Модель вскипающей жидкости

Abstract

Представлена модель вскипающей жидкости, построенная на базе ранее предложенной автором обобщенно-равновесной модели смеси. В модели учтена сжимаемость жидкой фракции. Проведен характеристический анализ уравнений модели и показана их гиперболичность. Приведены расчетные формулы узлового метода характеристик, с использованием которого рассчитано течение при распаде произвольного разрыва во вскипающей жидкости. A model of a boiling liquid is presented, built on the basis of a one-speed two-temperature mixture model previously proposed by the author, in which the forces of interfractional interaction are taken into account. The liquid fraction was considered compressible. A characteristic analysis of the equations of the model is carried out and their hyperbolicity is shown. Relations for characteristic directions and differential relations along these lines are written. An analytical formula for calculating the speed of sound in a boiling liquid is obtained. It is noted that the speed of sound in a liquid when taking into account phase transformations is somewhat lower than is predicted by the Wood formula. The calculation formulas of the iterative algorithm of the nodal method of characteristics are presented, which implies that the flow is calculated during the decay of an arbitrary rupture in a boiling liquid. In the calculations, it was assumed that the phase transition during the boiling process occurs under conditions of an overheated state, when the temperature of the liquid exceeds the saturation temperature. It is shown that taking phase transformation into account leads to a significant increase in the vapor concentration in the unloading wave, as well as to a small increase in both the speed of the mixture and pressure. The concentration of the vapor fraction behind the shock front decreases.