A simple physical theory of weak Mach reflection over plane surfaces
The author shows that simple physical principles coupled with the inviscid shock jump relation can be applied to the problem of weak Mach reflection, so that the triple point path can be predicted from the incident shock Mach number, gas specific heat ratio, and the inclination angle of reflecting surface to the shock normal. The position of the triple point is determined by the following mechanism: (a) the component of velocity normal to the surface following the initial impact of incident shock at the corner trips off a reflected wave which propagates as a finite-strength cylindrical wave into the moving flow downstream of the incident wave. This cylindrical wave meets the incident wave at the triple point if the corner angle is far from the transition angle for Mach reflection; (b) for angles close to the transition angle the pressure rise behind the normal Mach stem shock at the surface, influences the triple point, and `forces' the intersection to occur beyond that of the cylindrical wave. The limit for the case (a) for zero corner angle is the 'glancing incidence' case where the reflected wave is a cylindrical sound wave, while the limit in case (b) is the transition angle based on the detachment angle, and gives the correct reflected shock angle for regular reflection. Between these two cases there is a region of overlap of corner angles where the triple point changes smoothly from (a) to (b). A cubic fit to the full range covered by (a) and (b) can be used to interpolate over this overlap region. Comparison with Euler code data and with experiments show close agreement for conditions both far from and close to transition, and demonstrate that the general shapes of reflected and Mach stem shocks follow simple curves except in a neighbourhood of the triple point. The conflict at the triple point in matching the flow deflection angles and pressures across the contact discontinuity remains. The author shows, however, that the simple model presented in this paper gives a close match to the CFD and experimental overall shock and contact surface shapes, although it cannot predict these or the flow properties in any detail.
scientific article; zbMATH DE number 1452894