Physical and mathematical problems of 1D modelling of transonic two-phase flow in a convergent-divergent nozzle

This work addresses the challenges associated with one-dimensional modelling of steady transonic two-phase flows illustrated through simulations of selected flow cases of the famous Moby Dick experiment. It primarily concentrates on the method for a fast determination of the transonic trajectory. The second proposed approach allows for determining trajectories describing the transonic flow with a normal shock wave. The first method is successfully verified by comparing its results with simulation results obtained from the (widely known and thoroughly verified) Wavefront Algorithm for High-speed Aerodynamics code, utilizing the Delayed Equilibrium Model. The first method mentioned is the author's proposition that is competitive to conven-tional (time-expensive) approaches such as the Newton Critical Point or achieving a steady flow description by asymptotical convergence of the time-dependent model's solutions, and it is a completely new consistent solution method. The second pro-posed method is an adaptation of the Rankine–Hugoniot jump conditions to a two-phase flow described by the Delayed Equi-librium Model. In the case of this method, the presented here analysis and results serve only as a proof of concept. Similar methods have been described before, but the results presented in this article, obtained with the Delayed Equilibrium Model, are unique. Also, a limited but coherent model of thermodynamic properties of a superheated liquid is presented and physically justified. This model was formulated earlier and is often used, but its comprehensive derivation has not been presented before.