26 2 2009 3 CHINESE JOURNAL OF COMPUTATIONAL PHYSICS Vol. 26,No. 2 Mar., 2009 Article ID : 10012246 X(2009) 0220231210 Aerodynamic Investigation of a 2D Wing and Flows in Ground Effect YANG Wei, YANG Zhigang ( Shanghai Automotive Wind Tunnel Center, Tongji University, Shanghai 201804, China) Abstract : A numerical investigation is performed to study aerodynamics of a 2D NACA0012 wing and flows in ground effect ( IGE). Lift and drag forces are obtained and pressure distribution on airfoil surfaces is recorded at different angles of attack and ground clearances. Viscous flow near ground and air compressibility are taken into account. High lift is obtained as the airfoil is in close proximity to the ground. The stall angle decreases with reduction of the ground clearance, due to higher adverse pressure gradient. Viscous effect of floor shows less effect on airfoil. Compressibility should be taken into account at lower ground clearances. Key words : wing in ground effect ; aerodynamics ; viscous effect ; compressibility CLC number : U661171 ; V211141 Document code : A 0 Introduction It has long been recognized that flight in close ground proximity is more aerodynamically efficient than flight in freestream. This leads to design and construction of craft operating close to the ground and flying in ground effect. The effects of proximity to ground for an airfoil on lift and drag were studied as early as in 1920s [1,2 ]. At a given angle of attack, the lift increases with decreasing ground clearance. The air flow around wing is considerably modified in ground effect. The stagnation point moves down on lower surface, thereby more air flows around upper surface. Thus velocity above wing and pressure below wing are increased. An air cushion is created by high pressure under wing as it is in close ground proximity. Higher pressure under wing is achieved as a wing approaches the ground, which is called ramming action. Increased lift and lift2to2drag ( LΠD) ratio due to reduced ground clearance leads to much higher aerodynamic efficiency. Flight range of wing in ground effect at a given fuel consumption is larger than that of conventional aircraft [3,4 ]. A thorough investigation on characteristics of a wing in ground effect and WIG craft is required from both practical and fundamental considerations. Experiments and theoretical studies were made to investigate on aerodynamic characteristics of wing in ground effect. It was found that flight in close ground proximity provides increased lift and decreased drag. Zerihan and Zhang [5,6 ] reported pressure, lift and drag of a single element wing in ground effect with endplates. Force reduction and effect of height on a single reference incidence are focused. Force reduction was observed in very close proximity to the ground and separation of boundary layer occurred near trailing edge of the suction surface. Ahmed and Sharma [7 ] studied a symmetrical airfoil in ground effect. It is found that suction effect on upper surface results in adverse pressure gradient and leads to a rapid decay of kinetic energy over the upper surface. Higher pressure extends to almost entire lower Received date : 2007-12 - 03 ; Revised date : 2008-05 - 26 Biography : Yang Wei (1980 - ),male, Weifang, Shandong, Ph. D,engaged in fields of aerodynamics.
232 26 surface due to ramming action. Numerical studies by Young [8 ] and Xing, et al [9,10 ] based on RANS illuminated that results in ground effect by solving incompressible Navier2Stokes equations agree well with experiments. The lift increases non2linearly with reduction of hπc under 011. It was concluded by Young et al. that increase of camber clearly enhances lift by lowering stagnation point at leading edge, and reduction of thickness decreases drag by moderating adverse pressure gradient along the upper surface of airfoil. Most studies are limited to force study. Some involved surface pressure measurements and few focuse on flow in ground effect. Detailed investigation on angle of stall and flow in ground effect are needed. 1 Computational methodology Aerodynamics of a two2dimensional wing in ground effect for airfoil of NACA0012 is numerically investigated by solving incompressible two2dimensional Reynolds2averaged Navier2Stokes equations in a k2 Πsst turbulence model [11 ]. In the present study, aerodynamic characteristics of airfoil NACA0012 are investigated, at various ground clearances and angles of attack and a Reynolds number of 6 10 6 (based on chord length). Governing equations are written as where - 9 U i 9 x i = 0, 9 U i 9 t + 9 ( U iu j ) 9 x j = - 1 9 P + 92 U i + 9 ( - 9 x i 9 x j 9 x j 9 x i u j ), j i u j is Reynolds stress term. Menter s k2 Πsst ( shear stress transport) turbulence closure model [11 ] is used. Transport equations of k and are written as D k D t 9 u i = 2 S ij - 3 k + 9 ( + 9 k 9 x j 9 k t ), x j 9 x j D = 9 u i D t ij - 2 + 9 ( + t 9 x j 9 t ) 9 1 + 2 (1 - F x j 9 x 1 ) 9 k 9 2. j 9 x j 9 x j Wilcox s k2 model behaves well in near wall region and thus low2reynolds2number corrections are not required. It is generally very sensitive to freestream value of, but behaves poorly in near wake region. A combined k2 Πk2 model proposed by Menter uses parameter F 1 to switch from k2 to k2 in the wake region to prevent sensitivity to freestream conditions. The blending function is defined as = tanh ( 4 1), where 1 F 1 = min max k 0109 y, 500 y 2 ; 4 2 k CD k y 2, 1 9 k 9 CD k = max 2 2 ; 10-20. 9 x i 9 x i In this study, model constants used refer to Ref. [ 12 ]. Navier2Stokes equations are solved by SIMPLE algorithm with a second2order upwind scheme applied to convection terms. C2H type multi2block grids are adopted for 2D wings. For resolution of turbulent boundary layer profiles, a minimum normal spacing of 1 10-5 c is selected so that y + at the wall is around 1 along airfoil surfaces. Figure 1 shows meshes in computation domain. Ground clearance is defined by distance
2 YANG Wei et al. : Aerodynamic Investigation of a 2D Wing and Flows in Ground Effect 233 from the ground to trailing edge of airfoil. Fig11 Computational grid and domain, hπc = 012, = 4 2 Computational results and discussion The present work aims at studying aerodynamic characteristics of two2dimensional airfoil of NACA0012 and viscous flow in ground effect, at various angle of attack and ground clearance. Influence of air compressibility in ground effect on aerodynamic characteristics of wing is investigated. 211 Validation of computational method Aerodynamic characteristics of NACA0012 airfoil are simulated at a Reynolds number of 6 10 6. Lift and drag are compared with experimental data [13 ] with free transition in Fig. 2. Good agreement of lift is achieved while drag is not predicted accurately. A possible reason is that more viscous effect is introduced and viscous drag is overestimated. Fig12 Lift and drag coefficient 212 Aerodynamic characteristics of airfoil in ground effect Ground effect brings two characteristics in numerical simulation. Firstly, grids are re2generated for each relative ground clearance and angle of attack, and it costs more time. Secondly, larger number of grids are needed between the lower surface of airfoil and ground, because aerodynamic characteristics of airfoil is sensitive to flow in this region. The relative ground clearance varies from 011 to 1151 Figure 3 presents lift and drag coefficients of two2dimensional airfoil NACA0012 at different ground
234 26 clearances and various angles of attack. It is found that running in close to the ground increases lift and decreases drag at some angle of attack, and smaller ground clearance comes with higher lift coefficient. The lift coefficient becomes negative at a small angle of attack, and the drag coefficient increases sharply with reduced angle of attack. Furthermore, small ground clearance brings about a considerable decrease of stall angle. The stall angle decreases from 18 to 14 with a relative ground clearance from 115 to 011. Fig13 Lift and drag coefficient It was pointed out that suction effect exists on the lower surface at ground clearances of hπc = 011 to hπc = 0125 [7 ]. Figure 4 shows pressure distribution at angles of attack of 0 and 12 in different ground clearances. At an angle of attack of 0, in lower ground clearances, the area between ground and airfoil is regarded as a convergent2divergent passage. Due to ramming action, pressure is high on the lower surface near the leading edge. Pressure reduces with acceleration of flow in convergent region. The NACA0012 section has maximum thickness at 30 % of the chord, where the gap between airfoil and ground is minimum. It is shown that a minimum pressure appears at this location in lower ground clearance. In the divergent region, pressure increases sharply to meet pressure of the upper surface near the trailing edge. Pressure distribution on the upper surface does not change significantly with ground clearance. Suction effect on the lower surface results in negative lift coefficient. The blocking effect, based on convergent2divergent passage under airfoil, enhances drag force in very low ground clearances. Fig14 Pressure coefficient distribution
2 YANG Wei et al. : Aerodynamic Investigation of a 2D Wing and Flows in Ground Effect 235 At higher angles of attack, there is no divergent region under wing. Higher pressures are found on the lower surface along the chord length of airfoil at lower ground clearance due to ramming effect. Dividing streamline and stagnation point move down along lower surface of the airfoil with increasing angle of attack. More air is forced to flow over the upper surface. Hence an increase of velocity as well as a decrease of pressure are recorded over airfoil. Then flow velocity decelerates towards the trailing edge. Figure 4 shows that recovery of pressure on the upper surface is sharper at hπc = 011 than that at hπc = 014. Reduction in pressure on the upper surface results in an adverse pressure gradient. The closer the wing flies over the ground, the greater the adverse pressure gradient on the upper surface is. Figure 5 and Figure 6 show contours of velocities at several ground clearances and angles of attack. Suction effect on the lower surface is prominent at an angle of attack of 0, in a relative ground clearance of 0111 As angle of attack is increased, suction effect on the lower surface is weakened, and then occurs on the upper surface. Simultaneously, a separation of boundary layer is shown at the trailing edge. At the same angle of attack, separation region at the trailing edge is decreased. A weakened suction effect is found with increase of ground clearance. It is clear that the suction effect shifts from lower surface to upper surface with increasing angle of attack and ground clearance. Separation of boundary layer occurs near trailing edge of the suction surface. Due to enhanced suction effect and increased pressure gradient, the angle of stall decreases with reduction of ground clearance (Fig. 3). Fig15 Contours of velocities at hπc = 011 Fig16 Contours of velocities at hπc = 014 213 Potential effect and viscous effect in ground effect region Studies on aerodynamic characteristics of WIG crafts show that lift and drag vary with ground clearance. Viscous characteristics of the flow near floor become important due to close ground proximity. In this study, potential effect and viscous effect in ground effect at an angle of attack of 4 are investigated with different boundary conditions of floor, including wall condition in which floor has zero velocity ; symmetry condition in which no viscous effect exists near floor and moving wall condition in which floor
236 26 has same velocity as air of inlet. Figure 7 shows variation of lift and drag with ground clearances, with different boundary conditions at an angle of attack of 4. The results with moving wall condition and symmetry condition are nearly the same. A fixed floor gives rise to an increase of lift and a decrease of drag. Difference between results with moving wall and fixed floor is reduced with increase of ground clearance. Fig17 Lift and drag coefficient It is reported that boundary condition of moving wall simulates actual flow with ground effect successfully. In Fig. 8, velocity near ground changes along the floor under the wing. A shear region exists near the ground. Figure 9 shows velocity between the wing and the ground at different locations. A great difference is shown with fixed ground condition. A detailed comparison between symmetry condition and moving wall condition indicates that velocity is in reasonably good agreement, except in a shear region near ground. Fig18 Velocity near the ground with moving wall condition, hπc = 011 WIG crafts are investigated with experiments in wind tunnels and numerical simulation. Besides Reynolds number and tunnel wall, boundary condition of floor in simulation is different from real flow in ground effect. It was shown in Fig. 7 and Fig. 9 that numerical simulations in ground effect with fixed floor are unacceptable. Since the shear region near floor extends to slightly above yπc = 01005 ( Fig. 8) and results with moving wall condition and symmetry condition agree well, the ground effect is mainly potential
2 YANG Wei et al. : Aerodynamic Investigation of a 2D Wing and Flows in Ground Effect 237 effect. Mirror2image method is employed in simulation of conventional wind tunnel experiments. 214 Compressibility effects in ground effect Fig19 Velocity between the wing and the ground, hπc = 011, = 4 Different from previous studies in low speeds, for large wing2in2ground effect vehicles with very high cruising speeds, compressibility of air have to be considered. Figure 10 shows lift and drag with different air conditions at Mach number of 013. It shows sensitivity of suction effect to compressibility of air. Suction effect is enhanced on the surface. Higher positive lifts are given with suction effect on the upper surface. Higher negative lifts are shown with suction effect on the lower surface. Compressibility of air leads to a distinct decrease of drag at an angle of attack of 2 and an increase at an angle of attack of 10. Air flows more fluently through convergent2 divergent passage with compressibility. As a result drag is decreased at lower angles of attack. increased suction effect on upper surface results in increased drag at higher angle of attack. Difference in lift and drag even at hπc = 110 indicates reasonable results as in freestream. A comparison is made between out ground effect (OGE) and in ground effect ( IGE) with a relative ground clearance of 011, on discrepancy of lift and drag coefficient considering compressibility effect. It is shown in Fig. 11 that compressibility effect is enlarged in ground effect. Due to the ground, compressibility of air becomes important. It shows that compressibility effect is not negligible in strong ground2effect region with a relative ground clearance less than 011. Compressibility effect is not only sensitive to Mach number but also to ground clearance in ground effect. The 3 Conclusions A detailed investigation on aerodynamic characteristics of a two2dimensional wing of NACA0012 in ground effect and flow characteristics in ground effect is carried out. It is conclued : 1) For airfoil of NACA0012, suction effect observed on the lower surface at lower ground clearance due to convergent2divergent passage causes a negative lift. Higher lifts are shown at certain angles of attack with lower ground clearance than that in freestream due to suction effect on the upper surface. Higher pressures are found near trailing edge on the upper surface. 2) Separation of the boundary layer occurs on surface with suction effect. Angle of stall is reduced with decreasing ground clearance due to enhanced suction effect and higher adverse pressure gradient at
238 26 Fig110 Lift and drag coefficient
2 YANG Wei et al. : Aerodynamic Investigation of a 2D Wing and Flows in Ground Effect 239 Fig111 Discrepancy of c L and c D due to compressibility lower ground clearance. 3) Viscous effect near floor extends to region slightly above yπc = 010051 It makes no difference to characteristics of the wing neglecting viscous effect of the floor. The ground effect is mainly position effect. 4) At lower relative ground clearance, compressibility of air becomes important and it should be considered in numerical simulation and experiment in wind tunnel. Acknowledgement :The authors would like to recognize support of Shanghai Automotive Wind Tunnel Center. This work was supported by Program for Changjiang Scholars and Innovative Research Team in University. References : [ 1 ] Raymond A E. Ground influence on airfoils[ R]. NACA Technical Note 67, 1921. [ 2 ] Reid E G. A full scale investigation of ground effect[ R]. NACA Technical Report 265, 1927. [ 3 ] Rozhdestvensky Kirill V. Wing2in2ground effect vehicles[j ]. Progress in Aerospace Science, 2006, 42 : 211-283. [ 4 ] Halloran M, O Mearn S. Wing in ground effect craft review[ R ]. DSTO2GD20201, Canberra (Australia) Technology Organization, 1999. [ 5 ] Zerihan J, Zhan X. Aerodynamics of a single element wing in ground effect[ R]. AIAA paper, 2000-0605, 2000. : Defense Science and [ 6 ] Zhang X, Zerihan J. Turbulent wake behind a single element wing in ground effect [ C ]ΠΠProceedings of the 11 th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Portugal, 2002. [ 7 ] Ahmed M R, Sharma S D. An investigation on the aerodynamics of a symmetrical airfoil in ground effect [J ]. Experimental Thermal and Fluid Science, 2005, 29 : 633-647. [ 8 ] Young J Moon. Aerodynamic investigation of three2dimensional wings in ground effect for aero2levitation electric vehicle[j ]. Aerospace Science and Technology, 2005, 9 : 485-494. [ 9 ] Xing Fu, Wu Baoshan. Investigation on numerical prediction of WIG s aerodynamics[j ]. Journal of Ship Mechanics, 2004, 6 (8) :19-30. [10 ] Wu Baoshan, Xing Fu. Investigation of hydrodynamic characteristics of submarine moving close to the sea bottom with CFD methods [J ]. Journal of Ship Mechanics, 2005,3 (9) :19-28. [11 ] Menter F R. Two2equation eddy2viscosity turbulence models for engineering applications[j ]. AIAA J, 1994, 32 : 1598-1605. [12 ] Forsythe J R, Strang W Z. Validation of several Reynolds2averaged turbulence models in a 32D unstructured grid code [ R ]. AIAA Paper 00-2552, 2000. [13 ] Abbot I H, von Doenhoff A E. Theory of wing sections[m]. Dover Publications Inc, 1959 : 64-79.
240 26, (, 201804) [ ], NACA0012,.,,,, ;,, ; ; 0. 1,. [ ] ; ; ; 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3, 2009 5 25 29, 2 ( ),3 ( )., : 11 : 1) ( ) ; 2) ( ) ; 3) ; 4) ( ). ( ),. 21,. 10 000,.,,,. 31 2009 3 1 ( A4 1 ), 4 20,. : :, : (010) 59872156, (010) 59872154 : (010) 62010108 E2mail :li - gang @iapcm. ac. cn ; shen - huayun @iapcm. ac. cn : 8009 16, :100088. 2008 11 20 [ ] 2007-12 - 03 ; [ ] 2008-05 - 26