Analysis of Steady and Unsteady Flows Past Airfoils in the Proximity of the Ground at Low Reynolds Numbers

Abstract

This paper presents the analysis of the steady and unsteady flows past fixed and oscillating airfoils at low Reynolds numbers in the proximity of the ground. Various flight evolutions of the micro-air-vehicles take place in the proximity of the ground or a ceiling, which require the aerodynamic solutions in these conditions at the low Reynolds numbers. The unsteady flow problem is solved in a rectangular computational domain, obtained from the physical domain by time-dependent coordinate transformations for various subdomains, in which the boundary conditions are efficiently and rigorously implemented. Solutions for the aerodynamic coefficients of airfoils executing pitching oscillations in the proximity of the ground at low Reynolds numbers are obtained with an efficient numerical method developed by the authors for the time-accurate solution of the Navier-Stokes equations, which is second-order accurate in time and space. This method uses a pseudotime relaxation procedure based on artificial compressibility and a factored Alternate Direction Implicit (ADI) scheme for integration in pseudo-time. A second-order central finite difference formulation is used on a stretched staggered grid (which avoids the oddand-even points decoupling). A special decoupling procedure based on the continuity equation reduces the problem to the solution of scalar tridiagonal systems of equations, which enhances substantially the computational efficiency of the method. The influence of various flow parameters (Reynolds number, airfoil relative thickness and the amplitude and frequency of oscillations) on the aerodynamic coefficients (lift, drag, pitching moment and lift-to-drag ratio) and the flow separation in the proximity of the ground is also studied.