Book Description

Shock wave/boundary-layer interactions (SBLIs) are ubiquitous to both the external vehicle body and internal propulsion flowpath. The external surfaces include for example the nose, wings, and tail, while internal surfaces include bounding walls of mixed compression inlets, diffusers, and isolators. To obtain predictions of these flowfields, Reynolds-averaged Navier-Stokes (RANS) computational fluid dynamics (CFD) solvers are preferred over computationally expensive scale-resolving methods like large-eddy simulation (LES), hybrid RANS/LES, and direct numerical simulation (DNS). However, RANS predictions are highly dependent on the choice of turbulence model. Reasons include the fundamental assumption (Boussinesq eddy-viscosity approximation) made in the development of turbulence models and the estimation of the terms that govern turbulence transport. In this work, key mechanisms in the exact Reynolds stress transport equation are examined with a view towards identifying important flow phenomena and improving prediction of flows with SBLIs. Upon linking the unsteady dynamics back to the Reynolds stress transport, significant mechanisms can be isolated, whose relative importance varies across the SBLI region. By discovering the importance of these mechanisms to SBLIs, current models can be improved and mechanisms generally assumed negligible due to the lack of experimental or high-fidelity data can be modeled. With this purpose in mind, wall-resolved LES (WRLES) of SBLI are considered at several Reynolds numbers. The flow conditions and geometry are based on the experiments performed at the Institut Universitaire des Systemes Thermiques Industriel (IUSTI) in Marseille, France at Mach 2.29 for an 8 degree deflection angle shock wave impinging on a turbulent boundary layer developing on the opposite surface. Due to a closely coupled relationship between the corner flow and centerline separation in small- to medium-aspect-ratio configurations, the full tunnel span that includes the two sidewalls and produce a three-dimensional SBLI is studied. Verification of the numerical strategy is achieved by investigating the dependence of the results on mesh resolution, choice of domain size, numerical dissipation of the WRLES framework, and the digital filter inflow generation method. This is followed by detailed validation against the particle image velocimetry data from the experiment to assess the accuracy of the simulations. A comparison between the periodic and full-span simulations confirms that the corner physics is integral to the prediction of the centerline separation. The compression waves, visualized by plotting isosurface of the pressure gradient magnitude, are shown to emanate from the blockage created by the corner separation and are responsible for the amplification of the centerline separation. Furthermore, the phenomenology within the interaction region is invariably linked to the perturbation of the incoming turbulent boundary layer by the reflected-shock foot. It leads to the formation of a band in which the turbulence statistics become prominent and consistent with the development of the shear layer and Kelvin-Helmholtz shedding. The interaction between the corner separation and secondary flow of the second kind, i.e., a pair of counter-rotating vortices symmetric about the corner bisector, significantly diminishes the size of the vortex pair. However, as the corner separation becomes sidewall biased, the clockwise-rotating vortex grows, while the counter clockwise-rotating vortex remains anchored near the corner origin. Unsteady dynamics at the centerline and corner locations are evaluated by computing the weighted power spectral densities (PSDs) of pressure and velocity fluctuations. By placing the probes at key locations, unsteadiness effects related to the reflected-shock foot (low frequency, St ≈ 0.015), shear-layer development (intermediate frequency, St ≈ 0.1), and Kelvin-Helmholtz shedding (high frequency, St ≈ 0.5) are identified. The streamwise and spanwise recirculation dynamics of the centerline separation bubble are explored by employing low-pass filtered PSDs of u′ and w′, where broadband energetic scales in the intermediate-frequency range are found. The same intermediate-frequency scales are also present in the PSDs of the probes located within the corner separation. The corner-centerline two-point correlations illustrate the dynamical coupling of the corner regions with the reflected-shock foot that persists for multiple forward and aft shock oscillation cycles. The corner-corner two-point correlations reveal that the opposing corners are either positively correlated, uncorrelated, or negatively correlated and the period of this behavior cycle is significantly longer than the reflected-shock foot unsteadiness. A rigorous analysis of the Reynolds stress transport budget is performed to evaluate the significance of production, diffusion, transport, redistribution, and dissipation mechanisms in regions of SBLI. The budget sum, computed to serve as a measure of error in the budget, is also a good indicator of non-equilibrium in the flowfield caused by the unsteadiness. The pressure-diffusion mechanism is found to be important at the reflected-shock foot location and in its downstream vicinity. Notably, the analysis of turbulent-diffusion and pressure-strain mechanisms corroborates their key roles in balancing production within the shear-layer development and Kelvin-Helmholtz shedding regions. The molecular diffusion contributes in balancing dissipation near the wall, but is inconsequential in the unsteady regions. Upon considering the behavior of three diffusion mechanisms, the evidence indicates that separate modeling of these mechanisms would be beneficial in RANS simulations of SBLIs. Although the turbulent mass flux mechanism was hypothesized to be significant for the entrainment and ejection of mass from the separation bubble, it is in fact negligible and not a modeling concern. Finally, the spanwise variation in budgets due to the flow three-dimensionality is studied by comparing the centerline, quarter-span, and corner bisector positions. The leading mechanisms in the corner region are convection, production, turbulent diffusion, and pressure strain, while the behavior of quarter-span budgets is dependent upon the streamwise location. Ultimately, these results lay the foundation for a more systematic procedure to close the RANS equations in the presence of three-dimensionality, pressure gradients, and other sources of mechanical non-equilibrium.