Efficient Time Spectral Algorithm for Time-Periodic Unsteady Problems

This paper demonstrates an algorithm for the simulation of time-periodic unsteady problems via the solution Unsteady Euler equations. This algorithm which is called Time Spectral method uses a Fourier representation in time and hence solve for the periodic state directly without resolving transients (which consume most of the resources in a time-accurate scheme). In contrast to the conventional Fourier-Based techniques which solve the governing equations in frequency space, the new algorithms perform all the calculations in time domain, and hence require inimal modifications to an existing solver. The Time Spectral method has been proposed for the fast and efficient computation of periodic unsteady flows. The algorithm has been validated with 2D external aerodynamics test cases. These test cases are NACA 0012 pitching airfoils (CT1 and CT5). The results presented by the Time Spectral method are compared with experimental and NLFD data. It has shown tremendous potential forreducing the computational cost compared to the conventional time-accurate methods, by enforcing periodicity and using Fourier representation in time, leading to spectral accuracy. Results verify the small number of time intervals per pitching cycle required to capture the flow physics.

Keywords:

Time Spectral Method , Time-periodicunsteady flow , Discrete Fourier transform , Pitchingairfoil