EDUCTION SCHEME FOR CONVECTIVE STRUCTURES IN TURBULENT COMPRESSIBLE SEPARATED FLOW

Evidence of coherent convective vortical structures in a statistical sense is obtained for a turbulent compressible separated flow. Structures are detected and tracked in unsteady data from a Large Eddy Simulations of shock waveboundary layer interaction by means of a new algorithm. This one is based on the detection of the modulations of the instantaneous zero mass flux lines induced by the travelling structures. The educed structures are spatially characterized and their frequencies, convection velocities and dimensions are given. Their effect on the wall pressure and the skin friction coefficients are also described. INTRODUCTION Shock-wave/boundary-layer interaction (SWBLI) has been largely studied for several decades due to their practical interest in aeronautical applications. One critical feature of such flows is the occurrence of low-frequency unsteadiness if the shock-induced adverse pressure gradient is strong enough to induce a separation of the incoming boundary layer. The physics resulting in these lowfrequency unsteadiness, also encountered in many subsonic separated flow (Cherry et al., 1984; Kiya & Sasaki, 1983) is not yet fully understood, see Babinsky & Harvey (2011). However, possible links between the low-frequency unsteadiness and the coherent structures of the mixing layer developing downstream the separation point have been highlighted in recent works, both in subonic (Ehrenstein & Gallaire, 2008) and supersonic regime (Piponniau et al., 2009). It is therefore of importance to obtain a comprehensive description of the characteristics of these structures. Difficulty arise in turbulent flows from the energy preeminence of the structures issued from the incoming boundary layer over the mixing layer ones. Some information where nonetheless obtained in SWBLI from two-point statistics and instantaneous PIV measurements of Dupont et al. (2006); Piponniau et al. (2009). The purpose of the present work is to complete these data by providing a statistical description of the dynamics associated with these Figure 1. Spark Schlieren visualization of the interaction. structures. A conditional averaging method relying on a new eduction scheme of the coherent structures is proposed to this end. As an illustration, it is applied to data obtained from a Large-Eddy Simulation of a Mach 2.3 shock reflection for flow deflection angle of 9.5◦ including a large separation, as described in Agostini et al. (2012). The unsteady properties have been widely validated against the experimental results obtained for the same interaction geometry Agostini et al. (2012). The spatial organization of the flow is illustrated with a short time exposure Schlieren of the interaction in figure 1. The origin of the longitudinal coordinate x was fixed at the mean position (X0) of the unsteady reflected shock. This position was derived from unsteady wall pressure. It was normalized by the length of interaction L defined as the distance between X0 and the extrapolation down to the wall of the incident shock. The size of the interaction was of 54.5 mm. The dimensionless longitudinal coordinate X∗ = (x−X0)/L was used to present the results. One key feature of this database is the very long physical time of 150 periods of the low frequency phenomenon that has been computed. It therefore ensure a rather good statistical convergence of the conditionally averaged data.