THE CHARACTER OF 2-PHASE GAS PARTICULATE FLOW EQUATIONS

In classical (single-phase)fluid mechanics, it is a matter of experien ce that, away from flow boundaries, inviscid models often give excelle nt results. For lime-dependent two-phase flows, an attractive possibil ity is to likewise ignore viscosity in the ''mainstream '' flow. Howev er, such equations are generally not hyperbolic, and possess complex e igenvalues. This creates severe technical difficulties as the initial value problem is then ill-posed, and serious numerical problems that m ay render accurate computation impossible. This ill-posedness has been the subject of heated controversy, but the conclusion is clear: Doubt remains over the correct equations even for simple two-phase flows. C omplex characteristics arise as a result of multiphase flow averaging, and the consequent omission of important physical terms. With care, h owever, these effects may be reintroduced into the equations. Using su ch an approach, the specific case of gas/particulate two-phase flow is considered. The aim is not to propose a definitive, demonstrably ''co rrect'' system of equations for unsteady two-phase gas/particulate flo w; the assumptions made are too general and specific cases must be tre ated on their individual merits. Rather a methodology of analysis is i llustrated and qualitative results concerning the nature of added term s in the equations are obtained. The effect of each term and also of c ombinations of terms is studied, and general conclusions are drawn con cerning the hyperbolicity of the equations.