Unconditionally Energy Stable Linear Schemes for a Two-Phase Diffuse Interface Model with Peng-Robinson Equation of State

Many problems in the fields of science and engineering, particularly in materials science and fluid dynamic, involve flows with multiple phases and components. From mathematical modeling point of view, it is a challenge to perform numerical simulations of multiphase flows and study interfaces between phases, due to the topological changes, inherent nonlinearities and complexities of dealing with moving interfaces. In this work, we investigate numerical solutions of a diffuse interface model with Peng-Robinson equation of state. Based on the invariant energy quadratization approach, we develop first and second order time stepping schemes to solve the liquid-gas diffuse interface problems for both pure substances and their mixtures. The resulting temporal semi-discretizations from both schemes lead to linear systems that are symmetric and positive definite at each time step, therefore they can be numerically solved by many efficient linear solvers. The unconditional energy stabilities in the discrete sense are rigorously proven, and various numerical simulations in two and three dimensional spaces are presented to validate the accuracies and stabilities of the proposed linear schemes

Studying of the fluid's property adjustment and its application in metal foam industry

The main aim of this study is to find criteria influencing the shapes of a gas bubbles rising in stagnant liquid experimentally to form foam. A testing facility with the high-speed camera was designed. The results obtained are presented in terms of dimensionless parameters i.e. Reynolds's, Morton's and Eötvös. Factors varied to test their dependency such as nozzle diameter (3 - 5 mm), rate of flow rate (15 and 130 l/h), viscosity, surface tension and density were changed in order to see their effect on the shape of the bubble, its velocity in the liquid, surface tension force, drag force and buoyancy force. In order to vary such parameters a water-ethanol mixture was used in the tank. Also the foam formed was examined using water ethanol mixture in predicting the Foam bubble behavior in multi-phase flow. The study compares the concept of formation of foam at the surface of the mixture with the procedure of producing aluminum foam by direct gas injection. Material properties such as kinematic viscosity, density and surface tension on the foaming process will be studied experimentally, while the foam bubble size will be studied by means of digital image processing.The main aim of this study is to find criteria influencing the shapes of a gas bubbles rising in stagnant liquid experimentally to form foam. A testing facility with the high-speed camera was designed. The results obtained are presented in terms of dimensionless parameters i.e. Reynolds's, Morton's and Eötvös. Factors varied to test their dependency such as nozzle diameter (3 - 5 mm), rate of flow rate (15 and 130 l/h), viscosity, surface tension and density were changed in order to see their effect on the shape of the bubble, its velocity in the liquid, surface tension force, drag force and buoyancy force. In order to vary such parameters a water-ethanol mixture was used in the tank. Also the foam formed was examined using water ethanol mixture in predicting the Foam bubble behavior in multi-phase flow. The study compares the concept of formation of foam at the surface of the mixture with the procedure of producing aluminum foam by direct gas injection. Material properties such as kinematic viscosity, density and surface tension on the foaming process will be studied experimentally, while the foam bubble size will be studied by means of digital image processing.

A componentwise convex splitting scheme for diffuse interface models with Van der Waals and Peng Robinson equations of state

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