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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Sensitivities of time-dependent temperature profile predictions for NSTX with the multi-mode model

The Multi-Mode Model (MMM) for turbulent transport was applied to a large set of well-analyzed discharges from the National Spherical Torus Experiment (NSTX) in order to evaluate its sensitivities to a wide range of plasma conditions. MMM calculations were performed for hundreds of milliseconds in each discharge by performing time-dependent predictive simulations with the 1.5D tokamak integrated modeling code TRANSP. A closely related study (Lestz et al 2025 Plasma Phys. Control. Fusion 67 105029) concluded that MMM predicted electron and ion temperature profiles that were in reasonable agreement with NSTX observations, generally outperforming a different reduced transport model, TGLF. This finding motivates the more thorough investigation of the characteristics of the MMM predictions conducted in this work. The simulations with MMM have electron energy transport dominated by electron temperature gradient modes in the examined discharges with relatively low plasma β (ratio of kinetic plasma pressure to magnetic field pressure) and high collisionality, transitioning to a mixture of different modes for higher β and lower collisionality. The thermal ion diffusivity predicted by MMM is much smaller than the neoclassical contribution, in line with previous experimental analysis of NSTX. Nonetheless, the electron and ion temperature profiles are coupled via collisional energy exchange and thus sensitive to which transport channels are predicted. The time-dependent simulations with MMM are robust to the simulation start time, converging to remarkably similar temperature profiles later during the discharge. MMM typically overpredicts confinement relative to NSTX observations, leading to the prediction of overly steep temperature profiles. Plasmas with spatially broader temperature profiles, higher plasma β, and longer energy confinement times tend to be predicted by MMM with better agreement with the experiment. As a result, these findings provide useful context for understanding the regime-dependent tendencies of MMM in anticipation of self-consistent, time-dependent predictive simulations of NSTX-U discharges with these same modeling tools.

MMM↗
DOE OSTI2022

Effect of the Nuclear Equation of State on Relativistic Turbulence-induced Core-collapse Supernovae

Abstract The nuclear equation of state (EOS) is an important component in the evolution of core-collapse supernovae. In this paper we make a survey of various EOSs in the literature and analyze their effect on spherical core-collapse models in which the effects of three-dimensional turbulence is modeled by a general relativistic formulation of Supernova Turbulence In Reduced-dimensionality (STIR). We show that the viability of the explosion is quite EOS dependent and that it best correlates with the early-time interior entropy density of the proto–neutron star. We check that this result is not progenitor dependent, although the lowest-mass progenitors show different explosion properties, due to the different pre-collapse nuclear composition. Larger central entropies also induce more vigorous proto–neutron star convection in our one-dimensional turbulence model, as well as a wider convective layer.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Combined effects of horizontal and vertical resolution on reliable turbulence prediction at tidal energy sites: A systematic study in the Salish Sea, WA

Predicting turbulence characteristics with coastal ocean models is essential for tidal energy converter deployment. While large eddy simulation provides a detailed turbulence representation, computational limitations restrict its use to smaller domains. We systematically evaluate whether well-configured coastal models can provide reliable turbulence prediction through progressive refinement of 3D model representation. We implemented four model configurations (Levels 1–4) using terrain-following coordinates, isolating the impacts of horizontal resolution, vertical resolution, and layer distribution. We validated all configurations against field measurements from the Salish Sea, WA. Results show that tidal current velocity predictions remain unchanged regarding model configuration, but turbulence properties are sensitive to resolution refinement. Increasing vertical resolution alone proved insufficient; even with vertical sigma-levels rising from 11 to 41, significant underprediction persisted until finer horizontal resolution better captured bathymetric variations. The Level 4 configuration, incorporating geometric sigma-levels distribution, achieved turbulence prediction skill scores exceeding 0.90. Turbulence closure comparison revealed Mellor- Yamada 2.5 outperformed k-epsilon in TKE prediction (skill scores 0.84–0.94 versus 0.72–0.81) due to better boundary layer parameterization. This study shows that well-configured coastal models effectively bridge the gap between simplified tools and costly high-fidelity modeling, offering the tidal energy industry practical and cost-effective turbulence data at commercially relevant scales.

Marine Energy↗
DOE OSTI2022

Dry Deposition Methods Based on Turbulence Kinetic Energy: 1. Evaluation of Various Resistances and Sensitivity Studies Using a Single‐Point Model

Different functions are used to account for turbulence strength in the atmospheric boundary layer for different stability regimes. These functions are one of the sources for differences among different atmospheric models' predictions and associated biases. Also, turbulence strength is underrepresented in some of the resistance formulations. Here, to address these issues with dry deposition, firstly we take advantage of three‐dimensional (3‐D) turbulence information in estimating resistances by proposing and validating a 3‐D turbulence velocity scale that is relevant for different stability regimes of boundary layer. Secondly, we hypothesize and validate that friction velocity measured by 3‐D sonic anemometer can be effectively replaced by the new turbulence velocity scale multiplied by the von Karman constant. Finally, we (a) present a set of resistance formulations for ozone (O 3 ) based on the 3‐D turbulence velocity scale; (b) intercompare estimations of such resistances with those obtained using existing formulations; and, (c) evaluate simulated O 3 fluxes using a single‐point dry deposition model against long‐term observations of O 3 fluxes at the Harvard Forest (MA) site. Results indicate that the new resistance formulations work very well in simulating surface latent heat and O 3 fluxes when compared to respective existing formulations and measurements at a decadal time scale. Findings from this research may help to improve the capability of dry deposition schemes for better estimation of dry deposition fluxes and create opportunities for the development of a community dry deposition model for use in regional/global air quality models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Turbulence-parameter estimation for current-energy converters using surrogate model optimization

Surrogate models maximize information utility by building predictive models in place of computational or experimentally expensive model runs. Marine hydrokinetic current energy converters require large-domain simulations to estimate array efficiencies and environmental impacts. Meso-scale models typically represent turbines as actuator discs that act as momentum sinks and sources of turbulence and its dissipation. An OpenFOAM model was developed where actuator disc k-ε turbulence was characterized using an approach developed for flows through vegetative canopies. Turbine-wake data from laboratory flume experiments collected at two influent turbulence intensities were used to calibrate parameters in the turbulence-source terms in the k-ε equations. Additionally, parameter influences on longitudinal wake profiles were estimated using Gaussian process regression with subsequent optimization minimizing the objective function within 3.1% of those obtained using the full model representation, but for 74% of the computational cost (far fewer model runs). This framework facilitates more efficient parameterization of the turbulence-source equations using turbine-wake data.

16 TIDAL AND WAVE POWER↗
DOE OSTI2020

Spatiotemporally dynamic implicit large eddy simulation using machine learning classifiers

In this article, we utilize machine learning to dynamically determine if a point on the computational grid requires implicit numerical dissipation for large eddy simulation (LES). The decision making process is learnt through a priori training on quantities derived from direct numerical simulation (DNS) data. In particular, we compute eddy-viscosities obtained through the coarse-graining of DNS quantities and utilize their projection onto a Gaussian distribution to categorize areas that may require dissipation. If our learning determines that closure is necessary, an upwinded scheme is utilized for computing the non-linear Jacobian. In contrast, if it is determined that closure is unnecessary, a symmetric and second-order accurate energy and enstrophy preserving Arakawa scheme is utilized instead. This results in a closure framework that precludes the specification of any model-form for the small scale contributions of turbulence but deploys an appropriate numerical dissipation from explicit closure driven hypotheses. Here, this methodology is deployed for the Kraichnan turbulence test-case and assessed through various statistical quantities such as angle-averaged kinetic energy spectra and vorticity structure functions. Our framework thus establishes a link between the use of explicit LES ideologies for closure and numerical dissipation-based modeling of turbulence leading to improved statistical fidelity of a posteriori simulations.

42 ENGINEERING↗
DOE OSTI2020

Simulating Real Atmospheric Boundary Layers at Gray-Zone Resolutions: How Do Currently Available Turbulence Parameterizations Perform?

Recent computational and modeling advances have led a diverse modeling community to experiment with atmospheric boundary layer (ABL) simulations at subkilometer horizontal scales. Accurately parameterizing turbulence at these scales is a complex problem. The modeling solutions proposed to date are still in the development phase and remain largely unvalidated. This work assesses the performance of methods currently available in the Weather Research and Forecasting (WRF) model to represent ABL turbulence at a gray-zone grid spacing of 333 m. We consider three one-dimensional boundary layer parameterizations (MYNN, YSU and Shin-Hong) and coarse large-eddy simulations (LES). The reference dataset consists of five real-case simulations performed with WRF-LES nested down to 25 m. Results reveal that users should refrain from coarse LES and favor the scale-aware, Shin-Hong parameterization over traditional one-dimensional schemes. Overall, the spread in model performance is large for the cellular convection regime corresponding to the majority of our cases, with coarse LES overestimating turbulent energy across scales and YSU underestimating it and failing to reproduce its horizontal structure. Despite yielding the best results, the Shin-Hong scheme overestimates the effect of grid dependence on turbulent transport, highlighting the outstanding need for improved solutions to seamlessly parameterize turbulence across scales.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Numerical Analysis of Novel Plate Type Heat Exchanger with Oval-Twisted Channels

The novel heat exchanger (HX) designs implementing geometrical and surface modification combinations are expected to perform better than traditional HX technologies. Applied enhancement techniques seek to achieve (1) higher overall heat transfer performance, (2) increased compactness, and (3) simplified or comparable manufacturability. One innovative enhancement technique is to generate swirling flow vortices induced by channel or tube twisting. The turbulence generated by the twisted cross-section greatly enhances the heat transfer rate with minimal increases in pressure drop. Plate-type HXs and Printed Circuit Heat Exchangers (PCHXs) are compact designs that achieve high heat transfer rates per unit volume by utilizing several small channels, which maximizes the heat transfer surface area between the hot and cold fluids. Currently, advanced manufacturing technologies enable the design and fabrication of compact-type units with complicated channel geometries to achieve the highest performance and meet the compactness criteria of innovative HX technology. The proposed HX design concept combines the compactness of plate-type HXs and twisted channels, which provide additional turbulence and flow swirl enhancement. The plate-type oval-twisted HX (PTOTHX) is a crossflow configuration, with 16 short channels on one side (for hot fluid) and 8 long channels on the perpendicular side (for cold fluid). The inlet plenums have flow guide vanes to redirect flow and produce uniformity across the various flow paths. The compact size and purportedly improved heat transfer performance of the PTOTHX investigated herein prove its viability in various applications. Some notable potential nuclear applications of the PTOTHX include reactor core, spent fuel cooling, and residual heat dissipation. To establish a reference case, circular channels (PTCHX) are also considered in the present study for comparison with (PTOTHX). This paper aims to outline the numerical analysis procedures for determining the viability of the PTOTHX by comparing its heat transfer performance with the PTCHX units. The computational study used STAR-CCM+, a commercial computational fluid dynamics (CFD) code. Sensitivity analysis and model selection studies are conducted to determine the appropriate mesh density and turbulence model to provide the reported results. Numerical analyses comparing the Nusselt number (Nu) of the PTOTHX design with a comparable HX unit, including a circular cross-section and no twisting (PTCHX), show an overall heat transfer performance increase of 29-55% for balanced flow and 29-59% for imbalanced flow. Oval-cross-sectional twisted channels induce swirling flow vortices, enhancing the working fluid's convective heat transfer capabilities.

25 ENERGY STORAGE↗
DOE OSTI2022

Local correlation-based transition models for high-Reynolds-number wind-turbine airfoils

Abstract. Modern wind-turbine airfoil design requires robust performance predictions for varying thicknesses, shapes, and appropriate Reynolds numbers. The airfoils of current large offshore wind turbines operate with chord-based Reynolds numbers in the range of 3–15 million. Turbulence transition in the airfoil boundary layer is known to play an important role in the aerodynamics of these airfoils near the design operating point. While the lack of prediction of lift stall through Reynolds-averaged Navier–Stokes (RANS) computational fluid dynamics (CFD) is well known, airfoil design using CFD requires the accurate prediction of the glide ratio (L/D) in the linear portion of the lift polar. The prediction of the drag bucket and the glide ratio is greatly affected by the choice of the transition model in RANS CFD of airfoils. We present the performance of two existing local correlation-based transition models – one-equation model (γ− SA) and two-equation model (γ-Reθt‾- SA) coupled with the Spalart–Allmaras (SA) RANS turbulence model – for offshore wind-turbine airfoils operating at a high Reynolds number. We compare the predictions of the two transition models with available experimental and CFD data in the literature in the Reynolds number range of 3–15 million including the AVATAR project measurements of the DU00-W-212 airfoil. Both transition models predict a larger L/D compared to fully turbulent results at all Reynolds numbers. The two models exhibit similar behavior at Reynolds numbers around 3 million. However, at higher Reynolds numbers, the one-equation model fails to predict the natural transition behavior due to early transition onset. The two-equation transition model predicts the aerodynamic coefficients for airfoils of various thickness at higher Reynolds numbers up to 15 million more accurately compared to the one-equation model. As a result, the two-equation model predictions are more comparable to the predictions from eN transition model. However, a limitation of this model is observed at very high Reynolds numbers of around 12–15 million where the predictions are very sensitive to the inflow turbulent intensity. The combination of the two-equation transition model coupled with the Spalart–Allmaras (SA) RANS turbulence model is a good method for performance prediction of modern wind-turbine airfoils using CFD.

17 WIND ENERGY↗
DOE OSTI2020

On the character of turbulent-like flows in self-consistent models of core-collapse supernovae

Neutrino-driven convection plays a crucial role in the development of core-collapse supernova (CCSN) explosions. However, the complex mechanism that triggers the shock revival and the subsequent explosion has remained inscrutable for many decades. Multidimensional simulations suggest that the growth of fluid instabilities, especially development of convection, will determine the morphology of the explosion. We have performed 3D simulations using spherical-polar coordinates covering a reduced angular extent (90° computational domain), and with angular resolutions of 2°, 1°, 1/2°, and 1/4°, to study the development of turbulent-like flows in core-collapse supernova explosions on a time scale of order 100 ms. We have employed the multi-physics Chimera code that includes detailed nuclear physics and spectral neutrino transport. Coarse resolution models do not develop an inertial range, presumably due to the bottleneck effect, such that the energy is prevented from cascading down to small scales and tends to accumulate at large scales. High-resolution models instead, start to recover the k −5/3 scaling of Kolmogorov's theory. Stochasticity and few simulation samples limit our ability to predict the development of explosions. Over the simulated time period, our models show no clear trend in improving (or diminishing) conditions for explosion as the angular resolution is increased. However, we find that disordered flow provides an effective pressure, as characterized by the Reynolds stress, behind the shock. This contribution, ~40%–50% of the thermal pressure, aids shock revival and thus the development of the explosion. Finally, we show that the kinetic energy power spectrum of reduced angular extent and full 4π models are consistent, thus indicating that a 90° computational domain is an adequate configuration to study the character of turbulence in CCSNe.

Casanova Bustamante, Jordi↗
DOE OSTI2025

Atwood effects on nonlocality of the scalar transport closure in Rayleigh-Taylor mixing

The importance of nonlocality is assessed in modeling mean scalar transport for turbulent Rayleigh-Taylor (RT) mixing at different Atwood numbers. Building on the two-dimensional incompressible work of Lavacot et al. [J. Fluid Mech. 985, A47 (2024)], the present work extends the macroscopic forcing method to variable density problems in three-dimensional space to measure moments of the generalized eddy diffusivity kernel in RT mixing for increasing Atwood numbers (𝐴 = 0.05, 0.3, 0.5, 0.8). It is found that as 𝐴 increases, (1) the eddy diffusivity moments become asymmetric and (2) the higher-order eddy diffusivity moments become larger relative to the leading-order diffusivity, indicating that nonlocality becomes more important at higher 𝐴. There is a particularly strong temporal nonlocality at higher 𝐴, suggesting stronger history effects. In conclusion, the implications of these findings for closure modeling for finite-Atwood RT are discussed.

general physics↗
DOE OSTI2021

Self-organized confinement in whole-device modeling of laboratory magnetospheres

Turbulent self-organization driven by global ideal interchange modes in a dipole-confined plasma is explored with self-consistent, whole-plasma simulations using a flux-tube averaged magnetohydrodynamic model in dipole magnetic geometry. We show the existence of robust particle pinch driven by ideal interchange-mode fluctuations, in which the particles are transported up the density gradient. It is found that the plasma profiles in a dipole field spontaneously relax to a marginally stable state as centrally peaked pressure and density are created by global interchange-mode transport.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Intelligent Sampling of Extreme-Scale Turbulence Datasets for Accurate and Efficient Spatiotemporal Model Training

With the end of Moore’s law and Dennard scaling, efficient training increasingly requires rethinking data volume. Can we train better models with significantly less data via intelligent subsampling? To explore this, we develop SICKLE, a sparse intelligent curation framework for efficient learning, featuring a novel maximum entropy (MaxEnt) sampling approach, scalable training, and energy benchmarking. We compare MaxEnt with random and phase-space sampling on large direct numerical simulation (DNS) datasets of turbulence. Evaluating SICKLE at scale on Frontier, we show that subsampling as a preprocessing step can, in many cases, improve model accuracy and substantially lower energy consumption, with observed reductions of up to 38×.

Brewer, Wes [ORNL] (ORCID:0000000236393956)↗
DOE OSTI2021

Two-dimensional turbulence in a massless fluid with a relativistic lattice Boltzmann model

We investigate a relativistic adaptation of the lattice Boltzmann method that reproduces the equations of motion for a turbulent, two-dimensional, massless hydrodynamic system. The classical lattice Boltzmann method and its extension to relativistic fluid dynamics are described. The numeric formulation is evaluated using a zero-averaged stirring force introduced into the numerics to induce turbulence, and the flow characteristics produced are compared to properties of a classical turbulent hydrodynamic flow. The model can reasonably be expected to offer quantitative simulations of electron fluid flows in graphene or Kagome lattices.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Characterizing in-stream turbulent flow for tidal energy converter siting in Cook Inlet, Alaska

Cook Inlet in Alaska is the most promising location for tidal energy development in the U.S. due to its significant tidal range of approximately 10 meters and high volume flux. The inlet's unique geometry and flow characteristics make it the most energetic tidal stream in the nation, with GW-scale potential energy capacity. With the growing interest in tidal energy converter (TEC) deployment in this area, we implemented a regional-scale, 3D hydrodynamic modeling framework to predict tidal current and turbulence characteristics that can assist TEC designers and project managers. We validated the model results extensively using various datasets collected with bottom-mounted acoustic Doppler current profilers and velocimeters. The comparison between the model outputs and observational data highlighted the effectiveness of the 3D FVCOM model and the Mellor-Yamada Level 2.5 Turbulence Model in accurately assessing macro-scale kinetic energy, turbulence intensity, and the production and dissipation rates at a prospective TEC site. Using two months of model simulation data, we examined the channel cross-section for TEC deployment, focusing on undisturbed power density and macro-scale turbulent properties. Further, our findings indicate that understanding the turbulence characteristics and flow properties can enhance Stage I/II resource characterization by identifying optimal locations for TECs and their layouts within the channel. Furthermore, we demonstrated that TEC designers can utilize macro-scale turbulence data from 3D coastal models as boundary conditions for other turbulence models, allowing for a more detailed resolution of the turbulence structure at TEC siting locations. Ultimately, this work emphasizes the importance of estimating flow and turbulence conditions in energetic systems to understand turbulent sites better and improve resource characterization.

16 TIDAL AND WAVE POWER↗
DOE OSTI2020

Diffusional growth of cloud droplets in homogeneous isotropic turbulence: DNS, scaled-up DNS, and stochastic model

This paper presents a novel methodology to use direct numerical simulation (DNS) to study the impact of isotropic homogeneous turbulence on the condensational growth of cloud droplets. As shown by previous DNS studies, the impact of turbulence increases with the computational domain size, that is, with the Reynolds number, because larger eddies generate higher and longer-lasting supersaturation fluctuations that affect growth of individual cloud droplets. The traditional DNS can only simulate a limited range of scales because of the excessive computational cost that comes from resolving all scales involved, that is, from large scales at which the turbulent kinetic energy (TKE) is introduced down to the Kolmogorov microscale, and from following every single droplet. The novel approach is referred to as the “scaled-up DNS”. The scaling up is done in two parts, first by increasing both the computational domain and the Kolmogorov microscale and second by using super-droplets instead of real droplets. To ensure proper dissipation of TKE and scalar variance at small scales, molecular transport coefficients are appropriately scaled up with the grid length. For the scaled-up domains, say, meters and tens of meters, one needs to follow billions of real droplets. This is not computationally feasible, and so-called super-droplets are applied in scaled-up DNS simulations. Each super-droplet represents an ensemble of identical real droplets, and the number of real droplets represented by a super-droplet is referred to as the multiplicity attribute. After simple tests showing the validity of the methodology, scaled-up DNS simulations are conducted for five domains, the largest of 64 3 m 3 volume using a DNS of 256 3 grid points and various multiplicities. All simulations are carried out with vanishing mean vertical velocity and with no mean supersaturation, similarly to past DNS studies. As expected, the supersaturation fluctuations as well as the spread in droplet size distribution increase with the domain size, with the droplet radius variance increasing in time t as t 1∕2 as identified in previous DNS studies. Scaled-up simulations with different multiplicities document numerical convergence of the scaled-up solutions. Finally, we compare the scaled-up DNS results with a simple stochastic model that calculates supersaturation fluctuations based on the vertical velocity fluctuations updated using the Langevin equation. Overall, the results document similar scaling to previous small-domain DNS simulations and support the notion that the stochastic subgrid-scale model is a valuable tool for the multi-scale simulation of droplet spectral evolution applying a large-eddy simulation model.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Recent advances in computational mathematics and applications

We are honored to bring you this special issue dedicated to recent advances in computational mathematics and applications in science and engineering. The papers in this special issue were presented in ”Conference on Computational Mathematics and Applications (CCMA)” held at the University of Nevada Las Vegas (UNLV) during October 25–27, 2019. The conference has attracted about 90 attendees from six countries. The 15 papers in the special issue comprise a diverse collection of theoretical numerical analysis as well as applications in various subjects. Topics cover optimal control of PDEs, discontinuous Galerkin methods, fluid flow in porous media, turbulence flow, static and moving interface problems, complex fluids composed by the mixture of Newtonian fluid and nematic (liquid crystal) flows, modeling of ocean–atmosphere system, image segmentation algorithm, uncertainty quantification problems for turbulence model and Maxwell’s equations, iterative solver for systems resulting from mixed methods, and novel methods for solving systems of nonlinear equations. As the Guest Editors we would like to thank Dr. Leland Jameson at NSF (National Science Foundation) for kindly supporting our conference proposal which made this conference possible. We would also like to thank Darren Sugrue from Elsevier who provided partial support for our conference, and Thennarasu Gunasekaran and his production team from Elsevier who produced this nice special issue. We are grateful to many people (Dr. Zhijian Wu, Lori Ornelas, Elsa Juarez, and many Ph.D. students) at the Department of Mathematical Sciences of UNLV who provided tremendous support for the conference. Finally, we very much appreciate all authors who contributed their precious results to this special issue.

97 MATHEMATICS AND COMPUTING↗