Numerical Modeling of Unsteady, Separated Viscous Flow

Abstract

Numerical solutions of the equations governing the laminar flow of an incompressible fluid through a two-dimensional sudden expansion are discussed. The fluid motion is started impulsively from rest and is examined in detail during the transient phase to the steady-state condition. Solutions are obtained by two independent finite-difference methods which are discussed. The development of the flow in the zone of separation is investigated, and, during the earliest phases of motion, the generation of vorticity at the solid boundaries and its spatial diffusion is studied in the region of uniform flow. The numerical treatment of the boundary conditions is discussed. Characteristics of the transient solution for two different Reynolds numbers in the laminar range are presented. Included with the results is the temporal development of the streamline dividing the zone of separation from the main flow.