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Wall-Resolved Large Eddy Simulations of Transonic Shock-Induced Flow Separation

This paper reports the wall-resolved large eddy simulations of shock-induced boundary layer separation over an axisymmetric bump for a flow Mach number of 0.875 and a chord-based Reynolds number of 2.763 million. The incoming boundary layer has a momentum-thickness Reynolds number of 6600 at one and a half chord lengths upstream of the leading edge. The calculations simulate the experiment by Bachalo and Johnson (AIAA Journal, Vol. 24, No. 3, 1986), except that the tunnel walls are ignored and the simulations are performed assuming free air with as many as 24 billion grid points. The effects of domain span, grid resolution and time step on the predictions are examined. The results are found to show some sensitivity to the studied parameters. Owing to the outer boundary conditions, the predicted surface pressure distribution as well as the flow separation and reattachment locations tend to agree better with the experimental results from the larger (6 × 6 ft) tunnel than those from the smaller (2 × 2 ft) tunnel. The predicted Reynolds shear stress profiles in the separated region differ by as much as 31%from the experimental results that were only obtained in the smaller tunnel. The most accurate surface pressure distribution obtained in this study lies within the scatter of the measurements taken in the two facilities.

Uzun, Ali↗

Wall-Resolved Large-Eddy Simulations of Transonic Shock-Induced Flow Separation

Wall-resolved large-eddy simulations of shock-induced flow separation over an axisymmet- ric bump for a Mach number of 0.875 and a chord-based Reynolds number of 2.763 million are performed. The incoming boundary layer has a momentum-thickness Reynolds number of 6600 at 1.5 chords upstream of the bump. The calculations, which employ up to 24 billion grid points, simulate the experimental model of Bachalo and Johnson (AIAA Journal, Vol. 24, No. 3, 1986), except that the tunnel walls are ignored and free air is assumed. The effects of domain span and grid resolution are examined along with the main flowfield features. The predicted shock position as well as separation and reattachment locations agree well with the experiment. Grid convergence is observed in the attached region well upstream of separation. Two-point azimuthal correlations suggest that a span of at least 20 degrees is needed in the attached region, while a 120-degree span might be barely large enough in the separated region. Computed root-mean-square surface pressure fluctuations at the shock foot reach about 5 percent of ambient pressure and the level at reattachment location drops to about half of the primary peak. Simulations reveal evidence of the low-frequency shock unsteadiness; however, a much longer statistical sample is needed to investigate this phenomenon.

Uzun, Ali↗

Wall-Resolved Large-Eddy Simulation of Flow Separation Over NASA Wall-Mounted Hump

This paper reports the findings from a study that applies wall-resolved large-eddy simulation to investigate flow separation over the NASA wall-mounted hump geometry. Despite its conceptually simple flow configuration, this benchmark problem has proven to be a challenging test case for various turbulence simulation methods that have attempted to predict flow separation arising from the adverse pressure gradient on the aft region of the hump. The momentum-thickness Reynolds number of the incoming boundary layer has a value that is near the upper limit achieved by recent direct numerical simulation and large-eddy simulation of incompressible turbulent boundary layers. The high Reynolds number of the problem necessitates a significant number of grid points for wall-resolved calculations. The present simulations show a significant improvement in the separation-bubble length prediction compared to Reynolds-Averaged Navier-Stokes calculations. The current simulations also provide good overall prediction of the skin-friction distribution, including the relaminarization observed over the front portion of the hump due to the strong favorable pressure gradient. We discuss a number of problems that were encountered during the course of this work and present possible solutions. A systematic study regarding the effect of domain span, subgrid-scale model, tunnel back pressure, upstream boundary layer conditions and grid refinement is performed. The predicted separation-bubble length is found to be sensitive to the span of the domain. Despite the large number of grid points used in the simulations, some differences between the predictions and experimental observations still exist (particularly for Reynolds stresses) in the case of the wide-span simulation, suggesting that additional grid resolution may be required.

Uzun, Ali↗

High-Fidelity Simulation of Turbulent Flow Past a Gaussian Bump

A spanwise-periodic computation of a turbulent flow past a Gaussian bump is performed in the form of a hybrid direct numerical simulation and wall-resolved large-eddy simulation. A fourth-order spatially-accurate flow solver is employed to perform the simulation, using 10.2 billion grid points for a Reynolds number of 170000 based on the bump height. The key findings from the simulation are reported in the acceleration and deceleration flow regions associated with the bump shape. Significant anisotropy in the normal Reynolds stresses, along both the wall-normal and streamwise directions, is observed within the acceleration region. The ratio between the Reynolds shear stress and turbulent kinetic energy in that region also experiences significant deviations from the norms of a zero pressure gradient turbulent boundary layer. The chosen Reynolds number generates strong flow separation in the adverse pressure gradient region, which is in contrast with a previous simulation at half the Reynolds number that only indicated incipient separation. An internal layer generated in the acceleration region evolves into a free shear layer that develops in the deceleration region and separates. Proper modeling of this inner layer appears crucial to predict the flow separation. Surface curvature effects on the attached flow development are also discussed.

Turbulent Boundary Layer↗

Implicit Large-Eddy Simulation of Axisymmetric and Asymmetric Turbulent Shock Wave Boundary Layer Interaction at Mach 2.5

High-speed inlet flows feature turbulent shock wave boundary layer interactions at supersonic Mach numbers. A canonical Mach 2.5 shock wave boundary layer interaction experiment at the NASA Glenn Research Center was designed for axisymmetric and asymmetric interactions depending on the placement of the shock generator. Four different wall-resolved implicit large-eddy simulations of the experiment were carried out at one-tenth of the Reynolds number of the experiment: (1) Two axisymmetric interactions with shock generator radii of 9.2% and 14.7% of the test section diameter and (2) two asymmetric interactions with 14.7% shock generator radius and shock generator centerline offsets of one-third and one-fourth of the test section radius. For the two axisymmetric interactions, various sub-domains upstream of the interaction, within the interaction, and downstream of the interaction were analyzed with the proper orthogonal decomposition. For all three regions, the dominant modes are streamwise coherent structures with Strouhal numbers based on separation length of 0.15 and below. Fourier spectra of the wall-pressure coefficient for the interaction region have peaks at Strouhal numbers based on separation length of 0.15 and 0.04. For the two asymmetric interactions, the streamwise extent of the separation varies considerably in the azimuthal direction. For both shock generator offsets, the interaction is strongest for the azimuthal location that is closest to the shock generator. Compared to the axisymmetric interaction, the streamwise extent of the separated flow region is noticeably reduced and a substantial crossflow is observed. Fourier analyses of the unsteady flow indicate low-frequency content f or the upstream part of the interaction which is more two-dimensional. Away from the upstream region, with increasing sweep angle and crossflow, the low-frequency content is diminished.

Computational Fluid Dynamics↗

Sidewall Effects on Exact Reynolds-Stress Budgets in an Impinging Shock Wave/Boundary Layer Interaction

Large-eddy simulations are performed using wall-resolved mesh for a Mach 2.29 impinging shock wave/boundary-layer interaction. Flow conditions are based on an experiment and therefore entire span was simulated, including the two sidewalls. Mean flow comparison with the experimental data showed that the interaction was larger in the simulation. Time-series analysis of a rake of pressure probes immediately downstream of the mean reflected shock position showed a peak in weighted power spectral density occurred about $St_{Lint}=0.01$, owing to a larger interaction length. Budgets of Reynolds-stress transport calculated across the span and along the corner bisector showed high degree of anisotropy. Merging of the secondary flows and separation along the corner gives rise to unstablecounter rotating vortices, which straddle the corner and grow in size. This also leads to a development of new behavior in the viscous sublayer along the corner bisector, where the pressure strain andmolecular diffusion mechanisms become prominent.

Vyas, Manan A.↗

LES Analysis of Loss Anomaly in a Turbine Blade with Large Trailing Edge Radius

There is great interest in the usage of Ceramic Matrix Composites (CMC) as a turbine blade material. CMCs can tolerate higher temperatures than alloyed metallic blades, resulting in better thermal efficiency of gas turbine engines. However, depending on the manufacturing process of the CMC, blades may have a larger trailing edge thickness. The design space therefore needs to be updated due to the resulting flow physics. Recently, experimental results acquired at NASA Glenn Transonic Turbine Blade Cascade Rig showed that a loss measure generally increased with increasing trailing edge thickness. For one case however, the losses initially decreased with increasing Reynolds number but rose and peaked at Re ~1.24x10 6 and then subsequently dropped to the original pre-peak trend. A possible cause of this intriguing phenomenon was speculated to be transonic vortex shedding, which is the mechanism of vortex shedding promoted by reflected shed pressure waves at the trailing edge at relatively high Reynolds numbers and higher Mach numbers. A Reynolds-averaged Navier-Stokes (RANS) analysis or a low-resolution large eddy simulation (LES) does not reproduce this apparent anomaly and thus it is worth performing a wall-resolved LES (the total mesh count of ~290 million cells) to investigate the aerodynamics of the CMC blade in the context of transonic vortex shedding. Our numerical results at Re=1,246,350 show that the pressure waves generated by the vortex shedding in the wake travel upstream and significantly influence the transition and separation on the suction side thus enhancing the said vortex shedding in the wake. This feedback seems not to hold under a low-Re condition (Re=621,900). The Reynolds number dependence was also examined by numerical perturbation of the pressure waves in the wake and by examining how such perturbation attenuates or endures. It is confirmed that the perturbation of the pressure waves is quickly damped.

LES↗

A Dynamic Nonlinear Subgrid-Scale Model for Large-Eddy Simulation of Complex Turbulent Flows

We present a new dynamic nonlinear subgrid-scale (SGS) model for large-eddy simulations (LES) and apply it to compute a flow involving pressure gradients, surface curvature and separation, for which data from a direct numerical simulation are available for comparison. The model, inspired by the triple model idea of Bardina et al. (“Improved Turbulence Models Based on Large Eddy Simulation of Homogeneous, Incompressible, Turbulent Flows,” Report No. TF-19, Thermosciences Division, Department of Mechanical Engineering, Stanford University, 1983), includes a Galilean-invariant term called the modified Leonard stress tensor, and two nonlinear terms comprised of the products of the strain-rate and rotation-rate tensors for an improved representation of the subgrid-scale dissipation, backscatter and anisotropy effects. The model does not employ any ad hoc averaging or clipping procedures, and does not require the specification of a characteristic length scale; hence, it naturally avoids the ambiguities associated with defining a proper length scale for anisotropic grids. Results from the wall-resolved LES of flow past a Gaussian bump using the new model demonstrate improved prediction of skin-friction, flow separation, mean flow profiles and turbulent quantities when compared to implicit LES as well as explicit LES using the Vreman SGS model on the same grid.

Turbulence↗