Моделирование развития вихревых структур в сверхзвуковом газовом потоке

Abstract

With the help of mathematical modeling methods we studied the evolution of whirl structures moving in a gas behind a shock wave front. This shock wave is defined by the Hugoniot relations. The Hugoniot relations allow finding the parameters of the gas behind the shock wave front, if the Mach number and gas parameters before the pressure jump are known. We developed a parallel algorithm and a numerical code for solving 2D gas dynamics equations. We made numerical simulations that modeled the shock wave interaction with whirl structures of different configurations (single whirl, two whirls with different directions of their vectors). We demonstrated the results of test simulations in a supercomputer with a different number of processors. It was shown that using 40 processors allows decreasing the duration of a test simulation approximately by the factor of 30. We described the results of the calculation of interaction of one/two whirls with the incident wave and the reflected waves. The gas dynamics parameters at the moment t = 0 were set with the help of Bernoulli law. Besides, we made a comparison with a similar program based on another algorithm (particle-in-cell method). It was shown that the interaction of two whirls with opposite directions does not lead to their compensation, but the interaction area (turbulent zone) has a complicated shape. The possibility of natural experiments with the help of a shock tube and a laser shock tube is discussed in the article. Such research would allow comparing the experimental data with the results of numerical simulations and developing more complicate models of the turbulent motion.