The character of two-phase gas/particulate flow equations

• Published in: Applied mathematical modelling Vol. 17; no. 7; pp. 338 - 354
• Main Author: Fitt, A.D.
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 1993; Elsevier Science
• Subjects: Computational methods in fluid dynamics; Exact sciences and technology; flow modelling; Fluid dynamics; Fundamental areas of phenomenology (including applications); gas/particulate flow; hyperbolicity maps; ill-posedness; Multiphase and particle-laden flows; Nonhomogeneous flows; nonhyperbolicity; Physics; two-phase flow; gas/particulate flow; nonhyperbolicity; hyperbolicity maps; flow modelling; ill-posedness; two-phase flow; Gas particle flow; Averaging method; Two-phase flow; Hyperbolic equation; Ill posed problem; Particle suspension; Modeling
• ISSN: 0307-904X
• DOI: 10.1016/0307-904X(93)90059-P

In classical (single-phase) fluid mechanics, it is a matter of experience that, away from flow boundaries, inviscid models often give excellent results. For time-dependent two-phase flows, an attractive possibility is to likewise ignore viscosity in the “mainstream” flow. However, such equations are generally not hyperbolic, and possess complex eigenvalues. This creates severe technical difficulties as the initial value problem is then ill-posed, and serious numerical problems that may 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. Complex characteristics arise as a result of multiphase flow averaging, and the consequent omission of important physical terms. With care, however, these effects may be reintroduced into the equations. Using such an approach, the specific case of gas/particulate two-phase flow is considered. The aim is not to propose a definitive, demonstrably “correct” system of equations for unsteady two-phase gas/ particulate flow; the assumptions made are too general and specific cases must be treated on their individual merits. Rather a methodology of analysis is illustrated and qualitative results concerning the nature of added terms in the equations are obtained. The effect of each term and also of combinations of terms is studied, and general conclusions are drawn concerning the hyperbolicity of the equations.