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Triple shock wave configurations, together with two shock ones, play a determining role in all prob lems of both internal and external aerodynamics [1]. These shock wave configurations appear at the entrance of air inlets during supersonic flights (Fig. 1a), where incident wave IA at the wedge vertex cannot be reflected from the axis of symmetry in a reg ular manner. When a supersonic nozzle operates in an overexpanded mode a bridge like system of shock waves appears that represents a sequence of three shock configurations. In a quasi steady case, the reflection of a shock wave from a planar wedge with an angle below the critical value also leads to the appear ance of a Mach configuration (Fig. 1b). In this case, the triple point moves at a constant angle relative to the surface. Thus, in the system of reference related to the point A, we observe a steady state three shock config uration.The arrangement and intensities of shock waves in these configurations depend on the Mach number M 1 of the incident flow, initial angle of incidence ω 1 , and ratio of specific heats γ (adiabatic index). As is known, in the case of strong shock waves, these configurations can be calculated using a three shock theory [2, 3]. According to this, it is suggested that, in a certain vicin ity of the triple point where all waves are direct, each shock obeys the laws of conservation and the boundary conditions are as follows: (i) flow through the incident and reflected waves is parallel to flow through the Mach wave and (ii) pressures on both sides of the tangential discontinuity surface AT are the same. For strong shock waves, the three shock theory provides a quite satisfac tory agreement with experiment. However, it should be noted that this theory cannot determine the Mach stem height in a steady case and the angle of motion of the triple point in a quasi steady case.Abstract-Triple configurations of shock waves with negative reflection angles are considered. These config urations have been observed in quasi steady cases of shock wave reflection from a planar wedge in real gases, while in steady cases three shock configurations are only known to occur with positive reflection angles. Boundaries for the appearance of a three shock configuration with a negative reflection angle in steady cases are analytically determined as dependent on the initial Mach number of the flow, angle of incidence, and adi abatic index. The formation of a three shock configuration with a negative reflection angle in a steady flow must lead to a change in the character of the wave pattern, and under certain conditions it can lead to insta bility.

Three and two shock wave configurations play a determining role in all problems of both internal and external aerodynamics. These shock wave configura tions appear, e.g., at the entrance of air inlets during supersonic flight and at the exit of supersonic nozzles operating in overexpanded regimes. Previously [1][2][3], we have demonstrated for gas flows at large Mach numbers and small adiabatic indices γ that, in addition to the well known regular and nonregular (Mach type) reflection, there must exist a new triple shock config uration (Fig. 1a) in which the reflected shock wave AR occurs below the line of incident flow. This pattern will be referred to as the triple shock configuration with a negative reflection angle (ω 2 < 0). The domains of existence of this configurations were determined, and it was established that it does not exist for the effective adiabatic index γ ≥ 1.4 [4]. The boundary of the domain of existence of a triple shock configuration with a negative reflection angle is shown in Fig. 1b. It was also suggested that, if a negative reflection angle appears in a certain vicinity of triple point A, the entire flow pattern must change so that the flow will become unstable. For example, if the reflected wave AR crosses the symmetry axis 0-0 ( Fig. 1a), the flow will be blocked and either the entire flow pattern will become unstable or the system will oscillate, so that the flying vehicle or a rocket engine will enter a critical operation regime.The new configuration has not been observed before, since all experiments are conventionally per formed in wind tunnels with airflow Mach numbers and drag parameters such that air can be treated as an ideal gas with γ = 1.4, for which a domain with nega tive reflection angle does not exist. Investigations involving the regions of existence of the shock wave configurations with negative reflection angles can only be performed by numerical methods. This Letter pre sents the results of such numerical simulations.Numerical calculations were performed using a STAR CCM+ (v.6.06) program package, which is intended for solving problems of continuum mechan ics. This program employs the method of Reynolds averaged Navier-Stokes (RANS) equations [5]. The system of equations was closed, with allowance for the appearance of new functions that characterize turbu lent stresses, using the Spalart-Allmaras model of tur bulence [6]. The system analysis was based on the model problem of shock wave reflection from a sym metry plane during the interaction of shocks generated by two symmetric wedges in a supersonic flow (Fig. 1a). Calculations were performed for various wedge angles within θ = 10°-50° in a broad range of flow parameters (M 1 = 3-10; γ = 1.05-1.4).Simulations were carried out in an extended hori zontal rectangular region with a wedge situated at the entrance. With allowance for the symmetry of the sys tem, the problem was solved for the upper half of geometry with the condition of symmetry on the lower boundary. Conditions on the left boundary were set as the flow ...

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