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 20δ 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

Shock-wave/boundary-layer interactions (SWBLI) remain challenging for the physical understanding and for numerical simulations, in particular when they lead to flow separation, which is in general unsteady. In the past, in pioneering work performed at Princeton University and at the University of Austin, some aspects of the unsteadiness of SWBLI were examined (see for example Dolling (2001) and Smits & Dussauge (2006) for reviews). Many cases were investigated, such as corner flows, blunt body interactions and 3D interactions; they provided in many cases measurements of wall pressure fluctuations, and led to first understanding of shock unsteadiness and separated flow breathing. The European program UFAST organised considerable effort to study and document this question. Among all the possible interactions, particular attention was paid to the case of oblique shock reflection, which imposes severe compression to boundary layers. Moreover, this occurs in many particular situations, such as air intakes, compressors, turbines etc., and can be very detrimental for the structures. It was felt that there was a need for experiments at moderate Reynolds numbers to serve as test cases for advanced turbulence modelling like LES or DES. Several cases were studied experimentally at Mach numbers of 1.7, 2.0 and 2.25 respectively at Delft University of Technology (TU Delft), at the Institute of Theoretical and Applied Mechanics (ITAM) Novosibirsk and at the Institut Universitaire des Systèmes Thermiques Industriels (IUSTI) Marseille. All the experiments include statistical measurements of the flow field (mean and fluctuating) and a characterization of unsteadiness by the measurements of spectra. Details of the experiments can be found in Doerffer (2009). Numerical simulations within UFAST include a large number of turbulence modelling approaches, together with 2D and 3D computations. The simulations were performed by NUMECA (Brussels), IMF Toulouse, UAN (Karkhov), SOTON (University of Southampton), and ONERA/DAAP. Table 1, taken from Garnier (Chapter 10 in Doerffer et al. 2010), sums up the different attempts by the different groups.

As reported in Doerffer (2009) and in Doerffer et al. (2010), it is interesting to focus on the IUSTI experiments, both because they are extensively documented, including some three-dimensional aspects, and because the associated computations have led to comparisons between RANS, URANS, hybrid methods like DES, and LES. RANS methods by principle cannot catch the unsteadiness. They can however give some indications, provided they can predict the size of the interactions. In some analyses, this size is related to the characteristic frequency of the shock motion, so that it can indirectly provide indications on its time dependent behaviour. However, the conclusions show of course the potential of LES and DES to determine unsteadiness. The results have also underlined the importance of 3D effects in nozzles of finite span, which contribute to the organization of the separated zone. The present document is based on the numerical simulations of ONERA/DAAP (DES and LES) and SOTON (LES), although we make some reference to RANS simulations.

	Temporal Scheme	Spatial Scheme	Modelling	Remark
NUMECA	Runge-Kutta + IRS	Jameson	RANS: SA, k-ε, SST, v2-f Hybrid: DES-SA	Multigrid
IMFT	DTA	Roe (Van Leer limiter)	RANS: SA Hybrid: DES, OES
UAN	Implicit O(2)	ENO Godunov O(2)	RANS: k-ω, SST	Realisabilty cond. in turb. model
SOTON	RK3	Centred O(4) + TV model	LES: MTS, DYN	Digital filter for inf. cond.
ONERA	Implicit O(2)	Roe O(2) + TVD filter	RANS: MSM, SA Hybrid: DDES SA based, SDES SA based	Synthetic Eddy Method (SEM) inflow conditions

Table 1: Brief description of the codes from Garnier (2010)

Contributed by: Jean-Paul Dussauge (*), P. Dupont (*) , N. Sandham (**), E. Garnier (***) — (*) Aix-Marseille Université, and Centre National de la Recherche Scientifique UM 7343, (**) University of Southampton, (***) ONERA/DAAP, Meudon, France