Numerical study of wave propagation in compressible two-phase flow

• Published in: International journal for numerical methods in fluids Vol. 54; no. 4; pp. 393 - 417
• Main Authors: Zeidan, D., Romenski, E., Slaouti, A., Toro, E. F.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 10.06.2007; Wiley
• Subjects: Compressible flows; shock and detonation phenomena; compressible two-phase flow; Computational methods in fluid dynamics; Exact sciences and technology; extended thermodynamics; Fluid dynamics; Fundamental areas of phenomenology (including applications); hyperbolic conservative two-fluid model; Multiphase and particle-laden flows; Nonhomogeneous flows; Physics; Shock-wave interactions and shock effects; TVD centred schemes; Gas liquid interface; Compressible fluid; Riemann problem; Digital simulation; Air water interface; hyperbolic conservative two-fluid model; compressible two-phase flow; Shock waves; Thermodynamics; Pressure wave; Wave propagation; Two-phase flow; extended thermodynamics; Modelling; TVD centred schemes; Heat transfer
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.1404

We propose a new model and a solution method for two‐phase two‐fluid compressible flows. The model involves six equations obtained from conservation principles applied to a one‐dimensional flow of gas and liquid mixture completed by additional closure governing equations. The model is valid for pure fluids as well as for fluid mixtures. The system of partial differential equations with source terms is hyperbolic and has conservative form. Hyperbolicity is obtained using the principles of extended thermodynamics. Features of the model include the existence of real eigenvalues and a complete set of independent eigenvectors. Its numerical solution poses several difficulties. The model possesses a large number of acoustic and convective waves and it is not easy to upwind all of these accurately and simply. In this paper we use relatively modern shock‐capturing methods of a centred‐type such as the total variation diminishing (TVD) slope limiter centre (SLIC) scheme which solve these problems in a simple way and with good accuracy. Several numerical test problems are displayed in order to highlight the efficiency of the study we propose. The scheme provides reliable results, is able to compute strong shock waves and deals with complex equations of state. Copyright © 2006 John Wiley & Sons, Ltd.