Subgrid-scale Turbulence Model Research Articles

Invariance embedded physics-infused deep neural network-based sub-grid scale models for turbulent flows

In this paper, we present two novel physics-infused neural network (NN) architectures that satisfy various invariance conditions for constructing efficient and robust Deep Learning (DL)-based sub-grid scale (SGS) turbulence models for use in Large Eddy Simulation (LES) procedures widely used in various fluid engineering applications. The first architecture, called tensor basis neural networks (TBNN), recently proposed in the context of Reynolds-averaged Navier–Stokes (RANS) modeling, and introduced herein for SGS modeling of wall-bounded turbulence, embeds the analytical expansion of the SGS turbulence stresses into integrity basis tensors composed of the symmetric and anti-symmetric parts of the resolved velocity gradient tensor, thus incorporating the Galilean, rotational and reflectional invariances. In our second approach, a relatively simple yet powerful architecture, called Galilean Invariance embedded Neural Network (GINN) incorporates the Galilean invariance, and takes in as inputs the independent components of the integrity basis tensors in addition to the invariant inputs in a single input layer. Explicit filtering of data from direct simulations of the canonical channel flow at two friction Reynolds numbers Reτ≈395 and 590 provided accurate data for training and testing these models. Both sets of models are used to predict the SGS stresses for feature datasets generated with different filter widths, and at different Reynolds numbers. The GINN model yields less prediction error on test datasets (mean squared error ∼0.4) compared to the TBNN model (mean squared error ∼0.5). Upon comparison, it is revealed that GINN has better feature extraction capacity owing to its ability to establish relations between and extract information from cross-components of the integrity basis tensors and the SGS stresses. Based on their predictive performance, both models proposed herein have shown great promise for use in a posteriori actual LESs. The present work illustrates the significance of physics infusion as well as invariance embedding into NN architecture for constructing efficient and robust DL-based SGS turbulent models in achieving superior predictive efficacy.

Influence of wall shear stress on the secondary flow in square ducts

We investigate turbulent duct flows with a square cross section using well-resolved large-eddy simulations (LES). A physically consistent subgrid-scale turbulence model based on the Adaptive Local Deconvolution Method (ALDM) for implicit LES is used. The wall shear stress is artificially modified at one of the four walls to analyse the influence on the secondary flow. A direct numerical simulation (DNS) of a symmetrical duct flow is used as reference to assess the influence of a modified wall shear stress. The modification results in an asymmetrical distribution of the secondary flow source terms, affecting the momentum distribution. Further, the anisotropy of the Reynolds stress tensor, which induces the secondary flow vortices is considerably affected by the wall shear stress modulation.

Effect of turbulence and viscosity models on wall shear stress derived biomarkers for aorta simulations

Ascending aorta simulations provide insight into patient-specific hemodynamic conditions. Numerous studies have assessed fluid biomarkers which show a potential to aid clinicians in the diagnosis process. Unfortunately, there exists a large disparity in the computational methodology used to model turbulence and viscosity. Recognizing this disparity, some authors focused on analysing the influence of either the turbulence or viscosity models on the biomarkers in order to quantify the importance of these model choices. However, no analysis has yet been done on their combined effect. In order to fully understand and quantify the effect of the computational methodology, an assessment of the combined effect of turbulence and viscosity model choice was performed. Our results show that (1) non-Newtonian viscosity has greater impact (2.9–5.0%) on wall shear stress than Large Eddy Simulation turbulence modelling (0.1–1.4%), (2) the contribution of non-Newtonian viscosity is amplified when combined with a subgrid-scale turbulence model, (3) wall shear stress is underestimated when considering Newtonian viscosity by 2.9–5.0% and (4) cycle-to-cycle variability can impact the results as much as the numerical model if insufficient cycles are performed. These results demonstrate that, when assessing the effect of computational methodologies, the resultant combined effect of the different modelling assumptions differs from the aggregated effect of the isolated modifications. Accurate aortic flow modelling requires non-Newtonian viscosity and Large Eddy Simulation turbulence modelling.

Momentum boundary layers in transcritical channel flows

We present well-resolved large-eddy simulations (LES) of a channel flow solving the fully compressible Navier–Stokes equations in conservative form. An adaptive look-up table method is used for thermodynamic and transport properties. We apply a physically consistent subgrid-scale turbulence model, that is based on the Adaptive Local Deconvolution Method (ALDM) for implicit LES. The wall temperatures are set to enclose the pseudo-boiling temperature at a supercritical pressure, leading to strong property variations within the channel geometry. In total seven cases are computed covering different Reynolds numbers, pseudo-boiling positions and pressure values. The hot wall at the top and the cold wall at the bottom produce asymmetric mean velocity and temperature profiles which result in different momentum layer thicknesses. All cases feature a turbulent mass flux which is essential in turbulence modelling. Furthermore, we analyse the turbulent kinetic energy budgets, perform a quadrant and octant analysis of the Reynolds shear stress and employ an invariant map to study the anisotropy in transcritical turbulent channel flows.

Development and assessment of algorithms for DEM-LES simulations of fluidized bed

The use of high-fidelity Discrete Element Method (DEM) coupled with Computational Fluid Dynamics (CFD) for particle-scale simulations demands extensive simulation times and restricts application to small particulate systems. DEM-CFD simulations require good performance and satisfactory scalability on high-performance computing platforms. A reliable parallel computing strategy must be developed to calculate the collision forces, since collisions can occur between particles that are not on the same processor, or even across processors whose domains are disjoint. The present paper describes a parallelization technique and a numerical verification study based on a number of tests that allow for the assessment of the numerical performance of DEM used in conjunction with Large-Eddy Simulation (LES) to model dense flows in fluidized beds. The fluid phase is computed through solving the volume-averaged four-way coupling Navier-Stokes equations, in which the Smagorinsky sub-grid scale tensor model is used. Furthermore, the performance of Sub-Grid Scale (SGS) turbulence models applied to Fluidized Bed Reactor (FBR) configurations has been assessed and compared. The developed numerical solver represents an interesting combination of techniques that work well for the present purpose of studying particle formation in fluidized beds.

Comparison of effects of four subgrid-scale turbulence models in large eddy simulation of a large wind farm

Comparison of effects of four subgrid-scale turbulence models in large eddy simulation of a large wind farm

Large eddy simulation of atmospheric boundary layer flow over complex terrain in comparison with RANS simulation and on-site measurements under neutral stability condition

Large eddy simulation (LES) of the atmospheric boundary layer (ABL) flow over complex terrain is presented with a validation using meteorological tower (met-tower) data through an improved neutral stability sampling approach. The proposed stability sampling procedure includes a condition based on the most-likely occurrence time-periods of the neutral ABL and reduces the variabilities of the conditional wind statistics calculated at the met-towers in comparison to our previous work. The ABL flow simulations are carried out over a potential wind site with a prominent hill based using the OpenFOAM-based simulator for on/off-shore wind farm applications by applying the Lagrangian-averaged scale-invariant dynamic sub-grid scale turbulence model. A low-dissipative scale-selective discretization scheme for the non-linear convection term in the LES governing equation is adopted implicitly to ensure both the second-order accuracy and bounded solution. The LES inflow is generated through a precursor method with a “tiling” approach based on the flow driving parameters obtained from a corresponding Reynolds-averaged Navier–Stokes (RANS) simulation. Overall, the averaged wind velocity profiles predicted by the LES approach at all met-tower locations show a similar tendency as the RANS results, which are also in reasonable agreement with the met-tower data. An obvious difference in wind speed standard deviation profiles is seen between LES and RANS, especially at regions downstream of the hill edge, where the LES shows under-predicted results at the highest measurement levels in comparison to the tower data. The computational costs of the LES are found to be about 20 times higher than the RANS simulations.

Can a Machine Learning–Enabled Numerical Model Help Extend Effective Forecast Range through Consistently Trained Subgrid-Scale Models?

Abstract The development of machine learning (ML) techniques enables data-driven parameterizations, which have been investigated in many recent studies. Some investigations suggest that a priori-trained ML models exhibit satisfying accuracy during training but poor performance when coupled to dynamical cores and tested. Here we use the evolution of the barotropic vorticity equation (BVE) with periodically reinforced shear instability as a prototype problem to develop and evaluate a model-consistent training strategy, which employs a numerical solver supporting automatic differentiation and includes the solver in the loss function for training ML-based subgrid-scale (SGS) turbulence models. This approach enables the interaction between the dynamical core and the ML-based parameterization during the model training phase. The BVE model was run at low, high, and ultrahigh (truth) resolutions. Our training dataset contains only a short period of coarsened high-resolution simulations. However, given initial conditions long after the training dataset time, the trained SGS model can still significantly increase the effective lead time of the BVE model running at the low resolution by up to 50% relative to the BVE simulation without an SGS model. We also tested using a covariance matrix to normalize the loss function and found it can notably boost the performance of the ML parameterization. The SGS model’s performance is further improved by conducting transfer learning using a limited number of discontinuous observations, increasing the forecast lead-time improvement to 73%. This study demonstrates a potential pathway to using machine learning to enhance the prediction skills of our climate and weather models. Significance Statement Numerical weather prediction is performed at limited resolution for computational feasibility, and the schemes to estimate unresolved processes are called parameterization. We propose a strategy to develop better deep learning–based parameterization in which an automatic differentiable numerical solver is employed as the dynamic core and interacts with the parameterization scheme during its training. Such a numerical solver enables consistent deep learning, because the parameterization is trained with a direct target of making the numerical model (dynamic core and parameterization together) forecast match observations as much as possible. We demonstrate the feasibility and effectiveness of such a strategy using a surrogate model and advocate that such machine learning–enabled numerical models provide a promising pathway to developing next-generation weather forecast and climate models.

Particulate Matter Dispersion Modeling in Agricultural Applications: Investigation of a Transient Open Source Solver

Agriculture is a major emitter of particulate matter (PM), which causes health problems and can act as a carrier of the pathogen material that spreads diseases. The aim of this study was to investigate an open-source solver that simulates the transport and dispersion of PM for typical agricultural applications. We investigated a coupled Eulerian–Lagrangian solver within the open source software package OpenFOAM. The continuous phase was solved using transient large eddy simulations, where four different subgrid-scale turbulence models and an inflow turbulence generator were tested. The discrete phase was simulated using two different Lagrangian solvers. For the validation case of a turbulent flow of a street canyon, the flowfield could be recaptured very well, with errors of around 5% for the non-equilibrium turbulence models (WALE and dynamicKeq) in the main regions. The inflow turbulence generator could create a stable and accurate boundary layer for the mean vertical velocity and vertical profile of the turbulent Reynolds stresses R11. The validation of the Lagrangian solver showed mixed results, with partly good agreements (simulation results within the measurement uncertainty), and partly high deviations of up to 80% for the concentration of particles. The higher deviations were attributed to an insufficient turbulence regime of the used validation case, which was an experimental chamber. For the simulation case of PM dispersion from manure application on a field, the solver could capture the influence of features such as size and density on the dispersion. The investigated solver is especially useful for further investigations into time-dependent processes in the near-source area of PM sources.

Effects of drag and subgrid-scale turbulence modeling on gas–solid hydrodynamics of a pilot-scale circulating fluidized bed

Large eddy simulation is performed on a circulating fluidized bed (CFB) based on an Eulerian-Eulerian approach. The riser of the CFB has two axial sections of different diameters joined by a diffuser. The effects of drag and subgrid-scale models are examined on hydrodynamic parameters, such as solids volume fraction (εs), solids circulation rate (Gs), and full loop pressure profiles. A hybrid energy minimization multi-scale (EMMS) drag model is applied that combines EMMS drag models for the bubbling and the fast fluidized bed regimes. Experiments are conducted on a pilot-scale CFB model, and numerical results are validated against the experimental measurements of pressure and Gs. The change in the riser diameter has a significant influence on axial- and radial profiles of εs, particularly in the upper riser section. The hybrid EMMS drag model and the sgs-TKE turbulence model give the best agreement to the experimental data.

Numerical assessment of LES subgrid-scale turbulence models for expandable particles in fire suppression

Numerical assessment of LES subgrid-scale turbulence models for expandable particles in fire suppression

Large-eddy simulation of flow around an isolated building: A step-by-step analysis of influencing factors on turbulent statistics

We designed and exclusively performed a wind tunnel experiment to obtain high-quality and high-resolution measurement results for three components of mean and fluctuating velocities around a 1: 1: 2 isolated building to establish a benchmark case for large-eddy simulation (LES) as a part of the activities of the Architectural Institute of Japan. Subsequently, we conducted LES to investigate the effect of computational grid arrangement on turbulent statistics by changing three grid arrangements. Finally, we performed a comparison by changing spatial discretization schemes, sub-grid scale (SGS) turbulence models, and convergence criteria. A grid in which the width of a building was discretized into 20 grids yielded sufficient resolution to reproduce the mean flow and second-order turbulent statistics. Under this appropriate grid arrangement, in the condition that the blending ratio of the first-order upwind interpolation scheme with the second-order linear interpolation scheme from 5 to 10%, the appropriate second-order statistics of wind velocity around the isolated building was obtained and numerical oscillation was effectively removed. Then, with this grid, any SGS model yielded appropriate results. In addition, the convergence criteria had little effects on the LES results if stable solution was obtained. Because the convergence criteria greatly affect the total calculation cost, weaker appropriate criteria should be set.

Embedded training of neural-network subgrid-scale turbulence models

The weights of a deep neural network model are optimized in conjunction with the governing flow equations to provide a model for sub-grid-scale stresses in a temporally developing plane turbulent jet at Reynolds number $Re_0=6\,000$. The objective function for training is first based on the instantaneous filtered velocity fields from a corresponding direct numerical simulation, and the training is by a stochastic gradient descent method, which uses the adjoint Navier--Stokes equations to provide the end-to-end sensitivities of the model weights to the velocity fields. In-sample and out-of-sample testing on multiple dual-jet configurations show that its required mesh density in each coordinate direction for prediction of mean flow, Reynolds stresses, and spectra is half that needed by the dynamic Smagorinsky model for comparable accuracy. The same neural-network model trained directly to match filtered sub-grid-scale stresses -- without the constraint of being embedded within the flow equations during the training -- fails to provide a qualitatively correct prediction. The coupled formulation is generalized to train based only on mean-flow and Reynolds stresses, which are more readily available in experiments. The mean-flow training provides a robust model, which is important, though a somewhat less accurate prediction for the same coarse meshes, as might be anticipated due to the reduced information available for training in this case. The anticipated advantage of the formulation is that the inclusion of resolved physics in the training increases its capacity to extrapolate. This is assessed for the case of passive scalar transport, for which it outperforms established models due to improved mixing predictions.

Large-eddy simulation of turbulent channel flow at transcritical states

We present well-resolved large-eddy simulations (LES) of a channel flow solving the fully compressible Navier–Stokes equations in conservative form. An adaptive look-up table method is used for thermodynamic and transport properties. A physically consistent subgrid-scale turbulence model is incorporated, that is based on the Adaptive Local Deconvolution Method (ALDM) for implicit LES. The wall temperatures are set to enclose the pseudo-boiling temperature at a supercritical pressure, leading to strong property variations within the channel geometry. The hot wall at the top and the cold wall at the bottom produce asymmetric mean velocity and temperature profiles which result in different momentum and thermal boundary layer thicknesses. Different turbulent Prandtl number formulations and their components are discussed in context of strong property variations.

Impact of the Sub-Grid Scale Turbulence Model in Aeroacoustic Simulation of Human Voice

In an aeroacoustic simulation of human voice production, the effect of the sub-grid scale (SGS) model on the acoustic spectrum was investigated. In the first step, incompressible airflow in a 3D model of larynx with vocal folds undergoing prescribed two-degree-of-freedom oscillation was simulated by laminar and Large-Eddy Simulations (LES), using the One-Equation and Wall-Adaptive Local-Eddy (WALE) SGS models. Second, the aeroacoustic sources and the sound propagation in a domain composed of the larynx and vocal tract were computed by the Perturbed Convective Wave Equation (PCWE) for vowels [u:] and [i:]. The results show that the SGS model has a significant impact not only on the flow field, but also on the spectrum of the sound sampled 1 cm downstream of the lips. With the WALE model, which is known to handle the near-wall and high-shear regions more precisely, the simulations predict significantly higher peak volumetric flow rates of air than those of the One-Equation model, only slightly lower than the laminar simulation. The usage of the WALE SGS model also results in higher sound pressure levels of the higher harmonic frequencies.

Spectral Properties of High-Order Element Types for Implicit Large Eddy Simulation

The use of high-order schemes continues to increase, with current methods becoming more robust and reliable. The resolution of complex turbulent flows using Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) can be computed more efficiently with high-order methods such as the Flux Reconstruction approach. We make use of the implicit form of LES, referred to as ILES, in which the numerical dissipation of the spatial scheme passively filters high-frequency modes, and no subgrid-scale turbulence model is explicitly implemented. Therefore, given the inherent three-dimensional behaviour of turbulent flows, it is important to understand the spectral characteristics of spatial discretizations in three dimensions. The dispersion and dissipative properties of hexahedra, prismatic and tetrahedral element types are compared using Von Neumann analysis. This comparison is performed on a per degree of freedom basis to assess their suitability for ILES in terms of computational cost. We observe dispersion relations that display non-smooth behaviour for tetrahedral and prismatic elements. In addition, the periodicity of the dispersion relations in one dimension is generally not observed in three-dimensional configurations. Semilogarithmic plots of the numerical error are presented. We observe that the amount of numerical dissipation and dispersion added by hexahedral elements is the least, followed by prisms and finally tetrahedra. We validate our analysis comparing results obtained on computational domains with comparable computational cost against DNS data. Hexahedral elements have the best agreement with the reference data, followed by prismatic and finally tetrahedral elements, which is consistent with the spectral analysis.

Investigation of wake characteristics of the MEXICO wind turbine using lattice Boltzmann method

AbstractThis paper investigates the characteristics of turbine wake which is the major factor determining the turbulence in wind farm and overall wind farm performance. Using the lattice Boltzmann method (LBM) and the large eddy simulation (LES) approach, dynamic simulations of detailed fluid flow and wake trajectory induced by the MEXICO wind turbine were carried out. Moreover, with the help of adaptive mesh refinement (AMR) method, the lattice units were allowed to be automatically refined to allocate more grid points on the solid walls and in the wake region. The simulation results were firstly compared with the experimental data for validation of the numerical model, as well as for investigation of the impact of sub‐grid scale (SGS) turbulence models. Within the present modeling framework, the characteristics of transient wake propagation, detailed flow field, and rotor‐tower interaction were investigated, and the effect of tip‐speed ratio was also analyzed. The present work indicates that, with a suitable SGS turbulence model, the LBM‐LES method is an effective way for dynamic simulations of wake structures induced by a wind turbine with a rotating rotor.

CFD analysis of cross-ventilation flow in a group of generic buildings: Comparison between steady RANS, LES and wind tunnel experiments

Computational fluid dynamics (CFD) results generated by the steady Reynolds-averaged Navier-Stokes equations (SRANS) model and large eddy simulation (LES) are compared with wind tunnel experiments for investigating a cross-ventilation flow in a group of generic buildings. The mean flow structure and turbulence statistics are compared for SRANS based on different two-equation turbulence models with LES based on the Smagorinsky subgrid-scale turbulence model. The LES results show very close agreement with the experimental results in the prediction of the time-averaged velocity, wind surface pressure around and inside the building, and crossing flow through the openings. In contrast, SRANS fails to predict the most important features of cross-ventilation. LES reproduces well the anisotropic turbulence property around and inside the cross-ventilated building, which is closely related to the transient momentum transfer caused in street canyon flows and has a significant influence on the mean flow structure. In contrast, SRANS could not inherently reproduce such transient fluctuations and anisotropic turbulence property, which results in low accurate predictions for the time-averaged velocity components, wind surface pressure distribution and crossing airflow rate up to 100% error.

Study of Human Phonation with Attention on Sub-Grid Scale Turbulence Models and Initialization Effects

The first aim of this paper is to compare three cases, where two cases contain turbulence sub-grid scale (SGS) models, which are commonly applied in wall-bounded flows. They use a bit different formulation of how to estimate the eddy-viscosity fields in a vicinity of walls. The SGS effect is obvious on flow rates through an intra-glottal gap. The second aim is to attend to a direct impact of the specific SGS model onto the sound pressure levels of frequency components (human formants). The third aim is focused on the effect of an initial time, when the vocal folds are in a start convergent phase itself and when the flow is suddenly accelerated due to boundary conditions. The effect is shown at aeroacoustic spectra.

Validation study for Large-Eddy Simulation of Forest Flow

The publication presents Large-Eddy Simulation (LES) of flow over a reduced-scale wind tunnel model of a forest canopy. The final aim of the study is to determine factors responsible for damage in forests by strong winds. The wind tunnel forest was represented by an open-porous foam material for the crown layer and wooden dowels for the trunk layer. The forest model was installed in the open test section of a Goettingen-type wind tunnel and Particle Image Velocimetry (PIV) measurements were made for the acquisition of the flow field data. The numerical simulations were performed with OpenFOAM®. The forest was modelled by an additional sink term in the momentum transport equations based on the leaf area density and a characteristic drag coefficient for the underlying tree specimen. Large-eddy simulations with different subgrid-scale (SGS) turbulence models were carried out and compared to wind tunnel data. The Smagorinsky SGS model outperformed the dynamic Lagrangian SGS model in the windward edge region (within a distance of approximately 2 tree heights from the leading edge) whereas the dynamic Lagrangian SGS model showed a better performance for regions farther downstream.