Correct numerical simulation of a two-phase coolant

Resumo

Different models used in calculating flows of a two-phase coolant are analyzed. A system of differential equations describing the flow is presented; the hyperbolicity and stability of stationary solutions of the system is studied. The correctness of the Cauchy problem is considered. The models’ ability to describe the following flows is analyzed: stable bubble and gas-droplet flows; stable flow with a level such that the bubble and gas-droplet flows are observed under and above it, respectively; and propagation of a perturbation of the phase concentration for the bubble and gas-droplet media. The solution of the problem about the breakdown of an arbitrary discontinuity has been constructed. Characteristic times of the development of an instability at different parameters of the flow are presented. Conditions at which the instability does not make it possible to perform the calculation are determined. The Riemann invariants for the nonlinear problem under consideration have been constructed. Numerical calculations have been performed for different conditions. The influence of viscosity on the structure of the discontinuity front is studied. Advantages of divergent equations are demonstrated. It is proven that a model used in almost all known investigating thermohydraulic programs, both in Russia and abroad, has significant disadvantages; in particular, it can lead to unstable solutions, which makes it necessary to introduce smoothing mechanisms and a very small step for describing regimes with a level. This does not allow one to use efficient numerical schemes for calculating the flow of two-phase currents. A possible model free from the abovementioned disadvantages is proposed.