Convergence studies of the time accurate and non-linear frequency domain methods for optimum shape design

Abstract

This paper presents convergence studies of the time accurate and non-linear frequency domain (NLFD) methods for optimum shape design. The NLFD method provides an attractive alternative for aerodynamic shape optimisation for unsteady flows. It dramatically reduces the number of time steps required to resolve the periodic flow field. In this work, the convergence of the gradients are investigated as the number of time steps are increased to determine the required number of modes that is adequate for shape optimisation for unsteady flows. The formulation of the adjoint equations for both the time accurate and NLFD techniques are presented. The techniques are employed for the redesign of a pitching airfoil to reduce the time-averaged drag coefficient while maintaining the lift coefficient.