Simulation of propagation and diffraction of a shock wave in a planar curvilinear channel

Abstract

Subject of Research. Numerical simulation of a shock wave propagation in a plane curved channel is considered on the basis of numerical simulation data. Method. Calculations of an inviscid compressible gas were carried out on the basis of unsteady two-dimensional Euler equations. Discretization of the basic equations was carried out using the finite volume method. Calculations were carried out for different channels with different radius of curvature and Mach numbers of the initial wave. To find the angular position of the front at the current time, the absolute value of the derivative of the density with respect to the angular coordinate was used. The calculation results were compared with the data of a physical experiment. Main Results. The features of the emerging shock-wave flow pattern and its development in time are discussed. The shock-wave configuration observed in channels with different radii of curvature is compared. Some differences in the curvature change of the front of shock waves formed in channels with different radius of curvature are shown. The size of the Mach leg and its change with time depending on the intensity of the initial wave and the size of the annular gap is the angular coordinate function corresponding to the position of the shock wave at the current time. While the maximum Mach number on the outer wall is relatively weakly dependent on the initial wave velocity, the Mach number on the bottom wall decreases with increasing Mach number at the channel entrance. The performed numerical studies show that in all variants there are no non-physical oscillations of the solution. Practical Relevance. The study of shock-wave and detonation processes is of interest for using their potential in pulsed installations and power systems for aircraft and rockets. The calculation results are important for the search of the new flow patterns that guarantee the formation of self-sustained detonation combustion in the combustion chambers of promising propulsion systems. Adjusting the size of the annular gap gives the possibility to select a geometric configuration that will provide the formation of an optimal triple shock wave structure, as well as the required intensity and size of the Mach wave.

Keywords

• shock wave
• diffraction
• channel
• numerical simulation
• gas dynamics