Literature Survey

LITERATURE SURVEY Analytic or Semi-analytic Study 2-Dimensional

Wieselsberger,C Tomotika et al Havelock,T.H. Green, A. E. Tuck,E.O Plotkin, A. and Kennelle, C.G

3-Dimensional

Plotkin,A. and Dodbele,S.S Newman,J.N. Tan,C.H. and Plotkin,A Teruhiko,Kida and Yoshihiro, Miyai Qian-Xi Wang Sheila E Widnall and Timothy M. Barrows Tuck,E.O

LITERATURE SURVEY Analytic or Semi-analytic Study 2-Dimensional Wieselsberger,C.,”Wing Resistance Near the Ground,” NACA TM77, April 1922. The first to solve this problem. Used the method of images, thus satisfying the no penetration boundary condition on the ground surface automatically.

Tomotika et al.,”The lift on a Flat Plate Placed Near a Plane Wall, with Special Reference to the Effect of Ground Upon the Lift of a Monoplane Aerofoil,” Aeronautical Research Inst., Rept. 97, Tokyo Imperial Univ., Tokyo, Aug.1933(as reported in Pistolesi,1935) Used the conformal mapping technique to obtain the exact solution for the flow around a flat plate near ground.

Havelock,T.H.,”The Lift and Moment on a Flat Plate in a Stream of Finite Width,” Proceedings of the Royal Society of London, Series A, Vol.166, No.2, London,1940, pp.19-54. Obtained an exact solution for the flow past an elliptic cylinder between two parallel plates by conformal mapping. Using a limiting process he obtained a series solution for the flow past a flat plate near a single wall(ground) which matched Tomotika’s solution far from the wall.

Green, A. E., ”The Forces Acting on the Circular-Arc Aerofoil in a Stream Bounded by a Plane Wall,” Proceedings, London Mathematical Society, Vol.46, No.2, London, 1940,pp.19-54. Green, A. E., ”The Two-Dimensional Aerofoil in a Bounded Stream,” Quarterly Journal of Mathematics, Vol.18, 1947,pp.167-177. Obtained the solution for a circular-arc airfoil and later for an airfoil with finite thickness near a olane wall also using conformal mapping. He showed that camber tends to increase the lift, while thickness tends to decrease it first and then increase it as the ground is approached. Based on the opposite effects of camber and thickness, one may expect the results of a flat plate in ground proximity to give a reasonable approximation for actual airfoils.

Plotkin, A. and Kennelle, C.G.,”Thickness-Induced Lift on a Thin Airfoil in Ground Effect, ” AIAA Journal, Vol.19, Nov. 1981,pp.1984-1986. Used the perturbation analysis the effect of thickness of the airfoil on the lift coefficient was calculated to the 2nd order in the thickness ratio. Analytical results was presented for the Joukowski airfoil. The first-order angle-of-attack solution for the flat plate was presented. The liftforce experienced by the airfoil in an infinite fluid is decreased by the effect of thickness and increased by the effect of angle of attack.

Tuck,E.O.,”Steady Flow and Static Stability of Airfoils in Extreme Ground Effect,” Journal of Engineering Mathematics, Vol.15, 1981,pp.89-102 For incompressible, irrotational flow, solutions for small values of wall clearance have been obtained for airfoils.

3-Dimensional Plotkin,A. and Dodbele,S.S.,”Slender Wing in Ground, ” AIAA Vol.28, No.4,1988. Determine analytically the lift coefficient for a slender(low-aspect ratio) wing in ground effect for large values of wall clearance by using perturbation analysis.

Newman,J.N.,”Analysis of Small-Asprct-Ratio Lifting Surfaces in Ground Effect.,” Journal of Fluid Mechanics, Vol.117, 1982,pp.305-314 For incompressible, irrotational flow, solutions for small values of wall clearance have been obtained for slender wings. The gap flow beneath the lifting surfaces is represented by a simple nonlinear solution in the cross-flow plane, and appropriate conditions are imposed at leading and trailing edges. For steadystate motion of a delta wing with sufficiently large angle of attack, the transition point is upstream of the tail. For oscillatory heaving motion of a delta wing the transition point is cyclic if the heave velocity is sufficiently large.

Tan,C.H. and Plotkin,A.,”Lifting-Line Solution for a Symmetrical Thin Wing in Ground Effect., ” AIAA Journal Vol.24, No.7.,1985. For a symmetrical thin wing, a lifting-line solution is obtained and effect of thickness on lift was considered in both the lifting-line and vortex-lattice formulations. For small values of h/c, the presence of the ground introduces a nonlinearity in angle of attack much stronger than in infinite fluid problem.

Teruhiko,Kida and Yoshihiro, Miyai, “Jet-Flapped Wings in Very Colse Proximity to the Ground.,”AIAA Journal Vol.10, No.5.,1971. The method of matched asymptotic expansions is applied to the problem of jet-flapped wings of finite span in very close proximity to the ground. For linearization, angle of attack and jet deflection are assumed to be smaller than the ratio of the ground clearance to the root chord. This study treats the flow in the confined region beneath the wing and jet sheet with a 2-D channel flow with known boundaries and mass addition, coming from the boundary condition of the flow tangency.

Timothy M. Barrows and Sheila E.Windall,”Optimum Lift-Drag Ratio for Ram Wing Tube Vehicle, ” AIAA Journal 1970. Munk’s theorem specifying the downwash condition for minimum drag is generalized to include lifting surfaces operating in proximity to solid boundaries. By developing a method for finding optimum lift distribution on a wing and extending it to the case of finding optimum configuration for a ram wing in a tube, this study concludes that the ram wing concept looks very promising as a method of supporting vehicles in a tube.

Qian-Xi Wang, ”Flow around an unsteady thin wing close to curved ground,” J. Fluid Mech. Vol.226, pp. 175-187., 1985. The method of matched asymptotic expansions is applied to the flow analysis of a 3-D thin wing moving uniformly in very close proximity to a curved ground surface. Flow above the wing is reduced to a direct problem, and the flow beneath it appears to be a 2-D channel flow. An equivalence is found between the extreme curved-ground effect and the corresponding flat-ground effect, which can be treated by the image method.

Tuck,E.O.,”Nonlinear extreme ground effect on thin wings of arbitrary aspect ratio,” J. Fluid Mech. Vol.136, pp.73-84.,1983. Nonlinear problem from nonlinear gap was studied.A semi-numerical solution for a wing of circular planform was given. In the special case of an exponentially varying clearance, it is possible to write down a solution in the form of a Bessel-function expansion, and good accuracy is achievable by truncating this series to a small number of terms.

Tuck,E.O.,”A nonlinear unsteady one-dimensional theory for wings in extreme ground effect.,”J. Fluid Mech. Vol.98, pp.33-47.,1980. Flow induced by a body moving near a plane wall is analyzed. The gap-flow problem in the case of unsteady motion is reduced to a nonlinear first-order ordinary differential equation in the time variable. As an illustration of the unsteady theory, the problem is solved of a flat plate falling toward the ground under its own weight, while moving forward at uniform speed.

Sheila E Widnall and Timothy M. Barrows,”An analytic solution for two- and three-dimensional wings in ground effect,” J. Fluid Mech. Vol.41, pp.769-792.,1970. The method of matched asymptotic expansions is applied to the problem of a wing of finite span in very close proximity to the ground. The lifting surface problem is shown to be a direct problem, represented by a sourcesink distribution on the upper surface of the wing and the wake, with concentrated sources around the leading and trailing edges plus a separate confined channel flow region under the wing and wake. An expression for the lift at small clearance at small clearance and angle of attack, valid for moderate aspect ratio, is derived.

Numerical Study - Panel Method 2-Dimensional Yen-Sen Chen,”Dynamic Ground Effects on a Two-Dimensional Flat Plate,” J. Aircraft.Vol.22, No.7,pp.638-640.,1985. 2-D unsteady ground effect was studied by using QVLM and modeling the wake with a sequence of discrete vortices. But their results are limited and their approach does not seem to be rigorous in the treatment of the path of the wake.

A.O. Nuhait and M.F.Zedan,”Numerical simulation of Unsteady Flow Induced by a Flat Plate Moving near Ground., ” J. Aircraft.,Vol.30, No.5, Sept.-Oct.,1993. General unsteady 2-dimensional vortex-lattice method and the method of images was developed to predict the unsteady ground effect on the aerodynamic characteristics of a flat plate. The wake is computed as a part of solution by allowing it to deform and roll up into its natural force-free position. For large sink rates, the wake becomes very close to the flight path with its position less dependent on the height above the ground.

D.T.Mook, S.Roy,G.Choski, and B.Dong,” Numerical Simulation of the Unsteady Wake Behind an Airfoil,” J. Aircraft.Vol.26, No.6, pp.509-514.,1989. The unsteady wake behind an airfoil is simulated numerically by a system of discrete vortex cores, also called point vortices. At each time step, a core is added to the wake at the trailing edge, and the cores already in the wake are convected at the local particle velocity.

3-Dimensional A.O. Nuhait and D.T.Mook,” Numerical Simulation of Wings in Steady and Unsteady Ground Effects,” J. Aircraft.Vol.26, No.12, pp.1081-1089.,1989. A numerical simulation of steady and unsteady ground effect is developed. The simulation is based on the general unsteady vortex-lattice method and computed results are compared with limited exact solutions and experimental data. This study showed the influences of various parameters on the aerodynamic coefficients for both steady and unsteady flows. Generally aerodynamic coefficients increase with proximity to the ground, the greater the sink rates the greater the increases. Increasing the aspect ratio increases both the steady and unsteady ground effects for both rectangular and delta planforms.

Katz,J., ” Calculation of the Aerodynamic Forces on Automotive Lifting Surfeces,” Journal of Fluid Enginnering. Vol.107,Dec. pp.438-443.,1985. Used a vortex-lattice method that included a freely deforming wake to investigate the performance of lifting surfaces close to the ground, such as those found on racing cars. Katz found that the increases in aerodynamic loads due to the unsteady ground effect are about 100% greater than those due to the steady ground effect.

A.O. Nuhait,” Unsteady Ground Effects on Aerodynamic Coefficients of Finite Wings with Camber,” J. Aircraft.Vol.32, No.1, pp.186-192.,1995. A numerical investigation on finite thin cambered wings moving near ground in unsteady flow was conducted. Increasing the aspect ratio increases the ground effect, causing wings to start feeling at higher position. The greater the sink rate, the weaker the increase. The ground effects are weaker as the camber ratio increases, consistent with the results of two dimensional plates. Moving the position of maximum camber backward has a similar effect. Meanlines of NACA five-digit series showed bigger increase in CL and CM compared to NACA four-digit and six-digit series meanlines. Increasing the angle of attack increases the ground effects in conflict with the results of two-dimensional plates.

Numerical Study -CFD Deese,J.E. and Agarwal,R.K.,”Euler Calculation for Flow Over a Wing In Ground Effect., ” AIAA Paper 86-1765 CP,1986. Hashiguchi, M.,Ohta,T.,and Kuwahara,K.,”Computational Study of Aerodynamic Behavior of a Car Configuration., ” AIAA Paper 87-1386,1987. Noboyuki Hirata and Takanori Hino., ” Investigation of a Three-Dimensional Power-Augmented Ram Wing in ground Effect.,” AIAA-97-0822 ,1997. The Navier-Stokes solver used was MUSCL-type third-order accurate upwind differencing, finite-volume, artificial compressibility code based on multi-block grid approach. In order to understand the mechanism of the power-augmentation effect, two boundary conditions on the ground were considered. (1) a moving belt ground plane condition (2) a fixed ground plate condition corresponding to a wind-tunnel test. Thrust was represented using prescribed body-force distributions. The flow around a rectangular wing with end plates and propellers which were placed forward of the wing and blew under the wing, were computed by the solver with different trailing edge heights.

Yen-Sen Chen,”Dynamic Ground Effects on a Two-Dimensional Flat Plate,” J. Aircraft.Vol.22, No.7,pp.638-640.,1985. 2-D unsteady ground effect was studied by using QVLM and modeling the wake with a sequence of discrete vortices. But their results are limited and their approach does not seem to be rigorous in the treatment of the path of the wake.

Chih-Min Hsiun and Chao-Kuang Chen.,Aerodynamic Characteristics of a 2Dimensional Airfoil ” J. Aircraft.Vol.33, No.2,pp.386-392.,1985. Applied steady, incompressible Navire-Stokes equations to treat the aerodynamic problem of an airfoil in ground proximity. The standard k-e two equation model was used to account for turbulent flow at high Reynolds number. But wrong boundary condition was imposed on the wall. So slip boundary condition should be imposed.

Experimental Study Ray Chung Chang and Vincent U. Muirhead,”Effect of Sink rate on Ground Effect of Low-Aspect-Ratio Wings,” J. Aircraft.Vol.24, No.3,pp.176-180.,1987. An experimental investigation of dynamic ground effect was conducted using delta wings of 60-,70-, and 75-deg sweep, the XB-70 wing, and the F-104A wing. Both static and dynamic tests were made at a Reynolds number of 700,000.

Toyohiko Kono, Yasuaki Kohama and Nobuaki Matsui, ”Stability of Guide Way Type Wing in Ground Effect Vehicle,” Proceedings of the third JSME-KSME Fluids Engineering Conference, July 25-27, 1994,Sendai, Japan. Aerofoil interference and dynamics of tandem was investigated. Numerical investigation is introduced to find out an optimum wing profile. The condition when chord and attack angle of front wing is bigger, stability of the system is more stable.