A momentum-variable calculation procedure for solving flow at all speeds

Abstract

The main purpose of this PhD research is to develop a numerical method for solving flow at all speeds using momentum component variables instead of the regular velocity ones. The different nature of compressible and incompressible governing equations of fluid flow generally classify the solution techniques into two main categories of compressible and incompressible methods. However, one extended purpose of this research is to develop an approach which permits incompressible methods to be extended to compressible ones using the analogy of flow equations. The proposed momentum component variables play a significant role for transferring the individual characteristics of the two formulations to each other in their adapted forms. In this regard, the two-dimensional Navier-Stokes equations are treated to solve time-dependent laminar flows from very low speeds, i.e. real incompressible flow, to supersonic flow. The approach is fully implicit and employs a control-volume-based finite-element method with momentum components, pressure, and temperature as dependent variables. The proper definitions for considering the dual role of momentum components at control surfaces plus the strong connective expressions between the variables on control volume surfaces and the main nodal values remove the possibility of velocity-pressure decoupling and allow the use of a colocated grid arrangement.

The performance of this ne w formulation is illustrated by solving different types of flow including incompressible and compressible (subsonic to supersonic), viscid and inviscid, and steady and unsteady options. No CFL number limit was encountered for the test models except in supersonic cases. The results demonstrate excellent performance of the flow analogy.