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Mach reflection subjected to the influence of an upstream shock wave from the same side is studied here. This situation occurs when two incident shock waves induced by a double wedge reflect at the same point of the reflecting surface and when the downstream incident shock wave is stronger than the upstream one. A shock polar analysis is used to show that this configuration produces an inverted Mach stem and a type IV shock interference between the Mach stem and the upstream shock wave. This shock interference produces a jet that divides the flow stream downstream of the Mach stem into two ducts with different sonic throats, thus complicating the mechanism by which the Mach stem size is determined. A transition analysis shows that the Mach reflection of the downstream shock wave is promoted by the upstream one. Computational fluid dynamics is used to assess the flow pattern anticipated by shock polar analysis and demonstrates how the heights of Mach stem and jet depend on the inflow Mach number and wedge turning angle.
The asymmetrical Mach reflection configuration is studied analytically in this paper, using an asymmetrical model extended from a recent symmetrical model and accounting for the new features related to asymmetry of the two wedges. It is found that the two sliplines do not turn parallel to the incoming flow at the same horizontal location and the sonic throat locates at the position where the difference of slopes of the two sliplines vanishes. This allows us to define a new sonic throat compatibility condition essential to determine the size of the Mach stem. The present model gives the height of the Mach stem, declined angle of the Mach stem from vertical axis, sonic throat location and shape of all shock waves and sliplines. The accuracy of the model is checked by computational fluid dynamics (CFD) simulation. It is found that the Mach stem height is strongly dependent on asymmetry of the wedge angles and almost linearly dependent on the asymmetry of the wedge lower surface lengths. The Mach stem height is shown to be insensitive to the asymmetry of the horizontal positions of the two wedges. The mechanisms for these observations are explained. For instance, it is demonstrated that the Mach reflection configuration remains closely similar when there is horizontal shift of either wedge.