Unified turbulence models for LES and RANS,FDF and PDF simulations

A review of existing basic turbulence modeling approaches reveals the need for the development of unified turbulence models which can be used continuously as filter density function (FDF) or probability density function (PDF) methods, large eddy simulation (LES) or Reynolds-averaged Navier–Stokes (RANS) methods. It is then shown that such unified stochastic and deterministic turbulence models can be constructed by explaining the dependence of the characteristic time scale of velocity fluctuations on the scale considered. The unified stochastic model obtained generalizes usually applied FDF and PDF models. The unified deterministic turbulence model that is implied by the stochastic model recovers and extends well-known linear and nonlinear LES and RANS models for the subgrid-scale and Reynolds stress tensor.      

An Attempt to Combine Large Eddy Simulation with the k-ε Model in a Channel-Flow Calculation

Large eddy simulation (LES) is combined with the Reynolds-averaged Navier–Stokes (RANS) equation in a turbulent channel-flow calculation. A one-equation subgrid-scale model is solved in a three-dimensional grid in the near-wall region whereas the standard k–ε model is solved in a one-dimensional grid in the outer region away from the wall. The two grid systems are overlapped to connect the two models smoothly. A turbulent channel flow is calculated at Reynolds numbers higher than typical LES and several statistical quantities are examined. The mean velocity profile is in good agreement with the logarithmic law. The profile of the turbulent kinetic energy in the near-wall region is smoothly connected with that of the turbulent energy for the k–ε model in the outer region. Turbulence statistics show that the solution in the near-wall region is as accurate as a usual LES. The present approach is different from wall modeling in LES that uses a RANS model near the wall. The former is not as efficient as the latter for calculating high-Reynolds-number flows. Nevertheless, the present method of combining the two models is expected to pave the way for constructing a unified turbulence model that is useful for many purposes including wall modeling. Received 11 June 1999 and accepted 15 December 2000     

A Hybrid RANS/LES Simulation of Turbulent Channel Flow

Hybrid models combining large eddy simulation (LES) with Reynolds-averaged Navier–Stokes (RANS) simulation are expected to be useful for wall modeling in the LES of high Reynolds number flows. Some hybrid simulations of turbulent channel flow have a common defect; the mean velocity profile has a mismatch between the RANS and LES regions due to a steep velocity gradient at the interface. This mismatch is reproduced and examined using a simple hybrid model; the Smagorinsky model is switched to a RANS model increasing the filter width. It is suggested that a rapid spatial variation in the eddy viscosity is responsible for an underestimate of the grid-scale shear stress and for the steep velocity gradient. To reduce the mean velocity mismatch a new scheme is proposed; additional filtering is introduced to define two kinds of velocity components at the interface between the two regions. The two components are used to remove inconsistency in the velocity equations due to a rapid variation in the filter width. Using the new scheme, simulations of channel flow are carried out with the simple hybrid model. It is shown that the grid-scale shear stress becomes large enough and most of the mean velocity mismatch is removed. Simulations for higher Reynolds numbers are carried out with the k–ε model and the one-equation subgrid-scale model. Although it is necessary to improve the turbulence models and the treatment of the buffer region, the new scheme is shown to be effective for reducing the mismatch and to be useful for developing better hybrid simulations. Received 5 April 2002 and accepted 8 January 2003 Published online 25 March 2003 Communicated by M.Y. Hussaini     

From single-scale turbulence models to multiple-scale and subgrid-scale models by Fourier transform

A theoretical method based on mathematical physics formalism that allows transposition of turbulence modeling methods from URANS (unsteady Reynolds averaged Navier–Stokes) models, to multiple-scale models and large eddy simulations (LES) is presented. The method is based on the spectral Fourier transform of the dynamic equation of the two-point fluctuating velocity correlations with an extension to the case of non-homogenous turbulence. The resulting equation describes the evolution of the spectral velocity correlation tensor in wave vector space. Then, we show that the full wave number integration of the spectral equation allows one to recover usual one-point statistical closure whereas the partial integration based on spectrum splitting gives rise to partial integrated transport models (PITM). This latter approach, depending on the type of spectral partitioning used, can yield either a statistical multiple-scale model or subfilter transport models used in LES or hybrid methods, providing some appropriate approximations are made. Closure hypotheses underlying these models are then discussed by reference to physical considerations with emphasis on identification of tensorial fluxes that represent turbulent energy transfer or dissipation. Some experiments such as the homogeneous axisymmetric contraction, the decay of isotropic turbulence, the pulsed turbulent channel flow and a wall injection induced flow are then considered as typical possible applications for illustrating the potentials of these models.      

Unsteady CFD simulations of a pump in part load conditions using scale-adaptive simulation

The scope of this work is to demonstrate the applicability of an eddy resolving turbulence model in a turbomachinery configuration. The model combines the Large Eddy Simulation (LES) and the Reynolds Averaged Navier Stokes (RANS) approach. The point of interest of the present investigation is the unsteady rotating stall phenomenon occurring at low part load conditions. Since RANS turbulence models often fail to predict separation correctly, a LES like model is expected to give superior results. In this investigation the scale-adaptive simulation (SAS) model is used. This model avoids the grid dependence appearing in the Detached Eddy Simulation (DES) modelling strategy. The simulations are validated with transient measurement data. The present results demonstrate, that both models are able to predict the major stall frequency at part load. Results are similar for URANS and SAS, with advantages in predicting minor stall frequencies for the turbulence resolving model.     

Computational analysis of impinging shock-wave boundary layer interaction under conditions of incipient separation

The interaction of an oblique shock wave with a turbulent boundary layer under conditions of incipient separation is analyzed by means of large-eddy simulation (LES) and Reynolds-averaged Navier–Stokes (RANS) turbulence models, with the objective to explore their predictive capabilities, in particular with respect to the unsteady features of the interaction. Consistent with earlier direct numerical simulations, we have found that the flow dynamics in the interaction zone is characterized by strong intermittency associated with the formation of scattered spots of flow reversal near the nominal position of the reflected shock. Comparison with experimental results (at much larger Reynolds number) show that the qualitative features of the interaction are predicted reasonably well by both LES and RANS models. RANS models supplemented with a semi-empirical closure are also found to provide reasonable estimate of the fluctuating pressure loads at the wall.     

LES Validation from Experiments

This paper addresses issues relating to the validation of LES from experiments. It highlights the differences between large eddy simulations (LES) and Reynolds averaged Navier–Stokes simulations (RANS) and how LES puts higher demands on the validation process than RANS. Some popular validation experiments are outlined, which are part of the Workshop on Turbulent Non-Premixed Flames. Important features of validation experiments are discussed to help modellers with the selection of suitable experiments, and experimentalists with the design. An LES validation using the typical approach is then presented, together with some unusual, more innovative approaches that deviate from common RANS practice. The final section considers experimental errors, with examples of their effects, and how LES can contribute to their analysis and compensation. This paper does not aim to provide a complete review of the field, but rather to communicate some ideas that were presented at an invited Workshop presentation.     

Large Eddy Simulations Using the Subgrid-Scale Estimation Model and Truncated Navier–Stokes Dynamics

We describe a procedure for large eddy simulations of turbulence which uses the subgrid-scale estimation model and truncated Navier–Stokes dynamics. In the procedure the large eddy simulation equations are advanced in time with the subgrid-scale stress tensor calculated from the parallel solution of the truncated Navier–Stokes equations on a mesh two times smaller in each Cartesian direction than the mesh employed for a discretization of the resolved quantities. The truncated Navier–Stokes equations are solved through a sequence of runs, each initialized using the subgrid-scale estimation model. The modeling procedure is evaluated by comparing results of large eddy simulations for isotropic turbulence and turbulent channel flow with the corresponding results of experiments, theory, direct numerical simulations, and other large eddy simulations. Subsequently, simplifications of the general procedure are discussed and evaluated. In particular, it is possible to formulate the procedure entirely in terms of the truncated Navier–Stokes equation and a periodic processing of the small-scale component of its solution. Received 27 April 2001 and accepted 16 December 2001     

Investigation of the sensitivity of turbulent closures and coupling of hybrid RANS‐LES models for predicting flow fields with separation and reattachment

Hybrid models have found widespread applications for simulation of wall‐bounded flows at high Reynolds numbers. Typically, these models employ Reynolds‐averaged Navier–Stokes (RANS) and large eddy simulation (LES) in the near‐body and off‐body regions, respectively. A number of coupling strategies between the RANS and LES regions have been proposed, tested, and applied in the literature with varying degree of success. Linear eddy‐viscosity models (LEVM) are often used for the closure of turbulent stress tensor in RANS and LES regions. LEVM incorrectly predicts the anisotropy of Reynolds normal stress at the RANS‐LES interface region. To overcome this issue, use of non‐linear eddy‐viscosity models (NLEVM) have started receiving attention. In this study, a generic non‐linear blended modeling framework for performing hybrid simulations is proposed. Flow over the periodic hills is used as the test case for model evaluation. This case is chosen due to complex flow physics with simplified geometry. Analysis of the simulations suggests that the non‐linear hybrid models show a better performance than linear hybrid models. It is also observed that the non‐linear closures are less sensitive to the RANS‐LES coupling and grid resolution. Copyright © 2016 John Wiley & Sons, Ltd.     

Prediction of separation flows around a 6：1 prolate spheroid using RANS/LES hybrid approaches

This paper presents hybrid Reynolds-averaged Navier–Stokes (RANS) and large-eddy-simulation (LES) methods for the separated flows at high angles of attack around a 6:1 prolate spheroid. The RANS/LES hybrid methods studied in this work include the detached eddy simulation (DES) based on Spalart–Allmaras (S–A), Menter’s k–ω shear-stress-transport (SST) and k–ω with weakly nonlinear eddy viscosity formulation (Wilcox–Durbin+, WD+) models and the zonal-RANS/LES methods based on the SST and WD+ models. The switch from RANS near the wall to LES in the core flow region is smooth through the implementation of a flow-dependent blending function for the zonal hybrid method. All the hybrid methods are designed to have a RANS mode for the attached flows and have a LES behavior for the separated flows. The main objective of this paper is to apply the hybrid methods for the high Reynolds number separated flows around prolate spheroid at high-incidences. A fourth-order central scheme with fourth-order artificial viscosity is applied for spatial differencing. The fully implicit lower–upper symmetric-Gauss–Seidel with pseudo time sub-iteration is taken as the temporal differentiation. Comparisons with available measurements are carried out for pressure distribution, skin friction, and profiles of velocity, etc. Reasonable agreement with the experiments, accounting for the effect on grids and fundamental turbulence models, is obtained for the separation flows. The project supported by the National Natural Science Foundation of China (10502030 and 90505005).     

Towards a Unified Turbulence Simulation Approach for Wall-Bounded Flows

A hybrid Reynolds-averaged Navier–Stokes/Large-Eddy Simulation (RANS/LES) methodology has received considerable attention in recent years, especially in its application to wall-bounded flows at high-Reynolds numbers. In the conventional zonal hybrid approach, eddy-viscosity-type RANS and subgrid scale models are applied in the RANS and LES zones, respectively. In contrast, the non-zonal hybrid approach uses only a generalized turbulence model, which provides a unified simulation approach that spans the continuous spectrum of modeling/simulation schemes from RANS to LES. A particular realization of the non-zonal approach, known as partially resolved numerical simulation (PRNS), uses a generalized turbulence model obtained from a rescaling of a conventional RANS model through the introduction of a resolution control function F _R , where F _R is used to characterize the degree of modeling required to represent the unresolved scales of turbulent motion. A new generalized functional form for F _R in PRNS is proposed in this study, and its performance is compared with unsteady RANS (URANS) and LES computations for attached and separated wall-bounded turbulent flows. It is demonstrated that PRNS behaves similarly to LES, but outperforms URANS in general.     

An advanced switching parameter for a hybrid LES/RANS model considering the characteristics of near-wall turbulent length scales

In this study, we proposed an idea for an advanced switching parameter used in a hybrid approach connecting large eddy simulation (LES) with Reynolds-averaged Navier–Stokes modeling [the hybrid LES/RANS (HLR) model]. Although the HLR model is promising way to predict engineering turbulent flows, an important problem is that RANS is always adopted in the near-wall region, even if the grid resolution is fine enough for LES. To overcome this difficulty, the switching parameter proposed here introduced knowledge of the Kolmogorov microscale that is thought to be reasonable for representing the near-wall turbulence. This parameter enabled the present HLR model to be smoothly replaced by a full LES if a grid resolution was fine enough in the near-wall region. To confirm model performance, the present HLR model was applied to numerical simulations of a periodic hill flow as well as fundamental plane channel flows. The model generally provided reasonable predictions for these test cases that include complex turbulence with massive flow separation.     

Possibilities and Limitations of Computer Simulations of Industrial Turbulent Dispersed Multiphase Flows

We give an overview on the usage of computer simulations in industrial turbulent dispersed multiphase flows. We present a few examples of industrial flows: bubble columns and bubbly pipe flows, stirred tanks, cyclones, and a fluid catalytic cracking unit. The fluid catalytic cracking unit is used to illustrate the complexity of the physical phenomena involved, and the possibilities and limitations of the different approaches used: Eulerian–Lagrangian (particle-tracking) and Eulerian–Eulerian (two-fluid). In the first approach, the continuous phase is solved using either RANS simulations (Reynolds-Averaged Navier–Stokes simulations) or DNS/LES (Direct Numerical Simulations/Large-Eddy Simulations), and the individual particles are tracked. In the second approach, the dispersed phase is averaged, leading to two sets equations, which are quite similar to the RANS equations of single-phase flows. The Eulerian–Eulerian approach is the most commonly used in industrial applications, however, it requires a significant amount of modelling. Eulerian–Lagrangian RANS can be simpler to use; in particular in situations involving complex boundary conditions, polydisperse flows and agglomeration/breakup. The key issue for the success of the simulations is to have good models for the complex physics involved. A major weakness is the lack of good models for: the turbulence modification promoted by the particles, the inter-particle interactions, and the near-wall effects. Eulerian–Lagrangian DNS/LES can play an important role as a research tool, in order to get a better physical understanding, and to improve the models used in the RANS simulations (either Eulerian–Eulerian or Eulerian–Lagrangian).     

End-to-end differentiable learning of turbulence models from indirect observations

The emerging push of the differentiable programming paradigm in scientific computing is conducive to training deep learning turbulence models using indirect observations. This paper demonstrates the viability of this approach and presents an end-to-end differentiable framework for training deep neural networks to learn eddy viscosity models from indirect observations derived from the velocity and pressure fields. The framework consists of a Reynolds-averaged Navier–Stokes(RANS) solver and a neuralnetwork-represented turbulence model, each accompanied by its derivative computations. For computing the sensitivities of the indirect observations to the Reynolds stress field, we use the continuous adjoint equations for the RANS equations, while the gradient of the neural network is obtained via its built-in automatic differentiation capability. We demonstrate the ability of this approach to learn the true underlying turbulence closure when one exists by training models using synthetic velocity data from linear and nonlinear closures. We also train a linear eddy viscosity model using synthetic velocity measurements from direct numerical simulations of the Navier–Stokes equations for which no true underlying linear closure exists. The trained deep-neural-network turbulence model showed predictive capability on similar flows.     

Joint RANS/LES Approach to Premixed Flame Modelling in the Context of the TFC Combustion Model

We present an original timesaving joint RANS/LES approach to simulate turbulent premixed combustion. It is intended mainly for industrial applications where LES may not be practical. It is based on successive RANS/LES numerical modelling, where turbulent characteristics determined from RANS simulations are used in LES equations for estimation of the subgrid chemical source and viscosity. This approach has been developed using our TFC premixed combustion model, which is based on a generalization of the Kolmogorov’s ideas. We assume existence of small-scale statistically equilibrium structures not only of turbulence but also of the reaction zones. At the same time, non-equilibrium large-scale structures of reaction sheets and turbulent eddies are described statistically by model combustion and turbulence equations in RANS simulations or follow directly without modelling in LES. Assumption of small-scale equilibrium gives an opportunity to express the mean combustion rate (controlled by small-scale coupling of turbulence and chemistry) in the RANS and LES sub-problems in terms of integral or subgrid parameters of turbulence and the chemical time, i.e. the definition of the reaction rate is similar to that of the mean dissipation rate in turbulence models where it is expressed in terms of integral or subgrid turbulent parameters. Our approach therefore renders compatible the combustion and turbulent parts of the RANS and LES sub-problems and yields reasonable agreement between the RANS and averaged LES results. Combining RANS simulations of averaged fields with LES method (and especially coupled and acoustic codes) for simulation of corresponding nonstationary process (and unsteady combustion regimes) is a promising strategy for industrial applications. In this work we present results of simulations carried out employing the joint RANS/LES approach for three examples: High velocity premixed combustion in a channel, combustion in the shear flow behind an obstacle and the impinging flame (a premixed flame attached to an obstacle).     

Effect of Boundary-Layer Thickness on the Structure of a Near-Wall Flow with a Two-Dimensional Obstacle

Results of physical and numerical experiments on investigating the effect of the depth of immersion of a two-dimensional obstacle with a square cross section into a developed turbulent boundary layer on the length of the separated flow region are presented. The numerical simulation is based on solving averaged Navier–Stokes equations with the use of the k– model of turbulence. The near-wall flow is visualized in the experiments, and the fields of mean and fluctuating velocities are measured. Flow regions where the results of numerical simulation agree with experimental data are determined. It is shown that the length of the recirculation flow region in the near wake increases with decreasing depth of immersion of the two-dimensional obstacle into the turbulent boundary layer.     

A multiscale approach to hybrid RANS/LES wall modeling within a high-order discontinuous Galerkin scheme using function enrichment

We present a novel approach to hybrid Reynolds-averaged Navier-Stokes (RANS)/ large eddy simulation (LES) wall modeling based on function enrichment, which overcomes the common problem of the RANS-LES transition and enables coarse meshes near the boundary. While the concept of function enrichment as an efficient discretization technique for turbulent boundary layers has been proposed in an earlier article by Krank & Wall (A new approach to wall modeling in LES of incompressible flow via function enrichment. J Comput Phys. 2016;316:94-116), the contribution of this work is a rigorous derivation of a new multiscale turbulence modeling approach and a corresponding discontinuous Galerkin discretization scheme. In the near-wall area, the Navier-Stokes equations are explicitly solved for an LES and a RANS component in one single equation. This is done by providing the Galerkin method with an independent set of shape functions for each of these two methods; the standard high-order polynomial basis resolves turbulent eddies, where the mesh is sufficiently fine and the enrichment automatically computes the ensemble-averaged flow if the LES mesh is too coarse. As a result of the derivation, the RANS model is applied solely to the RANS degrees of freedom, which effectively prevents the typical issue of a log-layer mismatch in attached boundary layers. As the full Navier-Stokes equations are solved in the boundary layer, spatial refinement gradually yields wall-resolved LES with exact boundary conditions. Numerical tests show the outstanding characteristics of the wall model regarding grid independence, superiority compared to equilibrium wall models in separated flows, and achieve a speed-up by two orders of magnitude compared to wall-resolved LES.     

Progress in subgrid-scale transport modelling for continuous hybrid non-zonal RANS/LES simulations

The partially integrated transport modelling (PITM) method can be viewed as a continuous approach for hybrid RANS/LES modelling allowing seamless coupling between the RANS and the LES regions. The subgrid turbulence quantities are thus calculated from spectral equations depending on the varying spectral cutoff location [Schiestel, R., Dejoan, A., 2005. Towards a new partially integrated transport model for coarse grid and unsteady turbulent flow simulations. Theoretical and Computational Fluid Dynamics 18, 443–468; Chaouat, B., Schiestel, R., 2005. A new partially integrated transport model for subgrid-scale stresses and dissipation rate for turbulent developing flows. Physics of Fluids, 17 (6)] The PITM method can be applied to almost all statistical models to derive its hybrid LES counterpart. In the present work, the PITM version based on the transport equations for the turbulent Reynolds stresses together with the dissipation transport rate equation is now developed in a general formulation based on a new accurate energy spectrum function E(κ) valid in both large and small eddy ranges that allows to calibrate more precisely the c_sgs2 function involved in the subgrid dissipation rate _sgs transport equation. The model is also proposed here in an extended form which remains valid in low Reynolds number turbulent flows. This is achieved by considering a characteristic turbulence length-scale based on the total turbulent energy and the total dissipation rate taking into account the subgrid and resolved parts of the dissipation rate. These improvements allow to consider a large range of flows including various free flows as well as bounded flows. The present model is first tested on the decay of homogeneous isotropic turbulence by referring to the well known experiment of Comte-Bellot and Corrsin. Then, initial perturbed spectra E(κ) with a peak or a defect of energy are considered for analysing the model capabilities in strong non-equilibrium flow situations. The second test case is the classical fully turbulent channel flow that allows to assess the performance of the model in non-homogeneous flows characterised by important anisotropy effects. Different simulations are performed on coarse and refined meshes for checking the grid independence of solutions as well as the consistency of the subgrid-scale model when the filter width is changed. A special attention is devoted to the sharing out of the energy between the subgrid-scales and the resolved scales. Both the mean velocity and the turbulent stress computations are compared with data from direct numerical simulations.     

Improvement of double-buffer problem in LES–RANS interface region by introducing an anisotropy-resolving subgrid-scale model

The “double-buffer problem” has been regarded as a crucial concern for the strategy behind the hybrid large eddy simulation (LES)/Reynolds-averaged Navier–Stokes (RANS) model (or HLR model, for short). Such models are likely to show unphysical mean-velocity distributions in the LES–RANS interface region, where “super-streak structures” also appear that look like low-speed streaks generated in the near-wall region of wall turbulence. To overcome this difficulty, the stochastic backscatter model, in which the vortex structures in the interface region are divided into smaller scales, holds promise due to the effect of random source term imposed in the momentum equation. Although this method is effective, several parameters must be prescribed and their specification process is arbitrary and ambiguous. An alternative advanced HLR model has been proposed, in which an anisotropy-resolving subgrid-scale (SGS) model was adopted in the LES region as well as a one-equation nonlinear eddy viscosity model in the RANS region. Previous investigations indicated that this HLR model did not exhibit or, at least, largely reduced the “double-buffer problem” in the mean-velocity distribution, with no special treatment being applied. The main purpose of the present study is to reveal why this HLR model improves the predictive performance in the LES–RANS interface region. Specifically, we focus on the role of the extra anisotropic term introduced in the SGS model, finding that it plays an important role in enhancing vortex structures in the interface region, leading to a considerable improvement in model performance.     

Large Eddy Simulation of Premixed Turbulent Combustion Using Ξ Flame Surface Wrinkling Model

One commonly-used method for deriving the RANS equations for multicomponent flow is the technique of conditional averaging. In this paper the concept is extended to LES, by introducing the operations of conditional filtering and surface filtering. Properties of the filtered indicator function are investigated mathematically and computationally. These techniques are then used to derive conditionally filtered versions of the Navier–Stokes equations which are appropriate for simulating multicomponent flow in LES. Transport equations for the favre-averaged indicator function and the unresolved interface properties (the wrinkling and the surface area per unit volume) are also derived. Since the paper is directed towards modelling premixed combustion in the flamelet regime, closure of the equations is achieved by introducing physical models based on the picture of the flame as a wrinkled surface separating burnt and unburnt components of the fluid. This leads to a set of models for premixed turbulent combustion of varying complexity. The results of applying one of this set of models to propagation of a spherical flame in isotropic homogeneous turbulence are analysed. This revised version was published online in July 2006 with corrections to the Cover Date.