Steady and Unsteady Three-Dimensional Flows in Confined Configurations With Constant and Variable Inflow Velocity

This paper presents a three-dimensional analysis of the unsteady confined viscous flows generated by the variations in time of the inflow velocities (fluctuations) which often are present during the operation cycle of various engineering systems, and have to be taken into account in the study of flow-induced vibration and instability of these systems. Time-accurate solutions of the Navier-Stokes equations for these unsteady flows are obtained with a numerical method developed by the authors, which is second-order accurate in space and time and is based on a finite difference formulation on a stretched staggered grid and uses artificial compressibility. A factored alternate direction implicit (ADI) scheme and a special decoupling procedure, based on the utilization of the continuity equation, are used to substantially enhance the computational efficiency of the method by reducing the problem to the solution of scalar tridiagonal systems of equations. This method is applied to obtain solutions for the benchmark unsteady confined flow past a downstream-facing step, generated by the harmonic variations in time of the inflow velocity. The formation of the flow separation regions is thoroughly analyzed in the paper, including the influence on the flow separations of the Reynolds number, and of the oscillation frequency and amplitude of the inflow velocity variations.