LARGE EDDY SIMULATION OF THE TRANSITION PROCESS FROM REGULAR TO IRREGULAR SHOCK-WAVE/BOUNDARY-LAYER INTERACTION

Abstract

The transition process from regular to irregular shockwave/boundary-layer interaction (SWBLI) at M∞ = 2 is studied both numerically and theoretically. The classical twoand three-shock theory is applied for carefully analyzing a data base of well resolved large-eddy simulations (LES). Inviscid theory appears to be a descriptive tool for the interpretation of the highly transient flow field of the SWBLI. Disturbances related to the incoming turbulent boundary layer can be identified as a source of bidirectional transition processes between regular and irregular SWBLI at a critical deflection angle across the incident shock wave. INTRODUCTION A shock wave represents a highly nonlinear phenomenon. The state of the medium that passes the wave changes instantaneously and irreversibly. The complexity of this process increases when more than one shock occurs, for example, in the case of the interaction of a shock with a symmetry plane, a solid surface or the asymmetric intersection of shock waves. The reflection phenomenon was first described by Ernst Mach in 1887, who experimentally observed two different wave configurations, namely the regular reflection (RR) and the irregular reflection / Mach reflection (MR). The symmetric reflection of shock waves in an inviscid framework can be briefly summarized as follows: Characteristic wave pattern of shock reflections (RR and MR) are restricted to certain domains depending on the free stream Mach number M∞ and the deflection angle θ01 across the incident shock. Criteria beyond which RR and MR are theoretically impossible are given by the detachment and the von Neumann condition, respectively; see Ben-Dor (2010) for a comprehensive review. Both RR and MR wave configurations are possible within the parameter space spanned by these two conditions. The existence of such a domain led Hornung et al. (1979) to hypothesize that a hysteresis process could exist in the transition process between both wave patterns. As the deflection across the incident shock increases, transition from RR to MR occurs near the detachment criterion, while in the opposite case transition from MR to RR occurs at the von Neumann condition. Recently, asymmetric intersections of shock waves got into the focus of classical gas-dynamic research, such as shown in Fig. 1a, see Li et al. (1999) and Hu et al. (2009), e.g.. Li et al. (1999) proposed transition criteria for the reflection of asymmetric shock waves corresponding to the (b) (a) Figure 1: (a) Experimental schlieren image of the quasiinviscid MR at M∞ = 4.96, θ01 = 28○ and θ02 = 24○, courtesy of Li et al. (1999). (b) Experimental schlieren image of the ISWBLI at M∞ = 1.965 and θ01 = 15.2○, courtesy of Bardsley & Mair (1950). detachment and von Neumann criteria. In the following, it will become apparent that methods (e.g. shock polars) and transition criteria (θN , θD) developed for inviscid flow in the recent decades also constitute a descriptive tool for analyzing the interaction of shock waves with viscous boundary layers. Shock-wave/boundary-layer interaction (SWBLI) is one of the most prevalent phenomena occurring in highspeed flight and has received much attention in the past decades; see the comprehensive review paper of Delery & Marvin (1986). Geometric configurations are wide-ranging in nature, however, four basic SWBLI configurations can be identified: the ramp flow, the oblique shock reflection, and the forward and backward facing step. Fig. 2a schematically depicts the strong regular SWBLI (RSWBLI) for the case of an oblique shock reflection. The strong interaction is characterized by a noticeable separation of the boundarylayer leading to a wall pressure distribution that clearly exhibits three inflection points. As can be seen in Fig. 2a, the boundary-layer separates well upstream from the point ximp where the incident shock C1 would impinge in an inviscid flow. The adverse pressure gradient affects the upstream flow through the subsonic layer, causing a displacement of the streamlines away from the wall and eventually boundary layer separation. Compression waves are formed that propagate into the potential outer flow. These compression waves coalesce into the separation shock C2. It is important to note that the interaction between shock and boundary layer can feature several other phenomena. For a more detailed discussion, see Henderson (1967) and Delery & Marvin (1986), who gave a review of the various types of shock reflections in the presence of a boundary-layer.