Unsteadiness characterisation of shock wave/turbulent boundary-layer interaction at moderate Reynolds number

Abstract

A direct numerical simulation of an oblique shock wave impinging on a turbulent boundary layer at Mach number 2.28 is carried out at moderate Reynolds number, simulating flow conditions similar to those of the experiment by Dupont et al. (J. Fluid Mech., vol. 559, 2006, pp. 255–277). The low-frequency shock unsteadiness, whose characteristics have been the focus of considerable research efforts, is here investigated via the Morlet wavelet transform. Owing to its compact support in both physical and Fourier spaces, the wavelet transformation makes it possible to track the time evolution of the various scales of the wall-pressure fluctuations. This property also makes it possible to define a local intermittency measure, representing a frequency-dependent flatness factor, to pinpoint the bursts of energy that characterise the shock intermittency scale by scale. As a major result, wavelet decomposition shows that the broadband shock movement is actually the result of a collection of sparse events in time, each characterised by its own temporal scale. This feature is hidden by the classical Fourier analysis, which can only show the time-averaged behaviour. Then, we propose a procedure to process any relevant time series, such as the time history of the wall pressure or that of the separation bubble extent, in which we use a condition based on the local intermittency measure to filter out the turbulent content in the proximity of the shock foot and to isolate only the intermittent component of the signal. In addition, wavelet analysis reveals the intermittent behaviour also of the breathing motion of the recirculation bubble behind the reflected shock, and allows us to detect a direct, partial correspondence between the most significant intermittent events of the separation region and those of the wall pressure at the foot of the shock.

Mach number effects on shock-boundary layer interactions over curved surfaces of supersonic turbine cascades

“…For all Mach numbers, the results show the presence of localized bursts (red regions) at low frequencies, confirming the presence of intermittent events in the flow. A closer inspection of the time signals reveals that these bursts are associated with large positive tangential velocity fluctuations, as well as strong bubble contractions, which conforms with the findings from Bernardini et al [15] and Jenquin et al [38]. Furthermore, one can also observe that increasing the inlet Mach number leads to an increase in the time scales of the intermittent events, as anticipated given the larger length scales of the separation bubbles.…”

“…The unsteadiness of SBLIs has been mostly studied for canonical two-dimensional configurations (statistically spanwise-homogeneous) such as flat plates [8][9][10][11][12][13][14][15], compression ramps [16][17][18][19], and steps [20,21]. In some cases, three-dimensional flows are also investigated over canonical geometries such as cylinders [22,23] and fins [24][25][26] installed on plates, as well as swept compression ramps [27,28], tunnel sidewalls [29,30], and double fins [31,32].…”

Direct numerical simulation of supersonic boundary layers over a microramp: effect of the Reynolds number

“…The DNS database considered in this work has been generated using STREAmS 2.0 (https://github.com/STREAmS-CFD/STREAmS-2) (Bernardini et al 2021(Bernardini et al , 2023bSathyanarayana et al 2023). The open-source finite-difference compressible flow solver, STREAmS, developed by our group, is designed to solve the compressible Navier-Stokes equations for a perfect, heat conducting gas.…”

“…The open-source finite-difference compressible flow solver, STREAmS, developed by our group, is designed to solve the compressible Navier-Stokes equations for a perfect, heat conducting gas. The solver targets canonical wall-bounded turbulent high-speed flows, and is oriented to modern HPC platforms with the capability to run on both NVIDIA (Bernardini et al 2021(Bernardini et al , 2023b and AMD (Sathyanarayana et al 2023) GPUs.…”

“…Shock wave/boundary layer interactions (SBLIs) can be found in a wide range of flows including transonic airfoils, high-speed inlets, control surfaces of high-speed aircraft, space launchers base flows and overexpanded nozzles. In the interaction region, extreme, unsteady, mechanical and thermal loads are typically observed (Clemens & Narayanaswamy 2014), and the adverse pressure gradient imposed by the shock often causes the boundary layer to separate intermittently (Bernardini et al 2023a). This problem represents, for example, a critical issue for high-speed intakes, since the low-momentum separated flow affects the mass flow rate entering the engine, producing flow distortions, total pressure losses and potential inlet unstarts (Herrmann & Koschel 2002).…”