Time Spectral Method for Unsteady Three-Dimensional Confined Viscous Flows with Variable Inflow Velocity at Low Reynolds Numbers

摘要

This paper presents a time spectral method for the analysis of the unsteady three-dimensional confined viscous flows generated by the variation in time of the inflow velocities at low Reynolds numbers, which are present in many engineering systems. In this time spectral method developed for incompressible flows, the authors use truncated Fourier series expansions for the non-dimensional fluid velocity components and pressure and reduce the solution of the unsteady Navier-Stokes equations to the solution of several steady harmonic flow components problems which arc solved sequentially. The Navier-Stokes and continuity equations obtained are complex and each of them represents two equations corresponding to the real and imaginary parts. A special decoupling procedure based on the utilization of the continuity equation is used in conjunction with a factored alternative direction implicit (ADI) scheme to reduce the problem to the solution of scalar tridiagonal system of equations. The method is successfully validated by comparison with experimental results and numerical solutions obtained using time accurate techniques for the same dimensions of the duct. The time spectral method is applied to obtain solutions for the benchmark unsteady confined flows past a downstream facing-step, generated by the variation in time of the inflow velocity during the operation cycle, which may substantially affect the flow-induced vibrations and instabilities of the engineering systems. The influence of the inflow velocity amplitudes, the oscillation frequencies, the Reynolds numbers, and the duct aspect ratio on the formation of the flow separation regions are completely analyzed in this paper.