Dynamic Modeling of Phase Crossings in Two-Phase Flow (Communications in Computational Physics, 2012)
Two-phase flow and heat transfer, such as boiling and condensing flows, arecomplicated physical phenomena that generally prohibit an exact solution and evenpose severe challenges for numerical approaches. If numerical solution time is also anissue the challenge increases even further. We present here a numerical implementation and novel study of a fully distributed dynamic one-dimensional model of two-phase flow in a tube, including pressure drop, heat transfer, and variations in tubecross-section. The model is based on a homogeneous formulation of the governingequations, discretized by a high resolution finite difference scheme due to Kurganovand Tadmore.The homogeneous formulation requires a set of thermodynamic relations to cover theentire range from liquid to gas state. This leads a number of numerical challengessince these relations introduce discontinuities in the derivative of the variables and areusually very slow to evaluate. To overcome these challenges, we use an interpolationscheme with local refinement.The simulations show that the method handles crossing of the saturation lines forboth liquid to two-phase and two-phase to gas regions. Furthermore, a novel resultobtained in this work, the method is stable towards dynamic transitions of the inlet/outlet boundaries across the saturation lines. Results for these cases are presentedalong with a numerical demonstration of conservation of mass under dynamicallyvarying boundary conditions. Finally we present results for the stability of the code ina case of a tube with a narrow section.