The Diffraction of a Two-Dimensional Curved Shock Wave Using Geometric Shock Dynamics
The diffraction of a cylindrical shock wave segment around convex sharp corners is considered. This investigation is approached from a numerical and analytical perspective. The numerical investigation was carried out using ANSYS Fluent while Whitham’s theory of geometric shock dynamics was used as a basis for the analytical approach. A model based on Whitham’s theory was developed, wherein the cylindrical shock profile is viewed as being composed of connected plane shocks with varying orientation. As the length of these plane shocks approaches zero, their combined shape approximates the cylindrical shock’s profile. Upon diffraction, disturbance waves propagate along this sequence of plane shocks; the theory of sound was used to model the propagation of these disturbances (taking into account the variation of shock orientation). Using this method, the inflection point (the point where the disturbed and undisturbed portions of the shock meet) was calculated. The results from the calculation were compared to those from ANSYS Fluent and they showed good correlation. A further attempt was made at modelling an elliptical shock, which produced unexpected results. In plane and cylindrical shocks, the disturbed region grows weaker; yet, it grows stronger in elliptical shock producing another wave between the reflected shock and the wall.
- 1.Chester, W.: The quasi–cylindrical shock tube. Philos. Mag. 45, 1293–1301Google Scholar
- 2.Chisnell, R.F.: The motion of shock waves in a channel with applications to cylindrical and spherical shock waves. J. Fluid Mech. 2, 286–298Google Scholar
- 3.Itoh, S., Okazaki, N., Itava, M.: On the transition between regular and mach reflection in truly non-stationary flows. J. Fluid Mech. 108, 384–400Google Scholar
- 4.Milton, B.E.: Mach reflection using ray shock theory. AIAA. 13, 1531–1533Google Scholar
- 5.Skews, B.W.: The shape of a diffracting shock wave. J. Fluid Mech. 29, 297–304Google Scholar
- 6.Whitham, G.B.: A new approach to problems of shock dynamics, Part 1: Two dimensional problems. J. Fluid Mech. 2, 146–171Google Scholar