Mass Conservation Based Algorithms for Multi-Fluid Flow at All Speeds 2 Nomenclature

In this paper seven segregated single-fluid pressure-based algorithms are extended to predict multi-fluid 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, transonic, and supersonic regimes. Solutions are generated for several grid densities using the single grid (SG), the prolongation grid (PG), and the full non-linear multi-grid (FMG) methods and their effects on convergence behavior studied. The main outcomes of this study are the clear demonstrations of: (i) the capability of all MCBA algorithms to deal with multi-fluid flow situations; (ii) the ability of the FMG method to tackle the added non-linearity of multi-fluid flows; (iii) and the capacity of the MCBA algorithms to predict multi-fluid 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, the use of the PG and FMG methods speed-up acceleration with the FMG method being more efficient 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