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Large-Eddy Simulation of Aeroacoustic Applications

This report summarizes work accomplished under a one-year NASA grant from NASA Langley Research Center (LaRC). The effort culminates three years of NASA-supported research under three consecutive one-year grants. The period of support was April 6, 1998, through April 5, 1999. By request, the grant period was extended at no-cost until October 6, 1999. Its predecessors have been directed toward adapting the numerical tool of large-eddy simulation (LES) to aeroacoustic applications, with particular focus on noise suppression in subsonic round jets. In LES, the filtered Navier-Stokes equations are solved numerically on a relatively coarse computational grid. Residual stresses, generated by scales of motion too small to be resolved on the coarse grid, are modeled. Although most LES incorporate spatial filtering, time-domain filtering affords certain conceptual and computational advantages, particularly for aeroacoustic applications. Consequently, this work has focused on the development of subgrid-scale (SGS) models that incorporate time-domain filters.

Pruett, C. David↗

The Impact of Parameterized Lateral Mixing on the Antarctic Circumpolar Current in a Coupled Climate Model

This study examines the impact of changing the lateral diffusion coefficient ARedi on the transport of the Antarctic Circumpolar Current (ACC). The lateral diffusion coefficient ARedi is poorly constrained, with values ranging across an order of magnitude in climate models. The ACC is difficult to accurately simulate, and there is a large spread in eastward transport in the Southern Ocean (SO) in these models. This paper examines how much of that spread can be attributed to different eddy parameterization coefficients. A coarse-resolution, fully coupled model suite was run with A Redi = 400, 800, 1200, and 2400 m 2 s -1 . Additionally, two simulations were run with two-dimensional representations of the mixing coefficient based on satellite altimetry. Relative to the 400 m 2 s -1 case, the 2400 m 2 s -1 case exhibits 1) an 11% decrease in average wind stress from 50° to 65°S, 2) a 20% decrease in zonally averaged eastward transport in the SO, and 3) a 14% weaker transport through the Drake Passage. The decrease in transport is well explained by changes in the thermal current shear, largely due to increases in ocean density occurring on the northern side of the ACC. In intermediate waters these increases are associated with changes in the formation of intermediate waters in the North Pacific. We hypothesize that the deep increases are associated with changes in the wind stress curl allowing Antarctic Bottom Water to escape and flow northward.

54 ENVIRONMENTAL SCIENCES↗

Turbulent Premixed Flame Propagation in Microgravity

A facility in which turbulent Couette flow could be generated in a microgravity environment was designed and built. To fit into the NASA Lewis drop tower the device had to be very compact. This means that edge effects and flow re-circulation were expected to affect the flow. The flow was thoroughly investigated using LDV and was found to be largely two dimensional away from the edges with constant turbulence intensities in the core. Slight flow asymmetries are introduced by the non symmetric re-circulation of the fluid outside the test region. Belt flutter problems were remedied by adding a pair of guide plates to the belt. In general, the flow field was found to be quite similar to previously investigated Couette flows. However, turbulence levels and associated shear stresses were higher. This is probably due to the confined re-circulation zone reintroducing turbulence into the test section. An estimate of the length scales in the flow showed that the measurements were able to resolve nearly all the length scales of interest. Using a new LES method for subgrid combustion it has been demonstrated that the new procedure is computational feasible even on workstation type environment. It is found that this model is capable of capturing the propagation of the premixed names by resolving the flame in the LES grid within 2-3 grid points. In contrast, conventional LES results in numerical smearing of the flame and completely inaccurate estimate of the turbulent propagation speed. Preliminary study suggests that there is observable effect of buoyancy in the 1g environment suggesting the need for microgravity experiments of the upcoming experimental combustion studies. With the cold flow properties characterized, an identical hot flow facility is under construction. It is assumed that the turbulence properties ahead of the flame in this new device will closely match the results obtained here. This is required since the hot facility will not enable LDV measurements. The reacting flow facility is also being constructed with planned drop tower experiments in mind. Therefore, issues related to safety and structural integrity are being take into account. Further development of the numerical model will also be carried out to include finite-rate kinetics for representative premixed cases. More detail analysis of the flame structure and propagation nature will be investigated. Simulations will also be compared to the flame properties observed in the experiments.

Menon, S.↗

Large eddy simulations of compressible turbulent flows

An evaluation of existing models for Large Eddy Simulations (LES) of incompressible turbulent flows has been completed. LES is a computation in which the large, energy-carrying structures to momentum and energy transfer is computed exactly, and only the effect of the smallest scales of turbulence is modeled. That is, the large eddies are computed and the smaller eddies are modeled. The dynamics of the largest eddies are believed to account for most of sound generation and transport properties in a turbulent flow. LES analysis is based on an observation that pressure, velocity, temperature, and other variables are the sum of their large-scale and small-scale parts. For instance, u(i) (velocity) can be written as the sum of bar-u(i) and u(i)-prime, where bar-u(i) is the large-scale and u(i)-prime is the subgrid-scale (SGS). The governing equations for large eddies in compressible flows are obtained after filtering the continuity, momentum, and energy equations, and recasting in terms of Favre averages. The filtering operation maintains only large scales. The effects of the small-scales are present in the governing equations through the SGS stress tensor tau(ij) and SGS heat flux q(i). The mathematical formulation of the Favre-averaged equations of motion for LES is complete.

Porter-Locklear, Freda↗

Effects of wall curvature on turbulence statistics

A three-dimensional, time-dependent, direct numerical simulation of low-Reynolds number turbulent flow in a mildly curved channel was performed, and the results examined to determine the mechanism by which curvature affects wall-bounded turbulent shear flows. A spectral numerical method with about one-million modes was employed, and no explicit subgrid scale model was used. The effects of curvature on this flow were determined by comparing the concave and convex sides of the channel. The observed effects are consistent with experimental observations for mild curvature. The most significant difference in the turbulence statistics between the concave and convex sides is in the Reynolds shear stress. This is accompanied by significant differences in the terms of the Reynolds shear stress balance equations. In addition, it was found that stationary Taylor-Goertler vortices were present and that they had a significant effect on the flow by contributing to the mean Reynolds shear stress, and by enhancing the difference between the wall shear stresses.

Moser, R. D.↗

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↗

Application of a dynamic subgrid-scale model to turbulent recirculating flows

The dynamic subgrid-scale model of Germano et al. is implemented in a finite volume formulation and applied to the simulation of turbulent flow in a three-dimensional lid-driven cavity at Reynolds number of 7500. The filtering operation is carried out in physical space, and the model coefficient is calculated locally. The computed mean and rms velocities as well as the Reynolds stress are compared with experimental data. It is shown that backscatter from small to large scales is necessary to sustain turbulent fluctuations. The model is being applied to the simulation of turbulent flows in a stratified and rotating environment in complex geometries.

Zang, Y.↗

A new non-eddy viscosity subgrid-scale model and its application to channel flow

To date, most large-eddy simulations (LES) have been carried out with eddy viscosity subgrid scale (SGS) models, with only a few exceptions that used the mixed model. Even though the assumptions behind Smagorinsky's model are rather stringent, it has been applied successfully to a variety of turbulent flows. This success is attributed to the ability of eddy viscosity models to drain energy from large scales, thus simulating the dissipative nature of turbulence. Most SGS models are absolutely dissipative, i.e. they remove energy from the large scales at every instant. However, SGS stresses may transfer energy back to the large scales intermittently; this reverse transfer or backscatter is especially important in geophysical flows and in transition. In a fully developed channel flow, there is reverse flow of energy from small to large scales near the walls, but eddy viscosity models are unable to account for this important feature. The dynamic localization eddy viscosity model of Ghosal et al. (1995) allows backscatter by co-evolving an auxiliary equation for the SGS energy; however, the computational cost is considerably larger than for conventional SGS models (Cabot 1994). In this report, a new non-eddy viscosity model based on local approximation of total quantities in terms of filtered ones is introduced; the scale similarity model of Bardina (1983) is a special case of this model. This procedure does not require the assumption of homogeneity, permits backscatter of energy from small to large scales, and is readily implemented in finite difference codes. The results of applying the proposed model to second order finite volume simulation of plane channel flow at high Reynolds numbers (Re(sub b) = 38,000) is described in this report. Greater emphasis is placed on the high Reynolds number flow since it provides a more rigorous test of the SGS model and its potential application. The results are compared to ones produced by the conventional and dynamic Smagorinsky models and the spectral LES of Piomelli (1993).

Shah, K. B.↗

Scientific challenges to characterizing the wind resource in the marine atmospheric boundary layer

Abstract. With the increasing level of offshore wind energy investment, it is correspondingly important to be able to accurately characterize the wind resource in terms of energy potential as well as operating conditions affecting wind plant performance, maintenance, and lifespan. Accurate resource assessment at a particular site supports investment decisions. Following construction, accurate wind forecasts are needed to support efficient power markets and integration of wind power with the electrical grid. To optimize the design of wind turbines, it is necessary to accurately describe the environmental characteristics, such as precipitation and waves, that erode turbine surfaces and generate structural loads as a complicated response to the combined impact of shear, atmospheric turbulence, and wave stresses. Despite recent considerable progress both in improvements to numerical weather prediction models and in coupling these models to turbulent flows within wind plants, major challenges remain, especially in the offshore environment. Accurately simulating the interactions among winds, waves, wakes, and their structural interactions with offshore wind turbines requires accounting for spatial (and associated temporal) scales from O(1 m) to O(100 km). Computing capabilities for the foreseeable future will not be able to resolve all of these scales simultaneously, necessitating continuing improvement in subgrid-scale parameterizations within highly nonlinear models. In addition, observations to constrain and validate these models, especially in the rotor-swept area of turbines over the ocean, remains largely absent. Thus, gaining sufficient understanding of the physics of atmospheric flow within and around wind plants remains one of the grand challenges of wind energy, particularly in the offshore environment. This paper provides a review of prominent scientific challenges to characterizing the offshore wind resource using as examples phenomena that occur in the rapidly developing wind energy areas off the United States. Such phenomena include horizontal temperature gradients that lead to strong vertical stratification; consequent features such as low-level jets and internal boundary layers; highly nonstationary conditions, which occur with both extratropical storms (e.g., nor'easters) and tropical storms; air–sea interaction, including deformation of conventional wind profiles by the wave boundary layer; and precipitation with its contributions to leading-edge erosion of wind turbine blades. The paper also describes the current state of modeling and observations in the marine atmospheric boundary layer and provides specific recommendations for filling key current knowledge gaps.

17 WIND ENERGY↗

Strongly Heated Turbulent Flow in a Channel with Pin Fins

Large-eddy simulations (LES) were performed to study the turbulent flow in a channel of height H with a staggered array of pin fins with diameter D = H/2 as a function of heating loads that are relevant to the cooling of turbine blades and vanes. The following three heating loads were investigated—wall-to-coolant temperatures of Tw/Tc = 1.01, 2.0, and 4.0 - where the Reynolds number at the channel inlet was 10,000 and the back pressure at the channel outlet was 1 bar. For the LES, two different subgrid-scale models—the dynamic kinetic energy model (DKEM) and the wall-adapting local eddy-viscosity model (WALE)—were examined and compared. This study was validated by comparing with data from direct numerical simulation and experimental measurements. The results obtained show high heating loads to create wall jets next to all heated surfaces that significantly alter the structure of the turbulent flow. Results generated on effects of heat loads on the mean and fluctuating components of velocity and temperature, turbulent kinetic energy, the anisotropy of the Reynolds stresses, and velocity-temperature correlations can be used to improve existing RANS models.

42 ENGINEERING↗

Improved turbulence models based on large eddy simulation of homogeneous, incompressible turbulent flows

The physical bases of large eddy simulation and subgrid modeling are studied. A subgrid scale similarity model is developed that can account for system rotation. Large eddy simulations of homogeneous shear flows with system rotation were carried out. Apparently contradictory experimental results were explained. The main effect of rotation is to increase the transverse length scales in the rotation direction, and thereby decrease the rates of dissipation. Experimental results are shown to be affected by conditions at the turbulence producing grid, which make the initial states a function of the rotation rate. A two equation model is proposed that accounts for effects of rotation and shows good agreement with experimental results. In addition, a Reynolds stress model is developed that represents the turbulence structure of homogeneous shear flows very well and can account also for the effects of system rotation.

Bardino, J.↗

Dynamic Smagorinsky Modeled Large-Eddy Simulations of Turbulence Using Tetrahedral Meshes

Eddy-resolving numerical computations of turbulent flows are emerging as viable alternatives to Reynolds Averaged Navier-Stokes (RANS) calculations for flows with an intrinsically steady mean state due to the advances in large-scale parallel computing. In these computations, medium to large turbulent eddies are resolved by the numerics while the smaller or subgrid scales are either modeled or taken care of by the inherent numerical dissipation. To advance the state of the art of unstructured-mesh turbulence simulation capabilities, large eddy simulations (LES) using the dynamic Smagorinsky model (DSM) on tetrahedral meshes are carried out with the space-time conservation element, solution element (CESE) method. In contrast to what has been reported in the literature, the present implementation of dynamic models allows for active backscattering without any ad-hoc limiting of the eddy viscosity calculated from the subgrid-scale model. For the benchmark problems involving compressible isotropic turbulence decay as well as the shock/turbulent boundary layer interaction benchmark problems, no numerical instability associated with kinetic energy growth is observed and the volume percentage of the backscattering portion accounts for about 38-40% of the simulation domain. A slip-wall model in conjunction with the implemented DSM is used to simulate a relatively high Reynolds number Mach 2.85 turbulent boundary layer over a 30° ramp with several tetrahedral meshes and a wall-normal spacing of either Δγ& = 10 or Δγ& = 20. The computed mean wall pressure distribution, separation region size, mean velocity profiles, and Reynolds stress agree reasonably well with experimental data.

CESE method↗

Towards Surrogate Modeling of Subgrid Turbulent Transport for 3D Radiative Hydrodynamic Simulations of the Quiet Sun

In this work, we investigate the use of deep learn-ing techniques as surrogate models, to enhance the estimationof effects of subgrid turbulent transport for 3D radiatuve hy-drodynamic simulations of the quiet Sun. We develop two dis-tinct 3D Convolutional Neural Networks (3DCNNs) to capturespatio-temporal dependencies in 3D velocity fields, leveragingdifferent activation functions and architectural designs. Thesemodels integrate both averaged velocity vector components andscalar features such as plasma density to enhance predictionaccuracy. Additionally, a Multilayer Perceptron (MLP) modelis employed to approximate complex nonlinear relationships,offering a comparison in performance between convolutionaland fully connected architectures. Logarithmic transformationis applied to the targets to handle heavily skewed data, im-proving model performance. All models are compared againsta physics-based Gradient Model. Results show that the 3DCNNmodels excel at approximating Reynolds stress tensors, makingthem a candidate for assisting in producing reduced resolutionsimulations, and thereby reducing computational overheadwhile maintaining higher accuracy than the baseline. Thesefindings demonstrate the potential of deep learning, particu-larly CNNs, to advance scalable and accurate simulations ofsolar dynamics, offering a promising alternative to traditionalturbulence models.

Heliophysics↗

Reynolds-Averaged Turbulence Modeling Using Deep Learning with Local Flow Features: An Empirical Approach

Reynolds-Averaged Navier-Stoke (RANS) models offer an alternative avenue in predicting flow characteristics when the corresponding experiments are difficult to achieve due to geometry complexity, limited budget, or knowledge. RANS models require the knowledge of subgrid scale physics to solve conservation equations for mass, energy, and momentum. Mechanistic turbulence models, such as k-epsilon, are generally evaluated and calibrated for specific flow conditions with various degrees of uncertainty. These models have limited capability to assimilate a substantial amount of data due to model form constraints. Meanwhile, deep learning (DL) has been proven to be universal approximators with the potential to assimilate available, relevant, and adequately evaluated data. Moreover, deep neural networks (DNNs) can create surrogate models without knowing function forms. Such a data-driven approach can be used in updating fluid models based on observations as opposed to hard-wiring models with precalibrated correlations. The paper presents progress in applying DNNs to model Reynolds stress using two machine learning (ML) frameworks. A novel flow feature coverage mapping is proposed to quantify the physics coverage of DL-based closures. It can be used to examine the sufficiency of training data and input flow features for data-driven turbulence models. The case of a backward-facing step is formulated to demonstrate that not only can DNNs discover underlying correlation behind fluid data but also they can be implemented in RANS to predict flow characteristics without numerical stability issues. Finally, the presented research is a crucial stepping-stone toward the data-driven turbulence modeling, which potentially benefits the design of data-driven experiments that can be used to validate fluid models with ML-based fluid closures.

42 ENGINEERING↗

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↗

Toward Simplification of Dynamic Subgrid-Scale Models

We examine the relationship between the filter and the subgrid-scale (SGS) model for large-eddy simulations, in general, and for those with dynamic SGS models, in particular. From a review of the literature, it would appear that many practitioners of LES consider the link between the filter and the model more or less as a formality of little practical effect. In contrast, we will show that the filter and the model are intimately linked, that the Smagorinsky SGS model is appropriate only for filters of first- or second-order, and that the Smagorinsky model is inconsistent with spectral filters. Moreover, the Germano identity is shown to be both problematic and unnecessary for the development of dynamic SGS models. Its use obscures the following fundamental realization: For a suitably chosen filter, the computible resolved turbulent stresses, property scaled, closely approximate the SGS stresses.

Pruett, C. David↗

Large-Eddy Simulation of Flow Over Boeing Gaussian Bump Using Multiagent Reinforcement Learning Wall Model: Preprint

We develop a wall model for large-eddy simulation (LES) that takes into account various pressure-gradient effects using multi-agent reinforcement learning. The model is trained using low-Reynolds-number flow over periodic hills with agents distributed on the wall at various computational grid points. It utilizes a wall eddy-viscosity formulation as the boundary condition to apply the modeled wall shear stress. Each agent receives states based on local instantaneous flow quantities at an off-wall location, computes a reward based on the estimated wall-shear stress, and provides an action to update the wall eddy viscosity at each time step. The trained wall model is validated in wall-modeled LES of flow over periodic hills at higher Reynolds numbers, and the results show the effectiveness of the model on flow with pressure gradients. The analysis of the trained model indicates that the model is capable of distinguishing between the various pressure gradient regimes present in the flow. To further assess the robustness of the developed wall model, simulations of flow over the Boeing Gaussian bump are conducted at a Reynolds number of 2 x 10^6, based on the free-stream velocity and the bump width. The results of mean skin friction and pressure on the bump surface, as well as the velocity statistics of the flow field, are compared to those obtained from equilibrium wall model (EQWM) simulations and published experimental data sets. The developed wall model is found to successfully capture the acceleration and deceleration of the turbulent boundary layer on the bump surface, providing better predictions of skin friction near the bump peak and exhibiting comparable performance to the EQWM with respect to the wall pressure and velocity field. We also conclude that the subgrid-scale model is crucial to the accurate prediction of the flow field, in particular the prediction of separation.

boundary layer↗

Numerical simulations of turbulent thermal convection with differential rotation

The solar nebula, from which the planets in our solar system formed, featured a disk of gas and dust grains in rapid, differential rotation, and at some stage was likely to have been unstable to thermal convection. This situation is suspected by many to lead to significant turbulent Reynolds stress production and angular momentum transport in such systems, and estimates of transport rates have been attempted from unsubstantiated phenomenological models. In order to determine the circumstances and physical conditions under which our own planetary system formed and to explain recent observations of young stellar systems, it is necessary to develop realistic models of heat and angular momentum transport for such flows. Developing an understanding of complicated flows featuring thermal convection, rotation, and shear is also of wide interest in stellar astrophysics and in planetary and terrestrial atmospheric studies. The ultimate objective is to develop workable models based on the numerical simulations for constructing global solar nebula models; viz., relatively simple prescriptions for heat and angular momentum fluxes from given system parameters (e.g., ratios of rotation, shear, and convective lapse rates) are characterized, quantified, and developed. Toward this end, our program has been to attempt to understand the behavior of the direct numerical simulations of Boussinesq convection, which, despite the complexity of the results, is still an overly simplified approximation to the real system and should be more amenable to analysis. These results are also intended to be tested against turbulence models, especially those designed for atmospheric boundary layers, and may provide a basis for subgrid-scale models. In order to make the numerical simulations more realistic with regard to the solar nebula problem, a fully compressible code that will allow incorporation of large density stratifications and realistic thermodynamic and radiative properties is developed. In order to explore the properties of these flows at the very high values of Re found in natural systems and the very low values of Pr found in most astrophysical contexts, we will need to employ large-eddy simulations for which we want to determine the most appropriate subgrid-scale model to incorporate.

Cabot, William H.↗