Numerical simulation of incompressible and compressible flow
This thesis describes the development of a numerical solution procedure which is valid for both incompressible flow and compressible flow at any Mach number. Most of the available numerical methods are for incompressible flow or compressible flow only and density is usually chosen as a main dependent variable by almost all the methods developed for compressible flow. This practice limits the range of the applicability of these methods since density changes can be very small when Mach number is low. Even for high Mach number flows the existing time-dependent methods may be inefficient and costly when only the finial steady-state is of concern. The presently developed numerical solution procedure, which is based on the SIMPLE algorithm, solves the steady-state form of the Navier-stokes equations, and pressure is chosen as a main dependent variable since the pressure changes are always relatively larger than the density changes. This choice makes it possible that the same set of variables can be used for both incompressible and compressible flows. It is believed that Reynolds stress models would give better performance in some cases such as recirculating flow, highly swirling flow and so on where the widely used two equation k-e model performs poorly. Hence, a comparative study of a Reynolds stress model and the k-e model has been undertaken to assess their performance in the case of highly swirling flows in vortex throttles. At the same time the relative performance of different wall treatments is also presented. It is generally accepted that no boundary conditions should be specified at the outflow boundary when the outflow is supersonic, and all the variables can be obtained by extrapolation. However, it has been found that this established principle on the outflow boundary conditions is misleading, and at least one variable should be specified at the outflow boundary. It is also shown that the central differencing scheme should be used for the pressure gradient no matter whether it is subsonic or supersonic flow.