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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Boundary Layer Climatology at ARM Southern Great Plains

Operational since 1992, the Atmospheric Radiation Measurement (ARM) southern great plains (SGP) site at Oklahoma, USA has become a reference research site for meteorological studies. Due to an open data policy the ARM data are used by researchers all over the world. In this report, we review the long-term climatology of the atmospheric boundary layer, SGP instrumentations, the site and some site-specific atmospheric conditions which potentially effect wind turbines within the region. As the atmospheric boundary layer is bounded and influenced by the surface, observations of surface radiation components and heat fluxes are crucial in understanding land-atmosphere interactions. The entrainment of air, updrafts, downdrafts and boundary layer height characteristics is needed for understanding the structure and growth of the atmospheric boundary layer. Therefore, measurements from both surface in-situ and remote sensing observations at SGP provide an overall climatology and their interactions from surface up to the boundary layer. Measurements from a 60 m meteorological tower, surface flux stations, disdrometers, soil temperature and moisture flux plates, coherent Doppler lidar, Raman lidar, radiosondes, and satellite data at SGP central facility were analyzed. All the measurements were generally within a few square kilometers of each other at the central facility. This report focuses on data from January 2010 to June 2020 at SGP central facility. The various sections describe the ARM SGP site and surrounding wind turbines; in-situ and remote sensing instrumentation used in the report; provides mathematical equations to analyze fluxes, turbulence and other boundary layer parameters; a climatological analysis of surface winds, fluxes and thermodynamic parameters for several years; an analysis of observed winds in the framework of Monin-Obukhov Similarity Theory; an analysis of the boundary layer winds and direction from a Doppler lidar; multi-year turbulence estimates through the boundary layer from a Doppler lidar; atmospheric boundary layer water vapor and relative humidity profiles from Raman lidar; cloud base height and boundary layer height from multiple sensors and satellite data; and finally site specific atmospheric conditions, such as nocturnal low-level jets. Diurnal, seasonal and yearly variations of surface, sub-surface and boundary layer quantities, such as wind speed, direction, temperature, atmospheric stability, soil temperature, and various atmospheric fluxes at SGP showed distinct trends useful for focused modeling studies. The applicability of surface similarity theory on ARM SGP data is also evaluated, which showed northerly flows are aligned with MO theory estimates compared to southerly flows. Boundary layer winds and direction profiles for several years from a Doppler lidar shows a consistent presence of a nocturnal low-level jet and predominant southerly wind directions through the boundary layer at SGP. The inter-annual variability at SGP is low (<3.5%), with a mean annual wind speed of approximately 7 m s -1 at 100 m above ground level. Boundary layer turbulence and moisture transport from Doppler and Raman lidars are evaluated, which provides evidence of increased water vapor mass flux into the great plains during nocturnal low-level jets. The moisture flux from nocturnal low-level jets is observed to be maximum during summer periods. A novel machine learning algorithm is implemented to accurately estimate the planetary boundary layer height, providing further insights into growth and destruction of the convective boundary layer height during various seasons and land-atmosphere conditions. The high frequency of low-level clouds during winter, spring and fall seasons is validated using the multi-sensor array and satellite estimates of cloud top height. Satellite vegetative fraction data provides insight into seasonal surface roughness and vegetation variability around SGP site.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Design and Modeling of an 80 bar Oxy-Combustor for Direct Fired Supercritical CO2 Applications

As supercritical CO2 power cycles for fossil energy power generation continue to generate interest, there are significant issues and unanswered questions regarding injector design, flame stabilization, wall heat transfer, CO emissions, combustion dynamics and other combustion phenomenon. For natural gas, direct-fired cycles with carbon capture it is believed that Computational Fluid Dynamics (CFD) modeling will play an essential role in the combustor design process. To accurately model turbulent reacting flows at these unique conditions, experimental data is needed to validate CFD codes and sub-models and is currently lacking at conditions relevant for these cycles. This paper presents the conceptual design and CFD simulations of an experimental 80 bar oxy-combustion facility and test article currently under construction at NETL. The facility is targeted towards the testing of a single injector, direct-fired sCO2 combustor at the 100 kW thermal output level. While these conditions do not reflect the actual Allam cycle operating conditions (300 bar) they are viewed as a stepping stone in the model validation process at supercritical conditions. Reynolds Averaged Navier-Stokes as well as Large Eddy Simulation are used to model the turbulent combustion process and aid in the design of the combustor and injector. Process parameters including oxidizer preheat temperature and combustor flowrate are investigated.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

Editorial: Resolving atmospheric flow in complex environments: recent experiments in terrain and forest canopies

The characterization of atmospheric flows in complex environments, which may include steep terrain slopes and heterogeneous vegetation and/or forest cover, is a long-standing challenge in boundary-layer meteorology. Atmospheric observations are complicated by the presence of transient, terrain-induced flow features, forest-canopy-atmosphere interactions, and atmospheric stability effects, not to mention the logistical hurdles involved with instrument deployment, data analysis, and quality control. Furthermore, challenges in atmospheric modeling arise due to numerical errors associated with complex terrain flows, as well as reliance on simplified parameterizations for unresolved processes such as turbulent mixing and land-surface or forest-canopy-atmosphere interactions. These modeling challenges are exacerbated in the so-called “gray zone,” wherein features of interest have length scales that are similar to the model grid spacing, or when the principal flow layer is smaller than the grid spacing (e.g., slope flows).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Adaptive mesh based combustion simulations of direct fuel injection effects in a supersonic cavity flame-holder

Here, we present high-fidelity reacting simulations of a supersonic cavity flame-holder configuration. The focus of this work is on flame stabilization brought about by varying the location of fuel injection in a cavity stabilized supersonic flow of air. Central to our approach is a compressible multi-species reacting flow solver that uses adaptive-mesh-refinement (AMR), enabling the resolution of flame, shock-waves, boundary-layers, and small-scale structures in the computational domain. Our analysis indicates that fuel injection closer to the ramp at the aft end of the cavity allows for greater mixing and lower peak temperatures compared to fuel injection upstream that is closer to the backward facing step of the cavity. This difference is mainly due to greater turbulent fluctuations generated from the shear-layer towards the cavity ramp, thereby enhancing the mixing of fuel and air. A low frequency oscillatory behaviour in heat-release and pressure was also observed for the upstream injection case while a much higher-frequency phenomena was observed in the near-ramp injection case. By identifying the important physical determinants of the combustion processes, this study illustrates a promising pathway to design and optimize direct fuel injection strategies in supersonic cavity flame-holders that can improve flame stability, combustion efficiency, and reduce emissions.

42 ENGINEERING↗
DOE OSTI2021

Describing the Mechanism of Instability Suppression Using a Central Pilot Flame With Coupled Experiments and Simulations

Pilot flames are commonly used to extend combustor operability limits and suppress combustion oscillations in low-emissions gas turbines. Combustion oscillations, a coupling between heat release rate oscillations and combustor acoustics, can arise at the operability limits of low-emissions combustors where the flame is more susceptible to perturbations. While the use of pilot flames is common in land-based gas turbine combustors, the mechanism by which they suppress instability is still unclear. In this study, we consider the impact of a central jet pilot on the stability of a swirl-stabilized flame in a variable-length, single-nozzle combustor. Previously, the pilot flame was found to suppress the instability for a range of equivalence ratios and combustor lengths. We hypothesize that combustion oscillation suppression by the pilot occurs because the pilot provides hot gases to the vortex breakdown region of the flow that recirculate and improve the static, and hence dynamic, stability of the main flame. This hypothesis is based on a series of experimental results that show that pilot efficacy is a strong function of pilot equivalence ratio but not pilot flow rate, which would indicate that the temperature of the pilot products as well as the combustion intensity of the pilot flame play more of a role in oscillation stabilization than the length of the pilot flame relative to the main flame. Further, the pilot-flame efficacy increases with pilot-flame equivalence ratio until it matches the main-flame equivalence ratio; at pilot equivalence ratios greater than the main equivalence ratio, the pilot-flame efficacy does not change significantly with pilot equivalence ratio. To understand these results, we use large-eddy simulation (LES) to provide a detailed analysis of the flow in the region of the pilot flame and the transport of radical species in the region between the main flame and pilot flame. Furthermore, the simulation, using a flamelet/progress variable-based chemistry tabulation approach and standard eddy viscosity/diffusivity turbulence closure models, provides detailed information that is inaccessible through experimental measurements.

42 ENGINEERING↗
DOE OSTI2024

Implementation and Validation of a Generalized Actuator Disk Parameterization for Wind Turbine Simulations Within the FastEddy Model

ABSTRACT Fast and accurate large‐eddy simulation (LES) of the atmospheric boundary layer plays a crucial role in advancing wind energy research. Long‐duration wind farm studies at turbine‐resolving scales have become increasingly important to understand the intricate interactions between large wind farms and the atmospheric boundary layer. However, the prohibitive computational cost of these turbulence‐ and turbine‐resolving simulations has precluded such modeling to be exercised on a regular basis. To that end, we implement and validate the generalized actuator disk (GAD) model in the computationally efficient, graphics processing unit (GPU)–resident, LES model FastEddy. We perform single‐turbine simulations under three atmospheric stabilities (neutral, unstable, and stable) and compare them against observations from the Scaled Wind Farm Technology (SWiFT) facility and other LES codes from the recent Wakebench turbine wake model benchmark. Our idealized LES results agree well with observed wake velocity deficit and downstream recovery across stability regimes. Turbine response in terms of rotational speed, generated power, torque, and thrust coefficient are well predicted across stability regimes and are consistent with the LES results from the benchmark. The FastEddy simulations are found to be at least two orders of magnitude more efficient than the traditional CPU‐based LES models, opening the door for realistic LES simulations of full wind plants as a viable standard practice.

17 WIND ENERGY↗
DOE OSTI2025

Optimization and active stabilization of a far-infrared laser for NSTX-U high poloidal wavenumber scattering diagnostics

The far-infrared (FIR) laser output beam power and profile are important parameters in the laser-aided diagnostics, directly influencing the spatial resolution and signal-to-noise ratio of measurements. Here, this work focuses on developing a systematic control method to enhance FIR laser beam quality through optimized mirror alignment and real-time feedback-based precision cavity length tuning. A 150 W CO 2 laser, aligned with the waveguide axis using a HeNe reference laser, serves as the pump source. The sensitivity of FIR beam intensity to pump gas pressure and thermal expansion is investigated, revealing that even a 1 µm cavity expansion can significantly degrade output power stability to about two-thirds of its original value. To address this, a feedback control module has been designed and implemented for active cavity length adjustment, stabilizing the output power at ∼30 mW. In addition, maintaining a high formic acid gas pressure ($>$190 mTorr) within the cavity ensures reliable operation. The optimized FIR laser will be deployed on the National Spherical Torus eXperiment-U high poloidal wavenumber scattering system for studying electron-scale turbulence in tokamak plasmas.

Xu, Xinhang [Univ. of California, Davis, CA (Unite↗
DOE OSTI2025

Evolution of intermittent filaments in the scrape-off layer of NSTX

Filamentary structures naturally arise from background turbulence in the scrape-off layer (SOL) of plasmas, leading to significant particle and heat transport that can degrade overall plasma confinement. This enhanced transport can contribute to unacceptably high heat loads on plasma-facing components. As such, understanding the physics of SOL plasma filaments is critical for predicting and mitigating their effects in future fusion devices. On the National Spherical Torus Experiment (NSTX), plasma filaments—commonly referred to as “blobs”—were investigated using the gas-puff imaging (GPI) diagnostic in the edge and SOL regions. The analysis involved identifying, segmenting, and tracking the characteristic contours of the blobs in each frame of the GPI video sequences. Their evolution was characterized through shape descriptors, velocity, and angular velocity derived from their contour coordinates. The results indicate that as the blob area increases, their shapes become more concave and less circular, suggesting reduced structural stability in larger blobs. This result aligns with previous theoretical results where it was shown that larger blobs are more susceptible to instabilities [Krasheninnikov et al., J. Plasma Phys. 74, 679–717 (2008) and D'Ippolito et al., Phys. Plasmas 18, 060501 (2011)]. A positive correlation was observed between radial velocity and radial position, suggesting radially outward acceleration of the filaments, potentially driven by decreasing viscous drag toward the far SOL. Interestingly, blobs in background SOL turbulence exhibited minimal spinning in contrast to filaments originating from edge localized modes, which show substantial rotation during their paths [Lampert et al., Phys. Plasmas 29, 102502 (2022)]. Statistical analysis of the solidity and total curvature shape descriptors, along with their temporal evolution, revealed relatively broad, near-Gaussian distributions. This suggests that blob morphology is strongly influenced by stochastic turbulent processes in the surrounding plasma environment. Blob parameters were also compared with bulk plasma and radial profile measurements. Notable trends were found between blob rotation and poloidal velocity with collisionality and line-integrated density. These findings contribute to a deeper understanding of blob dynamics and provide valuable insights for refining SOL turbulence models.

Covariance and correlation↗
DOE OSTI2020

Mesh-Sequenced Realizations for Evaluation of Subgrid-Scale Models for Turbulent Combustion

This paper develops a new approach for analysis of subgrid closures for turbulent combustion as modeled using direct quadrature (finite-rate chemistry) techniques. The approach, termed multiresolution analysis through mesh-sequenced realizations (MRA-MSR), conducts simultaneous, constrained large-eddy simulations on a set of hierarchically coarsened meshes. Furthermore, the availability of underlying fine-mesh (subgrid) data corresponding to coarse-mesh locations allows a clearer assessment of the effects of unresolved fluctuations on apparent reactivity. A key to MRA-MSR is the correlation of eddy structures at coarser mesh levels, which is facilitated by the transfer of filtered fine-mesh velocity information. A seven-mesh MRA-MSR hierarchy using three resolution levels is applied to one of the Sydney bluff-body stabilized methane–hydrogen flames. Analysis of the simultaneously evolved data at different resolution levels reveals several interesting trends. First, at high Damköhler numbers, there is clear evidence of attenuation of apparent reactivity due to the effects of unresolved fluctuations. Secondly, single-point, single-time filtered density functions of a normalized subgrid Damköhler number show a characteristic beta probability density function (PDF) form and display evidence of scale similarity. Interrogation of the MRA-MSR database also shows that the recently-proposed least-squares minimization (LSM) turbulence–chemistry interaction model can account for the observed diminishment in reactivity at high Damköhler numbers but cannot reduce scatter significantly. A new form of the LSM model, which makes use of the normalized subgrid Damköhler number beta PDF distribution, performs slightly better than the original model, illustrating the potential of MRA-MSR both in assessing existing closure concepts and in developing new ones.

42 ENGINEERING↗
DOE OSTI2023

Predicting wind farm operations with machine learning and the P2D‐RANS model: A case study for an AWAKEN site

Abstract The power performance and the wind velocity field of an onshore wind farm are predicted with machine learning models and the pseudo‐2D RANS model, then assessed against SCADA data. The wind farm under investigation is one of the sites involved with the American WAKE experimeNt (AWAKEN). The performed simulations enable predictions of the power capture at the farm and turbine levels while providing insights into the effects on power capture associated with wake interactions that operating upstream turbines induce, as well as the variability caused by atmospheric stability. The machine learning models show improved accuracy compared to the pseudo‐2D RANS model in the predictions of turbine power capture and farm power capture with roughly half the normalized error. The machine learning models also entail lower computational costs upon training. Further, the machine learning models provide predictions of the wind turbulence intensity at the turbine level for different wind and atmospheric conditions with very good accuracy, which is difficult to achieve through RANS modeling. Additionally, farm‐to‐farm interactions are noted, with adverse impacts on power predictions from both models.

17 WIND ENERGY↗
DOE OSTI2023

Nonlinear second order electromagnetic gyrokinetic theory for a tokamak plasma

The steep plasma pressure gradient that forms at the edge of the high confinement, H-mode regime of tokamak operation provides free energy to drive electromagnetic micro-instabilities that are widely believed to influence the transport processes in this so-called pedestal region. This high pressure gradient also provides a high current density (bootstrap current), known to influence ballooning mode stability and to be important for driving kink modes in the ideal magneto-hydrodynamic plasma model (so-called peeling-ballooning modes). Furthermore, efficient, steady state future tokamak power plants must operate with a large bootstrap current in the core and especially concerning spherical tokamaks, confinement will be influenced by electromagnetic turbulence. To accommodate these important situations, conventional electromagnetic gyrokinetic theory is extended to incorporate neoclassical effects in the equilibrium drives, allowing $B_{\vartheta} ~ B_0$ (B0 is the confining magnetic field, and $B_{\vartheta}$ is its poloidal component). This provides a global gyrokinetic model that self-consistently captures the consequences of large bootstrap current fractions on the equilibrium distribution functions.

kink modes↗
DOE OSTI2022

Predicting the recovery and grade of a rougher flotation circuit from liberation data

A flotation model has been validated against the survey data obtained from a copper rougher flotation circuit with a circulating load. Here, the model was developed using the hydrophobic force as a kinetic parameter, which made it possible to use the contact angles of the free and composite particles as input parameters so that the model can predict both recoveries and grades. The model also recognizes the role of bubble coarsening in determining the froth phase recoveries and grades. The model predictions are in good agreement with the survey data. The size-by-size recovery curve as predicted from the model shows an optimum particle size range that is consistent with most of the operating data reported in the literature. The model suggests that the upper particle size limit may be determined by the instability of the froth phase rather than the turbulence in the pulp phase of a flotation cell.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Electro-mechanical Modeling of Wind Turbine and Energy Storage Systems with Enhanced Inertial Response

In this paper, a coordinated control scheme for wind turbine generator (WTG) and supercapacitor energy storage system (ESS) is proposed for temporary frequency supports. Inertial control is designed by using generator torque limit considering the security of WTG system, while ESS releases its energy to compensate the sudden active power deficit during the recovery process of turbine rotor. WTG is modeled using the fatigue, aerodynamic, structure, turbulence (FAST) code, which identifies the mechanical loadings of the turbine and addresses electro-mechanical interactions in the wind energy system. A damping controller is augmented to the inertial control to suppress severe mechanical oscillations in the shaft and tower of the turbine during frequency supports. Furthermore, the result of small-signal stability analysis shows that the WTG-ESS tends to improve the stability of the whole multi-energy power grid. The major contributions of this paper will be validated by utilizing the proposed control method that combines the grid support capability and maintaining the integrity of structural design of the turbine for normal operations.

17 WIND ENERGY↗
DOE OSTI2022

Low-Reynolds-number oscillating boundary layers on adiabatic slopes

We investigate the instabilities and transition mechanisms of Boussinesq stratified boundary layers on sloping boundaries when subjected to oscillatory body forcing parallel to the slope. We examine idealized forms of boundary layers on hydraulically smooth abyssal slopes in tranquil mid- to low-latitude regions, where low-wavenumber internal tides gently heave isopycnals up and down adiabatic slopes in the absence of mean flows, high-wavenumber internal tides, shelf breaks, resonant tide–bathymetry interactions (critical slopes) and other phenomena associated with turbulence ‘hot spots’. In non-rotating low-Reynolds-number flow, increased stratification on the downslope phase has a relaminarizing effect, while on the upslope phase we find transition-to-turbulence pathways arise from shear production triggered by gravitational instabilities. When rotation is significant (low slope Burger numbers) we find that boundary layer turbulence is sustained throughout the oscillation period, resembling stratified Stokes–Ekman layer turbulence. Simulation results suggest that oscillating boundary layers on smooth slopes at low Reynolds number ($Re\leqslant 840$), unity Prandtl number and slope Burger numbers greater than unity do not cause significant irreversible turbulent buoyancy flux (mixing), and that flat-bottom dissipation rate models derived from the tide amplitude are accurate within an order of magnitude.

42 ENGINEERING↗
DOE OSTI2025

Metastability of stratified magnetohydrostatic equilibria and their relaxation

Motivated by explosive releases of energy in fusion, space and astrophysical plasmas, we consider the nonlinear stability of stratified magnetohydrodynamic equilibria against two-dimensional interchanges of straight magnetic-flux tubes. We demonstrate that, even within this restricted class of dynamics, the linear stability of an equilibrium does not guarantee its nonlinear stability: equilibria can be metastable. We show that the minimum-energy state accessible to a metastable equilibrium under non-diffusive two-dimensional dynamics can be found by solving a combinatorial optimisation problem. These minimum-energy states are, to good approximation, the final states reached by our simulations of destabilised metastable equilibria for which turbulent mixing is suppressed by viscosity. To predict the result of fully turbulent relaxation, we construct a statistical mechanical theory based on the maximisation of Boltzmann's mixing entropy. This theory is analogous to the Lynden-Bell statistical mechanics of collisionless stellar systems and plasma, and to the Robert–Sommeria–Miller theory of two-dimensional vortex turbulence. Our theory reproduces well the results of our numerical simulations for sufficiently large perturbations to the metastable equilibrium.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Coupling a Lagrangian–Eulerian Spark-Ignition (LESI) model with LES combustion models for engine simulations

In the United States transportation sector, Light-Duty Vehicles (LDVs) are the largest energy consumers and CO 2 emitters. Electrification of LDVs is posed as a potential solution, but SI engines can still contribute to decarbonization. Car manufacturers have turned to unconventional engine operation to increase the efficiency of Spark-Ignition (SI) engines and reduce the carbon emissions of their fleets. Dilute, lean, and stratified-charge engine operation has the potential for engine efficiency improvements at the expense of increased cyclic variability and combustion instability. At such demanding engine conditions, the spark ignition event is key for flame initiation and propagation and for enhanced combustion stability. Reliable and accurate spark ignition models can help design ignition systems that reduce cyclic variability. Multiple computational spark-ignition models exist that perform well under conventional conditions, but the underlying physics needs to be expanded, for unconventional engine operation. In this paper, a hybrid Lagrangian–Eulerian Spark-Ignition (LESI) model is coupled with different turbulent flame propagation models for engine simulations. LESI relies on Lagrangian arc tracking and Eulerian energy deposition. The LESI model is coupled with the Well-Stirred Reactor (WSR), Thickened Flame Model (TFM), and g-equation model and used to simulate several cycles of a Direct-Injection Spark-Ignition (DISI) engine using a commercial Computational Fluid Dynamics (CFD) engine solver. The results showcase the successful coupling of LESI with the combustion models. Global engine metrics, such as pressure and Apparent Heat Release Rate (AHRR), for each simulation setup are compared to experimental engine results, for validation. In addition, results highlight the successful prediction of spark channel movement by comparing simulation images to experimental optical engine images. Finally, the successful coupling of LESI to combustion models, making it a usable model in the engine modeling community, is emphasized and future development details are discussed.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2024

Large eddy simulation of lean blow-off in swirl-stabilized flame with the subgrid dissipation concept

The lean blow-off mechanism of the premixed swirl flame is numerically investigated by large eddy simulation (LES) with the subgrid dissipation concept (SDC) combustion model. Three simulated cases cover stable, near blow-off, and transient conditions. Compared with the experiment, the LES-SDC approach captures the flow and combustion features for stable and near blow-off conditions. More importantly, the predictions of the blowoff procedure and duration agree satisfactorily with the experiment, indicating that the LES-SDC approach is a promising tool for predicting strong, unsteady turbulent combustion processes. Further, the numerical results are used to investigate the blow-off mechanism. Two stages in the blow-off procedure are specified. The first is the necking and extinction of the downstream flame surface, and the second is the shrinking of the upstream flame surface. The blow-off mechanism is well explained by the theory of stretched flame extinction. At the end of the recirculation zone, the large negative radial velocity pushes the flame to the central line. The combustion process here can be abstracted as the stretched counter-flame of the reactant-reactant configuration. The excessive flame stretch dominates the flame extinction and triggers the blow-off event. The upstream flame resists the intense stretch with the help of hot product recirculation, and the combustion here can be idealized as the counter-flame of the reactant-product configuration. The alignment of the temperature gradient and flow velocity, together with the excessive stretch, clearly indicates the tendency of flame local extinction. A Damköhler number-based blow-off criterion is raised from the mean flow strain rate and laminar flame bulk extinction strain rate.

42 ENGINEERING↗
DOE OSTI2022

Dynamic calibration of differential equations using machine learning, with application to turbulence models

We present a methodology for calibration of parametric ordinary and partial differential equation models, using off-the-shelf software for back-propagation in Neural Networks (NN). As a prototypical example, we consider calibration of a Reynolds-averaged Navier-Stokes (RANS) turbulence closure model, against ground truth data from direct numerical simulations (DNS) of two different turbulent flows. Numerical time integration is represented as a custom NN, where only the RANS model parameters are trainable. A loss function is defined to quantify the mismatch between the NN prediction and the ground truth over a predefined, finite time integration window. This loss function is then minimized using a gradient descent method utilizing the back-propagation algorithm. Furthermore, this dynamic approach to training is to be contrasted with a static approach, wherein a least square regression estimate for parameters is obtained in the limit of an infinitesimal time integration window. In a first test of static and dynamic approaches against ground truth data generated by the model, the former proves to be significantly faster and more accurate than the latter at recovering the parameters. When both calibration approaches are tested against DNS data, for which it is known that the model cannot achieve a perfect fit, the static approach yields a good prediction only for short times, while the dynamic approach results in physical and stable predictions over the entire integration window. After optimization of the dynamic approach for time step, spatial resolution, stability, and physics-based constraints, we obtain a 50% improvement of outcomes over those obtained from the existing, manually calibrated set of parameters, demonstrating the merits of this systematic and automated procedure.

97 MATHEMATICS AND COMPUTING↗