When simulating multiphase compressible flows using the diffuse-interface methods, the test cases presented in the literature to validate the modellings with regard to interface problems are always textbook cases: interfaces are sharp and the simulations therefore easily converge to the exact solutions. In real problems, it is rather different because the waves encounter moving interfaces which consequently have already undergone the effects of numerical diffusion. Numerical solutions resulting from the interactions of waves with diffused interfaces have never been precisely investigated and for good reasons, the results obtained are extremely dependent on the model used. Precisely, well-posed models present similar and important issues when such an interaction occurs, coming from the appearance of a wave-trapping phenomenon.To circumvent those issues, we propose to use a thermodynamically-consistent pressure-disequilibrium model with finite, instead of infinite, pressure-relaxation rate to overcome the difficulties inherent in the computation of these interactions. Because the original method to solve this model only enables infinite relaxation, we propose a new numerical method allowing infinite as well as finite relaxation rates. Solutions of the new modelling are examined and compared to literature, in particular we propose the study of a shock on a water-air interface, but also for problems of helium-air and water-air shock tubes, spherical and non-spherical bubble collapses.
In this study, cryogenic flows in rocket engine that may undergo a phase change because of a loss of pressure in pump, or any depressurization process are considered. We proposed a well-posed mathematical representation for this kind of flow as well as the numerical model for seeking the solutions. The two important points addressed in this study are: the compressibility of the phases and the use of a rotating reference frame. The compressibility effects are quite essentials to obtain a physical and realistic cavitation model through the equation of state of the fluids (liquid and vapor), while the moving reference frame being the way we chose to model the pump motion. The model we develop is based on conservation equations of mass, momentum and energy for each phase plus a non-conservative equation evolution for the volume fraction. The description of the flow is based on the diffuse interface method: the interfaces appear naturally in the flow (interfaces between vapor and liquid for example) and do not require any interface tracking method. The phase change process is based on a stiff relaxation procedure using thermodynamic equilibrium considerations. Results related to a pump application are then presented using the open-source platform ECOGEN where the present numerical method is implemented. The model is able to produce a quite realistic pump characteristic curve where the relationship between the pump overpressure and its operating mass flow rate is expressed. In these first calculations it will be shown that cavitation may occur in some regions of the flow and that the multiphase approach is suited for this study.
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