Shock Wave Turbulent Boundary Layer Research Articles

A deep learning super-resolution model for turbulent image upscaling and its application to shock wave–boundary layer interaction

Upscaling flow features from coarse-grained data is paramount for extensively utilizing computational physics methods across complex flow, acoustics, and aeroelastic environments where direct numerical simulations are computationally expensive. This study presents a deep learning flow image model for upscaling turbulent flow images from coarse-grained simulation data of supersonic shock wave–turbulent boundary layer interaction. It is shown for the first time that super-resolution can be achieved using only the coarsest-grained data as long as the deep learning training is performed using hundreds of fine-grained data. The unsteady pressure data are used in training due to their importance in aeroelasticity and acoustic fatigue occurring on aerospace structures. The effect on the number of images and their resolution features used in training, validation, and prediction is investigated regarding the model accuracy obtained. It is shown that the deep learning super-resolution model provides accurate spectra results, thus confirming the approach's effectiveness.

Interaction of a moving shock wave with a turbulent boundary layer

In the present study, the influence of a uniformly moving impinging shock on the resulting shock wave–turbulent boundary layer interaction is numerically investigated. The relative Mach number of the shock front travelling above a flat-plate model varied between 0 and 2.3, while the quasi-steady inflow conditions remained constant with a Mach number of 3. To quantitatively evaluate the effect of shock travelling speed, a well-known scaling method for interaction length in quasi-steady flows was applied as a reference after significant improvements in modelling the effects of Reynolds number and wall temperature using new and existing data. Moreover, previously obtained experimental results for a limited range of travelling speeds were employed to validate the obtained numerical results. Three ranges of shock travelling speeds with distinctly different properties were extracted and quantitatively described using a developed correlation-based approach built on the extended quasi-stationary scaling law. In the first range, the scaled interaction length reaches its maximum for the given interaction strength and can be directly described by the scaling law obtained for quasi-stationary interactions. In the second travelling-speed range, the dependence of the interaction length on the interaction strength is explicitly influenced by the shock movement. With increasing shock travelling speed, the scaled interaction length here decreases significantly faster than in the quasi-stationary reference case. The end of this speed range is reached when the absolute shock front speed has caught up with the maximum speed of sound in the interaction zone, and thus the interaction length has fallen to zero. This travelling-speed limit signifies the transition to the third range, where upstream influence is no longer possible.

Separation length scaling for dual-incident shock wave–turbulent boundary layer interactions with different shock wave distances

In this study, the length scaling for the boundary layer separation induced by two incident shock waves is experimentally and analytically investigated. The experiments are performed in a Mach 2.73 flow. A double-wedge shock generator with two deflection angles ( $\alpha _1$ and $\alpha _2$ ) is employed to generate two incident shock waves. Two deflection angle combinations with an identical total deflection angle are adopted: ( $\alpha _1 = 7^\circ$ , $\alpha _2 = 5^\circ$ ) and ( $\alpha _1 = 5^\circ$ , $\alpha _2 = 7^\circ$ ). For each deflection angle combination, the flow features of the dual-incident shock wave–turbulent boundary layer interactions (dual-ISWTBLIs) under five shock wave distance conditions are examined via schlieren photography, wall-pressure measurements and surface oil-flow visualisation. The experimental results show that the separation point moves downstream with increasing shock wave distance ( $d$ ). For the dual-ISWTBLIs exhibiting a coupling separation state, the upstream interaction length ( $L_{int}$ ) of the separation region approximately linearly decreases with increasing $d$ , and the decrease rate of $L_{int}$ with $d$ increases with the second deflection angle under the condition of an identical total deflection angle. Based on control volume analysis of mass and momentum conservations, the relation between $L_{int}$ and $d$ is analytically determined to be approximately linear for the dual-ISWTBLIs with a coupling separation region, and the slope of the linear relation obtained analytically agrees well with that obtained experimentally. Furthermore, a prediction method for $L_{int}$ of the dual-ISWTBLIs with a coupling separation region is proposed, and the relative error of the predicted $L_{int}$ in comparison with the experimental result is $\sim$ 10 %.

Turbulence Modelling for SWTBLI with Expansion Wave Interference Inside Scramjet Inlets

An accurate prediction of the flowfield inside the scramjet inlet/isolator is crucial for a stable and reliable aerodynamic design. However, the complex phenomena such as shock wave-expansion wave interactions and shock wave-turbulent boundary layer interactions (SWTBLI) inside the isolator pose great difficulties to the computational modelling community. In the current work, a numerical investigation is carried out for a practical mixed compression scramjet inlet/isolator using the extensively validated SST k − ω turbulence model, and the numerical results are compared against the experimental data. Although the simulations qualitatively predict the overall shock structures, major discrepancies are observed in the predictions of separation region (location, shape, and size) and subsequent positions of the separation and reflected shocks: similar discrepancies are observed in the literature with various models. Analysis reveals that although the turbulence model is capable of predicting SWTBLI, this discrepancy is primarily because of the improper estimation of turbulence levels in the separation region due to upstream expansion wave interference. The predictions are significantly improved by recalibrating a model constant, called structure parameter a 1 , when its value was decreased from the standard value of 0.31 to 0.28. The reduction in a 1 is in contrast to observations in the literature where the structure parameter was suggested to be increased beyond the default value for separated high-speed flows. This behaviour is due to the expansion wave interference whose effects, opposite to that of shock, need to be incorporated into the model for accurate predictions of scramjet flows.

Generalized Scaling Analysis of the Separation Zone Induced by Shock Wave–Turbulent Boundary Layer Interactions

Generalized Scaling Analysis of the Separation Zone Induced by Shock Wave–Turbulent Boundary Layer Interactions

Dynamic interaction between shock wave turbulent boundary layer and flexible panel

The high-speed fluid–structure interaction (FSI) occurring between a skin panel and a turbulent shock-boundary layer interaction (SBLI) are investigated with large eddy simulations (LES). The SBLI is comprised of a Mach 4 and unit Reynolds number of 2.375×107 (/m) flow interacting with an oblique shock of strength p3/p1≈8.5 and angle σ≈30deg. The inviscid point of impingement on the flexible panel occurs near the mid-chord length. The fully clamped rectangular panel has the aspect ratio and non-dimensional panel thickness of b/a=1.377 and h/a=0.003, respectively. The strong SBLI induces a large flow separation of length Lsep≈0.7a (or equivalently ≈23δin) with a wide range of turbulent scales, including the characteristic low-frequency unsteadiness. Fluid and structural responses are compared across different classes of interaction, namely: rigid surface; one-way application of SBLI loads to the structure; and two-way interaction between the flow and structure. The interplay between the SBLI and flexible panel is elucidated using detailed analysis that includes proper orthogonal decomposition (POD), dynamic mode decomposition (DMD), and the recently developed Lagrangian modal analysis (LMA) for the deforming meshes. The large panel deflections (∼1h) result in structural non-linearity associated with the coupling between bending and stretching of the panel, manifested in terms of increased modal frequencies of the panel deflection.

Evaluation of the SU2 Open-Source Code for a Hypersonic Flow at Mach Number 5

This paper presents the evaluation of the Stanford University Unstructured (SU2) open-source computational software package for a high Mach number 5 flow. The test case selected is an impinging shock wave turbulent boundary layer interaction (SWTBLI) on a flat plate where the experimental data of Sch¨ulein et al. [27] is used for validation purposes. Two turbulence models, the Spalart–Allmaras (SA) and the k-ω Shear Stress Transport (SST) within the SU2 code are evaluated in this study. Flow parameters, such as skin friction, wall pressure distribution and boundary layer profiles are compared with experimental values. The results demonstrate the performance of the SU2 code at a high Mach number flow and highlight its limitations in predicting fluid flow physics. At higher shock generator angles, the discrepancy between experimental and CFD data is more significant. Within the interaction and flow separation zones, a smaller separation bubble and delayed separation are predicted by the SA model while the k-ω SST model predicts early separation. Both models are able to predict wall pressure distribution correctly within the experimental values. However, discrepancies were observed in the prediction of skin friction due to the inability of the models to capture the boundary layer recovery after shock impingement.

Shock wave and turbulent boundary layer interaction in a double compression ramp

Direct numerical simulations of shock wave and supersonic turbulent boundary layer interaction in a double compression ramp with fixed ramp angles of 12o and 24o at Mach 2.9 are conducted. The characteristics of the shock interactions are investigated for four different length between the two ramp kinks, corresponding to Lc = 0.9δref, 1.8δref, 2.7δref, and 3.6δref (δref being the upstream turbulent boundary layer thickness). The influence of increasing Lc on flow structures, unsteadiness, Reynolds stress, turbulence kinetic energy, and Reynolds stress anisotropy tensor is assessed. The size of the separation region is significantly decreased and reattached flow appears between the two ramp kinks. Streamwise vorticity contours and streamline curvature show the decreased spanwise width and increased spanwise coherency of Görtler-like vortices. Analysis of fluctuating wall pressure indicates that the low-frequency unsteadiness is strongly suppressed in the interaction region. Profiles of Reynolds stress components and turbulence kinetic energy exhibit different turbulence evolution across the interaction, leading to substantial differences observed in the anisotropy invariant map. It is found that the near wall region is characterized by decreased anisotropy, becoming closer to the axisymmetric compression state, while a significant increase of turbulence is identified in the outer region, following the axisymmetric expansion limit. Moreover, downstream of the interaction, turbulence in the near-wall region experiences a faster recovery and the influence of Lc is found to be marginal. The main effect of Lc is observed in the outer region, an increase of Lc resulting in a monotonic decay of turbulence intensities and an inward movement of turbulent structures.

A Numerical Investigation on the Equivalence of Shock−Wave/ Boundary-Layer Interactions using a Two Equations RANS Model

A detailed numerical investigation of two different modes of shock wave-turbulent boundary layer interaction (SWBLI) is presented. Equivalence of ramp induced SWBLI (R-SWBLI), and impingement shock based SWBLI (I-SWBLI) is explored from the computational study using an in-house developed compressible flow solver. Multiple flow deflection angles and ramp angles are employed for this study. For all the investigated cases, a freestream Mach number of 2.96 and Reynolds number of 3.47×107m−1 are considered. The k−ε model with the improved wall function of present solver predicted wall pressure distributions and separation bubble sizes very close to the experimental measurements. However, the separation bubble size is slightly over overpredicted by the k−ω model in most of the cases. The effect of overall flow deflection angle and upstream boundary layer thickness on the SWBLI phenomenon is also studied. A nearly linear variation in separation bubble size is observed with changes in overall flow deflection angle and upstream boundary layer thickness. However, the equivalence of SWBLI is noted to be independent of these two parameters. The undisturbed boundary thickness at the beginning of the interaction is identified as the most adequate scaling parameter for the length of the separated region.

Flow physics and sensitivity to RANS modelling assumptions of a multiple shock wave/turbulent boundary layer interaction

Reynolds Averaged Navier Stokes simulation (RANS) using the in-house CFD solver of Glasgow University is utilised to investigate the flow physics and the sensitivity to modelling assumptions of a multiple shock wave turbulent boundary layer interaction in a rectangular duct (Mr=1.61, Reδr=162000). Such interactions often occur in high-speed intakes. Two-dimensional simulations were first performed to investigate the required grid resolution. Then the sensitivity of the solution to different turbulence models is considered. Based on the required grid resolution a series of three-dimensional simulations were performed to investigate the effect of spanwise confinement and turbulence models. Lastly, using the best approach based on the above investigations, results from two additional test cases were compared to their experiments, and conclusions are drawn as to the best way to simulate multiple shock wave turbulent boundary layer interactions.

Incident shock wave and supersonic turbulent boundarylayer interactions near an expansion corner

Direct numerical simulations of incident shock wave and supersonic turbulent boundary layer interactions near an expansion corner are performed at Mach number M∞ = 2.9 and Reynolds number Re∞ = 5581 to investigate the expansion effect on the characteristic features of this phenomenon. Four expansion angles, i.e. α = 00 (flat-plate), 20, 50 and 100 are considered. The nominal impingement point of the oblique shock wave with a flow deflection angle of 120 is fixed at the onset of the expansion corner, and flow conditions are kept the same for all cases. The numerical results are in good agreement with previous experimental and numerical data. Various flow phenomena, including the flow separation, the post-shock turbulent boundary layer and the flow unsteadiness in the interaction region, have been systematically studied. Analysis of the instantaneous and mean flow fields indicates that the main effect of the expansion corner is to significantly decrease the size and three-dimensionality of the separation bubble. A modified scaling analysis is proposed for the expansion effect on the interaction length scale, and a satisfactory result is obtained. Distributions of the mean velocity, the Reynolds shear stress and the turbulent kinetic energy show that the post-shock turbulent boundary layer in the downstream region experiences a faster recovery to the equilibrium state as the expansion angle is increased. The flow unsteadiness is studied using spectral analysis and dynamic mode decomposition, and dynamically relevant modes associated with flow structures originated from the incoming turbulent boundary layer are clearly identified. At large expansion angle (α=100), the unsteadiness of the separated shock is dominated by medium frequencies motions, and no low frequency unsteadiness is observed. The present study confirms that the driving mechanism of the low frequency unsteadiness is strongly related to the separated shock and the detached shear layer.

Wavelet-based adaptive delayed detached eddy simulations for wall-bounded compressible turbulent flows

A novel wavelet-based adaptive delayed detached eddy simulation (W-DDES) approach for simulations of wall-bounded compressible turbulent flows is proposed. The new approach utilizes anisotropic wavelet-based mesh refinement and its effectiveness is demonstrated for flow simulations using the Spalart–Allmaras DDES model. A variable wavelet thresholding strategy blending two distinct thresholds for the Reynolds-averaged Navier–Stokes (RANS) and large-eddy simulation (LES) regimes is used. A novel mesh adaptation on mean and fluctuating quantities with different wavelet threshold levels is proposed. The new strategy is more accurate and efficient compared to the adaptation on instantaneous quantities using a priori defined uniform thresholds. The effectiveness of the W-DDES method is demonstrated by comparing the results of the W-DDES simulations with results already available in the literature. Supersonic plane channel flow for two different configurations is tested as benchmark wall-bounded flows. Both the accuracy indicated by the threshold and efficiency in terms of degrees of freedom for the novel adaptation strategy are successfully gained compared with the wavelet-based adaptive LES method. Moreover, the newly proposed W-DDES resolves the typical log-layer match issue encountered in the conventional non-adaptive DDES method mainly due to the use of wavelet-based adaptive mesh refinement. The W-DDES capability for simulations of complex turbulent flows is validated by two other flow configurations – a subsonic channel flow with periodic hill constrictions and a supersonic flow over a compression ramp inducing the shock wave–turbulent boundary layer interaction. The current study serves as a crucial step towards construction of a unified wavelet-based adaptive hierarchical RANS/LES modelling framework, capable of performing simulations of varying fidelities from no-modelling direct numerical simulations to full-modelling RANS simulations.

Numerical analysis of shock wave and supersonic turbulent boundary interaction between adiabatic and cold walls

ABSTRACTDirect numerical simulations of shock wave and supersonic turbulent boundary layer interaction in a 24° compression ramp with adiabatic and cold-wall temperatures are conducted. The wall temperature effects on turbulence structures and shock motions are investigated. The results are validated against previous experimental and numerical data. The effects of wall cooling on boundary layer characteristics are analysed. Statistical data show that wall cooling has a significant effect on the logarithmic region of mean velocity profile downstream the interaction region. Moreover, the influence of wall temperature on Reynolds stress anisotropy is mainly limited in the near-wall region and has little change on the outer layer. As the wall temperature decreases, the streamwise coherency of streaks increases. Based on the analysis of instantaneous Lamb vector divergence, the momentum transport between small-scale vortices on cold-wall condition is significantly enhanced. In addition, spectral analysis of wall pressure signals indicates that the location of peak of low-frequency energy shifts toward higher frequencies in cold case. Furthermore, the dynamic mode decomposition results reveal two characteristic modes, namely a low-frequency mode exhibiting the breathing motion of separation bubble and a high-frequency mode associated with the propagation of instability waves above separation bubble. The shape of dynamic modes is not sensitive to wall temperature.

Heat transfer and wall temperature effects in shock wave turbulent boundary layer interactions

Heat transfer and wall temperature effects in shock wave turbulent boundary layer interactions

An experimental and computational study of the flow pattern in a refrigerant ejector. Validation of turbulence models and real-gas effects

This investigation presents a study based on experimental and numerical flow pattern in a R134-a ejector. Furthermore, the entrainment ratio has also been analysed. The geometry of the ejector has a long tapered mixing chamber designed to improve pressure recovery. The numerical simulation is used to explain the flow features related with the static pressure profiles measurements, as well as a test case for the CFD validation. In this regard, an initial study has been undertaken in order to gain an insight into the CFD uncertainties in three relevant cases related to the ejector flow physics, namely turbulence modelling, real gas thermodynamics and shock-wave turbulent boundary layer interaction.The double-choked and mixed regime have been realized in this study. Both the standard k−ε and the SST k−ω turbulence models show good agreement between the experimental and computed pressure profiles. Regarding the entrainment ratio prediction, it was better for the latter in the double-choked regime. However, for the mixed regime, it was found that the numerical analysis could not yield a reliable entrainment ratio value using any of the turbulence models employed, although the pressure profile was accurately computed. An explanation for this contradiction has been found in this investigation. Furthermore, the numerical analysis has helped to explain the differences found between the measured pressure profiles and the one-dimensional theory prediction.

Nonlinear spectral-like schemes for hybrid schemes

In spectral-like resolution-WENO hybrid schemes, if the switch function takes more grid points as discontinuity points, the WENO scheme is often turned on, and the numerical solutions may be too dissipative. Conversely, if the switch function takes less grid points as discontinuity points, the hybrid schemes usually are found to produce oscillatory solutions or just to be unstable. Even if the switch function takes less grid points as discontinuity points, the final hybrid scheme is inclined to be more stable, provided the spectral-like resolution scheme in the hybrid scheme has moderate shock-capturing capability. Following this idea, we propose nonlinear spectral-like schemes named weighted group velocity control (WGVC) schemes. These schemes show not only high-resolution for short waves but also moderate shock capturing capability. Then a new class of hybrid schemes is designed in which the WGVC scheme is used in smooth regions and the WENO scheme is used to capture discontinuities. These hybrid schemes show good resolution for small-scales structures and fine shock-capturing capabilities while the switch function takes less grid points as discontinuity points. The seven-order WGVC-WENO scheme has also been applied successfully to the direct numerical simulation of oblique shock wave-turbulent boundary layer interaction.

Numerical simulation of ramp induced shock wave/boundary-layer interaction in turbulent flow

AbstractA computational study has been carried out to analyse the shock wave turbulent boundary layer interaction in a two-dimensional compression ramp flow for a free stream Mach number of 2·94. Ramp angles ranging from 8° to 24° are used to produce the full range of possible flow fields, including flows with minor separation, moderate separation, and significant amount of separation. The model has been analysed using 2D numerical simulations based on a commercially available Computational Fluid Dynamics (CFD) Code, Fluent, that employs k-ω Shear Stress Transport (SST) turbulence model. The computed data for surface pressure distribution indicated a good agreement with experiment. Numerical results obtained through the present series of computations indicate an increased extent of separated zone, and thus show increased upstream influence when compared to experiment. Total pressure loss has shown to increase downstream of separation location and increase when corner angle increases. Secondary separation has been observed for higher angles.

Low-frequency unsteadiness in shock wave–turbulent boundary layer interaction

AbstractThe low-frequency unsteadiness is characterized in the direct numerical simulation of a shock wave–turbulent boundary layer interaction generated by a $2{4}^{\ensuremath{\circ} } $ compression ramp in Mach 2.9 flow. Consistent with experimental observations, the shock wave in the simulation undergoes a broadband streamwise oscillation at frequencies approximately two orders of magnitude lower than the characteristic frequency of the energetic turbulent scales in the incoming boundary layer. The statistical relation between the low-frequency shock motion and the upstream and downstream flow is investigated. The shock motion is found to be related to a breathing of the separation bubble and an associated flapping of the separated shear layer. A much weaker statistical relation is found with the incoming boundary layer. In order to further characterize the low-frequency mode in the downstream separated flow, the temporal evolution of the low-pass filtered flow field is investigated. The nature of the velocity and vorticity profiles in the initial part of the interaction is found to change considerably depending on the phase of the low-frequency motion. It is conjectured that these changes are due to an inherent instability in the downstream separated flow, and that this instability is the physical origin of the low-frequency unsteadiness. The low-frequency mode observed here is, in certain aspects, reminiscent of an unstable global mode obtained by linear stability analysis of the mean flow in a reflected shock interaction (Touber & Sandham, Theor. Comput. Fluid Dyn., vol. 23, 2009, pp. 79–107).

Reconstruction of velocity fields from wall pressure measurements in a shock wave/turbulent boundary layer interaction

We present here experimental results in a shock wave/turbulent boundary layer interaction at Mach number of 2.3 impinged by an oblique shock wave, with a deflection angle of 9.5°, as installed in the supersonic wind tunnel of the IUSTI laboratory, France. For such a shock intensity, strong unsteadiness are developing inside the separated zone involving very low frequencies associated with reflected shock motions.The present work consists in simultaneous PIV velocity fields and unsteady wall pressure measurements. The wall pressure and PIV measurements were used to characterize the pressure distribution at the wall in an axial direction, and the flow field associated. These results give access for the first time to the spatial-time correlation between wall pressure and velocity in a shock wave turbulent boundary layer interaction and show the feasibility of such coupling techniques in compressible flows. Linear Stochastic Estimation (LSE) coupled with Proper Orthogonal Decomposition (POD) has been applied to these measurements, and first results are presented here, showing the ability of these techniques to reproduce both the unsteady breathing of the recirculating bubble at low frequency and the Kelvin–Helmholtz instabilities developing at moderate frequency.

Time-Frequency Analysis of Rocket Nozzle Wall Pressures during Start-up Transients

Surveys of the fluctuating wall pressure were conducted on a sub-scale, thrust-optimized parabolic nozzle in order to develop a physical intuition for its Fourier-azimuthal mode behavior during fixed and transient start-up conditions. These unsteady signatures are driven by shock wave turbulent boundary layer interactions which depend on the nozzle pressure ratio and nozzle geometry. The focus however, is on the degree of similarity between the spectral footprints of these modes obtained from transient start-ups as opposed to a sequence of fixed nozzle pressure ratio conditions. For the latter, statistically converged spectra are computed using conventional Fourier analyses techniques, whereas the former are investigated by way of time-frequency analysis. The findings suggest that at low nozzle pressure ratios –where the flow resides in a Free Shock Separation state– strong spectral similarities occur between fixed and transient conditions. Conversely, at higher nozzle pressure ratios –where the flow resides in Restricted Shock Separation– stark differences are observed between the fixed and transient conditions and depends greatly on the ramping rate of the transient period. And so, it appears that an understanding of the dynamics during transient start-up conditions cannot be furnished by a way of fixed flow analysis.