Numerical simulation methods for phase-transitional flow

Abstract

The object of the present dissertation is a numerical study of multiphase flow of one fluid component. In particular, the research described in this thesis focuses on the development of numerical methods that are based on a diffuse-interface model (DIM). With this approach, the modeling problem posed by the presence of moving boundaries in the flow domain, namely the interfaces between different phases, can be solved in a way that preserves the characteristic physical features related to the interfaces, such as surface tension and phase transitions. The first, largest part of the dissertation describes how to apply the DIM formulation that has been adopted, commonly identified as Korteweg formulation, in numerical simulations, without altering the physical parameters of the fluid. The issues of stability and accuracy of the solution, which can be severely compromised by the elliptical and dispersive nature of the set of governing equations, are extensively discussed. Therefore, before discretizing the governing equations a transformation of variables is performed, which removes the most important dispersive terms and greatly increases the stability of the numerical method. The latter is tested on several benchmark two-phase flow problems and for various grid refinements, when a Van der Waals equation of state is used and the temperature is in the vicinity of the critical value. To study the behavior of the flow when the temperature and the velocity fields are coupled, not only isothermal but also non-isothermal simulations are performed and analyzed. This includes a phasetransitional flow where the initial temperature field is such that latent heat plays a major role. Next, the feasibility of a combination of the DIM formulation with Large Eddy Simulation (LES) for turbulent multiphase flow, which is typical in several industrial applications, is explored and tested on one of the isothermal flow simulations. First the various subgrid terms resulting from filtering the governing equations are assessed in an a priori analysis, and different models for the most important subgrid terms are evaluated. Subsequently, a real LES is performed with the best subgrid model based on this analysis and its results are compared with filtered results from a direct numerical simulation. The research carried out for DIM and DIM-LES simulations is intended as the first step towards the development of models for interface mass and heat transfer that can be applied in commercial flow solvers for turbulent phase-transitional flow on industrial problems. Therefore, this research represents an ideal bridge towards the last part of the dissertation, in which a CFD (Computational Fluid Dynamics) model is developed and tested for an industrial application of turbulent phase-transitional flow: the direct-contact condensation of superheated steam injected in water. This model is implemented in the commercial CFD software package ANSYS Fluent. The purpose of this work is twofold. On the one hand, a condensation model for the mass transfer rate at the steam–water interface, based on kinetic gas theory, is tested by comparison of the results with experiments conducted at the Department of Mechanical Engineering of TU/e within the scope of the same research project. By testing the phase change model, useful information can be obtained on the grid requirements and the turbulence model. On the other hand, comparison with experiments, also conducted at TU/e, can be made for the case of steam injected in a fully developed turbulent cross-flow of water in a square duct. To this purpose, results are shown for a three-dimensional simulation performed for the assigned geometry of the experimental setup and for one set of operating conditions used in the experiments. All simulations performed with Fluent are based on a Volume-of-Fluid (VOF) multiphase formulation and on the Reynolds-averaged Navier-Stokes (RANS) equations approach for turbulent flow. Both are typically adopted in the industrial two-phase flow CFD.