Finite Analytic Numerical Solution of Unsteady Laminar Flow Past Disc‐Valves

Abstract

The unsteady flow past a disc‐type valve in an axisymmetric tube has been calculated numerically from the governing Navier‐Stokes equations. The flow is assumed to be laminar and incompressible, and the fluid possesses constant properties. Numerical solutions for unsteady flow patterns and pressure drops across the valve are obtained. The finite analytic numerical method is used to solve the Navier‐Stokes equations expressed in terms of pressure and velocities. In the present investigation, the finite analytic solution has been obtained for pulsatile flow past the disc‐type valve at a Reynolds number of 100 based on the tube diameter and the maximum mean velocity during the pulsatile flow. A comparison of the results with that for steady flow at a corresponding Reynolds number showed that, in unsteady flow, larger shear stresses at the edge of the valve ring were observed along with substantial changes in the separation characteristics downstream to the valve. The applicability of the results to delineate the effect of flow past valve prosthesis in vivo is briefly discussed.