A novel five-equation model for inviscid, non-heat-conducting, compressible two-fluid flow is derived, together with an appropriate numerical method. The model uses flow equations based on conservation laws and exchange laws only. The two fluids exchange momentum and energy, for which source terms are derived from fundamental physical laws. The Riemann invariants of the governing equations are derived, and used in the construction of an Osher-type approximate Riemann solver. A consistent finite-volume discretization of the source terms is proposed. The source terms have distinct contributions in the cell domain and at the cell faces. For the source-term evaluation at the cell faces, the Riemann solver is elegantly exploited. Numerical results are presented for shock-tube and shock-bubble-interaction problems. The resemblance with experimental results is very good. Free-surface pressure oscillations do not occur, without any precaution. The paper contributes to state of the art in computing two-fluid flows.
Additional Metadata
Keywords compressible two-fluid flow, source terms, momentum and energy exchange, interface capturing, approximate Riemann solver, shock tube, shock-bubble interaction
MSC Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (msc 65M60), Gas dynamics, general (msc 76N15), Liquid-gas two-phase flows, bubbly flows (msc 76T10)
THEME Life Sciences (theme 5), Energy (theme 4)
Publisher CWI
Series Modelling, Analysis and Simulation [MAS]
Citation
Kreeft, J.J, & Koren, B. (2009). A physical five-equation model for compressible two-fluid flow, and its numerical treatment. Modelling, Analysis and Simulation [MAS]. CWI.