Marching approach for channels with lateral inflow and secondary currents

Abstract

Space marching approach has been widely applied for flows with a predominant direction of motion, small secondary currents and no lateral crossflow. These last restrictions cannot be satisfied for some channel flows in rotating machinery. The marching approach presented in this paper considers the three dimensional domain between two successive sections. A typical computation element has one side on the upstream section where the variables are known, and the second side on the downstream section where the variables should be determined. All three velocity components are obtained on the downstream section using penalty formulation of the three-dimensional momentum equations, without any restrictions on the magnitude of the secondary currents and lateral inflow. Finite element method and quadratic/linear 18-node elements (9-node quadratic elements on each upstream-downstream section, linear interpolation between sections) are used. The governing equations are written for single and two phase incompressible mixture flows. The separation velocity between phases is obtained from the dynamic equilibrium of the dispersed phase. The approach is tested for simple curved channel flows and applied to centrifugal pump casings.