In preparation of the study of liquefied natural gas (LNG) sloshing in ships and vehicles, we model and numerically analyze compressible two-fluid flow. We consider a five-equation two-fluid flow model, assuming velocity and pressure continuity across two-fluid interfaces, with a separate equation to track the interfaces. The system of partial differential equations is hyperbolic and quasi-conservative. It is discretized in space with a tailor-made third-order accurate finite-volume method, employing an HLLC approximate Riemann solver. The third-order accuracy is obtained through spatial reconstruction with a limiter function, for which a novel formulation is presented. The non-homogeneous term is handled in a way consistent with the HLLC treatment of the convection operator. We study the one-dimensional case of a liquid column impacting onto a gas pocket entrapped at a solid wall. It mimics the impact of a breaking wave in an LNG containment system, where a gas pocket is entrapped at the tank wall below the wave crest. Furthermore, the impact of a shock wave on a gas bubble containing the heavy gas R22, immersed in air, is simulated in two dimensions and compared with experimental results. The numerical scheme is shown to be higher-order accurate in space and capable of capturing the important characteristics of compressible two-fluid flow.

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Computers & Fluids
Sloshing of Liquefied Natural Gas: subproject Variability (14-10-project2)
Scientific Computing

De Böck, R., Tijsseling, A. S., & Koren, B. (2019). A monotonicity-preserving higher-order accurate finite-volume method for Kapila's two-fluid flow model. Computers & Fluids, 193, 104272:1–104272:16. doi:10.1016/j.compfluid.2019.104272