The direct numerical simulation of multiphase flow is a challenging research topic with various key applications. In the present work, a computational simulation of multi-phase compressible flow has been proposed for safety analysis of chemical reactors. The main objective of a pressure relief system is to prevent accidents occurring from over pressurisation of the reactor. We are particularly interested in understanding the phenomena associated with emergency pressure relief systems for batch-type reactors and storage vessels. Existence of multiphase flow is significantly influenced by the interface between the phases and the associated discontinuities across the phase. The approach, which builds on the method first introduced by Saurel and Ab-grall, was developed for solving two-phase compressible flow problems. Each phase is separately described by conservation equations. The interactions between two phases appear in the basic equations as transfer terms across the interface. The equations are complemented by state equations for the two phases and by additional correlations for the right-hand side coupling terms. The method is able to deal with multiphase mixtures and interface problems between compressible fluids. The key difference compared to classical two-fluid model is the presence of separate pressures fields associated with phases and introduction of pressure and velocity relaxation procedures. The relaxation operators tackle the boundary conditions at the interface and consequently the model is valid for fluid mixtures, as well as for pure fluids. The numerical technique requires the system to be decomposed and involves a non-conservative hyperbolic solver, an instantaneous pressure relaxation procedure and source term operators. The solution is obtained by succession of integrators using a second-order accurate scheme. The ultimate goal of this research is to use the method for studying the venting problem in reactor systems after verifying its performance on a series of standardised test cases documented in the literature.
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