Planar shock-wave boundary-layer interaction

Semi-confined Flows

Underlying Flow Regime 3-32

Description

Introduction

The problem of the unsteadiness in shock wave/boundary layer interactions (SWBLI) is challenging in many respects. A more general question is related to the unsteadiness or "breathing" of separated flows, whatever the regime, subsonic or supersonic. This is a problem that is important for both applications and basic research. In many aeronautical applications, such as aircraft profiles, air intakes, turbines or compressors, shock waves are formed and generally lead to separation. The resulting separation bubbles are unsteady, in the sense that they produce frequencies much lower (by at least two orders of magnitude) than the identified frequencies of the turbulent flow. Another difficulty arises if high-speed flows are considered, in which case the unsteadiness is also dependent on Mach number.

A first point is the understanding of the origin of these low frequencies: how is it possible to produce, from the turbulent fluctuations of the boundary layer, very low frequencies, involving scales differing from the turbulent layer itself generally by two orders of magnitude? Several possibilities have been examined in recent years. A first one assumes that the superstructures of the incoming layer (hairpin packets of length about 20 /?/ or more) make the shock wave and the separated zone move (Ganapathisubramani et al, 2007, 2009). A second one (Piponniau et al. 2009) considers that the low frequencies are produced by a process of emptying/filling of the separation bubble. Because of fluid entrainment, the air of the separation zone is drained by the large structures, Kelvin-Helmholtz-like, formed at the edge of the recirculating zone, and is progressively emptied, until it is filled again by air incoming in the reverse direction. The second scenario seems more appropriate, since it is able to reproduce the dominant frequencies in shock reflections, while the first one fails for this flow case. A point which can be underlined is that the scales involved in the unsteadiness are not directly related to the incoming boundary layer, and therefore cannot be reduced by some simple similarity to the characteristics of the boundary layer. This latter point is reinforced by a third approach (Touber & Sandham, 2011), based on a simplified momentum integral analysis, which shows how the low frequency can develop from uncorrelated broadband stochastic forcing of a separating boundary layer.

From the CFD point of view, such flows remain challenging. Many attempts have been made to compute SWBLI, to determine the mean and turbulent fields or the unsteadiness. The few attempts of applying compressibility flow corrections in turbulence modelling have demonstrated an insufficient predictive capability of unsteady flows with strong compressibility effects and attempts to 'extrapolate' turbulence modelling from incompressible flows have also proven insufficient for the accurate prediction of the buffeting phenomenon and of transonic-dip flutter (examples: research program ETMA, Vieweg, Vol. 65 and European research program UNSI, final report edited by Springer, Vol. 81), concerning the simulation of buffeting phenomenon and of shock unsteady motion. A difficulty for RANS methods comes probably from their tuning to simple, self-similar equilibrium situations, and hence cannot cope with the new scales which are typically out of equilibrium, having a particular dynamics. More recently the hybrid approach DES (Detached Eddy Simulation), that is an inherently 3D approach, has been applied to the transonic flows around airfoils, indicating the crucial need for improvement of flow-physics knowledge concerning the modification of the turbulence scales due to the unsteadiness and compressibility.

It seems that methods like LES do not suffer from the same limitations as RANS; a consequence is that hybrid methods like the different versions of DES may represent an interesting compromise by combining the flexibility of LES and the economy in computational resources of RANS. On the numerical side, such flows represent some challenging aspects: there are the usual requirements on meshes, since in LES computations the mesh size acts as a filter and therefore is part of the modelling, and there are other difficulties since unsteady shocks should be adequately represented by the computations, without being confused with turbulence.

For the present application to shock-wave/boundary-layer interaction, experiments provide detailed descriptions of the flow, for the mean and turbulent fields, and for the characterization of the unsteadiness. The data are compared to the results of computations, using LES, several types of DES, and URANS and RANS methods based on Spalart-Allmaras modelling. The discussions will also lead to the assessment of the importance of taking in account the 3D effects for predicting correctly the separated zone and in turn, the interaction unsteadiness.

Review of UFR studies and choice of test case

Provide a brief review of past studies of this UFR which have included test case comparisons of experimental measurements with CFD results. Identify your chosen study (or studies) on which the document will focus. State the test-case underlying the study and briefly explain how well this represents the UFR? Give reasons for this choice (e.g a well constructed test case, a recognised international comparison exercise, accurate measurements, good quality control, a rich variety of turbulence or physical models assessed etc.) . If possible, the study should be taken from established data bases. Indicate whether of not the experiments have been designed for the purpose of CFD validation (desirable but not mandatory)?

Contributed by: Jean-Paul Dussauge — Orange