drag ratio of the airfoil. The lift-to- drag ratio versus lift coefficient, as shown in Fig. 4c, indicates thatCL increase for the airfoil with a higher GF at a given L=D. When CL is relatively high,L=D increases aswell. It is also noted that whenCL is larger than 1.2, airfoils with GFs of 0.25% and 0:5%C heights can provide a higherL=D compared with a clean one. In particular, when CL reaches about 1.6, the increment of L=D is approximately 68% with a 1:5%CGF. Figure 4d shows that all the tested GFs can induce higher L=D at small AOAs, and when the AOAvaries from 0 12�, the maximum increment of L=D is obtained with a 0:25%C GF. Nowadays, the takeoff angle of general civil planes is usually about 10�. The detail data ofCL and L=D of the airfoil with different GFs at this angle are listed in Table 1. It is seen that �CL increases with theGF’s height. However,�L=D tends to be negative, except at 0:5%C GF, which can result in an increment of 3.4% for L=D. Although a numerical simulation may have some computational Fig. 1 GF on RAE-2822 airfoil. ¶Data available at http://www.grc.nasa.gov/WWW/wind/valid/raetaf/ raetaf.html [retrieved 13 April 2010]. 1566 YU, WANG AND ZHANG error, the variation trends of the results are fitted well with the experimental measurement data [8]. It is expected from the present study that a GFwith a height of about 0:5%C can apparently increase CL and L=D of the S-C airfoil at takeoff-and-landing conditions, which is applicable for improving the takeoff-and-landing perform- ance of the present civil planes, as well as the future lift-enhancement design. Figure 4e indicates that the nosedown pitching moment of the airfoil is also increased with GF height, and the slopes of the nosedown pitching moment curves almost remain constant; thus, the effect of the GF on the static stability of the airfoil is negligible. In addition to the force and moment variation induced by the GF, the variation of the pressure coefficient on theRAE-2822 airfoil with/ without a 2%C GF is illustrated in Fig. 5. With the GF, the Kutta condition in the vicinity of the trailing edge is changed, evidently leading to the increases of pressure difference between the upper and lower surfaces of the airfoil. This effect enhances the load capacity of the airfoil, and then it results in the substantially increased CL of the airfoil. With a large adverse pressure region in front of the flap due to the presence of the GF, it is expected to increase the pressure in the lower surface of the trailing edge; this phenomenon agrees well with the pressure distribution in previous studies [5,6]. Besides, for AOA� 14�, the flow separates on the upper surface of the airfoil trailing edge; the pressure increment caused by the GF seems to be relatively smaller (Fig. 5c). Figure 6 presents the wake velocity profiles taken at 70% chord length downstream from the trailing edge of airfoil. Compared with the clean airfoil, the magnitude of the wake velocity deficit and the width of the wake are all enlarged as the GF is used, it means that the airfoil drag is increased. Moreover, the wake velocity profile translates downward due to the existence of the GF, leading to an increased airfoil camber and Cl in sequence, which is consistent with that of the symmetry airfoil with the GF [8]. Therefore, the aerodynamic performances induced by the GF mentioned above, including the lift and drag variations, can be well explained by the wake velocity profile variation of the airfoil, with or without GF. Figures 7 and 8 present time-averaged streamlines and pressure contours near the training edge of the airfoil with/without a GF at AOA� 6� andAOA� 14�, respectively. It is quite clear that there is no separation on the trailing edge of the clean airfoil The fluid flows fairly along the upper surface at a small AOA (Fig. 7a, AOA� 6�). The pressure on the upper surface near the trailing edge is positive. However, as shown in Fig. 7b, there exists an adverse flow separation region between the upstream surface of the GF and the lower surface of the trailing edge, where the pressure is increased for the compression effect of the fluid. Note that there is a downward shift of the airfoil wakewith theGF,which can be expected for an airfoil with increased camber, resulting in negative pressure on the entire upper surface of the airfoil. Moreover, the GF also induces a suction pressure region downstream of the leeward side, in which there is a couple of counter-rotating vortex pairs enduring negative pressure for the expansion effect of the fluid. Since the GF acts as a point-unit vortex, which enlarges the circulation of the airfoil, the Kutta condition shifts from trailing-edge point of the airfoil to the lower edge of the GF, magnifying the pressure difference between the upper and lower trailing-edge surfaces, and ultimately results in CL increase. On the other hand, because the windward side of the GF endures positive pressure and is the leeward side with the negative one, the drag of the airfoil increases with the GF. Since theAOA is adequately large for theRAE-2822 airfoil at 14 �, a separation bubble appears on the upper surface of the airfoil near the trailing edge induced by the adverse pressure gradient, which significantly decreases the suction pressure of the upper surface (Fig. 8a). However, when the GF is used, the flow separation is restrained and results in a substantial increase of CL (Fig. 8b). Fig. 2 Grid system: a) C-mesh grid distribution around RAE-2822 airfoil and b) zoom-in view of girds in the vicinity of the trailing edge and GF. -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Xfoil Simulation,Re=1e+5 Present Re=5.8e+6 Han et al. [22] Re=6.5e+6,Ma=0.05 C L AOA 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.0 0.5 0.0 -0.5 -1.0 - C P x/C Exp, α=2.57° Re=6.3e+6 Num, α=2.57° Re=5.8e+6 a) b) Fig. 3 Lift coefficient and pressure distribution of RAE-2822 airfoil by numerical simulation compared with previous results. YU, WANG AND ZHANG 1567 III. Aerodynamic Performances During Cruise Phase A. Governing Equation and Numerical Method It can be concluded from Sec. II that the GF is capable of improving the aerodynamic performance of the RAE-2822 S-C airfoil, potentially shortening the takeoff-and-landing roll distance of civil airplanes. In this section, the aerodynamic characteristics improvement during the cruise phase of this airfoil with the GF will be demonstrated progressively. To examine the algorithm reliability of the present work in predicting the aerodynamic performance of an airfoil in cruising, case 9 [23] from AGARD is selected to verify the present simulation. The previously tested case 9 had the conditions as Ma� 0:730, �� 3:19�, and Re� 6:5 � 106 (based Fig. 4 Aerodynamic characteristic of RAE-2822 airfoil with/without GF. 1568 YU, WANG AND ZHANG on a chord length of 0.61 m), with slight separation near the trailing edge. For eliminating the influence caused by the wall of the wind tunnel, the Mach number and AOA selected by numerical simulation should be empirically modified in order to match the wind-tunnel results. The parameter correction method proposed by Coakley [24] is chosen, and the details of theflow condition are listed in Table 2. To solve the transonic viscosity flow, two-dimensional steady compressible RANS equations are adopted, and the governing equations are shown as follows: @Ui @xi � 0 (3) @��uiuj� @xj � @p @xi � @ @xj � � � @ui @xj � @uj @