PRESSURE-BASED ALGORITHMS FOR MULTIFLUID FLOW AT ALL SPEEDS—PART I: MASS CONSERVATION FORMULATION

Abstract

In this article, seven segregated single-fluid, pressure-based algorithms are extended to predict multifluid flow at all speeds. The extended algorithms form part of the mass conservation-based algorithms (MCBA) group, in which the pressure-correction equation is derived from overall mass conservation. The performance and accuracy of these algorithms are assessed by solving a variety of two-dimensional two-phase flow problems in the subsonic, transsonic, and supersonic regimes. Solutions are generated for several grid densities using the single-grid (SG), the prolongation-grid (PG), and the full nonlinear multigrid (FMG) methods, and their effects on convergence behavior are studied. The main outcomes of this study are clear demonstrations of: (1) the capability of all MCBA algorithms to deal with multifluid flow situations; (2) the ability of the FMG method to tackle the added nonlinearity of multifluid flows; (3) and the capacity of the MCBA algorithms to predict multifluid flow at all speeds. Moreover, results indicate that the performances of SIMPLE, SIMPLEC, and SIMPLEX are very close. The PRIME algorithm is the most expensive, due to the explicit treatment of the fluidic momentum equations. The PISO algorithm is generally more expensive than SIMPLE. In terms of CPU effort, SIMPLEM stands between PRIME and SIMPLE. For all algorithms, use of the PG and FMG methods speeds up acceleration, with the FMG method being more efficient at accelerating the convergence rate, for the problems solved on the densest grid used, over the SG method, by a factor reaching a value as high as 6.55.