An analytic solution for two- and three-dimensional wings in ground effect

Wing configuration is a parameter that affects the performance of wing-in-ground effect (WIG) craft. In this study, the aerodynamic characteristics of a new compound wing were investigated during ground effect. The compound wing was divided into three parts with a rectangular wing in the middle and two reverse taper wings with anhedral angle at the sides. The sectional profile of the wing model is NACA6409. The experiments on the compound wing and the rectangular wing were carried to examine different ground clearances, angles of attack, and Reynolds numbers. The aerodynamic coefficients of the compound wing were compared with those of the rectangular wing, which had an acceptable increase in its lift coefficient at small ground clearances, and its drag coefficient decreased compared to rectangular wing at a wide range of ground clearances, angles of attack, and Reynolds numbers. Furthermore, the lift to drag ratio of the compound wing improved considerably at small ground clearances. However, this improvement decreased at higher ground clearance. The drag polar of the compound wing showed the increment of lift coefficient versus drag coefficient was higher especially at small ground clearances. The Reynolds number had a gradual effect on lift and drag coefficients and also lift to drag of both wings. Generally, the nose down pitching moment of the compound wing was found smaller, but it was greater at high angle of attack and Reynolds number for all ground clearance. The center of pressure was closer to the leading edge of the wing in contrast to the rectangular wing. However, the center of pressure of the compound wing was later to the leading edge at high ground clearance, angle of attack, and Reynolds number.

I. Abstract HIS work details the design and computational analysis of a race car front wing. Using XFOIL, an airfoil was designed, based on the Selig 1223 airfoil, to produce high values of negative lift with a low corresponding drag at a fixed angle of attack. The modified airfoil achieved an 8.55% increase in lift and 45.6% decrease in drag over the Selig airfoil. The airfoil design was extruded into a 3-dimensional wing, which was then computationally analyzed using FLUENT under three different sets of conditions: wing out of ground effect, wing in ground effect, and wing with endplates in ground effect. The results of the computational analysis are presented in the form of pressure distribution, lift and drag coefficients, lift curves, drag polars, lift force, and drag force, as well as flow visualization output by FLUENT. The FLUENT case for the wing with endplates in ground effect achieved an 81% increase in lift while increasing its L/D from 6.9 to 9.0 from the case of the wing out of ground effect and without endplates. The results conclusively show that the completed design successfully accomplishes the goal of achieving appropriately high lift with corresponding low drag at a small angle of attack.

This paper deals with the influence of different RANS turbulence models on the numerical modelling of a 3D rectangular symmetrical wing in ground effect. Travelling near a solid surface, so-called ground effect, considerably alters the aerodynamic characteristics of a wing. This paper aims to investigate the performance of the widely used eddy viscosity turbulence models while predicting the changing aerodynamic behavior due to the ground effect. Three different RANS turbulence models, realizable , SST and Spalart-Allmaras models are taken into consideration. The effectiveness of the turbulence models were tasted in comparison with the experimental data in different angles of attack and ground heights. Results reveals that, the effect of the turbulence models on the numerical accuracy of the ground effect aerodynamics calculations are related to the altitude and the angle of attack. The choice of the turbulence model becomes important when the wing travels in very close proximity to the ground and the angle of attack is low or negative. The discrepancy of the calculated results mainly comes from the pressure distribution variations on the lower side of the wing. For high angles of attack, or relatively larger ground heights, the difference between the predictions of the turbulence models become negligible.

Aerodynamic characteristics of an airfoil, NACA 6409, flying over a wavy wall is investigated numerically. An Euler code based on the LU-factored algo rithm and higher-order upwind scheme is constructed and its accuracy is tested on two benchmark problems : NACA 4412 airfoil moving over a level ground and NACA 0012 airfoil in free-flight pitching oscillation. The calculated flow about NACA 6409 airfoil over the wavy ground represented by a moving sine function indicates that the aerodynamic property of the airfoil becomes sensitive if the wave number or amplitude of the wavy ground is increased, and/or if the proximity of the airfoil to the ground is smaller. Introduction When an aircraft flies near the ground, the aerodynamic performance of the wing is much changed from that of the free flight. In particular, a wing in proximity to the ground manifests reduced upwash, downwash, and tip vortices which cause enhancement of lift and pitching moment, and reduction of induced drag. These effects, in overall, are called ‘the ground effect’ whereas the wing taking advantage of these effects is called ‘wing in the ground effect’ or WIG, in short. There has been recently considerable interest in development of WIG crafts in such countries as Russia[1,2], Japan[3,4], Germany[5,6], and China[7] due to its energy saving feature as a means of passenger and cargo transportation. Preliminary design of a WIG airplane is under progress in South Korea[8] and the present research is motivated by this particular program. The gain in the lift-todrag ratio might be achieved by a WIG craft at the cost of stability due to the increased pitching moment. The flight properties of a WIG hence need to be investigated thoroughly during the aircraft development process. Recently, a few reports have appeared on the aerodynamic performance of WIG wings and airfoils[4-7,9] flying over a level *Doctoral candidate, Dept. of Aerospace Engineering. tprofessor, Dept. of Aerospace Engineering, Member AIAA. Copyright @ 2000 by YEHOO” Im. Kcun-Shik Chmg. Publidld by the Americ-n Institute of Aeronautica md Aatronautica. Inc. with permhion. ground. NACA Cdigit airfoils are, in general, known to have positive ground effect. However, a symmetric airfoil with large thickness, NACA 0012, for example, can exhibit negative ground effect at a small angle of attack[4,7]. The WIG craft operated over the sea is quite often expected to face with rough wavy surfaces. This rather periodic terrain will cause ground effect different from that of the level ground. In the literature, the unsteady flow past a twodimensional airfoil moving over a wavy ground has been investigated with the lifting surface theory by Ando et al.[lO], and with the unsteady panel method by Morishita and Ashihara[ll]. Mizutani and Suzuki[l2] used Rankine source and boundary element method to compute the wing aerodynamics over the coastal free surface. Their results have certainly offered some useful data for fundamental study of the lifting airfoils. However, the solutions of Euler and Navier-Stokes equations are still wanted in order to study the possible compressibility and viscosity effect of the WIG craft. In this paper we have numerically solved the Euler equations with the LU-factored algorithm[l3] and high-resolution upwind scheme for the unsteady WIG airfoil moving over a wavy wall. Fortunately, Mizutani and Suzuki[l2] have found that deformation of the free surface caused by the proximate flight of a WIG craft is only negligible. We verified accuracy of the present computer code by reproducing two earlier results : NACA 4412 airfoil over a level ground[l4], and the NACA 0012 airfoil in pitching oscillation[l5]. Various parameter effects on NACA 6409 airfoil flying over a wavy wall with a subsonic flight Mach number, M, = 0.3, is elaborated in this paper. Governing Equations We consider unsteady twodimensional Euler equations in the computational domain (t, 5, n), 1 OF 8 aQ ai aF z+-+-=O ac 877 with the flux vectors (1) AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS PAPER 2000-0657

Recently a new transport system "Aerotrain" has been proposed, and test using the first and second stage models are conducted in a 3 km guide way of old MAGLEV test facility in Miyazaki prefecture. "Aerotrain" has wings, and flies close to the ground of an open channel to take advantage of the ground effect. Characteristics of wing in ground effect (WIG) have been investigated using conventional wind tunnels. But this type of experiment cannot estimate the ground effect correctly because of the existence of boundary layer developed between bottom of the wings and the ground surface. Therefore, it is necessary to experiment using a towing wind tunnel to clarify characteristics of wing in the real ground effect. The aerodynamic charactersistis of two kinds of aerofoil sections: NAGA 4412 and circular arc aerofoil were clarified by the experriment towing the aerofoils in 3 km guide way of MAGLEV test facility. In addition, we examined problems to utilize the guide way of old MAGLEV as a towing wind tunnel.

Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter Facebook Reddit LinkedIn Tools Icon Tools Reprints and Permissions Cite Icon Cite Search Site Citation A. Tarmizi Baharun, Adi Maimun, Yasser M. Ahmed, M. Mobassher, M. Nakisa; Comparison of numerical simulation with experimental result for small scale one seater wing in ground effect (WIG) craft. AIP Conference Proceedings 15 May 2015; 1660 (1): 070120. https://doi.org/10.1063/1.4915838 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAIP Publishing PortfolioAIP Conference Proceedings Search Advanced Search |Citation Search

Effect of bleeding on aerodynamics of non-slender delta wing in ground effect

Micro-vortex generators (MVGs) are simple passive flow control devices mounted on the base surfaces to mitigate the boundary layer flow separation. The effect of the MVGs installed on the aircraft lifting surfaces, i.e., wing, operating close to the ground (ground effect), is not well understood. In this work, the aerodynamic performance of a National Advisory Committee for Aeronautics (NACA) 4412 wing in ground effect equipped with MVGs is numerically investigated. Installed at 10% or 25% chord of the wing, the MVGs are arranged in a row in a counter-rotating pattern. The analysis is carried out at 18°angle of attack, which is close to the stall angle of attack of the wing. Four different cases of h/b = 0.1, 0.5, 1, and free flight (no ground effect) are considered in this analysis. The Reynolds number based on the wing chord is around 3 million. In this work, the detached eddy simulation (DES) method is employed to accurately capture the high energy levels of the vortex formed behind the MVGs, the wing tip vortex, and their contact with the ground. The DES simulations accurately depict the intricate flow dynamics of the NACA 4412 wing, and the use of MVGs enhances its performance while in close proximity to the ground. A negative Cp peak at the leading edge of the wing increases as it approaches the ground, according to the analysis. For h/b = 0.1, the lower wing over pressure is much higher than for other cases. The Q-criterion shows flow unsteadiness and wing tip vortex evolution. The flow region's vortical structures increase as the wing descends. The flow has the most coherent vortical forms at 0.1 aspect ratio. The ground effect leads to an increase in lift and a decrease in drag as the wing gets closer to the ground.

This research reports the numerical results of the ground effect trend for a three-dimensional flapping insect wing at a very low Reynolds number (Re = 10). It demonstrates that the ground effect trend at this Re has a ‘single force regime,’ i.e. the forces only enhance as the ground distance decreases. This phenomenon is unlike the widely expected non-monotonic trend publicized in previous studies for higher Reynolds numbers, that shows ‘three force regimes,’ i.e. the forces reduce, recover, and also enhance as the ground distance decreases. The force trend in the ground effect correlates to a similar trend in wing–wake interaction or the downwash strength on the wing’s head. At very low Re (10), the very large viscosity causes diffused vortices and less advected vortex wake, while at relatively high Re, the vortices are easily separated from the wing and then advected downwards. This different development of the vortex wake caused different force trends for the flapping wing in the ground effect. Furthermore, by examining only the first stroke when there is no vortex wake, we found that the ‘ramming effect’ enhances the forces on the wing. This effect increases the pressure of the lower wing surface due to the squeezed air between the wing and the ground. The ‘ramming effect’, combined with the reduced downwash (or wing–wake interaction) effect, causes the force enhancement of the wing near the ground’s vicinity. It is further comprehended that the trend is dependent on Re. As the Re is increased, the trend becomes non-monotonic. The effect of varying angles of attack, flapping amplitude and wing planform at very low Re does not change this trend. This ground effect might help insects by enhancing their lift while they hover above the surface. This finding might prove beneficial for developing micro air vehicles.

SummaryThe problem of a non-planar wing of finite span very close to the ground is considered by the method of matched asymptotic expansions. This method is based on the work of Widnall and Barrows, in which a planar wing very close to the ground was examined in detail. A simple analytic solution, to first-order approximation, is obtained for a non-planar wing which is uncambered. Expressions for the lift coefficient, induced angle and induced drag coefficient, which are valid for small ground clearance and moderately small aspect ratio, are derived for the case when the configuration of the wing projected onto a transverse plane normal to the free stream is elliptic. The problem of the optimum lift distribution around the wing and the rolling-moment coefficient for the inclined flat wing are discussed.The distribution of camber and of aerofoil angle of attack is given analytically for an optimally loaded non-planar wing, to first-order approximation. Moreover, it is seen that, to first-order approximation, the aerodynamic forces given for the small aspect ratio are independent of the wing planform and depend only on the wing configuration at the trailing edge projected onto a transverse plane.

Animals can obtain excellent locomotion performance as they swim or fly under ground effect in nature. Inspired by this, fluid mechanisms of the flexible bionic wing oscillating and gliding in ground effect are investigated by fluid–solid interaction simulation in this study, respectively. For the oscillation motion, the flexible wing vertically moves up and down at different distances from the ground. Different parameters such as the average height from the ground, oscillation frequency of the flexible bionic wing, and airfoil flexibility are considered in the simulation. At the same time, the gliding motion of the flexible wing in the ground effect is also studied, compared with the oscillation motion. Several simulations are set for different parameters. The characteristics of the force and deformation of the flexible wing and the flow field around the flexible wing are analyzed in depth. The effects of different flexibilities on the force characteristics of oscillation and gliding motion are obtained. The results show that the influence of flexibility on the lift and drag force is different. Optimal motion performance can be achieved within a certain range of flexibility. The ground effect features of the flexible bionic wing with different locomotion modes are acquired.

Counter-rotating vortices form from the opposite edges of lifting surfaces, and gradually move laterally and dissipate as they travel downstream (as seen in a wing-fixed reference frame). Under ground effect conditions, the vortex from a lifting wing – such as that used in an aircraft application – moves laterally outboard from the wingtip as it progresses downstream; for a downforce wing in ground effect – such as that used in an automotive application – the vortex moves laterally inboard. An interesting case is the situation where the inboard moving vortices become in close proximity to each other. The objective of the present study was to investigate counter-rotating vortices produced from a low aspect ratio downforce wing operating in ground effect. The pair of vortices move towards each other and mutually induce an upwards directed motion which in turn reduces the inboard movement driven by the ground effect. Experimental data gained from three-dimensional Laser Doppler Anemometry in a moving ground wind-tunnel was used to validate a Large Eddy Simulation computational result.

In this study, Reynolds-averaged Navier-Stokes simulation (RANS) of the uniform blowing and suction (UB/US) control on a Clark-Y airfoil was performed aiming at improving an airfoil performance by friction drag reduction. First, the control effect when only the uniform blowing control or uniform suction control is applied on the airfoil surface was investigated by changing the control locations. The blowing or suction velocity was 0.14% of the free-stream velocity and the blowing/suction area was set at four different locations from the leading edge to the trailing edge on both the upper and lower surfaces. The Reynolds number based on the chord length is 1.5 × 106. The angle of attack is set to 0°. It was found that friction drag is decreased/increased by single UB/US control. It was also found that the lift-to-drag ratio improved with UB on the lower surface or US on the upper surface, and decreased with UB on the upper surface or US on the lower surface. In the combined control of UB and US, the blowing and suction velocity was 0.14% or 0.26% of the free-stream velocity and the locations of blowing/suction and flow conditions were the same as those in the cases with either UB or US. It seemed that the lift-to-drag ratio was improved by the combined control of UB on the lower surface and US on the upper surface. In particular, the lift-to-drag ratio was most improved by US on the lower rear surface and UB on the upper rear surface.

This paper focused on the development of a model to represent longitudinal aerodynamics of a wing and/or flight vehicle in ground effect when height is a function of time including high angles of attack. A general aerodynamic model of a wing and/or airplane in ground effect which includes high angles of attack was created. The aerodynamic coefficients of wings studied herein were obtained by the unsteady vortex lattice method with Kirchhoff-based correction (UVLM-K). Wind tunnel measurements presented in the literature were used to validate the UVLM-K. Then, a rectangular wing was simulated at high angles of attack in takeoff and flare, and the aerodynamic characteristics at different heights aboveground were obtained along with the h derivatives during these maneuvers. The mathematical model presented herein is capable to model unsteady aerodynamic phenomena in ground effect at high angles of attack. When this model was used in static ground effect, values of R2 equal to and greater than 0.999, 0.981, 0.993 were obtained for lift, induced drag, and pitching moment coefficient, respectively. In dynamic ground effect, the model can adjust the aerodynamic coefficient during the maneuvers.

Euler's equations, the shock wave relations, and the surface boundary condition are used to derive a hypersonic slender body theory applicable to angles of attack from zero to 90 degrees. The theory is not based on small disturbances, but it gives Van Dyke's theory for small angles of attack, Sychev's similarity for moderate angles of attack, and strip theory for large angles of attack. The new similarity parameters are Meo~, 0 cos a/~, and y (where ~=o cos a + sin a). They are shown to be a combination of Sychev's parameters and can be used to modify equations for pressure and force coefficients at small angles of attack for moderate and large angle of attack applications. B(X,y,Z) CA CA CD CD CN CN Cp Cp d D Db A n p,p S(x,y,Z) T Nomenclature scaled function for body geometry axial force coefficient, based on ref. area ::: 2Ld scaled axial force coefficient given by eq. (50) drag coefficient, based on ref. area ::: 2Ld scaled drag coefficient given by eq. (51) normal force coefficient based on ref. area ::: 2Ld scaled normal force coefficient given by eq. (19) pressure coefficient, eq. (47) ... scaled pressure coefficient given by eq. (47) base height of lower surface, see Fig. 1 parameter defined by eq. (2) parameter defmed by eq. (44) unit vectors in x, y, z directions, respectively similarity parameter, 0 cos a~ similarity parameter, Moo~ body length freestream Mach number unit vector normal (inner) to surface static pressure and scaled static pressure, eq. (25) scaled function for shock surface temperature * Professor of Mechanical and Aerospace Engineering, Associate Fellow AlAA. Copyright© 1992 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. 542 u,v,w u,v,w ~ Veo,VOQ x,y,z x,y,z a ~ y o ~ Cartesian velocity components in x,y,z directions, respectively scaled (nondimensional) velocity components freestream velocity vector and magnitude Cartesian coordinates, see Fig. 1 x/L, y/d, z/d, respectively angle of attack shockwave angle ratio of specific heats, 1.4 for air lower surface thickness ratio, d/L, see Fig. 1 --'> lower surface thickness ratio relative to V 00' see Fig. 1 and eq. (15) p,p density and scaled density, eq. (22) circumferential angle, =0 in windward plane SUbscripts c Cone b body s shock wave 00 freestream value Introduction Analysis of inviscid, hypersonic flow past slender bodies has been developed by Van Dyke l for small angles of attack and by Sychev2 for large angles of attack. The small angle of attack analysis is based on small disturbance theory and the similarity parameters are Moo 0, a/o, and y. At large angles of attack the Sychev similarity parameters are Moo sin a, 0 cot a, and y. Hemsch3 showed that the large angle of attack similarity parameters can be combined to yield the small angle of attack parameters when a is small, i.e. (MOQ sin a) (0 cot a) --'> Moo 0 and 0 cot a --'> o/a. Cox and Crabtree4 and Hayes and Probstein5 discuss hypersonic small disturbance theory and Sychev similarity. BarnweU6 showed that Sychev's analysis is applicable to all slender-body flows with crossflow Mach numbers greater than sonic and hence is not restricted to hypersonic values of the cross flow Mach number. In addition, he showed that Sychev similarity applied to a number of slender-body flows with subsonic crossflow Mach numbers, including incompressible flow. Hemsch3 demonstrated empirically that Sychev similarity holds for any value of the cross-flow Mach number if the axial flow component is 4