Theoretical and computational solutions of steady and unsteady aerodynamic problems

摘要

This paper, dedicated to Elie Carafoli, presents first a method of solutions based on velocity singularities for the analysis of finite-span wings in subsonic flows. This leads to efficient theoretical solutions in closed form for the spanwise variation of the circulation and lift, which were found in excellent agreement with the classical method developed by Carafoli. The second part of this paper is devoted to the analysis of unsteady viscous flows with oscillating walls and separation regions, which are present in many engineering applications. The method of solution presented in this paper is based on the accurate time-integration of the unsteady Navier-Stokes equations and uses artificial compressibility in a fixed computational domain obtained via a time-dependent coordinate transformation from the fluid domain with moving boundaries. This method is first validated for steady flows past a downstream-facing step by comparison with previous numerical solutions and experimental results. The method is then used to obtain solutions for the unsteady flows in channels with a downstream-facing step followed by an oscillating floor, for which there are no previously known solutions.