PRESSURE-BASED ALGORITHMS FOR MULTIFLUID FLOW AT ALL SPEEDS—PART II: GEOMETRIC CONSERVATION FORMULATION

Abstract

This work is concerned with the implementation and testing, within a structured collocated finite-volume framework, of seven segregated algorithms for the prediction of multiphase flow at all speeds. These algorithms belong to the geometric conservation-based algorithms (GCBA) group, in which the pressure-correction equation is derived from the constraint equation on volume fractions (i.e., the sum of volume fractions equals 1). The pressure-correction schemes in these algorithms are based on SIMPLE, SIMPLEC, SIMPLEX, SIMPLEM, SIMPLEST, PISO, and PRIME. The performance and accuracy of these algorithms are assessed by solving, using the single-grid method (SG), the prolongation-grid method (PG), and the full nonlinear multigrid method (FMG), the following four two-dimensional, two-phase-flow problems: (1) turbulent upward bubbly flow in a pipe, (2) turbulent air–particle flow in a pipe, (3) compressible dusty flow over a flat plate, and (4) transsonic dusty flow in a converging-diverging nozzle. Results are displayed in the form of convergence history plots and tabulated CPU times. The main outcomes of this study are the clear demonstrations of: (1) the capability of all GCBA algorithms to deal with multifluid flow situations; (2) the ability of the FMG method to tackle the added nonlinearity of multifluid flows; and (3) the capacity of the GCBA algorithms to predict multifluid flow at all speeds.