Subgrid-scale Models For Large-eddy Simulation Research Articles

Large Eddy Simulation of a Turbulent Polydisperse Spray Flow: a Comparative Study of Subgrid Scale Models and Droplet Injection Models

Abstract This study performs an investigation of the effects of the subgrid-scale and droplet injection models in the large eddy simulation (LES) of turbulent two-phase spray flows. Three LES subgrid-scale (SGS) models (Smagorinsky, wall-adapting local eddy viscosity, and dynamic Smagorinsky) and two droplet injection models (cone nozzle injection and conditional droplet injection) are validated to the experimental measurements. For both gaseous and liquid phases, all SGS models provide comparable results, indicating that the current two-phase flow field does not exhibit a pronounced sensitivity to the LES SGS model. As for different droplet injection models and spray dispersion angles, minimal differences are observed in the prediction of the gaseous mean and RMS velocity profiles. However, for the result of liquid phase, CDIM (conditional droplet injection model) predictions of the droplet mean diameter and velocity are in better agreement with experiments, and less sensitive to spray dispersion angle settings. While the CNIM (cone nozzle injection model) prediction of droplet diameter is less accurate when increasing the dispersion angle. The study suggests that turbulent two-phase spray flows are more influenced by the spray boundary conditions rather than the LES SGS models.

Evaluating anisotropic minimum dissipation, sigma and modulated gradient subgrid-scale models in large-eddy simulation of compressible mixing layers

We evaluate three subgrid-scale (SGS) models in large eddy simulations (LES) of compressible mixing layers up to convective Mach number ( M c ) 2.0. The initial momentum-thickness based Reynolds number is 1000 to match recent high-resolution simulations of the same configuration. The simulations employ the Localised Artificial Diffusivity (LAD) shock-capturing scheme and evaluate constant-coefficient and dynamic versions of Anisotropic Minimum Dissipation (AMD), Sigma, and Modulated Gradient (MGM) SGS models. The results show that the LAD scheme is crucial for stability at higher convective Mach numbers, for M c > 1.2 . The SGS models improve the accuracy of the LES predictions, particularly for dissipation and Reynolds stresses. Dynamic versions of all three SGS models give accurate results. The AMD kernel is found to be most sensitive to the flow conditions since the dynamically obtained model coefficient varies the least with M c . Dynamic versions of the SGS models enhance the agreement with reference results compared to the constant-coefficient versions, particularly for the eddy-viscosity AMD and Sigma models, and to a lesser extent for the MGM model. The results also emphasise the importance of retaining a non-zero artificial-shear-viscosity term, even in the presence of explicit SGS models.

Development of a subgrid-scale model for Burgers turbulence using statistical mechanics-based methods

Turbulent flows can be simulated using direct numerical simulations (DNS), but DNS is computationally expensive. Reduced-order models implemented into Reynolds-averaged Navier–Stokes and large eddy simulations (LES) can reduce the computational cost, but need to account for subgrid-scale (SGS) turbulence through closure relations. Turbulence modeling has presented a significant challenge due to the non-linearities in the flow and multi-scale behavior. Well-established features of the turbulent energy cascade can be leveraged through statistical mechanics to provide a characterization of turbulence. This paper presents a physics-based data-driven SGS model for LES using the concepts of statistical mechanics. The SGS model is implemented and tested using the stochastic Burgers equation. DNS data are used to calculate Kramers–Moyal (KM) coefficients, which are then implemented as an SGS closure model. The presented data-driven KM method outperforms traditional methods in capturing the multi-scale behavior of Burgers turbulence.

Ensemble data assimilation-based mixed subgrid-scale model for large-eddy simulations

An ensemble Kalman filter (EnKF)-based mixed model (EnKF-MM) is proposed for the subgrid-scale (SGS) closure in the large-eddy simulation (LES) of turbulence. The model coefficients are determined through the EnKF-based data assimilation technique. The direct numerical simulation (DNS) results are filtered to obtain the benchmark data for the LES. Reconstructing the correct kinetic energy spectrum of the filtered DNS (fDNS) data has been adopted as the target for the EnKF to optimize the coefficient of the functional part in the mixed model. The proposed EnKF-MM framework is subsequently tested in the LES of both the incompressible homogeneous isotropic turbulence and turbulent mixing layer. The performance of the LES is comprehensively examined through the predictions of the flow statistics including the velocity spectrum, the probability density functions (PDFs) of the SGS stress, the PDF of the strain rate, and the PDF of the SGS energy flux. The structure functions, the evolution of turbulent kinetic energy, the mean flow, the Reynolds stress profile, and the iso-surface of the Q-criterion are also examined to evaluate the spatial–temporal predictions by different SGS models. The results of the EnKF-MM framework are consistently more satisfying compared to the traditional SGS models, including the dynamic Smagorinsky model, the dynamic mixed model, and the velocity gradient model, demonstrating its great potential in the optimization of SGS models for the LES of turbulence.

Large Eddy Simulation Study on the Relationship Between Large-Scale Turbulence Vortices and Unsteady Cavitation Around a Hydrofoil

Abstract We conducted a large eddy simulation (LES) of cavitating turbulent flow around a Clark-Y11.7% hydrofoil at an angle of attack of 8 deg. We focused on the improvement of the reproducibility of hydrofoil performance under cavitating conditions when considering the unsteadiness of the flow field sufficiently by LES. A homogeneous cavitation model was adopted. The subgrid-scale model for LES was the one-equation dynamic model. The unsteady phenomena such as cavity oscillation and cloud cavity shedding accompanied by the reentrant jet were simulated. Large-scale spanwise vortices were also captured, which occurred intermittently from the onset of the sheet cavity. Then, the flow inside the sheet cavity was de-accelerated and the streamlines went around the sheet cavity. Streamline curvature formed a separation bubble behind the sheet cavity accompanied by a low-pressure region. Thus, the sheet cavity length was sufficient and the reproducibility of the pressure distribution around the hydrofoil and lift coefficient were improved.

A turbulent combustion model for soot formation at the LES subgrid-scale using virtual chemistry approach

Designing efficient and clean combustion devices to reduce soot formation in practical applications is a major concern nowadays. This could be achieved by performing predictive simulations in turbulent sooting combustors. Large Eddy Simulation (LES) is an attractive approach to predict flame/turbulence interactions at small scales including soot phenomena. However, because of the peculiarly complex nature of soot production phenomena, turbulent sooting flames remain very difficult to simulate and are computationally expensive. Thus, reduced gas-phase kinetics and soot models should be included in numerical simulations. The reduced virtual chemistry approach is a great alternative to address this problem since it introduces an optimized and flexible strategy to tackle multi-mode turbulent combustion and pollutants prediction. Also, the virtual chemistry approach has recently demonstrated its capability in reproducing soot phenomena in laminar flames including radiative heat transfer. In the present work, the virtual chemistry methodology is extended to resolve turbulent sooting flames using LES. Based on analysis of flame and soot chemical time scales along with turbulent time scale, an original hybrid turbulent combustion model formulation is proposed, which degenerates to the flamelet regime in the flame front region and to a PSR formalism in the post-flame zone, characterized by slow soot chemistry. The subgrid-scale model for turbulence-chemistry-soot interactions is then implemented in an LES framework. The model is challenged in the turbulent non-premixed sooting flame from Sandia Laboratory. Results indicate that the LES subgrid-scale model has a significant impact on soot formation and confirms previous observations from the literature in LES of non-premixed turbulent sooting flames. Additionally, results show that the virtual chemistry can reproduce flame-soot characteristics of a turbulent sooting jet flame and are comparable to other state-of-the-art works.

Deep reinforcement learning for large-eddy simulation modeling in wall-bounded turbulence

The development of a reliable subgrid-scale (SGS) model for large-eddy simulation (LES) is of great importance for many scientific and engineering applications. Recently, deep learning approaches have been tested for this purpose using high-fidelity data such as direct numerical simulation (DNS) in a supervised learning process. However, such data are generally not available in practice. Deep reinforcement learning (DRL) using only limited target statistics can be an alternative algorithm in which the training and testing of the model are conducted in the same LES environment. The DRL of turbulence modeling remains challenging owing to its chaotic nature, high dimensionality of the action space, and large computational cost. In this study, we propose a physics-constrained DRL framework that can develop a deep neural network-based SGS model for LES of turbulent channel flow. The DRL models that produce the SGS stress were trained based on the local gradient of the filtered velocities. The developed SGS model automatically satisfies the reflectional invariance and wall boundary conditions without an extra training process so that DRL can quickly find the optimal policy. Furthermore, direct accumulation of reward, spatially and temporally correlated exploration, and the pre-training process are applied for efficient and effective learning. In various environments, our DRL could discover SGS models that produce the viscous and Reynolds stress statistics perfectly consistent with the filtered DNS. By comparing various statistics obtained by the trained models and conventional SGS models, we present a possible interpretation of better performance of the DRL model.

Turbulence models and simulation method in the CFD simulation of 75-mm hydrocyclone

In this paper, an effective method for the classification process simulation in 75¬mm hydrocyclone is considered. The simulation results and computational time are compared using Reynolds stress model (RSM) and different large eddy simulation (LES) subgrid-scale models as turbulence models, and the volume of fluid model (VOF) as a multiphase model. The Lagrangian discrete phase model (DPM) is used to simulate the classification process of particles. As the experimental result for comparison of simulation results, Hsieh's experimental data are used. When the different LES subgrid-scale models are used, the solution converges stably by various solution convergence methods without increasing the grid numbers or reducing the size of time steps than RSM model. As a result, it is confirmed that when an appropriate simulation method is applied with the LES-WMLES S-Omega model, more accurate axial water flow velocity distribution and particle classification simulation results can be obtained at a computational cost similar to that of using the RSM model.

Experimental and LES study of unconfined jet impingement on a smooth flat heated plate with slots of different widths

ABSTRACT The present work focuses on the experimental and large-eddy simulation (LES) investigation of fluid flow and heat transfer due to the impingement of an unconfined turbulent slot jet on a smooth flat plate. Three LES sub-grid scale models are validated with the experimental observations for first time in terms effect of slot widths. A detailed parametric study is conducted considering nozzle to plate spacing ratio from 4 to 12, non-dimensional slot width from 0.015 to 0.035, and Reynolds number range from 4000 to 12000. The results show an appreciable change in the stagnation point and along the wall jet Nusselt numbers with the change in Reynolds number, nozzle-to-plate spacing and non-dimensional slot width. No significant effect of nozzle to plate spacing is observed along the wall jet Nusselt number beyond the streamwise location at 0.2. The local Nusselt number increases with an increase in Reynolds number while it decreases with an increase in nondimensional slot width. Comparison of various LES sub-grid models with RANS (k-ω SST) turbulence model is performed. The results show that turbulent kinetic energy plays a major role in enhancing the heat transfer rate. Dissipation of the turbulent kinetic energy increases with an increase in nozzle to plate spacing and non-dimensional slot width. Further, a correlation is proposed for the stagnation point and wall jet region Nusselt numbers in terms of effect of slots width, Reynolds number and non-dimensional nozzle to plate spacing.

Information-theoretic formulation of dynamical systems: Causality, modeling, and control

The problems of causality, modeling, and control for chaotic, high-dimensional dynamical systems are formulated in the language of information theory. The central quantity of interest is the Shannon entropy, which measures the amount of information in the states of the system. Within this framework, causality is quantified by the information flux among the variables of interest in the dynamical system. Reduced-order modeling is posed as a problem related to the conservation of information in which models aim at preserving the maximum amount of relevant information from the original system. Similarly, control theory is cast in information-theoretic terms by envisioning the tandem sensor-actuator as a device reducing the unknown information of the state to be controlled. The new formulation is used to address three problems about the causality, modeling, and control of turbulence, which stands as a primary example of a chaotic, high-dimensional dynamical system. The applications include the causality of the energy transfer in the turbulent cascade, subgrid-scale modeling for large-eddy simulation, and flow control for drag reduction in wall-bounded turbulence.

Density-unweighted subgrid-scale models for large-eddy simulations of compressible turbulence

Density-unweighted methods in large-eddy simulations (LES) of turbulence have received little attention, and the modeling of unclosed terms using density-unweighted methods even less. We investigate the density-unweighted subgrid-scale (SGS) closure problem for LES of decaying compressible isotropic turbulence at initial turbulent Mach numbers 0.4 and 0.8. Compared to the LES with Favre (density-weighted) filtering, there are more unclosed SGS terms for density-unweighted LES, which can be reconstructed using different SGS models, including the gradient model (GM), approximate deconvolution model (ADM), dynamic Smagorinsky model (DSM), dynamic mixed model (DMM), and the dynamic iterative approximate deconvolution (DIAD) models proposed by Yuan et al. “Dynamic iterative approximate deconvolution models for large-eddy simulation of turbulence,” Phys. Fluids 33, 085125 (2021). We derive GM models suitable for density-unweighted methods. We also, for the first time, apply the DIAD model to investigate compressible turbulence. In the a priori tests, the correlation coefficients of the GM, ADM, and DIAD models are larger than 0.9. Particularly, the correlation coefficients of DIAD models exceed 0.98 and the relative errors are below 0.2, which is superior to that in other SGS models. In the a posteriori tests of the density-unweighted LES, the DIAD model shows great advantages over other SGS models (including GM, ADM, DSM, and DMM models) in predicting the various statistics and structures of compressible turbulence, including the velocity spectrum, probability density functions (PDFs) of SGS fluxes and the instantaneous spatial structures of SGS heat flux, SGS kinetic energy flux, and vorticity.

Subgrid-scale models of isotropic turbulence need not produce energy backscatter

This investigation questions the importance of inverse interscale energy fluxes, the so-called energy backscatter, for the modelling of the energy cascade in large-eddy simulations (LES) of turbulent flows. The invariance of the filtered Navier–Stokes equations to divergence-preserving transformations of the subgrid-scale (SGS) stress tensor is exploited here to explore alternative representations of the local SGS energy fluxes. Numerical optimisation procedures are applied to the SGS stress tensor – obtained by filtering isotropic turbulence flow fields – to find alternative stresses that satisfy the filtered Navier–Stokes equations, but that produce negligible backscatter. These alternative SGS stresses show that backscatter represents not a flux of energy from the subgrid to the resolved scales, but conservative spatial fluxes, and that it need not be modelled to reproduce the local energetic exchange between the resolved and the subgrid scales in LES. From the perspective of statistical mechanics, it is argued that this is a consequence of the strong statistical irreversibility of inertial-range dynamics, which precludes inverse energy cascades even in a local sense. These findings show that the energy cascade is strongly unidirectional locally, and that it can be modelled as an irreversible sink of energy, justifying the extended use of purely dissipative SGS models in LES.

Data-driven model development for large-eddy simulation of turbulence using gene-expression programing

We apply the gene-expression programing (GEP) method to develop subgrid-scale models for large-eddy simulations (LESs) of turbulence. The GEP model is trained based on Galilean invariants and tensor basis functions, and the training data are from direct numerical simulation (DNS) of incompressible isotropic turbulence. The model trained with GEP has been explicitly tested, showing that the GEP model can not only provide high correlation coefficients in a priori tests but also show great agreement with filtered DNS data when applied to LES. Compared to commonly used models like the dynamic Smagorinsky model and the dynamic mixed model, the GEP model provides significantly improved results on turbulence statistics and flow structures. Based on an analysis of the explicitly given model equation, the enhanced predictions are related to the fact that the GEP model is less dissipative and that it introduces high-order terms closely related to vorticity distribution. Furthermore, the GEP model with the explicit equation is straightforward to be applied in LESs, and its additional computational cost is substantially smaller than that of models trained with artificial neural networks with similar levels of predictive accuracies in a posteriori tests.

A novel buoyancy-modified subgrid-scale model for large-eddy simulation of turbulent convection

PurposeThe purpose of this paper is to develop a subgrid-scale (SGS) model for large eddy simulation (LES) of buoyancy- and thermally driven transitional and turbulent flows and further examine its performance.Design/methodology/approachFavre-filtered, non-dimensional LES equations are solved using non-dissipative, fully implicit, kinetic energy conserving, finite-volume algorithm which uses an iterative predictor-corrector approach based on pressure correction. Also, to develop a new SGS model which accounts for buoyancy, turbulent generation term in SGS viscosity is properly modified and enhanced by buoyancy production.FindingsThe proposed model has been successfully applied to turbulent Rayleigh–Bénard convection. The results show that the model is able to reproduce the complex physics of turbulent thermal convection. In comparison with the original wall-adapting local eddy-viscosity (WALE) and buoyancy-modified (BM) Smagorinsky models, turbulent diagnostics predicted by the new model are in better agreement with direct numerical simulation.Originality/valueA BM variant of the WALE SGS model is newly developed and analyzed.

Development of a large-eddy simulation subgrid model based on artificial neural networks: a case study of turbulent channel flow

Abstract. Atmospheric boundary layers and other wall-bounded flows are often simulated with the large-eddy simulation (LES) technique, which relies on subgrid-scale (SGS) models to parameterize the smallest scales. These SGS models often make strong simplifying assumptions. Also, they tend to interact with the discretization errors introduced by the popular LES approach where a staggered finite-volume grid acts as an implicit filter. We therefore developed an alternative LES SGS model based on artificial neural networks (ANNs) for the computational fluid dynamics MicroHH code (v2.0). We used a turbulent channel flow (with friction Reynolds number Reτ=590) as a test case. The developed SGS model has been designed to compensate for both the unresolved physics and instantaneous spatial discretization errors introduced by the staggered finite-volume grid. We trained the ANNs based on instantaneous flow fields from a direct numerical simulation (DNS) of the selected channel flow. In general, we found excellent agreement between the ANN-predicted SGS fluxes and the SGS fluxes derived from DNS for flow fields not used during training. In addition, we demonstrate that our ANN SGS model generalizes well towards other coarse horizontal resolutions, especially when these resolutions are located within the range of the training data. This shows that ANNs have potential to construct highly accurate SGS models that compensate for spatial discretization errors. We do highlight and discuss one important challenge still remaining before this potential can be successfully leveraged in actual LES simulations: we observed an artificial buildup of turbulence kinetic energy when we directly incorporated our ANN SGS model into a LES simulation of the selected channel flow, eventually resulting in numeric instability. We hypothesize that error accumulation and aliasing errors are both important contributors to the observed instability. We finally make several suggestions for future research that may alleviate the observed instability.

Large Eddy Simulation of Film Cooling Over a Flat Plate in Supersonic Flow

Abstract In the present work, large eddy simulation (LES) was performed to access the film cooling performance in the supersonic flow over a flat plate with a perpendicular slot injection configuration. The study was carried out for three mainstream Mach No.; Mα = 1.2, 2.67, and 3.3 and three coolant stream Mach No.: 0.05, 0.1, and 0.15. In supersonic flow, temperature rise inside the boundary layer is a major issue considering it causes high rates of heat transfer to the coolant film. To select a suitable LES sub-grid scale (SGS) model, LES results obtained from the present study using the LES SGS models such as Smagorinky-Lilly, wall adapted local eddy viscosity (WALE), and wall-modeled LES (WMLES) models were compared with DNS results of Keller and Kloker. The parametric study showed that the higher mainstream Mach No. caused increased wall temperature and reduced effectiveness. The film cooling effectiveness appeared to reduce almost by 10% when the mainstream Mach No. is increased from 1.2 to 2.67; however, no apparent difference was observed in effectiveness between the mainstream Mach No. 2.67 and 3.3. It was found that doubling and tripling the coolant stream Mach No. from 0.05 to 0.1 and 0.15, the length of potential core region also doubled and tripled, respectively, from 4 X/S to 8 X/S and 13 X/S and hence significant improvement in the film cooling effectiveness was observed.

Evaluation of LES sub-grid scale models and time discretization schemes for prediction of convection effect in a buoyant pool fire

The identification of the type of regime has an essential effect on the selection of sub-grid scale and discretization methods, regarding the accuracy and computational time. In order to investigate the role of sub-grid scale and time discretization method in a pool fire modeling by the Large Eddy Simulation (LES), three sub-grid scales Smagorinsky, one-equation and Wall-Adapting Local Eddy-Viscosity (WALE) and three time discretization methods of first-order Euler method, second-order Crank Nicolson and backward second-order were investigated. The results indicate that WALE and one-equation sub-grid scale have an acceptable prediction, while Smagorinsky has a significant error with the experimental results. Different time discretization methods have little effects on the results of mean velocity and mean turbulent parameters of the pool fire. By considering the instantaneous distribution of parameters, all three methods perform similar results where the kinetic energy is less than 5 m2/s2. In areas where the perturbation is aggravated, the two second-order discretization methods have the same error with a little difference by the first-order Euler method. The accuracies of second-order methods are about 10% for the velocity prediction, compared to the experimental results, while the error of the Euler method is 15%.

Assessment of subgrid-scale models for large-eddy simulation of a planar turbulent wall-jet with heat transfer

In the present work, five different subgrid-scale (SGS) models and implicit large-eddy simulation (LES) are evaluated and compared against the DNS for the simulation of the planar turbulent wall-bounded jet with heat transfer. The SGS models tested are the classical constant coefficient Smagorinsky model and its dynamic version, the wall-adaptive local eddy-viscosity (WALE) model, the turbulent kinetic energy one-equation model, and its dynamic version. The effects of using variable turbulent Prandtl number and the near-wall damping function are also studied in these models. The mean, second-order flow and heat-transfer statistics with the evolution of Nusselt number along the jet downstream are used to assess the different SGS models. The quality of resolution of the present LES are evaluated using the activity parameter and the index of resolution quality. Among the models tested, the constant coefficient Smagorinsky model together with Van-Driest damping predicts the solution accurately in the near-wall region as well as in estimating the thermal parameters. However, the dynamic models performed better in evaluating the Reynolds stress profiles away from the wall in the outer region. Capabilities of the models to predict the turbulent kinetic energy budgets, pressure-velocity gradient correlations and triple velocity correlations are also studied. The implemented variable Prandtl number algorithm is noted to have minimal influence on the evolution of the solution.

Subgrid-scale model for large-eddy simulation of transition and turbulence in compressible flows

This article focuses on a subgrid-scale (SGS) eddy viscosity model based on helicity which is derived from our previous research [Yu et al., “Subgrid-scale eddy viscosity model for helical turbulence,” Phys. Fluids 25, 095101 (2013)] for large-eddy simulation of transition and turbulence in compressible flows. Based on the character of the compressible boundary layer over a flat plate, we obtain from theoretical analysis that this model can automatically distinguish laminar flow and turbulence and can also simulate turbulence well. Meanwhile, an a priori test using direct numerical simulation (DNS) data of a spatially developing flat-plate boundary layer at Ma = 2.25 shows that the helicity model can clearly differentiate laminar, transitional, and turbulent regions. Comparing the numerical simulation results with DNS and other SGS models in the spatially developing boundary-layer over a flat plate, we find that the suggested model could precisely predict the onset of transition, transition peak, skin-friction coefficient, mean velocity profile, mean temperature profile, and turbulence intensities. In the case of a compression ramp, the model can well simulate the bypass-type transition, the separated and reattached points, and the size of the separation bubble in the corner region. Furthermore, the prominent advantage of the proposed model can predict transitional flow exactly with no explicit filtering or dynamic procedure.

Large-Eddy Simulation of an Asymmetric Plane Diffuser: Comparison of Different Subgrid Scale Models

Large-eddy simulation (LES) of separated turbulent flow through an asymmetric plane diffuser is investigated. The outcome of an actual LES depends on the quality of the subgrid-scale (SGS) model, as well as the accuracy of the numerical method used to solve the equations for the resolved scales. In this paper, we focus on the influence of SGS models for LES of the diffuser flow through using a high-order finite difference method to solve the equations for the resolved scales. Six resolutions are computed to investigate the influence of mesh resolution. Four existing SGS models, a new one-equation dynamic SGS model and a direct numerical simulation (DNS) are conducted in the diffuser flow. A series of computational analyses is performed to assess the performance of different SGS models on the coarse grids. By comparison with the experiment and DNS, the results produced by the new one-equation dynamic model give better agreement with experiment and DNS than the four other existing SGS models.