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At least 397 records · Page 22

A Review of Physics-Informed Machine Learning in Fluid Mechanics

Physics-informed machine-learning (PIML) enables the integration of domain knowledge with machine learning (ML) algorithms, which results in higher data efficiency and more stable predictions. This provides opportunities for augmenting—and even replacing—high-fidelity numerical simulations of complex turbulent flows, which are often expensive due to the requirement of high temporal and spatial resolution. In this review, we (i) provide an introduction and historical perspective of ML methods, in particular neural networks (NN), (ii) examine existing PIML applications to fluid mechanics problems, especially in complex high Reynolds number flows, (iii) demonstrate the utility of PIML techniques through a case study, and (iv) discuss the challenges and opportunities of developing PIML for fluid mechanics.

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↗

Uniform momentum and temperature zones in unstably stratified turbulent flows

Wall-bounded turbulent flows exhibit a zonal arrangement, in which streamwise velocity organizes into uniform momentum zones (UMZs), separated by thin layers of elevated interfacial shear. While significant research efforts have focused on these structural features in neutrally stratified flows, the effects of unstable thermal stratification on UMZs and on analogous uniform temperature zones (UTZs) have not been considered previously. In this article, statistical properties of UMZs and UTZs are investigated using a suite of large eddy simulations of unstably stratified turbulent channel flow spanning weakly to highly convective conditions. When normalized by the friction velocity and stability-dependent mixing length, the mean velocity gradient based on UMZ interfacial velocity jumps and the vorticity thickness exhibits good collapse for all stabilities, establishing a link between UMZ properties and scaling predictions from Monin–Obukhov similarity theory. A similar relationship is found between UTZ properties and surface-layer scaling of the mean temperature gradient. In the mixed layer, mean UMZ depth is quasi-constant with wall-normal distance, while the deepest UTZs are found in the centre of the boundary layer. These instantaneous structures are found to be linked to the well-mixed velocity and temperature profiles in the convective mixed layer. Conditional averaging indicates that both UMZ and UTZ interfaces are associated with ejections of momentum and warm updrafts below the interface and sweeps of momentum and cool downdrafts above the interface. These results demonstrate a tangible connection between instantaneous structural features, mean properties and scaling laws in unstably stratified flows.

Mechanics↗

Convective and Turbulent Motions in Nonprecipitating Cu. Part II: LES Simulated Cloud Represented by a Starting Plume

The dynamic structure of a small trade wind cumulus (Cu) is analyzed using a novel approach. Cu developing in a shear-free environment is simulated by 10-m-resolution LES model with spectral bin microphysics. The aim is to clarify the dynamical nature of cloud updraft zone (CUZ) including entrainment and mixing in growing Cu. The validity of concept stating that a cloud at developing state can be represented by a parcel or a jet is tested. To investigate dynamical entrainment in CUZ performed by motions with scales larger than the turbulence scales, the modeled fields of air velocity were filtered by wavelet filter that separated convective motions from turbulent ones. Two types of objects in developing cloud were investigated: small volume ascending at maximal velocity (point parcel) and CUZ. It was found that the point parcel representing the upper part of cloud core is adiabatic. The motion of the air in this parcel ascending from cloud base determines cloud-top height. The top-hat (i.e., averaged) values of updraft velocity and adiabatic fraction in CUZ are substantially lower than those in the point parcel. Evaluation of the terms in the dynamical equation typically used in 1D cloud parcel models show that this equation can be applied for calculation of vertical velocities at the developing stage of small Cu, at least up to the heights of the inversion layer. Dynamically, the CUZ of developing cloud resembles the starting plume with the tail of nonstationary jet. Both the top-hat vertical velocity and buoyancy acceleration linearly increase with the height, at least up to the inversion layer. An important finding is that lateral entrainment of convective (nonturbulent) nature has a little effect on the top-hat CUZ velocity and cannot explain the vertical changes of conservative variables qt and θl. In contrast, entrained air lifting inside CUZ substantially decreases top-hat liquid water content and its adiabatic fraction. Possible reasons of these effects are discussed.

54 ENVIRONMENTAL SCIENCES↗

Scaling patch analysis of planar turbulent mixing layers

Proper scales for the mean flow and Reynolds shear stress in planar turbulent mixing layers are determined from a scaling patch analysis of the mean continuity and momentum equations. By seeking an admissible scaling of the mean continuity equation, a proper scale for the mean transverse flow is determined as V ref =(dδ/dx)U ref , where dδ/dx is the growth rate of the mixing layer width and U ref =U h –U l is the difference between the velocity of the high speed stream U h and the velocity of the low speed stream U l . By seeking an admissible scaling for the mean momentum equation, a proper scale for the kinematic Reynolds shear stress is determined as R uv,ref =U avg V ref =[$\frac{1}{2A_u}$$\frac{dδ}{dx}$]$U^{2}_{ref}$ where A u $_{=}^{def}$(U h –U l )/(U h +U l ) is the normalized velocity difference that emerges naturally in the admissible scaling of the mean momentum equation. Self-similar equations for the scaled mean transverse flow V* and Reynolds shear stress $R^{*}_{uv}$=R uv /R uv,ref are derived from the mean continuity and mean momentum equations. Finally, approximate equations for V* and $R^{*}_{uv}$ are developed and found to agree well with experimental data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Isotope effects on transport in LHD

Abstract Isotope effects are one of the most important issues for predicting future reactor operations. Large helical device (LHD) is the presently working largest stellarator/helical device using super conducting helical coils. In LHD, deuterium experiments started in 2017. Extensive studies regarding isotope effects on transport have been carried out. In this paper, the results of isotope effect studies in LHD are reported. The systematic studies were performed adjusting operational parameters and nondimensional parameters. In L mode like normal confinement plasma, where internal and edge transport barriers are not formed, the scaling of global energy confinement time ( τ E ) with operational parameters shows positive mass dependence ( M 0.27 ; where M is effective ion mass) in electron cyclotron heating plasma and no mass dependence ( M 0.0 ) in neutral beam injection heating plasma. The non-negative ion mass dependence is anti-gyro-Bohm scaling. The role of the turbulence in isotope effects was also found by turbulence measurements and gyrokinetic simulation. Better accessibility to electron and ion internal transport barrier (ITB) plasma is found in deuterium (D) plasma than in hydrogen (H). Gyro kinetic non-linear simulation shows reduced ion heat flux due to the larger generation of zonal flow in deuterium plasma. Peaked carbon density profile plays a prominent role in reducing ion energy transport in ITB plasma. This is evident only in plasma with deuterium ions. New findings on the mixing and non-mixing states of D and H particle transports are reported. In the mixing state, ion particle diffusivities are higher than electron particle diffusivities and D and H ion density profiles are almost identical. In the non-mixing state, ion particle diffusivity is much lower than electron diffusivity. Deuterium and hydrogen ion profiles are clearly different. Different turbulence structures were found in the mixing and non-mixing states suggesting different turbulence modes play a role.

Physics↗

The effects of turbulence on the flame structure and NO formation of ammonia turbulent premixed combustion at various equivalence ratios

Ammonia is carbon-free and is regarded as a potential fuel to address global warming issues. Here, in this work, three-dimensional direct numerical simulations (DNS) of ammonia/air turbulent premixed flames were performed to explore the influence of turbulence and equivalence ratio on the flame structure and NO formation characteristics. Two equivalence ratios were considered, i.e. Φ=0.9 and Φ=1.1. The general flame structures were presented and species distributions were examined. The NO mass fraction was found to be the highest in the product for the lean case and in the reaction zone for the rich case. The conditional mean values of species mass fractions and reaction rates were compared with those of the unstrained and strained laminar premixed flames to explore how well the laminar flame structures can approach those of the turbulent flame. The budget analysis of the species transport equations showed that turbulent diffusion plays an important role in species transport. The turbulent diffusivity D T was estimated using the gradient hypothesis based on the DNS data. Various laminar flame simulations with different diffusivities were carried out. It was shown that the conditional means of the DNS agree well with those of the laminar flames including D T in the transport property calculation. The global and local NO formation characteristics were investigated. It was found that the mean NO production conditioned on the progress variable is lower compared with the corresponding laminar flame in the rich case. However, the relative contributions from various NO pathways are rarely affected by turbulence. The NO mass fraction is higher in negative curvature regions compared with positive curvature regions of the flame surface for the rich case, which is due to the preferential diffusion of H 2 and other radicals and the enhanced NO pathways in negatively curved regions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Direct numerical simulation of open-channel flow over a heterogeneous particle bed at low relative submergence

In this article, this study investigates turbulent open-channel flows over beds of irregularly arranged particles, using direct numerical simulations at a friction Reynolds number of Re T = 300⁠. Two distinct cases are examined: a polydisperse bed (P800) composed of multiple layers of randomly distributed spheres of varying sizes, and a monodisperse bed (M1015) formed by a random distribution of uniform sized spheres, with a bottommost single layer of varied-sized particles to introduce realistic randomness. Our investigation unveils a rich network of low- and high-speed streaks within the flow field, exhibiting distinctive behaviors in different bed configurations. The P800 case presents a poorly organized flow pattern induced by the varied particle sizes and arrangements, while the M1015 case shows a more regular flow pattern, marked by larger streaks. We also observe that total wall shear stress is substantially influenced by surface roughness-induced drag, extending beyond the effects documented in existing studies of open-channel flows. The present study reveals intricate secondary flow patterns over irregular particle beds. Large-scale circulations are discerned around particle crests in the P800 case and localized circulations with increased turbulence in the M1015 case. Furthermore, analysis of Reynolds stress tensor components indicates that roughness disrupts coherent turbulent eddies, consequently mitigating peak stress. We quantify correlations between drag force and local fluid velocity fluctuations. Notably, a larger deviation in drag is observed in the P800 case compared to M1015, accentuating the influence of particle size and distribution on fluid–particle interactions.

42 ENGINEERING↗

Shear-free, inhomogeneous turbulence in a stably stratified fluid

High-resolution large eddy simulations are conducted of locally forced, shear-free turbulence in the presence of an initially sharp density interface. The simulations are reminiscent of oscillating grid turbulence experiments used to isolate the effect of turbulent diffusion and entrainment from background shear. By simulating such a flow we avoid common challenges of the experiments such as secondary-flow contamination due to sidewall effects and the inevitable interaction of the stratifying agent and forcing region. To address the latter concern, we add a heating term (potential energy sink) to the governing equations in the forcing layer, thereby preventing a heat flux through the source region. This modification sets up a continuous stratification in the mixed layer that is often assumed to be negligible in experiments. Despite this difference, we are able to make meaningful comparisons in terms of the overall entrainment rate, which varies as a power law with a turbulent Richardson number. Two exponents, −2 and −1, are measured depending on the definition of the Richardson number and entrainment rate used. The definition leading to −1 is consistent with most experiments, and we argue it is the superior choice if one is able to measure the relevant quantities. We also verify the self-similar scaling of turbulence velocity and length scales in the homogeneous fluid and propose ‘inner’ and ‘outer’ scalings for the stratified cases based on a local Froude number. The detailed scaling results are useful for turbulence model validation.

54 ENVIRONMENTAL SCIENCES↗

Near-cancellation of up- and down-gradient momentum transport in forced magnetized shear-flow turbulence

Visco-resistive magnetohydrodynamic turbulence, driven by a two-dimensional unstable shear layer that is maintained by an imposed body force, is examined by decomposing it into dissipationless linear eigenmodes of the initial profiles. The down-gradient momentum flux, as expected, originates from the large-scale instability. However, continual up-gradient momentum transport by large-scale linearly stable but nonlinearly excited eigenmodes is identified and found to nearly cancel the down-gradient transport by unstable modes. The stable modes effectuate this by depleting the large-scale turbulent fluctuations via energy transfer to the mean flow. This establishes a physical mechanism underlying the long-known observation that coherent vortices formed from nonlinear saturation of the instability reduce turbulent transport and fluctuations, as such vortices are composed of both the stable and unstable modes, which are nearly equal in their amplitudes. The impact of magnetic fields on the nonlinearly excited stable modes is then quantified. Furthermore, even when imposing a strong magnetic field that almost completely suppresses the instability, the up-gradient transport by the stable modes is at least two-thirds of the down-gradient transport by the unstable modes, whereas for weaker fields, this fraction reaches up to 98%. These effects are persistent with variations in magnetic Prandtl number and forcing strength. Finally, continuum modes are shown to be energetically less important, but essential for capturing the magnetic fluctuations and Maxwell stress. A simple analytical scaling law is derived for their saturated turbulent amplitudes. It predicts the falloff rate as the inverse of the Fourier wavenumber, a property which is confirmed in numerical simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Investigation of Main Bearing Fatigue Estimate Sensitivity to Synthetic Turbulence Models Using a Novel Drivetrain Model Implemented in OpenFAST

ABSTRACT A coupled medium‐fidelity drivetrain model is developed and implemented in OpenFAST for a 10‐MW land‐based reference turbine. The implementation is verified against a fully coupled multibody wind turbine model, including a detailed drivetrain. The new model can simultaneously and accurately estimate main bearing loads and represent elastic bending of the drivetrain. It has low computational cost and is useful for early design phases, sensitivity analyses and complex systems like wind farms (where computational expense must be expended elsewhere). Here, the model is implemented for a monopile offshore wind turbine and used to investigate the sensitivity of main bearing basic rating life to different synthetic turbulence models. Large‐eddy simulations (LES) targeting stable, neutral, and unstable atmospheric conditions at below‐, near‐ and above‐rated wind speeds are used as a reference. The turbulence models recommended by the International Electrotechnical Commission, the Mann spectral tensor model, and the Kaimal spectral model with exponential coherence are fitted to the LES data. Additionally, a constrained turbulence generator, PyConTurb (short for Python Constrained Turbulence ), based on LES data, is applied in the aero‐hydro‐servo‐elastic simulations. Taking PyConTurb as the baseline, the Kaimal model significantly underestimates fatigue of the downwind main bearing, with between 10% and 40% less damage. The Mann model also underestimates the downwind main bearing fatigue by up to 30%. The upwind main bearing damage is driven by mean loads, and differences between models are less significant, although the trends are similar. Reasons for these discrepancies are investigated and attributed to differences in spatial and temporal variations among the turbulence models.

17 WIND ENERGY↗

Pore-resolved investigation of turbulent open channel flow over a randomly packed permeable sediment bed

Pore-resolved direct numerical simulations are performed to investigate the interactions between streamflow turbulence and groundwater flow through a randomly packed porous sediment bed for three permeability Reynolds numbers, Re K = 2.56 , 5.17 and 8.94, representative of natural stream or river systems. Time–space averaging is used to quantify the Reynolds stress, form-induced stress, mean flow and shear penetration depths, and mixing length at the sediment–water interface (SWI). Here, the mean flow and shear penetration depths increase with Re K and are found to be nonlinear functions of non-dimensional permeability. The peaks and significant values of the Reynolds stresses, form-induced stresses, and pressure variations are shown to occur in the top layer of the bed, which is also confirmed by conducting simulations of just the top layer as roughness elements over an impermeable wall. The probability distribution functions (p.d.f.s) of normalized local bed stress are found to collapse for all Reynolds numbers, and their root-mean-square fluctuations are assumed to follow logarithmic correlations. The fluctuations in local bed stress and resultant drag and lift forces on sediment grains are mainly a result of the top layer; their p.d.f.s are symmetric with heavy tails, and can be well represented by a non-Gaussian model fit. The bed stress statistics and the pressure data at the SWI potentially can be used in providing better boundary conditions in modelling of incipient motion and reach-scale transport in the hyporheic zone.

turbulence simulation↗

Simulations of the churning mode: Toroidally symmetric plasma convection and turbulence around the X-points in a snowflake divertor

Using a reduced MHD model, extended to include field-aligned thermal conduction, we present numerical simulations of the churning mode (CM): a toroidally symmetric, non-linear plasma vortex in the vicinity of the null points in a snowflake (SF) divertor [D. D. Ryutov et al., Phys. Scr. 89, 088002 (2014)]. Simulations are carried out across a range of inter-null separations, d xx ⁠, and inter-null orientations, θ⁠, primarily in conditions relevant to the MAST-U tokamak. We find that, when d xx is small, the CM induces additional transport across the X-points when β pm ≳8%, where β pm is the ratio of the plasma pressure in the null region to poloidal magnetic pressure at the midplane. This transport also increases approximately linearly as d xx is reduced. A diffusive model of this transport is shown to predict the total transport across the null points, where diffusion coefficients of up to ∼ 10 2 m 2 s −1 centered on a small region around the X-points are used. However, the CM also results in significant changes to the flux surfaces in the null region, which is not captured by this diffusive model. The changes in magnetic geometry mean the fractional exhaust power delivered to each divertor leg is highly sensitive to β pm ⁠, d xx ⁠, and θ⁠. For small values of θ⁠, the CM can induce a change in topology, redirecting exhaust power from a secondary divertor leg on the high field side to one on the low field side. Similar behavior is found in the fraction of exhaust power going to the inner and outer divertor. Such changes in the flux surfaces may not be captured by Grad–Shafranov solvers and so may be a source of error in the magnetic reconstruction of SF experiments. We consistently find that the fractional exhaust power going to a secondary divertor leg on the high field side is small, consistent with SF experiments.

Computer simulation↗

A priori analysis on deep learning of subgrid-scale parameterizations for Kraichnan turbulence

In the present study, we investigate different data-driven parameterizations for large eddy simulation of two-dimensional turbulence in the a priori settings. These models utilize resolved flow field variables on the coarser grid to estimate the subgrid-scale stresses. We use data-driven closure models based on localized learning that employs a multilayer feedforward artificial neural network with point-to-point mapping and neighboring stencil data mapping, and convolutional neural network fed by data snapshots of the whole domain. The performance of these data-driven closure models is measured through a probability density function and is compared with the dynamic Smagorinksy model (DSM). The quantitative performance is evaluated using the cross-correlation coefficient between the true and predicted stresses. We analyze different frameworks in terms of the amount of training data, selection of input and output features, their characteristics in modeling with accuracy, and training and deployment computational time. We also demonstrate computational gain that can be achieved using the intelligent eddy viscosity model that learns eddy viscosity computed by the DSM instead of subgrid-scale stresses. Here, we detail the hyperparameters optimization of these models using the grid search algorithm.

42 ENGINEERING↗

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↗

Simulated meteorological impacts of offshore wind turbines and sensitivity to the amount of added turbulence kinetic energy

Offshore wind energy projects are currently in development off the east coast of the United States and may influence the local meteorology of the region. Wind power production and other commercial uses in this area are related to atmospheric conditions, and so it is important to understand how future wind plants may change the local meteorology. In the absence of measurements of potential wind plant impacts on meteorology, simulations offer the next-best possible insight into wake effects on boundary layer height, temperature, fluxes, and wind speeds. However, simulation tools that capture these effects offer multiple options for representing the amount of turbine-added turbulence that may impact assessments of micrometeorological effects. To explore this sensitivity, we compare 1 year of simulations from the Weather Research and Forecasting (WRF) model with and without wind plants incorporated, focusing on the lease area south of Massachusetts and Rhode Island. The simulations with wind plants are repeated to include both the maximum and minimum amounts of added turbulence to provide bounds on the potential impacts. We assess changes in wind speeds, 2 m temperature, surface heat flux, turbulence kinetic energy (TKE), and boundary layer height during different stability classifications and ambient wind speeds over the entire year and compare results for the degree of added turbulence in the wind plant simulations. Because the wake behavior may be a function of boundary layer stability, in this paper, we also present a machine learning algorithm to quantify the area and distance of the wake generated by the wind plant. This analysis enables us to identify the relationship between wake extent and boundary layer height. We find that hub-height wind speed is reduced within and downwind of the wind plant, with the strongest impacts occurring during stable conditions and faster wind speeds in region 3 of the turbine power curve, although impacts lessen as wind speeds increase past 15 m s−1. In contrast, wind speeds near the surface decrease when no turbine-added turbulence is included but can increase for stably stratified conditions when 100 % of possible TKE is included in the simulations. TKE increases at hub height in the simulations with added TKE for all stability classes, suggesting that atmospheric stability does not immediately modify the TKE generated by turbines. Negligible changes in hub-height TKE manifest in the simulations without the added TKE. At the surface, TKE increases in the simulations with maximum added turbulence only for unstable conditions. In the no-added-turbulence simulations, surface TKE decreases slightly in neutral and unstable simulations. Differences in 2 m temperatures and surface heat fluxes are small but vary considerably with atmospheric stability and the amount of added TKE. Boundary layer heights increase within the wind plant when turbine-added turbulence is included and decrease slightly downwind during stable conditions. In contrast, with no added turbulence, the boundary layer height is in general reduced in stable conditions with wind speeds less than 15 m s −1 and slightly increased in neutral conditions. Finally, shallower upwind boundary layer heights tend to correlate with larger wake areas and distances, though other factors likely also play a role in determining the extent of the wind plant wake. These simulation-based results provide a bound for micrometeorological impacts of wind plant wakes: simulations that couple the atmosphere to the ocean may reduce these impacts, and we await observational verification.

17 WIND ENERGY↗