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Simulation of Multiphase Flows with Strong Shocks and Density Variations
Author(s) -
Nowakowski Andrzej F.,
Jolgam Shaban A.,
Ballil Ahmed R.,
Nicolleau Franck C.G.A.
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110379
Subject(s) - benchmark (surveying) , euler equations , eulerian path , shock (circulatory) , conservation of mass , multiphase flow , compressible flow , momentum (technical analysis) , mechanics , flow (mathematics) , shock wave , mathematics , compressibility , component (thermodynamics) , computer science , physics , mathematical analysis , lagrangian , geology , medicine , geodesy , finance , economics , thermodynamics
Abstract The system of extended Euler type hyperbolic equations is considered to describe a two‐phase compressible flow. A numerical scheme for computing multi‐component flows is then examined. The numerical approach is based on the mathematical model that considers interfaces between fluids as numerically diffused zones. The hyperbolic problem is tackled using a high resolution HLLC scheme on a fixed Eulerian mesh. The global set of conservative equations (mass, momentum and energy) for each phase is closed with a general two parameters equation of state for each constituent. The performance of various variants of a diffuse interface method is carefully verified against a comprehensive suite of numerical benchmark test cases in one and two space dimensions. The studied benchmark cases are divided into two categories: idealized tests for which exact solutions can be generated and tests for which the equivalent numerical results could be obtained using different approaches. The ability to simulate the Richtmyer‐Meshkov instabilities, which are generated when a shock wave impacts an interface between two different fluids, is considered as a major challenge for the present numerical techniques. The study presents the effect of density ratio of constituent fluids on the resolution of an interface and the ability to simulate Richtmyer‐Meshkov instabilities by various variants of diffuse interface methods. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)