Session T10: Compressible Flows: Shock-Boundary Layer Interactions

Large eddy simulations of shock-boundary layer interactions in supersonic turbine cascades with adiabatic and isothermal walls

Large eddy simulations are employed to investigate the flow in a supersonic turbine cascade with adiabatic and cooled walls. The inlet Mach number is set as 2.0, and the Reynolds number based on the inlet velocity and axial chord is 200,000. For the isothermal case, the ratio of wall to inlet temperatures is 0.75. The effects of wall cooling on the shock-boundary layer interaction are evaluated through flow visualization and spectral analysis. The results indicate that the impinging shock penetrates deeper in the boundary layer for the cooled wall setup due to the displacement of the sonic line towards the wall. This, in turn, leads to a smaller suction side separation bubble. For the adiabatic case, strong heating effects are observed within the separation bubble, while higher temperatures are observed along the free shear layer downstream the bubble when cooling is applied. An analysis of the unsteadiness of the separation bubbles shows that their breathing patterns are similar, independently of the thermal conditions. Finally, the spectral characteristics of the separation bubbles and shock systems are also investigated.   

Analysis of shock-boundary layer interactions in a supersonic turbine cascade using LES.

A wall-resolved large eddy simulation is employed to investigate the unsteadiness of shock-boundary layer interactions (SBLIs) in a supersonic turbine cascade at Mach 2.0 and Reynolds number 395,000, based on the inlet velocity and the axial chord. The low-frequency dynamics of the interaction, including the separation bubble, shear layer and shock waves, is characterized using flow visualization and spectral analysis. The mean flowfield displays different impinging shock structures through the turbine cascade. On the suction side, an oblique shock interacts with the boundary layer, while a Mach reflection is formed on the pressure side. Instantaneous flow visualizations reveal the influence of upstream large-scale structures on the separation bubble motion. In addition, space-time correlations indicate that those structures drive the breathing of the separation bubble on the suction side. These correlations also suggest the existence of a π phase jump in the pressure fluctuations along the separation bubble. Despite some peculiarities regarding the curved wall of the turbine blade, the spectral analysis shows that the characteristic frequencies of the SBLIs are similar to those reported in impinging oblique shocks on flat plates, and compression-ramp interactions. However, some discrepancies are also reported, including the lack of a separation shock and the presence of low-frequency fluctuations on the reattachment location. The latter occurs due to the interaction between the streaky structures and the incident shock.   

Surface Flow Characteristics of Double-Fin Shock-Wave/Boundary-Layer Interactions

Shock-Wave/Boundary-Layer Interaction (SBLI) is ubiquitous for supersonic and hypersonic air vehicles, and can often lead to undesirable effects on internal and/or external aerodynamics. Even in simple geometries, SBLI flow fields are complex where the fundamental flow physics remains the subject of studies so that the adverse effects can be minimized or controlled for practical applications. In the present study, a crossing-shock SBLI generated by using a Double-Fin is experimentally investigated at Mach 2 and 3 as a canonical building block SBLI. Corresponding Single-Fin generated SBLI are also examined for comparison with the Double-Fin flowfield. Surface flow visualization is utilized to clearly document pertinent surface features such as the separation line, upstream influence and shock crossing. In order to capture the global surface pressure field beneath the interaction, conventional and fast response Pressure Sensitive Paint (PSP) are used to obtain mean and unsteady pressure maps. Spectral Proper Orthogonal Decomposition of the unsteady PSP fields reveals the existence of traveling pressure waves on the surface, originating from upstream influence. The behavior of these waves and other interesting interaction dynamics revealed through these experiments are discussed.   

Influence of Upstream Flow Perturbations on Blunt Fin Induced Shock-Wave / Boundary-Layer Interaction Unsteadiness

Detached eddy simulations were performed to study separation unsteadiness in a Mach 3, blunt fin induced shock-wave / boundary-layer interaction. Baseline simulations showed reasonable agreement with experimental measurements. The response of the separation unsteadiness to upstream flow perturbations was initially investigated by injecting synthetic turbulence, generated via a digital filter method, at the inflow boundary. A weak, but detectable correlation was found between the incoming turbulent fluctuations and the low-frequency separation motion. Inflow profiles of velocity perturbations, conditionally averaged based on separation motion, were used to design an artificial upstream time-periodic body force. With a forcing frequency representative of the characteristic large-scale separation unsteadiness in the baseline flow, the separation shock motion was phase locked to the applied force. These results demonstrate that upstream forcing of a certain form can modulate the separation motion of a strong interaction, where significant unsteadiness is exhibited even in the absence of upstream perturbations. These results are consistent with the findings from previous studies of weaker interactions, and imply possibilities for flow control of strong interactions.   

Study of fluid-structure interaction under a shock/boundary-layer interaction in Mach 2 flow using synchronous 50 kHz PIV and 5 kHz DIC

Fluid-structure interaction (FSI) is a phenomenon where the structural motion responds and couples to the flow field.  For instance, in supersonic/hypersonic flight, the frictional heating of the flow can lead to increased compliance and the presence of shock-induced separation can lead to rapid fatigue of the structure. To understand the physics of FSI, an experimental investigation of a thin panel response under a compression-ramp-induced shock/boundary-layer interaction using simultaneous 50 kHz PIV and 5 kHz stereoscopic DIC has been conducted. Streamwise (U), wall-normal (V) velocities and out-of-plane displacement have been measured. The effect of the mean panel deformation has been noticed: the average U velocity near the wall has been shown to change its magnitude in response to the streamwise slope of the panel deformation. Furthermore, the cross-correlation between the V-velocity fluctuation and the mean-subtracted panel displacement has been evaluated. The strong correlation results suggest that the flow remains tangent to the wall surface as the panel undergoes low-frequency deformation. Lastly, the possible coupling mechanism between the panel displacement and the unsteady dynamics of the separation shock motion will be discussed.

    

Numerical simulation of the interaction of oscillating oblique shock waves and turbulent boundary layers over flexible and rigid surfaces

Coupled fluid-structure interaction (FSI) simulations that integrate a finite-volume wall-modeled LES (WMLES) flow solver and a finite-element (FEM) solid mechanics solver are used to study the interaction of forced oscillating oblique shocks impinging on turbulent boundary layers (TBL) developed along rigid and flexible panels. The methodology of the coupled solver enables long integration times needed for spectral analysis while maintaining physical fidelity. Simulations are performed for a Mach 3 TBL interacting with a dynamic shock-expansion system generated by a wedge periodically rotating between 15.5 and 17.5 degrees, at different oscillating frequencies ranging from 50 to 800 Hz over rigid and elastic panels. The deflection of the flexible panel is found to be excited by wedge oscillation frequencies close to the primary natural frequency of the panel. Increasing the oscillation frequency over both rigid and flexible walls results in an attenuated response of the flow separation bubble. The gain and phase angle of several quantities of interest of the STBLI are studied as a function of the wedge oscillation frequency.   

Author not Attending

The transonic flow past airfoils and wings is associated with shock-wave/boundary layer interactions that induce flow separation. For particular combinations of Mach number and angle of attack, buffet (a large-scale periodic and self-sustained oscillation of the shock wave) occurs. As this highly unsteady phenomenon severely limits the aerodynamic performance and flight envelope, its understanding is crucial for the design of aircraft. Explanatory models predicting the phenomenon name pressure waves generated at the airfoil trailing edge as an integral driving force to the governing mechanism that maintains the shock oscillation. We study the propagation velocity of pressure waves along the airfoil upper surface, as well as the associated shedding frequency, on the basis of high-speed focusing-schlieren measurements. We captured the airfoil and a portion of the wake at an acquisition rate of 20 kHz. A thorough analysis of the pressure waves regarding the inherent variation in strength, propagation velocity, and frequency within the buffet cycle gives insight into the role of the waves regarding the back-and-forth motion of the shock wave.

We gratefully acknowledge the support of the German Research Foundation DFG in the framework of the Research Unit FOR 2895 (project number 406435057).

    

Author not Attending

The effect of the wall temperature on the shock boundary layer interaction over a 24° ramp at free-stream Mach number of 2.25 was investigated using high-fidelity simulation. Reynolds number of 1800 based on the momentum thickness transitioned to fully developed turbulent flow by employing a counterflow actuator.  Two wall conditions, adiabatic and hot wall thermal conditions were considered. Strong heat transfer through the wall produced a significant dilatation in the interaction region. Both the upstream and downstream turbulent statistics at each wall condition were studied to weigh the contribution to the low-frequency unsteadiness in the interaction region. The resulting Reynolds stress anisotropy tensor exhibited different patterns of turbulence development in the inner layer and outer layer in response to the heating effect. Turbulent statistics revealed that the flow separation frequency scaled with the incoming turbulent structures and heat transfer within the interaction region, which consequently altered the separation length.

    

Investigation of Wall Temperature Effects on Shock-Wave Turbulent Boundary Layer Interaction in a Compression Ramp using Large-Eddy Simulations

Shock-wave turbulent boundary layer interaction (STBLI) occurring within high-speed aerospace applications is characterized by unsteady and nonlinear multi-scale and multi-physics phenomena such as boundary layer thickening, shock dynamics, shock-induced separation/reattachment, intense thermo-mechanical loading, temperature effects, and low-frequency unsteadiness. The present study examines the effects of wall temperature on the features of STBLI in terms of the ratio of wall temperature to recovery temperature (T_w/T_r). The computational setup follows past studies and corresponds to a supersonic flow over a 24-degree compression ramp with a freestream Mach number of 2.9 and the freestream Reynolds number per unit millimeter of 5581.4. The dynamic one-equation model is used to perform wall-resolved large-eddy simulation (LES) at T_w/T_r = 0.6, 1.14, 1.4, and 2. The results are examined to assess the ability of LES to capture the effects of wall temperature on the statistics of the separation bubble by comparing with reference results from the literature. Additionally, the results are analyzed to examine the non-equilibrium aspects of the near-wall turbulence dynamics in the vicinity of the separation bubble.   

On low-frequency unsteadiness in three-dimensional shock/boundary layer interactions

We carry out DNS of shock/boundary layer interactions (SBLI) in the presence of cross flow, as a surrogate of genuine three-dimensional SBLI. Use of spanwise wide computational domains suggests the presence of organized, large-scale rippling of the instantaneous flow separation line, on a typical length scale proportional to the mean separation extent. We present evidence that In the presence of cross flow these ripples are advected at a fraction of the mean spanwise velocity. Based on the observed data we obtain a predictive formula for the typical frequency of the large-scale unsteadiness, which very well conforms with the computed frequency spectra. In agreement with what observed in experiments and DNS of three-dimensional SBLI, the typical frequency is predicted to increase with the flow skew angle.   

Not Participating

Hypersonic systems are characterized by high-dimensional, nonlinear dynamical systems with structures across a large range of scales. Despite the apparent complexity of such flows, persistent behaviors are often determined by the balance of a few dominant physical processes that might be and the governing equations can be dramatically simplified. High fidelity numerical simulations of shock wave/turbulent boundary layer interactions (STBLIs) are analyzed via dynamic mode decomposition (DMD) and spectral proper orthogonal decomposition (SPOD) to uncover dynamically significant low-frequency modes. The results of each modal analysis are presented and the three-dimensional modal reconstructions for the DMD and SPOD are compared. The sparse identification of nonlinear dynamics (SINDy) algorithm is applied to the modal coefficients to develop low-order models for the low frequency dynamics present in the STBLIs. The SINDy models are compared to the numerical data, and we assess and discuss their performance.   

Not Participating

High fidelity simulations of shock-turbulent boundary layer interactions (STBLI) solve the complex nonlinear governing equations requiring massive computational resources. However, local regions of the flow can often be reduced to a dominant subset of physical processes. Traditionally, simplification of the governing equations to approximate the local dominant physics have relied on analytical methods such as dimensional analysis and asymptotic methods. These approaches are however mathematically cumbersome for complex flows. In this work, the turbulent compressible governing equations for a canonical shock-separated ramp flow are reduced to local dominant subsets using machine learning methods. Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) data are used to generate data-driven models which are used to automatically identify distinct local regions of dominant physics. The method herein uses a Gaussian Mixture Model (GMM) probabilistic framework to cluster the data into dominant balance regions. Each cluster represents a set of active terms that approximates the full governing equations. Sparse Principal Components Analysis (SPCA) is then applied to combine redundant clusters. The resulting automatically identified local dominant balance regions and their physical interpretations are compared with apriori analyses. The prediction accuracy and viability of the method to uncover reduced-order mechanistic models in STBLI flows and for general application to multi-scale, multi-physics flows are discussed.