Large-eddy simulation of a supersonic turbulent boundary layer over a compression–expansion ramp Muzio Grilli ⇑ , Stefan Hickel, Nikolaus A. Adams Lehrstuhl für Aerodynamik und Strömungsmechanik, Technische Universität München, D-85748 Garching, Germany article info Article history: Received 8 October 2011 Received in revised form 13 August 2012 Accepted 24 December 2012 Available online xxxx Keywords: LES Compressible flow SWTBLI abstract Results of a large-eddy simulation (LES) of a supersonic turbulent boundary layer flow along a compres- sion–expansion ramp configuration are presented. The numerical simulation is directly compared with an available experiment at the same flow conditions. The compression–expansion ramp has a deflection angle of b = 25°. The flow is characterized by a free-stream Mach number of Ma 1 = 2.88 and the Reynolds number based on the incoming boundary layer thickness is Re d 0 ¼ 132840. The Navier Stokes equations for compressible flows are solved on a cartesian collocated grid. About 32.5  10 6 grid points are used to discretize the computational domain. Subgrid scale effects are modeled implicitly by the adaptive local deconvolution method (ALDM). A synthetic inflow-turbulence technique is used, which does not intro- duce any low frequency into the domain, therefore avoiding any possible interference with the shock/ boundary layer interaction system. Statistical samples are gathered over 800 characteristic time scales d 0 /U 1 . The numerical data are in good agreement with the experiment in terms of mean surface-pressure distribution, skin-friction, mean velocity profiles, velocity and density fluctuations. For the first time the full compression–expansion ramp configuration was taken into account. The computational results con- firm theoretical and experimental findings on fluctuation-amplification across the shockwave/boundary layer interaction region and on turbulence damping through the interaction with rarefaction waves. The LES provide evidence of the existence of Görtler-like structures originating from the recirculation region and traveling downstream along the ramp. An analysis of the wall pressure field clearly shows the pres- ence of a low frequency motion of the shock and strong influence of the Görtler-like vortices on the wall pressure spectra. Ó 2013 Elsevier Inc. All rights reserved. 1. Introduction The design process of supersonic and hypersonic air vehicles re- quires accurate simulation methods in order to predict aero-ther- modynamic loads. The need to achieve an optimal and safe design poses the requirement of an accurate estimation of critical quantities such as skin friction, heat-transfer rates, mean and fluc- tuating pressure. The interaction of turbulent boundary layers with shocks and rarefaction waves is one of the most prevalent phe- nomena occurring in high-speed flight, which can affect signifi- cantly the aero-thermodynamic loads. Accurate computations of such interaction are needed to gain a deeper insight into many as- pects of this phenomenon, such as the dynamics of shock unstead- iness, turbulence amplification through the shock, unsteady heat transfer near the separation and reattachment points, turbulence damping by the interaction with a Prandtl–Meyer expansion. For- ward- and backward-facing ramps configurations are often visible in engine inlets for scramjet applications as well as in supersonic planes. Given the importance of such flow configurations, com- pression–expansion and expansion–compression ramps configura- tion have been thoroughly investigated in previous experimental works. In the last three decades several experimental and numer- ical works focused their attention on such configuration. Most of the experimental contributions focused their attention on the com- pression ramp configuration, aiming to asses the main features of the shockwave turbulent boundary layer interaction phenomenon (SWTBLI). Settles et al. (1976, 1979) investigated 2D compression ramps with different inclination angles drawing a description of the mean flow features. Additional studies were carried out by Ardonceau et al. (1979) showing that the turbulence increases in intensity and gains a more pronounced anisotropy in passing the shock wave. Dolling and Murphy (1983), Dolling and Or (1985) and Muck et al. (1985) focused their attention on the fluctuating nature of the wall pressure signal in the interaction region of the compres- sion-ramp flow field, opening the way for a series of experimental contributions aiming to address the origin of the so called low fre- quency shock unsteadiness phenomenon which is actually respon- sible for the increase of wall pressure fluctuations in the vicinity of 0142-727X/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.ijheatfluidflow.2012.12.006 ⇑ Corresponding author. E-mail address: muzio.grilli@aer.mw.tum.de (M. Grilli). International Journal of Heat and Fluid Flow xxx (2013) xxx–xxx Contents lists available at SciVerse ScienceDirect International Journal of Heat and Fluid Flow journal homepage: www.elsevier.com/locate/ijhff Please cite this article in press as: Grilli, M., et al. Large-eddy simulation of a supersonic turbulent boundary layer over a compression–expansion ramp. Int. J. Heat Fluid Flow (2013), http://dx.doi.org/10.1016/j.ijheatfluidflow.2012.12.006