Calculation of steam drop mixture flows with boiling explosion mechanism using a multidimensional nodal method of characteristics

A hyperbolic model of a vapor-drop mixture is presented which takes into account the evaporation of drops by highlighting an explosive mechanism. The model is developed on the basis of the generalized-equilibrium model of a mixture previously proposed by the author. In this early model, the equations were hyperbolized by adding interfractional-interaction forces, and the liquid fraction was assumed to be incompressible. In the model proposed here, we assume that the phase transition at intense droplet evaporation occurs in an overheated state, when the fluid temperature exceeds the saturation temperature. A characteristic analysis of the model equations is carried out and their hyperbolicity is shown. An analytical formula is obtained for calculating the speed of sound in a vapor-drop mixture. It is noted that the speed of sound in the mixture in the presence of phase transformations turns out to be somewhat lower than that given by wood's formula. The multidimensional nodal method of characteristics for integrating hyperbolic systems, which is based on splitting the original system of equations into a number of one-dimensional subsystems, is described. Differential relations that hold true along the characteristic directions for each of the subsystems are derived. When calculating one-dimensional problems, an iterative algorithm of the inverse method of characteristics is applied. The computational method has been tested on a number of problems with self-similar solutions. Using the described method of integrating a multidimensional system of equations, the flow of a vapor-droplet flow near the disk was studied. It is shown that, in a number of cases, the explosive boiling of liquid droplets should be taken into account because it can significantly change the pattern of the flow around a disk.