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).     

Feedback-controlled forcing in hybrid LES/RANS

The computational cost of large eddy simulation (LES) increases rapidly with the Reynolds number when applied to attached boundary layers. This problem can be avoided by use of a Reynolds-averaged Navier–Stokes (RANS) model in the inner part of the boundary layer, which reduces the computational cost drastically. Such hybrid LES/RANS methods yield accurate results in general, but suffer from an artificial buffer layer and a shift in the velocity profile around the modeling interface. This velocity shift can be removed by use of additional forcing, but the results are very sensitive to the forcing amplitude.

The present paper proposes a feedback algorithm which efficiently finds the appropriate amplitude and thus yields accurate flow statistics. The feedback algorithm is relatively robust, both in that it is insensitive to the values of the parameters involved and that it yields accurate results with different forcing fields and for different Reynolds numbers. It is argued that the feedback algorithm is consistent with the underlying assumptions of hybrid LES/RANS and that it does not introduce additional empiricism into the method.     

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).     

The artificial buffer layer and the effects of forcing in hybrid LES/RANS

The present study is focused on large eddy simulations (LES) that use a statistical (RANS) turbulence model near solid walls, and on the artificial buffer layer that is formed at the interface between these two modeling regions. Additional forcing is used to trigger resolved motions in the LES region more quickly, and leads to improved results in several ways. The study investigates the artificial buffer layer and how it changes with the use of forcing in an in-depth manner, with the purpose of increased understanding of the increasingly popular hybrid LES/RANS group of methods.

The artificial buffer layer is shown to extend from below the modeling interface to well above it, in fact up to 20% of the boundary layer thickness for the cases studied here. The artificial buffer layer is found to be similar to the true buffer layer in many aspects, including a high correlation between the streamwise and wall normal velocity components in the ‘superstreaks’. This indicates that while the superstreaks are highly anisotropic and have unphysical length scales, they still contribute to the resolved shear stress. The forcing does not remove the artificial buffer layer, but it does reduce its extent and increases the resolved shear stress. This increase is mainly associated with increased fluctuations of the wall normal velocity.

A simple, low-dimensional forcing model is proposed and tested, with favorable results. The model is simple to implement and easily generalized to more complex geometries.     

Properties of the hybrid RANS/LES filter

One of the most important and challenging topics in the Large Eddy Simulation of turbulent flows is the connection of the LES technique to the well known and largely used RANS approach where the Navier–Stokes equations are Reynolds averaged. The hybridation of LES and RANS is not only important for its possible practical use, (a rational use of the computational means in different zones), but also from a theoretical point of view, and one possible procedure consists of blending RANS and LES models in the transition zone. In this paper a new filtering technique based on blending filters which transitions smoothly between LES and RANS is proposed and the associated universal model for the subgrid scale stresses is derived. PACS 47.27.Eq     

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.     

A hybrid RANS/LES approach with scale-adaptive capabilities for highly separated flows

A new hybrid RANS/LES approach with scale-adaptive capabilities is developed. The blending function in the SST model is adopted to prevent the invasion of the von Karman length scale to the RANS region, and the compressibility correction proposed by Wilcox is incorporated to produce a realistic shear layer development in compressible flows. The new model is validated for a subcritical flow past a circular cylinder and a supersonic base flow. Time-averaged turbulent statistics predicted by the new model show fairly good agreement with the experimental data, slight improvements over DES simulations, and are much better than SAS results. The main advantage of the new model over the DES method is that the distribution of the blending function reflects local vortex structures instead of grid spacing in the turbulent wake. The sequence of the effect intensity of the compressibility correction from strong to weak is SAS, the new model and DES.     

Hybrid RANS/LES computations of plane impinging jets with DES and PANS models

The qualities of a DES (Detached Eddy Simulation) and a PANS (Partially-Averaged Navier–Stokes) hybrid RANS/LES model, both based on the k–ω RANS turbulence model of Wilcox (2008, “Formulation of the k–ω turbulence model revisited” AIAA J., 46: 2823–2838), are analysed for simulation of plane impinging jets at a high nozzle-plate distance (H/B = 10, Re = 13,500; H is nozzle-plate distance, B is slot width; Reynolds number based on slot width and maximum velocity at nozzle exit) and a low nozzle-plate distance (H/B = 4, Re = 20,000). The mean velocity field, fluctuating velocity components, Reynolds stresses and skin friction at the impingement plate are compared with experimental data and LES (Large Eddy Simulation) results. The k–ω DES model is a double substitution type, following Davidson and Peng (2003, “Hybrid LES–RANS modelling: a one-equation SGS model combined with a k–ω model for predicting recirculating flows” Int. J. Numer. Meth. Fluids, 43: 1003–1018). This means that the turbulent length scale is replaced by the grid size in the destruction term of the k-equation and in the eddy viscosity formula. The k–ω PANS model is derived following Girimaji (2006, “Partially-Averaged Navier–Stokes model for turbulence: a Reynolds-Averaged Navier–Stokes to Direct Numerical Simulation bridging method” J. Appl. Mech., 73: 413–421). The turbulent length scale in the PANS model is constructed from the total turbulent kinetic energy and the sub-filter dissipation rate. Both hybrid models change between RANS (Reynolds-Averaged Navier–Stokes) and LES based on the cube root of the cell volume. The hybrid techniques, in contrast to RANS, are able to reproduce the turbulent flow dynamics in the shear layers of the impacting jet. The change from RANS to LES is much slower however for the PANS model than for the DES model on fine enough grids. This delays the break-up process of the vortices generated in the shear layers with as a consequence that the DES model produces better results than the PANS model.     

Simulation of wing-body junction flows with hybrid RANS/LES methods

In this paper, flows past two wing-body junctions, the Rood at zero angle of attack and NASA TN D-712 at 12.5° angle of attack, are investigated with two Reynolds-Averaged Navier-Stokes (RANS) and large eddy simulation (LES) hybrid methods. One is detached eddy simulation (DES) and the other is delayed-DES, both are based on a weakly nonlinear two-equation k–ω model. While the RANS method can predict the mean flow behaviours reasonably accurately, its performance for the turbulent kinetic energy and shear stress, as compared with available experimental data, is not satisfactory. DES, through introducing a length scale in the dissipation terms of the turbulent kinetic energy equation, delivers flow separation, a vortex or the onset of vortex breakdown too early. DDES, with its delayed effect, shows a great improvement in flow structures and turbulence characteristics, and agrees well with measurements.     

Performances of LES and RANS Models for Simulation of Complex Flows in a Coaxial Jet Mixer

Flow and mixing processes in a classical coaxial jet mixer have been investigated numerically. Calculations have been performed using three Large Eddy Simulation models and three unsteady RANS models. The time averaged mixture fraction and axial velocity, their rms values and energy spectra are compared with LIF and LDA measurements for both j- and r-modes of the jet mixer flow. A special attention is paid to the ability of different models to reproduce unsteady effects. The analysis demonstrates the superiority of the LES method with the dynamic mixed SGS model (DMM) with respect to other RANS and LES models.     

Turbulent flow and loading on a tidal stream turbine by LES and RANS

This paper presents results from numerical simulations of a 3-bladed horizontal axis tidal stream turbine. Initially, Reynolds Averaged Navier Stokes (RANS) k–ω Shear Stress Transport eddy-viscosity and Launder–Reece–Rodi models were used for code validation and testing of a newly implemented sliding mesh technique for an unstructured finite volume code. Wall- and blade-resolved large-eddy simulations (LES) were then performed to study the complete geometry at various tip speed ratios (TSR). Thrust and power coefficients were compared to published experimental measurements obtained from a towing tank for a range of TSR (4, 5, 6, 7, 8, 9 and 10) at a fixed hub pitch angle. A strong meandering is observed downstream of the supporting tower due to interaction between the detached tip vortices and vortex shedding from the support structure. The wake profiles and rate of recovery of velocity deficit show high sensitivity to the upstream turbulence intensities. However, the mean thrust and power coefficients were found to be less sensitive to the upstream turbulence. Comparisons between RANS and LES are also presented for the mean sectional blade pressures and mean wake velocity profiles. The paper also presents an overview of modelling and numerical issues relating to simulations for such rotating geometries.     

Assessment of Reynolds stresses tensor reconstruction methods for synthetic turbulent inflow conditions. Application to hybrid RANS/LES methods

Hybrid or zonal RANS/LES approaches are recognized as the most promising way to accurately simulate complex unsteady flows under current computational limitations. One still open issue concerns the transition from a RANS to a LES or WMLES resolution in the stream-wise direction, when near wall turbulence is involved. Turbulence content has then to be prescribed at the transition to prevent from turbulence decay leading to possible flow relaminarization. The present paper aims to propose an efficient way to generate this switch, within the flow, based on a synthetic turbulence inflow condition, named Synthetic Eddy Method (SEM). As the knowledge of the whole Reynolds stresses is often missing, the scope of this paper is focused on generating the quantities required at the SEM inlet from a RANS calculation, namely the first and second order statistics of the aerodynamic field. Three different methods based on two different approaches are presented and their capability to accurately generate the needed aerodynamic values is investigated. Then, the ability of the combination SEM + Reconstruction method to manufacture well-behaved turbulence is demonstrated through spatially developing flat plate turbulent boundary layers. In the mean time, important intrinsic features of the Synthetic Eddy method are pointed out. The necessity of introducing, within the SEM, accurate data, with regards to the outer part of the boundary layer, is illustrated. Finally, user’s guidelines are given depending on the Reynolds number based on the momentum thickness, since one method is suitable for low Reynolds number while the second is dedicated to high ones with a transition located around Re_θ = 3000.     

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.     

Hybrid RANS/LES of flow and heat transfer in round impinging jets

Fluid flow and convective heat transfer predictions are presented of round impinging jets for several combinations of nozzle-plate distances H/D = 2, 6 and 13.5 (where D is the nozzle diameter) and Reynolds numbers Re = 5000, 23,000 and 70,000 with the newest version of the k-ω model of Wilcox (2008) and three hybrid RANS/LES models. In the RANS mode of the hybrid RANS/LES models, the k-ω model is recovered. Three formulations are considered to activate the LES mode. The first model is similar to the hybrid models of Davidson and Peng (2003) and Kok et al. (2004). The turbulent length scale is replaced by the grid size in the destruction term of the k-equation and in the definition of the RANS eddy viscosity. As grid size, a maximum measure of the hexahedral grid cell is used. The second model has the same k-equation, but the eddy viscosity is the minimum of the k-ω eddy viscosity and the Smagorinsky eddy viscosity, following a proposal by Batten et al. (2004). The Smagorinsky eddy viscosity is formed with the cube root of the cell volume. The third model has, again, the same k-equation, but has an eddy viscosity which is an intermediate between the eddy viscosities of the first and second models. This is reached by using the cube root of the cell volume in the eddy viscosity formula of the first model.The simulation results are compared with experimental data for the high Reynolds number cases Re = 23,000 and Re = 70,000 and LES data for the low-Reynolds number case Re = 5000. The Reynolds numbers are defined with the nozzle diameter and the bulk velocity at nozzle outlet. At low nozzle-plate distance (the impingement plate is in the core of the jet), turbulent kinetic energy is overpredicted by RANS in the stagnation flow region. This leads to overprediction of the heat transfer rate along the impingement plate in the impact zone. At high nozzle-plate distance (the impingement plate is in the mixed-out region of the jet), the turbulence mixing is underpredicted by RANS in the shear layer of the jet which gives a too high length of the jet core. This also results in overprediction of the heat transfer rate in the impingement zone caused by too big temperature gradients at impingement.All hybrid RANS/LES models are able to correct the heat transfer overprediction of the RANS model. For good predictions at low nozzle-plate distance, it is necessary to sufficiently resolve the formation and development of the near-wall vortices in the jet impingement region. At high nozzle-plate distance, the essence is to capture the evolution and breakup of the flow unsteadiness in the shear layer of the jet, so that accurate mean and fluctuating velocity profiles are obtained in the impingement region. Although the models have a quite different theoretical justification and generate a quite different eddy viscosity in some flow regions, their overall results are very comparable. The reason is that in zones that are crucial for the results, the models behave similarly.     

DNS,LES and RANS of turbulent heat transfer in boundary layer with suddenly changing wall thermal conditions

The objectives of this study are to investigate a thermal field in a turbulent boundary layer with suddenly changing wall thermal conditions by means of direct numerical simulation (DNS), and to evaluate predictions of a turbulence model in such a thermal field, in which DNS of spatially developing boundary layers with heat transfer can be conducted using the generation of turbulent inflow data as a method. In this study, two types of wall thermal condition are investigated using DNS and predicted by large eddy simulation (LES) and Reynolds-averaged Navier–Stokes equation simulation (RANS). In the first case, the velocity boundary layer only develops in the entrance of simulation, and the flat plate is heated from the halfway point, i.e., the adiabatic wall condition is adopted in the entrance, and the entrance region of thermal field in turbulence is simulated. Then, the thermal boundary layer develops along a constant temperature wall followed by adiabatic wall. In the second case, velocity and thermal boundary layers simultaneously develop, and the wall thermal condition is changed from a constant temperature to an adiabatic wall in the downstream region. DNS results clearly show the statistics and structure of turbulent heat transfer in a constant temperature wall followed by an adiabatic wall. In the first case, the entrance region of thermal field in turbulence can be also observed. Thus, both the development and the entrance regions in thermal fields can be explored, and the effects upstream of the thermal field on the adiabatic region are investigated. On the other hand, evaluations of predictions by LES and RANS are conducted using DNS results. The predictions of both LES and RANS almost agree with the DNS results in both cases, but the predicted temperature variances near the wall by RANS give different results as compared with DNS. This is because the dissipation rate of temperature variance is difficult to predict by the present RANS, which is found by the evaluation using DNS results.     

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.     

The complementary RANS equations for the simulation of viscous flows

A complementary set of Reynolds‐averaged Navier–Stokes (RANS) equations has been developed for steady incompressible, turbulent flows. The method is based on the Helmholtz decomposition of the velocity vector field into a viscous and a potential components. In the complementary RANS solver a potential solution coexists with a viscous solution with the purpose of contributing to a fastest decay of the viscous solution in the far field. The proposed complementary RANS equations have been validated for steady laminar and turbulent flows. The computational results show that the complementary RANS solver is able to produce less grid‐dependent solutions than a conventional RANS solver. Copyright © 2005 John Wiley & Sons, Ltd.