Unsteady mechanisms in shock wave and boundary layer interactions over a forward-facing step

Abstract

The flow over a forward-facing step (FFS) at $Ma_\infty =1.7$ and $Re_{\delta _0}=1.3718\times 10^{4}$ is investigated by well-resolved large-eddy simulation. To investigate effects of upstream flow structures and turbulence on the low-frequency dynamics of the shock wave/boundary layer interaction (SWBLI), two cases are considered: one with a laminar inflow and one with a turbulent inflow. The laminar inflow case shows signs of a rapid transition to turbulence upstream of the step, as inferred from the streamwise variation of $\langle C_f \rangle$ and the evolution of the coherent vortical structures. Nevertheless, the separation length is more than twice as large for the laminar inflow case, and the coalescence of compression waves into a separation shock is observed only for the fully turbulent inflow case. The dynamics at low and medium frequencies is characterized by a spectral analysis, where the lower frequency range is related to the unsteady separation region, and the intermediate one is associated with the shedding of shear layer vortices. For the turbulent inflow case, we furthermore use a three-dimensional dynamic mode decomposition to analyse the individual contributions of selected modes to the unsteadiness of the SWBLI. The separation shock and Görtler-like vortices, which are induced by the centrifugal forces in the separation region, are strongly correlated with the low-frequency unsteadiness in the current FFS case. Similarly as observed previously for the backward-facing steps, we observe a slightly higher non-dimensional frequency (based on the separation length) of the low-frequency mode than for SWBLI in flat plate and ramp configurations.

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

“…[40], and Hu et al [20,21]. This is also shown in figure 20, which displays an instantaneous z-y plane of u- the first caused by the leading edge bow shock, and the second by the reflected shock from the pressure side of the adjacent blade.…”

“…On the pressure side, bell-shaped and mushroom structures are also formed in the incoming boundary layer. At the leading edge of the bubble, the flow separation region conforms to the Several authors have investigated the presence of Görtler vortices in SBLIs [13,20,21,40,47,48].…”

“…Flow visualizations selected based on the previous analysis are then used in section 3.4 to study the effect of inlet Mach number on the dynamics of separation bubbles. Finally, in section 3.5 the occurrence of Görtler vortices is examined in the present configuration, since these coherent structures have been observed in SBLIs by several authors [13,20,21,40,47,48]. Here, we present an analysis of the development and spatial evolution of streamwise vortices developing on turbulent boundary layers over concave as well as convex surfaces, including their interaction with streaks and their role in the separation bubble.…”

“…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].…”

Passive Control of Shock-Wave/Turbulent Boundary-Layer Interaction Using Spanwise Heterogeneous Roughness

“…An explicit 3 rd -order Runge-Kutta-scheme is used for time marching. This solver has been extensively validated and successfully applied for various STBLI cases, including the compression ramp [17], shock impingement [18,19] and forward/backward facing step [20,21]. A cut-cell-based immersed boundary method (IBM) is utilized to represent the rough wall [22,23].…”