Prediciton of Dynamic Stability using Mapped Chebyshev Pseudospectral Method

摘要

Conventional time-marching approach is one of the most popular techniques to compute unsteady flow solutions. An application of the technique can be extended to stability analysis of aircraft, and this can be achieved by calculation of unsteady dynamic derivatives which produce quantitative information of a correlation between aircraft flight dynamics and aerodynamic coefficients. However, time-marching method can be very expensive to compute all transient flow solutions with a small physical time step. On the other hand, time-spectral approach was developed as an efficient method as it replaces a time-derivative term of governing equations by a spectral derivative operator to improve the solution efficiency. Recently, a mapped Chebyshev pseudospectral method is developed, which utilizes Chebyshev polynomials to compute unsteady flow solutions. In this paper, the mapped Chebyshev pseudospectral method is employed to approximate the solutions of the time-dependent flow past two- and three-dimensional bodies and perform stability analysis. Unsteady dynamic derivatives of bodies under a forced harmonic oscillation are calculated based on unsteady flow solutions from time-marching and time-spectral methods including the harmonic balance method and the mapped Chebyshev pesudospectral method. The unsteady flow solutions are compared with experimental data to validate the accuracy of the mapped Chebyshev pseudospectral method.