The paper investigates shock-induced vortical flows within inhomogeneous media of nonuniform thermodynamic properties. Numerical simulations are performed using a Eulerian type mathematical model for compressible multicomponent flow problems. The model, which accounts for pressure nonequilibrium and applies different equations of state for individual flow components, shows excellent capabilities for the resolution of interfaces separating compressible fluids as well as for capturing the baroclinic source of vorticity generation. The developed finite volume Godunov type computational approach is equipped with an approximate Riemann solver for calculating fluxes and handles numerically diffused zones at flow component interfaces. The computations are performed for various initial conditions and are compared with available experimental data. The initial conditions promoting a shock-bubble interaction process include weak to high planar shock waves with a Mach number ranging from 1.2 to 3 and isolated cylindrical bubble inhomogeneities of helium, argon, nitrogen, krypton, and sulphur hexafluoride. The numerical results reveal the characteristic features of the evolving flow topology. The impulsively generated flow perturbations are dominated by the reflection and refraction of the shock, the compression, and acceleration as well as the vorticity generation within the medium. The study is further extended to investigate the influence of the ratio of the heat capacities on the interface deformation.
The simulation of multiphase compressible flows through high pressure nozzles is presented. The study uses the developed numerical approach. There are many important engineering applications which are concerned with multiphase flows and convergent-divergent nozzles. This work presents the developed extension of the model and numerical algorithm based on the so called parent model earlier introduced by Saurel and Abgrall [Saurel, R. and Abgrall, R., A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows, J. Comput. Phys. 150 (1999), 425–467]. This model which consists of conservation laws for each phase complemented with the volume fraction evolution equation is modified by adding a source term to simulate area variation. The model is strictly hyperbolic and non-conservative due to the existence of non-conservative terms. The model is able to deal with compressible and incompressible flows. Moreover, it can deal with mixtures and pure fluids, where each fluid has its own pressure and velocity. The presence of velocity and pressure relaxation terms in the governing equations has made the velocity and pressure relaxation processes essential to tackle the boundary conditions at the interface. The interface separating phases is considered as a numerical diffusion zone in this method. The model is solved using an efficient Eulerian numerical method. A second order Godunov-type scheme with approximate Riemann solver is used to enable capturing of a physical interface by the resolution of the Riemann problem. The solution is obtained by splitting the hyperbolic part and source terms parts in the numerical algorithm. The source terms, including relaxation parts of the model, are tackled in succession using Strang splitting technique. The governing equations are solved at each computational cell using the same numerical algorithm for the whole domain including the interface. The main aim of this work has been to study different flow regimes with respect to pressure boundary conditions through the numerical solutions of single and multiphase flows. The performance of the programme has been verified via well established benchmark test problems for multiphase flows.
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.
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