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Sensitivity to Snapshot Frequency in the POD-Based Reduced-Order Modeling of Flow over a Gaussian Bump

The flow over a Gaussian bump at a Reynolds number of 10^6, based on the bump length and freestream conditions, and a Mach number of 0.2, was simulated using wall-modeled large eddy simulation (WMLES). The incoming turbulent flow exhibits relaminarization upstream of the bump apex, due to the favourable pressure gradient acceleration induced by the bump curvature, as well as separation, reattachment and a detached shear layer downstream of the apex. A Galerkin reduced-order model (ROM) was then constructed using a proper orthogonal decomposition (POD) modal basis. The complex, three-dimensional flow features are captured by spatial POD modes differently based on the frequency of the high-fidelity snapshots originally provided. POD modes constructed from differently sampled snapshot matrices were then truncated to retain 90% of the turbulence kinetic energy in the domain of interest. A parametric study is conducted to evaluate the effect of the frequency of snapshots used to construct the POD-ROM.

turbulence↗

Direct Numerical Simulation of Flow Past a Gaussian Bump at a High Reynolds Number

We present the results from a direct numerical simulation of a spanwise-periodic turbulent flow past a Gaussian bump. The problem setup is designed to investigate the interaction of an incoming turbulent boundary layer with the strong favorable and adverse pressure gradients generated by the Gaussian bump as the flow passes over it at a Reynolds number of 340000 based on the bump height, or 4 million based on the bump length. The statistical results from the present simulation are compared against our earlier results at a Reynolds number of 2 million. An internal layer, which forms beneath the strongly accelerated boundary layer over the windward side of the bump, is found to generate its near-wall turbulence stress peaks in closer proximity of the wall in the higher Reynolds-number case. Furthermore, the logarithmic layer of the higher Reynolds-number boundary layer appears more resistant to changes induced by strong acceleration and surface curvature effects over the same region. Despite a nearly identical flow separation point in the two flows, the detached shear layer grows at a faster rate and subsequently reattaches at an earlier point in the higher Reynolds-number flow. The surface pressure and skin-friction distributions over the attached flow region compare well against the corresponding experimental data for both flows. However, some differences appear in the separated flow region, which are attributed to the three-dimensionality of the experimental model setup that is not included in the simulation owing to the spanwise periodic assumption. Comparisons with the stereoscopic particle image velocimetry measurements on the central plane of the experimental model over the windward side of the bump show reasonable overall agreement in the mean velocity components, but the turbulence stress components do not agree well at some streamwise locations. Comparisons over the leeward side of the bump show that the mean separated shear layer in the simulation is tilted significantly more toward the wall than the experimental shear layer on the central plane. This mismatch in the mean shear layer orientation is due to the experimental model three-dimensionality and tunnel end-wall effects, which are not modeled in the present spanwise-periodic simulation.

Favorable and Adverse Pressure Gradients↗

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↗

Wall-modeled LES of Flow Over a Gaussian Bump

We perform wall-modeled large eddy simulations (WMLES) of turbulent flow over a Gaussian-shaped bump geometry, to assess its performance in the accelerating and separation regions of the flow. The flow conditions are based on the ongoing CFD validation experiments of Slotnick [NATO STO-MP-AVT-307, 2019]. The oncoming flow Mach number is 0.176, and two Reynolds numbers are simulated that are about 10000 and 36000 based on boundary layer thickness upstream of the bump. Preliminary Reynolds-averaged Navier-Stokes simulations are first performed to assess the effects of Mach number, Reynolds number, tunnel top and sidewall effects. Finally, WMLES results with an equilibrium wall model will be presented at two Reynolds numbers to assess their performance for this flow by making detailed comparisons with available experimental and higher-fidelity numerical data.

turbulence, wall model, large eddy simulation↗

Wall-modeled LES of Flow Over a Gaussian Bump

We perform wall-modeled large eddy simulations (WMLES) of turbulent flow over a Gaussian-shaped bump geometry, to assess its performance in the acceleration and separation regions of the flow. An unstructured finite-volume solver is used along with an equilibrium wall model. The Mach number of the oncoming flow selected for the simulation is 0.176, and two Reynolds numbers (Re) are simulated that are about 10000 and 36000 based on boundary layer thickness upstream of the bump. Spanwise periodic results for the lower Re case are compared with the available DNS data, while the full three-dimensional simulation results for the higher Re case are compared to available experimental data. Sensitivity of WMLES results are assessed for a number of factors including grid resolution, wall model exchange location, type of wall model, and unstructured grid topology. The WMLES results for the lower Re case agree well with available DNS data in terms of the wall pressure variation, velocity and turbulent stress profile comparisons. The skin-friction predictions show a reduced tendency to separate. This appears to be accentuated for the higher Re case, for the medium resolution grid used in this study, where WMLES does not predict any flow separation in the mean, which is in contrast to the large separation bubble observed in the experiments.

turbulence↗

Wall-modeled LES of Turbulent Flow Over a Two-dimensional Gaussian Bump

We perform wall-modeled large eddy simulations (WMLES) of turbulent flow over a nominally two-dimensional Gaussian-shaped bump geometry to assess its performance in the accelerating and separation regions of the flow. The flow conditions are based on high-fidelity numerical simulation of Uzun & Malik (AIAA Journal 2022). The oncoming flow Mach number is 0.2, with the bump length-based Reynolds number (ReL) of 2 million. In our previous study, while WMLES with the constant coefficient Vreman subgrid scale model and equilibrium wall model performed satisfactorily at lower ReL = 1 million, it failed to predict flow separation at the higher Re, contrary to the experimental observations. We investigate the sensitivity of WMLES to different subgrid scale models, wall models, and grid resolution and topology on flow separation by comparing with available data.

Computational Fluid Dynamics↗

Classification image analysis: estimation and statistical inference for two-alternative forced-choice experiments

We consider estimation and statistical hypothesis testing on classification images obtained from the two-alternative forced-choice experimental paradigm. We begin with a probabilistic model of task performance for simple forced-choice detection and discrimination tasks. Particular attention is paid to general linear filter models because these models lead to a direct interpretation of the classification image as an estimate of the filter weights. We then describe an estimation procedure for obtaining classification images from observer data. A number of statistical tests are presented for testing various hypotheses from classification images based on some more compact set of features derived from them. As an example of how the methods we describe can be used, we present a case study investigating detection of a Gaussian bump profile.

Non-NASA Center↗

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↗

Wall-modeled LES of the Three-dimensional Speed Bump Experiment

We evaluate the performance of wall-modeled large eddy simulation (WMLES) in predicting smooth-body turbulent flow separation for a three-dimensional Gaussian-shaped speed bump geometry. The Reynolds number based on the bump length is 2 million, and an unstructured compressible finite-volume solver is used with an equilibrium wall model and dynamic subgrid scale model. Spanwise periodic simulations of the centerline two-dimensional bump were used to assess grid resolution requirements, and resolving the thin internal layer in the accelerating region was found to be necessary to correctly capture the downstream separated flow region. Based on these insights, an optimized grid that was smaller by a factor of two provided comparable accuracy to a finer grid that has been used by us and other researchers in past studies. Using insights gained from the spanwise periodic simulation, an unstructured polyhderal grid with about 250 million cells was used for the three-dimensional (3D) configuration with inviscid tunnel side and top walls. Detailed comparisons of wall skin-friction coefficient, wall pressure, velocity and turbulent stresses with available experimental data indicated excellent agreement. While the low-Reynolds Number Spalart-Allmaras RANS model with rotation/curvature correction gave qualitatively good agreement with experiments, WMLES showed significantly more accurate quantitative predictions of the flowfield. The 3D WMLES showed good agreement with experiments in the separated region, and the centerplane results indicated a different separation topology compared to the spanwise periodic simulation.

Computational Fluid Dynamics↗

Turbulence Model Validation Through Joint Experimental /Computational Studies of Separated Flow Over A Three-Dimensional Tapered Bump: Part I - Experimental Investigation

The results of a three-year experimental campaign aimed at comprehensively documenting the separated flow over a three-dimensional bump are presented with the purpose of generating a benchmark experimental database useful in validating computational fluid dynamics (CFD) flow simulations. The bump model geometry was designed to provide well-defined and repeatable smooth-body flow separation conditions that were suitable for both experiments and simulations. The bump had a Gaussian streamwise profile with a constant height equal to 8.5% of its width over the central 60% of the test section width. The remaining 40% were outboard spanwise portions that gradually taper to zero using an error function profile to minimize side-wall boundary layer effects. The model was immersed in a turbulent boundary layer that was developed on a suspended flat plate in the Notre Dame Mach 0.6 Wind Tunnel. In order to document the effect of the incoming boundary layer thickness on the flow separation, the bump model could be located at two streamwise positions. The mean velocity and turbulence intensity of the wind tunnel freestream flow field and approaching turbulent boundary layer were fully documented. The measurements of the flow separation region included surface visualization, wall shear stress using oil-film interferometry, mean and dynamic surface pressure, and planar and stereoscopic particle image velocimetry. The experiments were conducted over a range of Mach numbers from 0.05 to 0.2 corresponding to a range of Reynolds numbers based on the test section spanwise dimension (0.914m) of 1.0 × 10 6 ≤ Re L = U ∞ L/ν ≤ 4.0 × 10 6 . The bulk of the results are presented for the higher Mach number conditions of 0.1 and 0.2 with Re L = 2.0 × 10 6 and 4.0 × 10 6 , respectively. Extensive uncertainty analysis of the data was performed. The data is archived in the NASA Langley Turbulence Modeling Resource website at https://turbmodels.larc.nasa.gov/Other_exp_Data/speedbump_sep_exp.html. In addition to the experiments, a computational effort was made in parallel by the CFD group at Boeing Research & Technology highlighting the usefulness of the data set, which is outlined in the accompanying CFD report.

Flow separation↗

Simulations of a Turbulent Flow Subjected to Favorable and Adverse Pressure Gradients

This paper reports the results from a direct numerical simulation of an initially turbulent boundary layer passing over a wall-mounted “speed bump” geometry. The speed bump, represented in the form of a Gaussian distribution profile, generates a favorable pressure gradient region over the upstream half of the geometry, followed by an adverse pressure gradient over the downstream half. The boundary layer approaching the bump undergoes strong acceleration in the favorable pressure gradient region before experiencing incipient or very weak separation within the adverse pressure gradient region. These types of flows have proven to be particularly challenging to predict using lower-fidelity simulation tools based on various turbulence modeling approaches and warrant the use of the highest-fidelity simulation techniques. Simulation results are utilized to examine the key phenomena present in the flowfield, such as relaminarization/stabilization in the strong acceleration region succeeded by retransition to turbulence near the onset of adverse pressure gradient, incipient/weak separation, and development of internal layers where the sense of streamwise pressure gradient changes at the foot, apex and tail of the bump. The present direct numerical simulation is performed using a flow solver developed exclusively for graphics processing units, which is found to provide a significant speedup compared to an earlier solver optimized for central processing unit architectures.

Ali Uzun↗

Deriving Deformable Mirror Performance Requirements in Simulation with Experimental Verification

Coronagraph instruments rely on predictable and stable deformable mirror (DM) surface displacement to achieve the contrast required to detect Earth-sized exoplanets orbiting nearby Solar-type stars. Anomalous DM behavior, such as unstable or pinned actuators, can limit contrast in coronagraphs. Simulating how these undesired behaviors affect the performance of a high contrast imaging architecture is important for developing requirements on their associated hardware. Simulating a vortex coronagraph (VC) with two deformable mirrors, this study quantifies how the number of pinned actuators affect the performance of Focal Plane Wavefront Sensing and Control algorithms using both Grid Search Electric Field Conjugation (EFC) and Planned EFC, which uses Beta-Bumping. The simulation also quantifies how various types of voltage noise such as zero-mean Gaussian noise, zero-mean periodic noise, and drift can affect the contrast of a VC during an observation run. A tolerance of a change in the Mean Normalized Intensity of ${1\times10^{-11}}$ is allocated to both types of error. If Planned EFC is used, only 1 pinned actuator on both DMs can be tolerated. If only pure Grid Search EFC is used the DMs cannot have any pinned actuators. For the case of zero-mean Gaussian noise and zero-mean periodic noise, one can tolerate a noise standard deviation of no more than ${\sigma = 0.45 \text{ mV}}$. For drift, we can only tolerate ${\sigma = 0.30 \text{ mV}}$ or less. These results show that the DM electronics and the DM themselves need to be nearly defect free to avoid having more than 1 pinned actuator. The electronics need to be tested for different types of noise statistics and that both the average and standard deviation of the noise should be measured.

Dean L. Palmer↗

Gravitational clustering in the expanding universe - Controlled high-resolution studies in two dimensions

Results are presented from a series of gravitational clustering simulations in two dimensions. These simulations are a significant departure from previous work, since in two dimensions one can have large dynamic range in both length scale and mass using present computer technology. Controlled experiments were conducted by varying the slope of power-law initial density fluctuation spectra and varying cutoffs at large k, while holding constant the phases of individual Fourier components and the scale of nonlinearity. Filaments are found in many different simulations, even with pure power-law initial conditions. By direct comparison, filaments, called 'second-generation pancakes' are shown to arise as a consequence of mild nonlinearity on scales much larger than the correlation length and are not relics of an initial lattice or due to sparse sampling of the Fourier components. Bumps of low amplitude in the two-point correlation are found to be generic but usually only statistical fluctuations. Power spectra are much easier to relate to initial conditions, and seem to follow a simple triangular shape (on log-log plot) in the nonlinear regime. The rms density fluctuation with Gaussian smoothing is the most stable indicator of nonlinearity.

Beacom, John Francis↗

On the Nature of the Compact Object in SS 433. Observational Evidence of X-Ray Photon Index Saturation

We present an analysis of the X-ray spectral properties observed from black hole , candidate (BHC) binary SS 433. We have analyzed Rossi X-ray Time Explorer (RXTE) data from this source, coordinated with Green Bank Interferometer/RATAN-600. We show that SS 433 undergoes a X-ray spectral transition from the low hard state (LHS) to the intermediate state (IS). We show that the X-ray broad-band energy spectra during all spectral states are well fit by a sum of so called "Bulk Motion Comptonization (BMC) component" and by two (broad and narrow) Gaussians for the continuum and line emissions respectively. In addition to these spectral model components we also find a strong feature that we identify as a" blackbody-like (BB)" component which color temperature is in the range of 4-5 keV in 24 IS spectra during the radio outburst decay in SS 433. Our observational results on the "high temperature BB" bump leads us to suggest the presence of gravitationally redshifted annihilation line emission in this source. In fact this spectral feature has been recently reproduced in Monte Carlo simulations by Laurent and Titarchuk. We have also established the photon index saturation at about 2.3 in index vs mass accretion correlation. This index-mass accretion correlation allows us to evaluate the low limit of black hole (BH) mass of compact object in SS 433, M(sub bh) approximately > 2 solar masses, using the scaling method using BHC GX 339-4 as a reference source. Our estimate of the BH mass in SS 433 is consistent with recent BH mass measurement using the radial-velocity measurements of the binary system by Hillwig & Gies who find that M(sub x)( = (4.3 +/- 0.8) solar masses. This is the smallest BH mass found up to now among all BH sources. Moreover, the index saturation effect versus mass accretion rate revealed in SS 433, like in a number of other BH candidates, is the strong observational evidence for the presence of a BH in SS 433.

Seifina, Elena↗