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At least 19 records

Final Report for Grant DOE DE-FG02-08ER64573 (Relating to Turbulence Modeling)

Turbulence enhances transport and mixing. Turbulent ocean currents can increase the encounter rate between fish larvae and their prey. Without turbulence, the fuel and air injected into the cylinder of an internal combustion engine would mix too slowly to be effective. Birds extract energy from turbulent winds to soar for great distances without flapping their wings. Turbulence can be detrimental as well. The efficiencies of vehicles, pipelines, and industrial equipment are all hindered by turbulence. Turbulence can also cause structural fatigue, generate unwanted noise, and distort the propagation of electromagnetic signals. These observations highlight the importance of turbulence research. Our ability to predict and control turbulence and, thus, to intensify or suppress its effects as circumstances warrant is contingent on our understanding of the underlying mechanisms. Turbulence is also immensely interesting from a purely scientific perspective and is a great source of fundamentally important, challenging problems for physicists, engineers, and mathematicians. Moreover, various methods and tools developed in the field have found applications in other fields, including nonlinear optics, nonlinear acoustics, pattern formation, image processing, data compression, and econophysics. It is possible, at least away from walls, to derive LES models of very high-order accuracy. However, these models also lead to correspondingly intense computational complexity for their numerical solution. Some also introduce yet more questions on the already difficult problem of specifying needed and sometimes artificial local boundary conditions for the inherently nonlocal flow averages. For these two (and other) reasons, there has been a resurgence of interest in basing simulations of turbulent flows on much simpler regularizations of the Navier–Stokes equations rather than on full models of local averages--i.e., LES models. Initially these were developed as pure theoretical tools. The influx of ideas from LES and the added constraint that the regularization be amenable to numerical simulation have breathed new perspective and thus new life into this thread of ideas.Over the past year, a significant portion of our research activity has focused on numerical studies of the Navier–Stokes-$αβ$ model and extensions thereof. Our results regarding these and other approaches to turbulence modeling are described below.

97 MATHEMATICS AND COMPUTING↗

An adaptive knowledge-based data-driven approach for turbulence modeling using ensemble learning technique under complex flow configuration: 3D PWR sub-channel with DNS data

This work describes a new approach to increase the accuracy of Reynolds-averaged Navier–Stokes (RANS) in modeling turbulence flow leveraging the machine learning technique. Traditionally, different turbulence models for Reynolds stress are developed for different flow patterns based on human knowledge. Each turbulence model has a certain application domain and prediction uncertainty. In recent years, with the rapid improvements of machine learning techniques, researchers start to develop an approach to compensate for the prediction discrepancy of traditional turbulence models with statistical models and data. However, the approach has deficiencies in several aspects. For example, the amount of human knowledge introduced to the statistical model couldn’t be controlled, which makes the statistical model learn from a very naïve stage and limits its application. In this work, a new approach is developed to address those deficiencies. Here, the new approach uses the “ensemble learning” technique to control the amount of human knowledge introduced into the statistical model. Therefore, the new approach could be adaptive to the multiple application domains. In conclusion, according to the results of case study, the new approach shows higher accuracy than both traditional turbulence models and the previous machine learning approach.

42 ENGINEERING↗

Particle dispersion in homogeneous turbulence using the one-dimensional turbulence model

Lagrangian particle dispersion is studied using the one-dimensional turbulence (ODT) model in homogeneous decaying turbulence configurations. The ODT model has been widely and successfully applied to a number of reacting and nonreacting flow configurations, but only limited application has been made to multiphase flows. Here, we present a version of the particle implementation and interaction with the stochastic and instantaneous ODT eddy events. The model is characterized by comparison to experimental data of particle dispersion for a range of intrinsic particle time scales and body forces. Particle dispersion, velocity, and integral time scale results are presented. The particle implementation introduces a single model parameter β{sub p}, and sensitivity to this parameter and behavior of the model are discussed. Good agreement is found with experimental data and the ODT model is able to capture the particle inertial and trajectory crossing effects. These results serve as a validation case of the multiphase implementations of ODT for extensions to other flow configurations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

K-ε Turbulence Model Parameter Estimates Using an Approximate Self-similar Jet-in-Crossflow Solution

The k-ε turbulence model has been described as perhaps “the most widely used complete turbulence model.” This family of heuristic Reynolds Averaged Navier-Stokes (RANS) turbulence closures is supported by a suite of model parameters that have been estimated by demanding the satisfaction of well-established canonical flows such as homogeneous shear flow, log-law behavior, etc. While this procedure does yield a set of so-called nominal parameters, it is abundantly clear that they do not provide a universally satisfactory turbulence model that is capable of simulating complex flows. Recent work on the Bayesian calibration of the k-ε model using jet-in-crossflow wind tunnel data has yielded parameter estimates that are far more predictive than nominal parameter values. In this paper, we develop a self-similar asymptotic solution for axisymmetric jet-in-crossflow interactions and derive analytical estimates of the parameters that were inferred using Bayesian calibration. The self-similar method utilizes a near field approach to estimate the turbulence model parameters while retaining the classical far-field scaling to model flow field quantities. Our parameter values are seen to be far more predictive than the nominal values, as checked using RANS simulations and experimental measurements. They are also closer to the Bayesian estimates than the nominal parameters. A traditional simplified jet trajectory model is explicitly related to the turbulence model parameters and is shown to yield good agreement with measurement when utilizing the analytical derived turbulence model coefficients. Finally, the close agreement between the turbulence model coefficients obtained via Bayesian calibration and the analytically estimated coefficients derived in this paper is consistent with the contention that the Bayesian calibration approach is firmly rooted in the underlying physical description.

42 ENGINEERING↗

One-dimensional turbulence modeling of a turbulent counterflow flame with comparison to DNS

The one-dimensional turbulence (ODT) model is applied to a reactant-to-product counterflow configuration and results are compared with DNS data. The model employed herein solves conservation equations for momentum, energy, and species on a one dimensional (1D) domain corresponding to the line spanning the domain between nozzle orifice centers. The effects of turbulent mixing are modeled via a stochastic process, while the Kolmogorov and reactive length and time scales are explicitly resolved and a detailed chemical kinetic mechanism is used. Comparisons between model and DNS results for spatial mean and root-meansquare (RMS) velocity, temperature, and major and minor species profiles are shown. The ODT approach shows qualitatively and quantitatively reasonable agreement with the DNS data. Scatter plots and statistics conditioned on temperature are also compared for heat release rate and all species. ODT is able to capture the range of results depicted by DNS. However, conditional statistics show signs of underignition.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Posterior comparison of model dynamics in several hybrid turbulence model forms

Hybrid turbulence models that can accurately reproduce unsteady three-dimensional flow physics across the entire range of grid scales and turbulence dynamics from Reynolds-averaged Navier–Stokes (RANS), through large-eddy simulation (LES), down to direct numerical simulations (DNS) are of increasing interest to the turbulence modeling community. However, despite decades of research and development, the basic tasks of eliminating poor-performing hybrid RANS-LES models and accelerating adoption of superior models through well-designed validation and verification have yet to occur. As a step in this direction, in this work we evaluate thirteen different hybrid RANS-LES models via systematic grid refinement of decaying homogeneous isotropic turbulence. We further derive a novel mathematical framework for assessing the energy partitioning dynamics of each Hybrid RANS-LES model, wherein model-to-model variations in energy partitioning can be interpreted as different feedback mechanisms operating on a low-dimensional nonlinear dynamical system. We found that model forms similar to the flow simulation methodology—also often termed very-large eddy simulation—are dynamically inconsistent with DNS at all resolutions. Additionally, we found a strong dynamical similarity in the feedback mechanisms of all models related to detached eddy simulation and partially averaged Navier–Stokes that is inherent to their general model forms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Advanced Turbulence Models for Large-Scale Atmospheric Boundary Layer Flows

We present high-fidelity large-eddy-simulation (LES) modeling approaches for the turbulent atmospheric boundary layer (ABL) flows. Wind energy is a prime example of an application driven by ABL. Generation of electrical energy from farms of wind turbines at night in the stable ABL is a particularly interesting situation. In this report, we consider the well-known GEWEX (Global Energy and Water Cycle Experiment) Atmospheric Boundary Layer Study (GABLS) stably stratified benchmark LES case. We use a high-order spectral element code Nek5000/RS, which is supported under the DOE's Exascale Computing Project (ECP) Center for Efficient Exascale Discretizations (CEED) project, targeting application simulations on various acceleration-device based exascale computing platforms. In our earlier ANL report, we demonstrated our newly developed subgrid-scale (SGS) models based on high-pass filter (HPF), mean-field eddy viscosity (MFEV), and Smagorinsky (SMG) with no-slip and traction boundary conditions, provided with low-order statistics, convergence and turbulent structure analysis. In this report, we extend the range of our SGS modeling approaches in the context of the mean-field eddy viscosity (MFEV), to include the solution of an SGS turbulent kinetic energy equation (TKE). We demonstrate the model fidelity of Nek5000/RS in comparison to that of AMR-Wind, a block-structured second-order finite-volume code with adaptive-mesh-refinement capabilities, with which we studied scaling performance for both codes in comparison on DOE's leadership computing platforms.

17 WIND ENERGY↗

Modeling turbulence–chemistry interaction in lean premixed hydrogen flames with a strained flamelet model

Premixed flames in the thin and broken reaction zones regime exhibit strong non-linear turbulence–chemistry interactions and are hence challenging to model. In the present study, a direct numerical simulation (DNS) database for a hydrogen–air flame is used to understand the effect of turbulence–chemistry interactions on the flame speed. To this end, statistics of the local flame front displacement speed are investigated and the roles of flame stretch due to curvature and strain are analyzed. The local flame speed is found to be on average around 30% lower than the laminar burning velocity, which is shown to be a consequence of strain. Strain effects are then modeled by a recently proposed strained flamelet model, which is validated a priori against the DNS in terms of the flame speed and the reaction source term. The strained flamelet model leads to a moderate improvement of the flame speed prediction and is able to reproduce the decrease of the local flame speed. Moreover, it significantly improves the source term closure, which is demonstrated on the basis of the optimal estimator approach and, overall, describes the investigated DNS flame with very good accuracy.

Energy & Fuels↗

Machine Learning for Turbulence Modeling

This work was conducted as part of a Harry S. Truman Fellowship Laboratory Directed Research and Development project. The goal was to use machine learning methods to provide uncertainty quantification and model improvements for Reynolds Averaged Navier Stokes (RANS) turbulence models. For applications of interest in energy, safety, and security, it is critical to be able to model turbulence accurately. Current RANS models are unreliable for many flows of engineering relevance. Machine learning provides an avenue for developing improved models based on the data generated by high fidelity simulations. In this project, machine learning methods were used to predict when current RANS models would fail. They were also used to develop improved RANS closure models. A key aim was developing a tight feedback loop between scientific domain knowledge and data driven methods. To this end, a methodology for incorporating known invariance constraints into the machine learning models was proposed and evaluated. This work demonstrated that incorporating known constraints into the data driven models provided improved performance and reduced computational cost. This research represents one of the first applications of deep learning to turbulence modeling.

42 ENGINEERING↗

Validation of URANS and STRUCT-ε turbulence models for stratified sodium flow

Simulations of a transient stratified sodium experiment are carried out using a classic unsteady RANS model and the second-generation URANS model, STRUCT-ε. Turbulence modeling challenges and their implications to stratified flow prediction are discussed in the context of other sources of error. Input errors are discussed and addressed; discretization error is calculated to be less than 5% of the inlet velocity, for 80% of the domain; and remaining errors in temperature distributions are attributed to the turbulence model. Qualitative flow features from the simulations are presented and discussed. Compared to the experiment, the STRUCT-ε turbulence model provides a more physically accurate prediction of temperature and momentum mixing in key regions of the domain. Quantitative measures such as the L 2 norm of the temperature discrepancy demonstrate the improved performance of the STRUCT-ε approach. In conclusion, the magnitude of the temperature fluctuations is very well-predicted by the STRUCT-ε, while URANS overpredicts them by approximately 50%.

42 ENGINEERING↗

Effect of Turbulence Modeling on the Melt Flow and Inclusions Transport in a Steel Filtration Experiment

The current article deals with the effect of turbulence modeling on inclusions transport and melt flow in an induction crucible furnace (ICF), which was employed in order to investigate the efficiency and the performance of a ceramic filter. Furthermore, the influence of the discrete random-walk dispersion model on the behavior of inclusions in the ICF was investigated. Different turbulence models were employed in order to predict the turbulent melt flow. The numerical results show that the flow field is affected by the turbulence modeling method. Moreover, the distribution of the turbulent kinetic energy depends considerably on the choice of the turbulence model. In addition, the turbulence model and dispersion model also affect the inclusion transport in the melt. The filtration rate is also affected by the choice of the turbulence model.

36 MATERIALS SCIENCE↗

Field Sensitivity Analysis of Turbulence Model Parameters for Flow Over a Wing

Reynolds-averaged-Navier-Stokes (RANS) turbulence models are a critical tool in computational-fluid-dynamics simulations of aerodynamic systems, but simulation results can be highly sensitive to RANS-model parameter choices. Sensitivity analysis can be used to quantify these impacts, and the objective of this study is to demonstrate field sensitivity analysis with respect to ten parameters in the 2003 Menter shear-stress-transport (SST) turbulence model. Here, the analysis is demonstrated for an application relevant to wind energy, namely, flow over a NACA 0015 wing at 12 degree angle of attack and a Reynolds number of 1.5 x 10 6 . We quantify sensitivity using Sobol indices and the mean-squared gradient, which are estimated using polynomial chaos and active subspace models, respectively. Our results indicate that there are substantial spatial variations in parameter sensitivities, with different sets of most-sensitive parameters near the wing, as well as in the downstream wake, consistent with the physical interpretations of the turbulence model inputs. We show that, for this particular turbulence model and flow, simultaneous dimension reduction is possible across all quantities of interest, enabling efficient exploration of model outcomes. Ultimately, this analysis provides new insights into turbulence model parameter sensitivities in incompressible flows, and also demonstrates the implementation of field sensitivity analysis for applications relevant to aerodynamics simulations.

17 WIND ENERGY↗

A multispecies turbulence model for the mixing and de-mixing of miscible fluids

A de-mix capable model for turbulence in compressible, variable density flows is proposed. The model is based on the Besnard-Harlow-Rauenzahn (BHR) family of models (Besnard D, Harlow F, Rauenzahn R, et al. Turbulence transport equations for variable-density turbulence and their relationship to two-field models. NM (United States): Los Alamos National Laboratory; 1992 (Technical Report LA-12303-MS), but is extended to track the evolution of the turbulent fluxes and fluctuations in the material mass fractions for each species present. The new evolution equations are introduced without requiring additional closures or new empirically tuned coefficients relative to previous BHR models, and are shown to improve the model’s ability to reproduce the behaviour of simulations containing mixing layers that are constrained by a stabilising force. As a result, the model is tested in a range of canonical flows including Rayleigh-Taylor driven, shock driven, and shear driven turbulence, and is shown to produce reasonable agreement with simulations and experiments in these scenarios.

42 ENGINEERING↗

Turbulence Model Study for Pressure and Velocity Distributions for Molten Salts in a Crossflow Tube Bundle

Empirical pressure drop correlations for various compositions of molten salts in crossflow across tube bundles/banks are limited due to the scarcity of experimental data for these fluids. This lack of experimental data presents a limitation when designing heat exchangers for Molten Salt Reactors (MSRs) that utilize cross-flow configurations with turbulent molten salts flowing in the shell side. In an effort to provide a starting point for future design and experimental work, a computational fluid dynamics (CFD) campaign is being conducted to estimate pressure drops over a range of Reynolds numbers, pitch to diameter ratios, and for both staggered and in-line tube banks. In an effort to continue this work, the study of various turbulence models were conducted to determine the applicability for steady RANS simulations. An in-line tube bank with FLiBe (LiF-BeF{sub 2}), a frequently selected molten salt in MSRs, was selected for these simulations. The estimated pressure drops and pressure and velocity distributions for each turbulence model was compared to determine the applicability. The k-ε turbulence model family was found to be the most appropriate model for steady Reynolds averaged Navier Stokes within this type of domain. Difference turbulence models were investigated for simulation of molten salt experiencing crossflow within an in-line tube bundle. The flow was simulated using a steady RANS formulation with different families of turbulence models. The different turbulence models provide a view of this specific flow behavior potential requirements and applicable for steady RANS. Of particular note, the k-ε models were able to converge easily within this domain. The predicted behavior for both models were observed to be mostly similar for both velocity and pressure distributions. Whereas, k-ω SST and SA models did not converge well and had observable differences for the predictions of pressure and velocity distributions. The global behaviors were generally similar, but the variations occurring suggest k-ω SST and SA turbulence models are not useful in the steady RANS formulation of this domain. When comparing to the empirical pressure drop, each turbulence model resulted in overpredictions ranging from 8.7% and 19.75% difference. The standard low-Re k-ε model having the lowest difference is likely the better model for simplified predictions for pressure drops. Further investigations will be conducted to determine the convergence issues for the k-ω SST and SA turbulence models. These might be due to the flow geometry or potentially a revision of the meshing is needed. The flow behavior may not be resolved using these models in a steady formulation due to inherent unsteadiness of the flow. (authors)

42 ENGINEERING↗

On turbulence models and lidar measurements for wind turbine control

Abstract. To provide comprehensive information that will assist in making decisions regarding the adoption of lidar-assisted control (LAC) in wind turbine design, this paper investigates the impact of different turbulence models on the coherence between the rotor-effective wind speed and lidar measurement. First, the differences between the Kaimal and Mann models are discussed, including the power spectrum and spatial coherence. Next, two types of lidar systems are examined to analyze the lidar measurement coherence based on commercially available lidar scan patterns. Finally, numerical simulations have been performed to compare the lidar measurement coherence for different rotor sizes. This work confirms the association between the measurement coherence and the turbulence model. The results indicate that the lidar measurement coherence with the Mann turbulence model is lower than that with the Kaimal turbulence model. In other words, the potential value creation of LAC based on simulations during the wind turbine design phase, evaluated using the Kaimal turbulence model, will be diminished if the Mann turbulence model is used instead. In particular, the difference in coherence is more significant for larger rotors. As a result, this paper suggests that the impacts of different turbulence models should be considered uncertainties while evaluating the benefits of LAC.

17 WIND ENERGY↗

Performance prediction applying different reduced turbulence models to the SMART tokamak

The SMall Aspect Ratio Tokamak (SMART) is currently being commissioned at the University of Seville and will be able to compare the performance of positive and negative triangularity plasmas at low aspect ratio. Predictive simulations have been performed for different machine scenarios and heating schemes using the TRANSP code. The objectives of these simulations are to predict the parameters expected in positive triangularity plasmas, to guide diagnostic development, and to validate transport models. Several reduced turbulence models have been used to predict electron and ion temperatures for the operational phase 2. All models provide similar results from approximately mid-radius to the separatrix but important discrepancies are found in the core region. These positive triangularity results are compared with experiments from a similar size machine like GLOBUS-M2. The multi-mode model (MMM) shows the best agreement. Simulations with different boundary conditions have been performed and no strong differences have been observed between them. The impact of neutral beam injection (NBI) on the predicted profiles has also been addressed. Rotation reduces turbulence levels so higher temperatures are achieved when included in the simulations. Studying the different contributions to the thermal diffusivities, it is observed that electron temperature gradient (ETG) turbulence dominates at the plasma core while micro-tearing modes (MTM) dominate at the edge in the electron channel. In the ion channel, the neoclassical contribution is dominant at the core and at the very edge while the Weiland component, which includes ion temperature gradient mode (ITG), trapped electron mode (TEM), kinetic ballooning mode (KBM), peeling mode (PM) and collisionless and collision dominated magnetohydrodynamic (MHD) modes governs the mid-radius region. For phase 3, two plasmas with different electron densities have been studied. The case with lower density matches well a specific discharge of GLOBUS-M2. The higher density plasma shows high performance with β N ≈ 3.8.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗