Compressible flows with pressure-dependent viscosity and slip through local constrictions

Speaker: Katrin Rohlf (Ryerson)

Abstract: Understanding the properties of flows through local constrictions is important for assessing potential vessel rupture in blood flow through constricted/stenosed arteries, and for assessing the flow properties in nanochannels just to name a few examples. The relatively recent use of particle-based methods for flow applications in both areas, especially for flows through constricted cylinders, has shown that the built-in compressibility of the particle-based method may be more pronounced in such geometries than expected. In order to quantify the compressibility, an approximate analytical velocity profile, as well as centerline pressure/density curves, are derived theoretically from the compressible Navier-Stokes equation with variable viscosity. The method uses the Karman-Pohlhausen approximation technique, which leads to an ODE for the pressure gradient that is solved numerically with Maple/Matlab to obtain the theoretical predictions. Analytical predictions will be used to demonstrate changes as a result of compressibility, slip and pressure-dependent viscosity parameter, and then compared to the velocity/pressure/density curves from particle-based flow simulations.