Last modified: 2018-08-09

#### Abstract

Due to recent advances in computing technologies, numerical modelling of thermal-hydraulic two-phase flows is becoming increasingly important in the computational sciences and engineering fields, to the point where these flows frequently approximated by a variety of computer algorithms. These approximations are due to certain advantages that are associated with numerical modelling. Numerical two-phase flow modelling is often much less expensive than mathematical models since they require no detailed physical stabilization and can be easily adapted to accommodate flow properties of interest. Further, all the required tools for simulations is the computer machine and software or numerical methods and many researchers know how to interpret the results. Although many numerical thermal-hydraulic two-phase flow models exist, there is always a level of difficulty associated with non-equilibrium behavior between phases leading mathematical and physical restrictions within the results. This work present some numerical results of an ongoing project that cover a wide range of fundamental investigations related to thermal-hydraulic two-phase flows of nuclear power plants. Fluid flows of such plants are commonly investigated by separated two-phase flow equations. However, these flows can also be studied by means two-phase mixture flows. A mathematical model for gas and liquid flows is presented in which mixture formulations are incorporated. This model enables the non-equilibrium phenomena between the two-phase flows and allow consideration of phase transients. Further, it provides the capability to explicitly investigate the relative motion between different phases by a balance equation rather than a source term appearing in the momentum equations of the individual phases. The governing equations, therefore, include a mixture mass, mixture momentum and mixture energy, and another set of equations represents the volume fraction and mass fraction for the gas phase and the relative velocity between the gas and liquid phases. In these equations, the conservative nature feature the resulting mathematical model among currently used two-phase fluid flow models. The equations also are fully hyperbolic without any physical stabilization and enables the use of any numerical method of interest. The model is numerically solved on the basis of the Riemann problem using Godunov methods of centred type. This solution becomes appropriate since it leads to making the relative velocity visible which is an advanced computational feature for thermal-hydraulic two-phase flows. The model provides successful results at high phase velocities with low and high void fractions. It is found that the inclusion of the relative velocity balance equation into the two-phase flow mixture equation produce physically realistic solutions for strong relative motion between the liquid and gas phases. Results are compared with other available numerical methods producing accurate, efficient and free from numerical dissipation and dispersion computations. Simulation and test results show that the model equations can effectively simulate non-equilibrium thermal-hydraulic two-phase flows, which may broaden the possible application areas of mixture formulations of two-phase flows such as Pressurized water reactor (PWR) and Light water reactor (LWR).