Unsteady aerodynamics of a WIG airfoil flying over a wavy wall

Abstract

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