Large Eddy Simulation Closure Research Articles

One-year-long turbulence measurements and modeling using large-eddy simulation domains in the Weather Research and Forecasting model

We present an intercomparison of a full year of turbulence measurements and simulations at Østerild, a site in northern Denmark with relatively flat terrain and high surface roughness, where a high-quality tall meteorological mast is deployed. Both sonic and cup anemometers are mounted on booms on the mast from 7 up to 244 m, thus covering the range of heights in which modern wind turbines operate. The simulations were performed using the Weather Research and Forecasting model in a multiscale setup, with large-eddy simulations (LESs) nested one-way within mesoscale simulations. The mesoscale domains thus simulated the evolving weather, while the two innermost domains used an LES closure, intending the largest scales of turbulence to be explicitly resolved. For a selected day, we show that the simulated turbulence is accurately resolved within the innermost LES domain, and agrees well with the observations at all vertical levels. For the full year, we show that the innermost domain accurately reproduces mean wind speed, direction, and turbulence levels, whereas the mesoscale simulations have difficulties matching the frequency of occurrence of both low and high turbulence ranges when compared to the observations. The largest differences between the simulated turbulence from the innermost domain and the observations are found under low wind speed conditions close to the surface, particularly during nighttime where the simulated mean wind and turbulence levels are higher and lower, respectively, than the observations, potentially due to the inability of the LES mesh to resolve the very small scales of turbulence and associated momentum transport that those features support.

Toward discretization-consistent closure schemes for large eddy simulation using reinforcement learning

This study proposes a novel method for developing discretization-consistent closure schemes for implicitly filtered large eddy simulation (LES). Here, the induced filter kernel and, thus, the closure terms are determined by the properties of the grid and the discretization operator, leading to additional computational subgrid terms that are generally unknown in a priori analysis. In this work, the task of adapting the coefficients of LES closure models is thus framed as a Markov decision process and solved in an a posteriori manner with reinforcement learning (RL). This optimization framework is applied to both explicit and implicit closure models. The explicit model is based on an element-local eddy viscosity model. The optimized model is found to adapt its induced viscosity within discontinuous Galerkin (DG) methods to homogenize the dissipation within an element by adding more viscosity near its center. For the implicit modeling, RL is applied to identify an optimal blending strategy for a hybrid DG and finite volume (FV) scheme. The resulting optimized discretization yields more accurate results in LES than either the pure DG or FV method and renders itself as a viable modeling ansatz that could initiate a novel class of high-order schemes for compressible turbulence by combining turbulence modeling with shock capturing in a single framework. All newly derived models achieve accurate results that either match or outperform traditional models for different discretizations and resolutions. Overall, the results demonstrate that the proposed RL optimization can provide discretization-consistent closures that could reduce the uncertainty in implicitly filtered LES.

A super-grid approach for LES combustion closure using the Linear Eddy Model

LES–LEM is a simulation approach for turbulent combustion in which the stochastic Linear Eddy Model (LEM) is used for sub-grid mixing and combustion closure in Large-Eddy Simulation (LES). LEM resolves, along a one-dimensional line, all spatial and temporal scales, provides on-the-fly local turbulent flame statistics, captures finite rate chemistry effects and directly incorporates turbulence-chemistry interaction. However, the approach is computationally expensive as it requires advancing an LEM-line in each LES cell. This paper introduces a novel turbulent combustion closure model for LES using LEM to address this issue. It involves coarse-graining the LES mesh to generate a coarse- level ‘super-grid’ comprised of cell-clusters. Each cell-cluster, instead of each LES cell, then contains a single LEM domain. This domain advances the combined advection–reaction–diffusion solution and also provides suitably conditioned statistics for thermochemical scalars such as species mass fractions. Local LES-filtered thermochemical states are then obtained by probability-density-function (PDF) weighted integration of binned conditionally averaged scalars, akin to standard presumed PDF approaches for reactive LES but with physics-based determination of the full thermochemical state for particular values of the conditioning variables. The proposed method is termed ‘super-grid LEM’ or ‘SG-LEM’. The paper describes LEM reaction–diffusion advancement, the LEM representation of turbulent advection, a novel splicing algorithm (a key feature of LES–LEM) formulated for the super-grid approach, a wall treatment, and a thermochemical LES closure procedure. To validate the proposed model, a pressure-based solver was developed using the OpenFOAM library and tested on a premixed ethylene flame stabilised over a backward facing step, a setup for which some DNS data is available. SG-LEM provides high resolution flame structures, temperature and mass fractions suitable for LES thermochemical closure. Additionally, it provides reaction-rate data at the coarse level, a unique feature compared to other mapping-type closure methods. Quantitative comparisons are made between the proposed model and time-averaged DNS data, focussing on velocity, temperature and species mass fraction. Results show good agreement downstream of the step. Furthermore, comparison with an equivalent Partially-Stirred Reactor (PaSR) simulation demonstrates the superior predictive capability of SG-LEM. Additionally, the paper briefly examines the sensitivity of the model to coarse-graining parameters and finally, explores computational efficiency highlighting the substantial speedup achieved when compared to the standard LES–LEM approach with potentially significant speedup relative to PaSR closure for the intensely turbulent regimes of principal interest.

Scientific multi-agent reinforcement learning for wall-models of turbulent flows

The predictive capabilities of turbulent flow simulations, critical for aerodynamic design and weather prediction, hinge on the choice of turbulence models. The abundance of data from experiments and simulations and the advent of machine learning have provided a boost to turbulence modeling efforts. However, simulations of turbulent flows remain hindered by the inability of heuristics and supervised learning to model the near-wall dynamics. We address this challenge by introducing scientific multi-agent reinforcement learning (SciMARL) for the discovery of wall models for large-eddy simulations (LES). In SciMARL, discretization points act also as cooperating agents that learn to supply the LES closure model. The agents self-learn using limited data and generalize to extreme Reynolds numbers and previously unseen geometries. The present simulations reduce by several orders of magnitude the computational cost over fully-resolved simulations while reproducing key flow quantities. We believe that SciMARL creates unprecedented capabilities for the simulation of turbulent flows.

A new K-profile parameterization for the ocean surface boundary layer under realistic forcing conditions

In this study, we present a new parameterization for the enhancement of vertical mixing brought by the inclusion of the Stokes drift for the turbulent mixing schemes in ocean circulation models. The new scheme (KPP-LT) uses the K-Profile Parameterization (Large et al., 1994) as a template, and attempts to include the effect of the penetration decay scale of the Stokes drift (δ) and the misalignment between the wind stress and Stokes drift (θww). The effect of the wind–wave angle of misalignment is guided by a set of idealized Large Eddy Simulations (LES) and the Langmuir Turbulence (LT) parameterization is developed based on LES of the ocean surface boundary layer at Ocean Weather Station Papa, for a period of 20 days under observed atmospheric and oceanic conditions. The KPP-LT model is implemented in the Navy Coastal Ocean Model (NCOM) and compared to in situ oceanographic measurements, LES and other Second Moment Closure (SMC) schemes available in NCOM, namely the model of Kantha and Clayson (2004) and Harcourt (2013, 2015). Comparisons with temperature observations suggest better performance of the KPP-LT model over SMC models within the boundary layer, which are supported by comparisons of inertially averaged eddy viscosity profiles estimated from LES.

A machine learning framework for LES closure terms

In the present work, we explore the capability of artificial neural networks (ANN) to predict the closure terms for large eddy simulations (LES) solely from coarse-scale data. To this end, we derive a consistent framework for LES closure models, with special emphasis laid upon the incorporation of implicit discretization-based filters and numerical approximation errors. We investigate implicit filter types that are inspired by the solution representation of discontinuous Galerkin and finite volume schemes and mimic the behavior of the discretization operator, and a global Fourier cutoff filter as a representative of a typical explicit LES filter. Within the perfect LES framework, we compute the exact closure terms for the different LES filter functions from direct numerical simulation results of decaying homogeneous isotropic turbulence. Multiple ANN with a multilayer perceptron (MLP) or a gated recurrent unit (GRU) architecture are trained to predict the computed closure terms solely from coarse-scale input data. For the given application, the GRU architecture clearly outperforms the MLP networks in terms of accuracy, whilst reaching up to 99.9% correlation between the networks' predictions and the exact closure terms for all considered filter functions. The GRU networks are also shown to generalize well across different LES filters and resolutions. The present study can thus be seen as a starting point for the investigation of data-based modeling approaches for LES, which not only include the physical closure terms, but account for the discretization effects in implicitly filtered LES as well.

Dynamic subgrid-scale LES model for turbulent non-Newtonian flows: A priori and a posteriori analyses of Burgers turbulence

Large Eddy Simulation (LES) of turbulent non-Newtonian flows involves two additional closures, namely the Non-Newtonian SubGrid-Scale (NNSGS) stress tensor and filtered viscosity. Here, dynamic closures are proposed for NNSGS, eliminating the need for model calibration. In addition, for the primary evaluation of LES closures, two canonical case studies are designed by the extension of Newtonian forced Burgers turbulence to include power-law viscosity rheology. The characteristics of the proposed non-Newtonian turbulence are studied carefully using direct numerical simulation. For instance, it is revealed that the shear-thinning effect intensifies the small-scale motions and elevates the energy spectrum function at high wave-numbers. The subsequent a priori and a posteriori studies manifest that the NNSGS modeling is important for the present test cases. The omission of this term results in the under-prediction of kinetic energy due to the substantial backscatter effect of NNSGS. The proposed dynamic Smagorinsky based closure is recommended, based on the correlation coefficient measure in the a priori tests and the energy spectrum function in the a posteriori tests, for LES of turbulence at high shear-thinning rheology. The use of the present NNSGS dynamic model improved the predictions, however, further effort to achieve more accurate closures for NNSGS and especially the filtered viscosity is still necessary in future studies.

A Scale-Adaptive Turbulence Model for the Dry Convective Boundary Layer

AbstractA scale-adaptive model is developed for the representation of dry convective boundary layer (CBL) turbulence in numerical models operating at O(100) m to O(1) km horizontal resolution, also known as the model gray zone of the CBL. The new model is constructed based on a planetary boundary layer (PBL) scheme and a large-eddy simulation (LES) closure that are both turbulence kinetic energy–based parameterizations. Scale adaptivity is achieved by “blending” the PBL scheme with the LES closure through an inverse averaging procedure that naturally accounts for vertical variations of the dominant turbulent length scales, hence the gray zone range. High-resolution wide-domain LES benchmark cases covering a broad range of CBL bulk stability are filtered to gray zone resolutions, and analyzed to determine the averaging coefficients. Stability dependence of the dominant length scales is revealed by the analysis and accounted for in the new model. The turbulence model is implemented into a community atmospheric model, and tested for idealized cases. Compared to two established gray zone models, the new model performs equally well under strongly convective conditions, and is more advantageous for the weakly unstable and near neutral CBL.

Scale-Similarity Subgrid-Scale Turbulence Closure for Supercell Simulations at Kilometer-Scale Resolutions: Comparison against a Large-Eddy Simulation

Abstract In numerical simulations of deep convection at kilometer-scale horizontal resolutions, in-cloud subgrid-scale (SGS) turbulence plays an important role in the transport of heat, moisture, and other scalars. By coarse graining a 50 m high-resolution large-eddy simulation (LES) of an idealized supercell storm to kilometer-scale grid spacings ranging from 250 m to 4 km, the SGS fluxes of heat, moisture, cloud, and precipitating water contents are diagnosed a priori. The kilometer-scale simulations are shown to be within the “gray zone” as in-cloud SGS turbulent fluxes are comparable in magnitude to the resolved fluxes at 4 km spacing, and do not become negligible until ~500 m spacing. Vertical and horizontal SGS fluxes are of comparable magnitudes; both exhibit nonlocal characteristics associated with deep convection as opposed to local gradient-diffusion type of turbulent mixing. As such, they are poorly parameterized by eddy-diffusivity-based closures. To improve the SGS representation of turbulent fluxes in deep convective storms, a scale-similarity LES closure is adapted to kilometer-scale simulations. The model exhibits good correlations with LES-diagnosed SGS fluxes, and is capable of representing countergradient fluxes. In a posteriori tests, supercell storms simulated with the refined similarity closure model at kilometer-scale resolutions show better agreement with the LES benchmark in terms of SGS fluxes than those with a turbulent-kinetic-energy-based gradient-diffusion scheme. However, it underestimates the strength of updrafts, which is suggested to be a consequence of the model effective resolution being lower than the native grid resolution.

Interpreting neural network models of residual scalar flux

Abstract

Large-eddy simulation of the flow in a direct injection spark ignition engine using an open-source framework

Direct injection spark ignition engines aim at reducing specific fuel consumption and achieving the strict emission standards in state of the art internal combustion engines. This can be achieved by research comprising experimental methods, which are normally expensive and limited, and computational fluid dynamics methods, which are often more affordable and less restricted than their experimental counterpart. In the latter approach, the costs are mainly related to the acquisition, usage, and maintenance of computational resources, and the license cost when commercial computational fluid dynamics codes are used. Therefore, in order to make the research of direct injection spark ignition engines and their internal processes more accessible, this article proposes a novel open-source and free framework based on the OpenFOAM computational fluid dynamics library for the simulation of the internal flow in direct injection spark ignition engines using a large-eddy simulation closure for modeling the turbulence within the gas phase. Finally, this framework is tested by simulating the Darmstadt engine in motored operation, validating the results with experimental data compiled by the Darmstadt Engine Workshop.

Structural vibration of an elastically supported plate due to excitation of a turbulent boundary layer

High-Reynolds number turbulent boundary layers are an important source for noise and structural vibration. Indeed small features of a structure can have important influence on the resulting noise and vibration. In this work we develop a new method to couple a high-fidelity fluid solver with a dynamic-finite-element solver for the structure. The flow solver is based on the OpenFOAM opensource CFD toolkit. The fluid solver uses the Large-Eddy Simulation closure for the unresolved turbulence. Specifically, a local and dynamic one-equation eddy viscosity model is employed. The fluid pressure fluctuation on the structure is mapped to the dynamic finite element model with a suitable interpolation routine. A modal decomposition of the dynamic finite-element model is used to reduce the number of degrees-of-freedom of the numerical structural model. The numerical method is validated for the turbulent flow over a flat plate. The plate is elastically supported along its edges, and the turbulence is excited upstream ...

Deep neural networks for data-driven LES closure models

In this work, we present a novel data-based approach to turbulence modeling for Large Eddy Simulation (LES) by artificial neural networks. We define the perfect LES formulation including the discretization operators and derive the associated perfect closure terms. We then generate training data for these terms from direct numerical simulations of decaying homogeneous isotropic turbulence. We design and train artificial neural networks based on local convolution filters to predict the underlying unknown non-linear mapping from the coarse grid quantities to the closure terms without a priori assumptions. We show that selecting both the coarse grid primitive variables as well as the coarse grid LES operator as input features significantly improves training results. All investigated networks are able to generalize from the data and learn approximations with a cross correlation of up to 47% and even 73% for the inner elements, demonstrating that the perfect closure can indeed be learned from the provided coarse grid data. Since the learned closure terms are approximate, a direct application leads to stability issues. We show how to employ the artificial neural network output to construct stable and accurate models. The best results have been achieved with a data-informed, temporally and spatially adaptive eddy viscosity closure. While further investigations into the generalizability of the approach is warranted, this work thus represents a starting point for further research into data-driven, optimal turbulence models.

Reynolds-Averaged, Scale-Adaptive and Large-Eddy Simulations of Premixed Bluff-Body Combustion Using the Eddy Dissipation Concept

A lean premixed propane/air bluff-body stabilized flame (Volvo test rig) is calculated using the Scale-Adaptive Simulation turbulence model (SAS) and Large-Eddy simulations (LES) as well as the conventional Reynolds-averaged approach (RAS). RAS and SAS are closed by the standard k-𝜖 and the k-ω Shear Stress Transport (SST) turbulence models, respectively. The conventional Smagorinsky and the k-equation sub-grid scales models are used for the LES closure. Effects of the sub-grid scalar flux modeling using the classical gradient hypothesis and Clark’s tensor diffusivity closures both for the inert and reactive LES flows are discussed. The Eddy Dissipation Concept (EDC) is used for the turbulence-chemistry interaction. It assumes that molecular mixing and the subsequent combustion occur in the ’fine structures’ (smaller dissipative eddies, which are close to the Kolmogorov scales). Assuming the full turbulence energy cascade, the characteristic length and velocity scales of the ’fine structures’ are evaluated using different turbulence models (RAS, SAS and LES). The finite-rate chemical kinetics is taken into account by treating the ’fine structures’ as constant pressure and adiabatic homogeneous reactors, calculated as a system of ordinary-differential equations (ODEs) described by a Perfectly Stirred Reactor (PSR) concept. Several further enhancements to model the PSRs are proposed, including a new Livermore Solver (LSODA) for integrating stiff ODEs and a new correction to calculate the PSR time scales. All models have been implemented as a stand-alone application $\text {edcPisoFoam}$ based on the OpenFOAM technology. Additionally, several RAS calculations were performed using the Turbulence Flame Speed Closure model in Ansys Fluent to assess effects of the heat losses by modeling the conjugate heat transfer between the bluff-body and the reactive flow. Effects of the turbulence Schmidt number on RAS results are discussed as well. Numerical results are compared with available experimental data. Reasonable consistency between experimental data and numerical results provided by RAS, SAS and LES is observed. In general, there is satisfactory agreement between present LES-EDC simulations, numerical results by other authors and measurements without any major modification to the EDC closure constants, which gives a quite reasonable indication on the adequacy and accuracy of the method and its further application for turbulent premixed combustion simulations.

A Framework for Characterizing Structural Uncertainty in Large-Eddy Simulation Closures

Motivated by the sizable increase of available computing resources, large-eddy simulation of complex turbulent flow is becoming increasingly popular. The underlying filtering operation of this approach enables to represent only large-scale motions. However, the small-scale fluctuations and their effects on the resolved flow field require additional modeling. As a consequence, the assumptions made in the closure formulations become potential sources of incertitude that can impact the quantities of interest. The objective of this work is to introduce a framework for the systematic estimation of structural uncertainty in large-eddy simulation closures. In particular, the methodology proposed is independent of the initial model form, computationally efficient, and suitable to general flow solvers. The approach is based on introducing controlled perturbations to the turbulent stress tensor in terms of magnitude, shape and orientation, such that propagation of their effects can be assessed. The framework is rigorously described, and physically plausible bounds for the perturbations are proposed. As a means to test its performance, a comprehensive set of numerical experiments are reported for which physical interpretation of the deviations in the quantities of interest are discussed.

Explicit and implicit LES closures for Burgers turbulence

In this work, we perform an aposteriori error analysis on implicit and explicit large eddy simulation closure models for solving the Burgers turbulence problem. Our closure modeling efforts include both functional and structural models equipped with various low-pass filters. We introduce discrete binomial smoothing filters and an enhanced version of the Van Cittert algorithm to accelerate the convergence of approximate deconvolution processes including regularization and relaxation filtering approaches. Our implicit modeling efforts consist of various high-order schemes including compact and non-compact fifth-order upwind schemes as well as weighted essential non-oscillatory (WENO) and compact reconstructed WENO (CRWENO) schemes, and the resulting schemes are shown to effectively converge to the direct numerical simulation (DNS) for increasing resolutions. Comparing with DNS and underresolved DNS computations, our numerical assessments illustrate the ability of these methods to capture the energy content near grid cut-off scale.

Structural vibration of an elastically supported plate due to excitation of a turbulent boundary layer

High-Reynolds number turbulent boundary layers are an important source for noise and structural vibration. Indeed small features of a structure can have important influence on the resulting noise and vibration. In this work we develop a new method to couple a high-fidelity fluid solver with a dynamic-finite-element solver for the structure. The flow solver is based on the OpenFOAM opensource CFD toolkit. The fluid solver uses the Large-Eddy Simulation closure for the unresolved turbulence. Specifically, a local and dynamic one-equation eddy viscosity model is employed. The fluid pressure fluctuation on the structure is mapped to the dynamic finite element model with a suitable interpolation routine. A modal decomposition of the dynamic finite-element model is used to reduce the number of degrees-of-freedom of the numerical structural model. The numerical method is validated for the turbulent flow over a flat plate. The plate is elastically supported along its edges, and the turbulence is excited upstream ...

Unstable flow structure around partially buried objects on a simulated river bed

The unsteady flow characteristics around two partially buried objects, a short cylinder and a truncated cone, were examined with a three-dimensional, non-hydrostatic hydrodynamic model under similar steady unidirectional currents with flow Reynolds numbers, Re, of 86,061 and 76,209, respectively. Model simulations were conducted with the two objects partially buried in a simulated rippled river bed. A Reynolds-averaged Navier–Stokes (RANS) equation model coupled with a κ-ε turbulence closure was used to validate the experimental velocity measurements. A large eddy simulation (LES) turbulence model was subsequently used to characterize the unsteady flow structure around the objects. The LES closure allowed for the characterization of highly unsteady coherent turbulent structures such as the horse-shoe vortex, the arch-shaped vortex, as well as vortex shedding in the wake of the object.

Grid and subgrid-scale interactions in viscoelastic turbulent flow and implications for modelling

ABSTRACTUsing direct numerical simulations of turbulent plane channel flow of homogeneous polymer solutions, described by the Finitely Extensible Nonlinear Elastic-Peterlin (FENE-P) rheological constitutive model, a-priori analyses of the filtered momentum and FENE-P constitutive equations are performed. The influence of the polymer additives on the subgrid-scale (SGS) energy is evaluated by comparing the Newtonian and the viscoelastic flows, and a severe suppression of SGS stresses and energy is observed in the viscoelastic flow. All the terms of the transport equation of the SGS kinetic energy for FENE-P fluids are analysed, and an approximated version of this equation for use in future large eddy simulation closures is suggested. The terms responsible for kinetic energy transfer between grid-scale (GS) and SGS energy (split into forward/backward energy transfer) are evaluated in the presence of polymers. It is observed that the probability and intensity of forward scatter events tend to decrease in the presence of polymers.

Towards a Framework for the Stochastic Modelling of Subgrid Scale Fluxes for Large Eddy Simulation

We focus on a mixed deterministic-stochastic subgrid scale modelling strategy currently under development for application in Finite Volume Large Eddy Simulation (LES) codes. Our concept is based on the integral conservation laws for mass, momentum and energy of a flow field. We model the space-time structure of the flux correction terms to create a discrete formulation. Advanced methods of time series analysis for the data-based construction of stochastic models with inherently non-stationary statistical properties and concepts of information theory based on a modified Akaike information criterion and on the Bayesian information criterion for the model discrimination are used to construct surrogate models for the non-resolved flux fluctuations. Vector-valued auto-regressive models with external influences form the basis for the modelling approach. The reconstruction capabilities of the modelling ansatz are tested against fully 3D turbulent channel flow data computed by direct numerical simulation and, in addition, against a turbulent Taylor-Green vortex flow showing a transition from laminar to a turbulent flow state. The modelling approach for the LES closure is different in both test cases. In the channel flow we consider an implicit LES ansatz. In the Taylor-Green vortex flow, it follows an explicit closure approach. We present here the outcome of our reconstruction tests and show specific results of the non-trivial time series data analysis. Started with a generally stochastic ansatz we found, surprisingly, that the deterministic model part already yields small residuals and is, therefore, good enough to fit the flux correction terms well. In the Taylor-Green vortex flow, we found additionally time-dependent features confirming that our modelling approach is capable of detecting changes in the temporal structure of the flow. The results encourage us to launch a more ambitious attempt at dynamic LES closure along these lines.