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Interactions between shock waves and turbulence are ubiquitous in high-speed flows of practical aeronautical interest. Recent advances in computational power have made implicit large-eddy simulatio...

Shock-wave/boundary-layer interactions (SBLI) are an important feature of high-speed gas dynamics. In many numerical studies of SBLI span-periodicity is assumed to reduce computational complexity. However, span-periodicity is not a valid assumption for aeronautical applications such as supersonic engine intakes where lateral confinement leads to highly three-dimensional behaviour. In this work transitional oblique SBLI are simulated for a rectangular duct with a $$\theta _{sg} = 5^{\circ }$$ θ sg = 5 ∘ shock generator ramp at Mach 2. The baseline configuration is a duct with an aspect ratio of 0.5. Time-dependent disturbances are added to the base laminar flow via wall localised blowing/suction strips to obtain intermittent transition upstream of the SBLI. Two forcing configurations are evaluated to assess the response of the SBLI to different tripping locations. The transition is observed to develop first in the low-momentum corners of the duct and spread out in a wedge shape. The central separation bubble is seen to react dynamically to oncoming turbulent spots, shifting laterally across the span. While instantaneous corner separations do occur, the time-averaged corner flow remains attached. Comparisons to a one-to-one aspect ratio duct show that the SBLI is heavily dependent on aspect ratio; the wider duct exhibited significantly larger regions of flow-reversal due to a strengthened interaction.

Counter-flow configurations, whereby two streams of fluid are brought together from opposite directions, are highly efficient mixers due to the high turbulence intensities that can be maintained. In this paper, a simplified version of the problem is introduced that is amenable to direct numerical simulation. The resulting turbulent flow problem is confined between two walls, with one non-zero mean velocity component varying in the space direction normal to the wall, corresponding to a simple shear flow. Compared to conventional channel flows, the mean flow is inflectional and the maximum turbulence intensity relative to the maximum mean velocity is nearly an order of magnitude higher. The numerical requirements and turbulence properties of this configuration are first determined. The Reynolds shear stress is required to vary linearly by the imposed forcing, with a peak at the channel centreline. A similar behaviour is observed for the streamwise Reynolds stress, the budget of which shows an approximately uniform distribution of dissipation, with large contributions from production, pressure-strain and turbulent diffusion. A viscous sublayer is obtained near the walls and with increasing Reynolds number small-scale streaks in the streamwise momentum are observed, superimposed on the large-scale structures that buffet this region. When the peak local mean Mach number reaches 0.55, turbulent Mach numbers of 0.6 are obtained, indicating that this flow configuration can be useful to study compressibility effects on turbulence.

High-speed compressible turbulent flows typically contain discontinuities and have been widely modeled using Weighted Essentially Non-Oscillatory (WENO) schemes due to their high-order accuracy and sharp shock capturing capability. However, such schemes may damp the small scales of turbulence and result in inaccurate solutions in the context of turbulence-resolving simulations. In this connection, the recently developed Targeted Essentially Non-Oscillatory (TENO) schemes, including adaptive variants, may offer significant improvements. The present study aims to quantify the potential of these new schemes for a fully turbulent supersonic flow. Specifically, DNS of a compressible turbulent channel flow with M = 1.5 and Re τ = 222 is conducted using OpenSBLI, a high-order finite difference computational fluid dynamics framework. This flow configuration is chosen to decouple the effect of flow discontinuities and turbulence and focus on the capability of the aforementioned high-order schemes to resolve turbulent structures. The effect of the spatial resolution in different directions and coarse grid implicit LES are also evaluated against the WALE LES model. The TENO schemes are found to exhibit significant performance improvements over the WENO schemes in terms of the accuracy of the statistics and the resolution of the three-dimensional vortical structures. The sixth-order adaptive TENO scheme is found to produce comparable results to those obtained with nondissipative fourth- and sixth-order central schemes and reference data obtained with spectral methods. Although the most computationally expensive scheme, it is shown that this adaptive scheme can produce satisfactory results if used as an implicit LES model.

Numerical work on shockwave/boundary-layer interactions (SBLIs) to date has largely focused on span-periodic quasi-2D configurations that neglect the influence lateral confinement has on the core flow. The present study is concerned with the effect of flow confinement on Mach 2 laminar SBLI in rectangular ducts. An oblique shock generated by a 2 degree wedge forms a conical swept SBLI with sidewall boundary layers before reflecting from the bottom wall of the domain. Multiple large regions of flow-reversal are observed on the sidewalls, bottom wall and at the corner intersection. The main interaction is found to be strongly three-dimensional and highly dependent on the geometry of the duct. Comparison to quasi-2D span-periodic simulations showed sidewalls strengthen the interaction by 31% for the baseline configuration with an aspect ratio of one. The length of the shock generator and subsequent trailing edge expansion fan position was shown to be a critical parameter in determining the central separation length. By shortening the length of the shock generator, control of the interaction and suppression of the central interaction is demonstrated. Parametric studies of shock strength and duct aspect ratio were performed to find limiting behaviours. For the largest aspect ratio of four, three-dimensionality was visible across 30% of the span width away from the wall. Topological features of the three-dimensional separation are identified and shown to be consistent with `owl-like' separations of the first kind. The reflection of the initial conical swept SBLIs is found to be the most significant factor determining the flow structures downstream of the main interaction., Comment: 31 pages

Laminar shock-wave/boundary-layer interactions were simulated using OpenSBLI, a Python-based source code generation framework. Shock-capturing was performed by a 5th order finite-difference Weighted Essentially Non-Oscillatory (WENO)-Z scheme applied in characteristic space. Oblique shock conditions were imposed for a shock angle of θ = 32 . 58 ∘ and Mach 2 free-stream, impinging on a laminar flat-plate boundary-layer. Performance of the code was assessed on different architectures for CPU, GPU and Xeon Phi.

This work introduces a new error indicator which can be used to determine areas of insufficient numerical resolution in unfiltered finite difference simulations. The background behind the methodology is that smaller scales (i.e. the flow features with higher wave numbers) are physically characterised by a smaller energy content in comparison with larger scales. This energy should decrease with increasing wavenumber at a minimum rate; if this rate is not attained it likely means that the smaller scales are not being properly resolved on the computational grid of solution points. An approach using spectral techniques is used to formulate two varieties of the error indicator – one integer-valued and one floating point-valued. These values are computed at a finite number of ‘blocks’ which span the domain. The indicator is implemented within the OpenSBLI finite difference-based modelling framework, and evaluated in the context of a three-dimensional Taylor-Green vortex problem and flow past a V2C laminar flow aerofoil.