Numerical investigation of the onset of instability of triple shock configurations in steady supersonic gas flows

Abstract

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 ...

Stationary Mach Configurations with Pulsed Energy Release on the Normal Shock

“…In this case, detonation polar (11) degenerates to a point " * " (see Figures 2a-c and 4), which corresponds to the critical flow velocity behind the normal detonation wave (it means that M III = 1). A further increase in pulsed energy release leads to the loss of the stability of the shock j 3 and of the triple configuration as a whole.…”

“…Relation (11) describes so-called detonation shock polar, whose name suggests that the pulsed energy release at the shock or in the immediate vicinity of it occurs as a result of detonation initiated by a sudden increase in temperature on the shock surface. Figure 2a-c demonstrates a family of detonation polars IIIa-IIIf, which correspond to the effective adiabatic index γ 3 = γ 12 = 1.4 and different values of pulsed energy release.…”

“…In the recent 15-20 years, a classification of triple configurations [1,2] was developed, their parametric analysis was obtained [2][3][4][5][6], configurations with special properties of individual shocks [4] and extreme ratios of flow parameters on both sides of the emanating slipstream [4,7] were found and studied, and the obtained solutions were generalized for triple configurations of propagating shock waves [8]. Possible additional studies in this direction in the near future can cover the problems of performability of triple configurations forming at Mach reflection with a negative inclination angle of the reflected shock [7,[9][10][11][12][13] or the analysis of differential characteristics of the flowfield applying the dynamic compatibility conditions [2,14].…”

The interaction of a Prandtl–Meyer wave and a quasi-one-dimensional flow region

“…2b) exists at the beginning of the flow considered (x ¼ 0). This slipstream can occur, in particular, at the Mach reflection of another interaction of the shocks that form the triple configuration [6][7][8]. The slipstream τ divides the flow regions 1 and 2.…”

Control of Triple-Shock Configurations and Vortex Structures Forming in High Speed Flows of Gaseous Media past an AD Body under the Action of External Energy Sources

“…Additionally, in the case of unsteady interaction of shock waves with plane surfaces, the decrease of the ratio of specific heats has been shown to lead to the appearance of a significant flow reconstruction connected with the formation of the double Mach reflection. Recently it has been found that, for a flow around a system of two wedges (a model of an intake) for the Mach numbers higher than 3 and γ < 1.4 it is possible for the oscillation flow mode to appear and destroy the steady flow mode [24][25][26][27].…”