Numerical investigation of metastable condensing flows with an implicit upwind method

This work proposes and assesses two numerical models for solving high-speed condensing flows in metastable conditions. Each model involves a set of governing equations (mass, momentum, and energy) for the mixture or the continuum phase, i.e. the vapor, and two additional transport equations to characterize the dispersed phase. Such relations are formulated through the so-called method of moments that allows to represent the wetness fraction and the number of droplets of the liquid. The transport relations are discretized in space by means of a new coupled up-wind scheme. A segregated implicit time integration strategy is exploited to hasten the convergence of the full system to steady-state. The performance and accuracy of both models are thoroughly investigated on a reference quasi-1D problem and confronted against experimental data and more advanced two-phase flow models. Results show that experimental observations are adequately predicted, especially concerning the droplets dimension. It is additionally inferred that the new upwind flux is beneficial to improve robustness of the underlying numerical methods. Finally, it is demonstrated that the continuum phase model outperforms the mixture one in terms of numerical stability and computational cost, thereby making it very promising for the extension to multi-dimensional problems.