Numerical Simulation of Steady and Unsteady Compressible Multiphase Flows

Abstract

The present work concerns the development of an advanced numerical approach to simulate steady and unsteady compressible multiphase flows in the CFD solver FLUENT. Compressible multiphase flows can be simulated under the framework of either the multiphase Mixture/VOF or the Eulerian multifluid model. The governing equations solved are the mixture (Mixture or VOF model) or phase (Eulerian multifluid model) momentum, energy, species transport equations and phase volume fraction equations. Turbulence effects are accounted for using a range of multiphase turbulence models. For the compressible multiphase model, it assumes that only one phase is a compressible gas/gaseous mixture with multiple species. In gas-liquid flows, all the liquid phases can be compressible /incompressible liquid, while in gas-solid flows the solid phase can be treated as a granular flow. To ensure numerical stability and obtain physical solutions, the absolute pressure is limited in a way to satisfy the constraints for both incompressible and compressible flows that may exist in different regions. The compressible effects are taken into account by adding extra terms related to sound speed and phase volume fractions in both the phase volume fraction and the pressure-correction equations. For flow conditions at inlets and exits, only pressure and mass-flow-rate boundaries are applicable. The mixture Mach numbers are defined and used to determine the subsonic or supersonic flows and thermal boundary conditions. The compressible multiphase model have been successfully used to simulate steady and unsteady, sub- and super-sonic compressible multiphase flows in a wide range of 2D and 3D multiphase systems. The examples presented in the paper include: (1). Gas-liquid separation in a vertical cylindrical container; (2). Transient pressure variations in compressible liquid and gas-liquid flows of water hammers; (3). Sub- and super-sonic gas-liquid two-phase flows in a nozzle; (4). Cavitating and ventilated super-cavitating flows; and (5). 3D gas-liquid flows in a three-stream injector. The solver robustness and convergence performance will be discussed. The solutions will be compared with available experimental data or numerical solutions. Emphasis will be focused on the solver performances on simulations of compressible multiphase flows. Overall, the results obtained from the present compressible multiphase model are in line with analytical/CFD solutions or available experimental data. The numerical approach is reasonably fast and robust, and suitable for practical compressible multiphase applications.