Computer modeling of supersonic gas flow in variable cross-section channels using OpenFOAM

Abstract

With the development of high-performance computing systems, various software products are being created for mathematical modeling of physical phenomena, including gas-dynamic processes. Today, there are a number of different software packages, both proprietary and open source. One of these open source packages is OpenFOAM. OpenFOAM has a wide range of capabilities to solve any problem - from complex fluid flows, including chemical reactions, turbulence, and heat transfer, to acoustics, sol-id mechanics, and electromagnetism. Let's consider the problem of mathematical modeling of supersonic gas flow in channels of variable cross-section. When considering problems related to the formation and propagation of disconti-nuity surfaces in gases, gas leakage from supersonic engine nozzles, interaction of strong compression surges with obstacles, etc., it becomes necessary to solve the equations of gas dynamics. We consider the flow of supersonic gas in channels of variable cross-section in one-dimensional, two-dimensional and three-dimensional formulations. The problem of decay of an arbitrary discontinuity was analyzed in detail by N.E. Kochin in 1928. The algorithm for solving this problem is described in detail. The system of equations for solving the problem of rupture decay in a 3-dimensional formulation for the Cartesian coordinate system in the form of column vectors. The results of the calculations show that the implemented numerical solution in OpenFOAM using the Godunov, HLLC, and Rowe methods coincide with the solutions of each other. Rusanov's method has a slight difference compared to the other methods. This can be seen in the system of jumps and numerical values of gas parameters.