Implicit large-eddy simulation applied to turbulent channel flow with periodic constrictions

The subgrid-scale (SGS) model in a large-eddy simulation (LES) operates on a range of scales which is marginally resolved by discretization schemes. Accordingly, the discretization scheme and the subgrid-scale model are linked. One can exploit this link by developing discretization methods from subgrid-scale models, or the converse. Approaches where SGS models and numerical discretizations are fully merged are called implicit LES (ILES). Recently, we have proposed a systematic framework for the design, analysis, and optimization of nonlinear discretization schemes for implicit LES. In this framework parameters inherent to the discretization scheme are determined in such a way that the numerical truncation error acts as a physically motivated SGS model. The resulting so-called adaptive local deconvolution method (ALDM) for implicit LES allows for reliable predictions of isotropic forced and decaying turbulence and of unbounded transitional flows for a wide range of Reynolds numbers. In the present paper, ALDM is evaluated for the separated flow through a channel with streamwise-periodic constrictions at two Reynolds numbers Re = 2,808 and Re = 10,595. We demonstrate that, although model parameters of ALDM have been determined for isotropic turbulence at infinite Reynolds number, it successfully predicts mean flow and turbulence statistics in the considered physically complex, anisotropic, and inhomogeneous flow regime. It is shown that the implicit model performs at least as well as an established explicit model.      

Parallel FEM LES with one-equation subgrid-scale model for incompressible flows

This article develops a parallel large-eddy simulation (LES) with a one-equation subgrid-scale (SGS) model based on the Galerkin finite element method and three-dimensional (3D) brick elements. The governing filtered Navier–Stokes equations were solved by a second-order accurate fractional-step method, which decomposed the implicit velocity–pressure coupling in incompressible flow and segregated the solution to the advection and diffusion terms. The transport equation for the SGS turbulent kinetic energy was solved to calculate the SGS processes. This FEM LES model was applied to study the turbulence of the benchmark open channel flow at a Reynolds number Re_τ = 180 (based on the friction velocity and channel height) using different model constants and grid resolutions. By comparing the turbulence statistics calculated by the current model with those obtained from direct numerical simulation (DNS) and experiments in literature, an optimum set of model constants for the current FEM LES model was established. The budgets of turbulent kinetic energy and vertical Reynolds stress were then analysed for the open channel flow. Finally, the flow structures were visualised to further reveal some important characteristics. It was demonstrated that the current model with the optimum model constants can predict well the organised structure near the wall and free surface, and can be further applied to other fundamental and engineering applications.     

An efficient very large eddy simulation model for simulation of turbulent flow

Among the various hybrid methodologies, Speziale's very large eddy simulation (VLES) is one that was proposed very early. It is a unified simulation approach that can change seamlessly from Reynolds Averaged Navier–Stokes (RANS) to direct numerical simulation (DNS) depending on the numerical resolution. The present study proposes a new improved variant of the original VLES model. The advantages are achieved in two ways: (i) RANS simulation can be recovered near the wall which is similar to the detached eddy simulation concept; (ii) a LES subgrid scale model can be reached by the introduction of a third length scale, that is, the integral turbulence length scale. Thus, the new model can provide a proper LES mode between the RANS and DNS limits. This new methodology is implemented in the standard k ? ? model. Applications are conducted for the turbulent channel flow at Reynolds number of Re_τ = 395, periodic hill flow at Re = 10,595, and turbulent flow past a square cylinder at Re = 22,000. In comparison with the available experimental data, DNS or LES, the new VLES model produces better predictions than the original VLES model. Furthermore, it is demonstrated that the new method is quite efficient in resolving the large flow structures and can give satisfactory predictions on a coarse mesh. Copyright © 2012 John Wiley & Sons, Ltd.     

Simulations of Turbulent Flow in a Plane Asymmetric Diffuser

Large-eddy simulations (LES) of a planar, asymmetric diffuser flow have been performed. The diverging angle of the inclined wall of the diffuser is chosen as 8.5°, a case for which recent experimental data are available. Reasonable agreement between the LES and the experiments is obtained. The numerical method is further validated for diffuser flow with the diffuser wall inclined at a diverging angle of 10°, which has served as a test case for a number of experimental as well as numerical studies in the literature (LES, RANS). For the present results, the subgrid-scale stresses have been closed using the dynamic Smagorinsky model. A resolution study has been performed, highlighting the disparity of the relevant temporal and spatial scales and thus the sensitivity of the simulation results to the specific numerical grids used. The effect of different Reynolds numbers of the inflowing, fully turbulent channel flow has been studied, in particular, Re _b  = 4,500, Re _b  = 9,000 and Re _b  = 20,000 with Re _b being the Reynolds number based on the bulk velocity and channel half width. The results consistently show that by increasing the Reynolds number a clear trend towards a larger separated region is evident; at least for the studied, comparably low Reynolds-number regime. It is further shown that the small separated region occurring at the diffuser throat shows the opposite behaviour as the main separation region, i.e. the flow is separating less with higher Re _b . Moreover, the influence of the Reynolds number on the internal layer occurring at the non-inclined wall described in a recent study has also been assessed. It can be concluded that this region close to the upper, straight wall, is more distinct for larger Re _b . Additionally, the influence of temporal correlations arising from the commonly used periodic turbulent channel flow as inflow condition (similar to a precursor simulation) for the diffuser is assessed.     

A Lagrangian Mixed Subgrid-Scale Model in Generalized Coordinates

This paper presents the formulation of a mixed dynamic subgrid-scale model in non-Cartesian geometries suitable for the study of complex flows. Following the approach developed by Jordan [J. Comput. Phys. 148, 322 (1999)], the variables are first transformed into a contravariant form and then filtered in the computational space. A dynamic localized mixed model, previously developed within the Cartesian framework has been entirely re-formulated for non-orthogonal meshes. The model performance was evaluated by carrying out two tests. First, a plane channel flow at Re_τ = 395 was simulated using both Cartesian and curvilinear grids; the results show that the model formulation is consistent and insensitive to grid distortion, and compares well with the reference data. Then, computations of the turbulent flow over a two-dimensional channel with a wavy wall were performed. Accurate first- and second-order statistics were obtained using relatively coarse grids. This revised version was published online in July 2006 with corrections to the Cover Date.     

Leray-α Regularization of the Smagorinsky-Closed Filtered Equations for Turbulent Jets at High Reynolds Numbers

The article reports on blending of the Leray-α regularization with the conventional Smagorinsky subgrid-scale closure as an option for large-eddy-simulation of turbulent flows at very high Reynolds number on coarse meshes. The model has been tested in the self-similar far-field region of a jet at a range of Reynolds numbers spanning over two decades (4×10³, 4×10⁴ and 4×10⁵) on two very coarse meshes of 2×10⁵ and 3×10⁴ mesh cells. The results are compared with the well-resolved DNS for $Re_D=4\times 10^3$ on 15 million cells and experimental data for higher Re numbers. While the pure Leray-α can fail badly at high Re numbers on very coarse meshes, a blending of the two strategies by adding a small amount of extra-dissipation performs well even at a huge jet Reynolds number of $Re_D=4\times 10^5$ on a very coarse mesh (2×10⁵ cells), despite the ratio of the typical mesh spacing to the Kolmogorov length exceeding 300. It is found that the main prerequisite for successful LES, both for the classic Smagorinsky and the blended Leray-α/Smagorinsky model, is to resolve the shear-length $L_s=\sqrt{\varepsilon/{\cal S}^3}$ (where ${\cal S}$ is the shear-rate modulus), defined by the constraint Δ/L _s ?<?1, where Δ is the typical mesh-cell size. For the mixed Leray-α/Smagorinsky model the regularization parameter should also be related to the shear-length rather than the local mesh size or Reynolds number, for which we propose a guide criterion α?=?0.15÷0.3 L _s .     

Surface‐sampled simulations of turbulent flow at high Reynolds number

A new approach to turbulence simulation, based on a combination of large eddy simulation (LES) for the whole flow and an array of non–space‐filling quasi‐direct numerical simulations (QDNS), which sample the response of near‐wall turbulence to large‐scale forcing, is proposed and evaluated. The technique overcomes some of the cost limitations of turbulence simulation, since the main flow is treated with a coarse‐grid LES, with the equivalent of wall functions supplied by the near‐wall sampled QDNS. Two cases are tested, at friction Reynolds number Re_τ=4200 and 20000. The total grid point count for the first case is less than half a million and less than 2 million for the second case, with the calculations only requiring a desktop computer. A good agreement with published direct numerical simulation (DNS) is found at Re_τ=4200, both in the mean velocity profile and the streamwise velocity fluctuation statistics, which correctly show a substantial increase in near‐wall turbulence levels due to a modulation of near‐wall streaks by large‐scale structures. The trend continues at Re_τ=20000, in agreement with experiment, which represents one of the major achievements of the new approach. A number of detailed aspects of the model, including numerical resolution, LES‐QDNS coupling strategy and subgrid model are explored. A low level of grid sensitivity is demonstrated for both the QDNS and LES aspects. Since the method does not assume a law of the wall, it can in principle be applied to flows that are out of equilibrium.     

LES and RANS for Turbulent Flow over Arrays of Wall-Mounted Obstacles

Large-eddy simulation (LES) has been applied to calculate the turbulent flow over staggered wall-mounted cubes and staggered random arrays of obstacles with area density 25%, at Reynolds numbers between 5 × 10³ and 5 10⁶, based on the free stream velocity and the obstacle height. Re = 5 × 10³ data were intensively validated against direct numerical simulation (DNS) results at the same Re and experimental data obtained in a boundary layer developing over an identical roughness and at a rather higher Re. The results collectively confirm that Reynolds number dependency is very weak, principally because the surface drag is predominantly form drag and the turbulence production process is at scales comparable to the roughness element sizes. LES is thus able to simulate turbulent flow over the urban-like obstacles at high Re with grids that would be far too coarse for adequate computation of corresponding smooth-wall flows. Comparison between LES and steady Reynolds-averaged Navier-Stokes (RANS) results are included, emphasising that the latter are inadequate, especially within the canopy region.     

Development of a Two-velocities Hybrid RANS-LES Model and its Application to a Trailing Edge Flow

The flow around a trailing edge is computed with a new hybrid method designed to more clearly separate the effects of total and sub-grid turbulent stress-modelling on the time-averaged and instantaneous velocity fields, and in turn, mean momentum and kinetic energy balances. These two velocity fields independently define Reynolds averaged and sub-grid-scale viscosities, and distinct stresses, at the same location. In particular, resolved eddies can emerge, or sweep in and out of the Reynolds averaged near wall layer, without being dampened by higher levels of the viscosity in this RANS dominated layer. The two-field hybrid model, first tested on channel flows, gives accurate predictions of mean velocities and stresses for different Reynolds numbers and coarse meshes. For the trailing edge flow the results of the hybrid model are close to the reference fine LES for mean velocity and turbulent content, whereas the DES-SST on the same coarse mesh gives too early separation.     

An improved anisotropy-resolving subgrid-scale model for flows in laminar–turbulent transition region

Some types of mixed subgrid-scale (SGS) models combining an isotropic eddy-viscosity model and a scale-similarity model can be used to effectively improve the accuracy of large eddy simulation (LES) in predicting wall turbulence. Abe (2013) has recently proposed a stabilized mixed model that maintains its computational stability through a unique procedure that prevents the energy transfer between the grid-scale (GS) and SGS components induced by the scale-similarity term. At the same time, since this model can successfully predict the anisotropy of the SGS stress, the predictive performance, particularly at coarse grid resolutions, is remarkably improved in comparison with other mixed models. However, since the stabilized anisotropy-resolving SGS model includes a transport equation of the SGS turbulence energy, k_SGS, containing a production term proportional to the square root of k_SGS, its applicability to flows with both laminar and turbulent regions is not so high. This is because such a production term causes k_SGS to self-reproduce. Consequently, the laminar–turbulent transition region predicted by this model depends on the inflow or initial condition of k_SGS. To resolve these issues, in the present study, the mixed-timescale (MTS) SGS model proposed by Inagaki et al. (2005) is introduced into the stabilized mixed model as the isotropic eddy-viscosity part and the production term in the k_SGS transport equation. In the MTS model, the SGS turbulence energy, k_es, estimated by filtering the instantaneous flow field is used. Since the k_es approaches zero by itself in the laminar flow region, the self-reproduction property brought about by using the conventional k_SGS transport equation model is eliminated in this modified model. Therefore, this modification is expected to enhance the applicability of the model to flows with both laminar and turbulent regions. The model performance is tested in plane channel flows with different Reynolds numbers and in a backward-facing step flow. The results demonstrate that the proposed model successfully predicts a parabolic velocity profile under laminar flow conditions and reduces the dependence on the grid resolution to the same degree as the unmodified model by Abe (2013) for turbulent flow conditions. Moreover, it is shown that the present model is effective at transitional Reynolds numbers. Furthermore, the present model successfully provides accurate results for the backward-facing step flow with various grid resolutions. Thus, the proposed model is considered to be a refined anisotropy-resolving SGS model applicable to laminar, transitional, and turbulent flows.     

Numerical study of an oscillatory turbulent flow over a flat plate

Oscillatory turbulent flow over a flat plate is studied using large eddy simulation (LES) and Reynolds-average Navier-Stokes (RANS) methods. A dynamic subgrid-scale model is employed in LES and Saffman's turbulence model is used in RANS. The flow behaviors are discussed for the accelerating and decelerating phases during the oscillating cycle. The friction force on the wall and its phase shift from laminar to turbulent regime are also investigated for different Reynolds numbers. The project supported by the Youngster Funding of Academia Sinica and by the National Natural Science Foundation of China     

On the performance of WENO/TENO schemes to resolve turbulence in DNS/LES of high‐speed compressible flows

High‐speed compressible turbulent flows typically contain discontinuities and have been widely modeled using Weighted Essentially Non‐Oscillatory (WENO) schemes due to their high‐order accuracy and sharp shock capturing capability. However, such schemes may damp the small scales of turbulence and result in inaccurate solutions in the context of turbulence‐resolving simulations. In this connection, the recently developed Targeted Essentially Non‐Oscillatory (TENO) schemes, including adaptive variants, may offer significant improvements. The present study aims to quantify the potential of these new schemes for a fully turbulent supersonic flow. Specifically, DNS of a compressible turbulent channel flow with M = 1.5 and Re_τ = 222 is conducted using OpenSBLI, a high‐order finite difference computational fluid dynamics framework. This flow configuration is chosen to decouple the effect of flow discontinuities and turbulence and focus on the capability of the aforementioned high‐order schemes to resolve turbulent structures. The effect of the spatial resolution in different directions and coarse grid implicit LES are also evaluated against the WALE LES model. The TENO schemes are found to exhibit significant performance improvements over the WENO schemes in terms of the accuracy of the statistics and the resolution of the three‐dimensional vortical structures. The sixth‐order adaptive TENO scheme is found to produce comparable results to those obtained with nondissipative fourth‐ and sixth‐order central schemes and reference data obtained with spectral methods. Although the most computationally expensive scheme, it is shown that this adaptive scheme can produce satisfactory results if used as an implicit LES model.     

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     

LES-based filter-matrix lattice Boltzmann model for simulating fully developed turbulent channel flow

In this paper, a three-dimensional filter-matrix lattice Boltzmann (FMLB) model based on large eddy simulation (LES) was verified for simulating wall-bounded turbulent flows. The Vreman subgrid-scale model was employed in the present FMLB–LES framework, which had been proved to be capable of predicting turbulent near-wall region accurately. The fully developed turbulent channel flows were performed at a friction Reynolds number Re_τ of 180. The turbulence statistics computed from the present FMLB–LES simulations, including mean stream velocity profile, Reynolds stress profile and root-mean-square velocity fluctuations greed well with the LES results of multiple-relaxation-time (MRT) LB model, and some discrepancies in comparison with those direct numerical simulation (DNS) data of Kim et al. was also observed due to the relatively low grid resolution. Moreover, to investigate the influence of grid resolution on the present LES simulation, a DNS simulation on a finer gird was also implemented by present FMLB–D3Q19 model. Comparisons of detailed computed various turbulence statistics with available benchmark data of DNS showed quite well agreement.     

Numerical study of oscillating boundary layer flow over a flat plate using k–kL–ω turbulence model

Oscillating boundary layer flow over an infinite flat plate at rest was simulated using the k–k_L–ω turbulence model for a Reynolds number range of 32 ⩽ Re_δ ⩽ 10,000 ranging from fully laminar flow to fully turbulent flow. The k–k_L–ω model was validated by comparing the predictions with LES results and experimental results for intermittently turbulent and fully turbulent flow regimes. The good agreement obtained between the k–k_L–ω model prediction with the experimental and LES results indicate that the k–k_L–ω model is able to accurately simulate transient intermittently turbulent flow and as well as accurately predict the onset of turbulence for such oscillatory flows.     

Large-eddy simulation of flow separation on an airfoil at a high angle of attack and Re = 105 using Cartesian grids

Incompressible flow separating from the upper surface of an airfoil at an 18° angle of attack and a Reynolds number of Re = 10⁵, based on the freestream velocity and chord length c, is studied by the means of large-eddy simulation (LES). The numerical method is based on second-order central spatial discretization on a Cartesian grid using an immersed boundary technique. The results are compared with an LES using body-fitted nonorthogonal grids and with experimental data.     

Turbulent Couette–Poiseuille flow with zero wall shear

A particular pressure-driven flow in a plane channel is considered, in which one of the walls moves with a constant speed that makes the mean shear rate and the friction at the moving wall vanish. The Reynolds number considered based on the friction velocity at the stationary wall (u_τ,S) and half the channel height (h) is Re_τ,S = 180. The resulting mean velocity increases monotonically from the stationary to the moving wall and exhibits a substantial logarithmic region. Conventional near-wall streaks are observed only near the stationary wall, whereas the turbulence in the vicinity of the shear-free moving wall is qualitatively different from typical near-wall turbulence. Large-scale-structures (LSS) dominate in the center region and their spanwise spacing increases almost linearly from about 2.3 to 4.2 channel half-heights at this Re_τ,S. The presence of LSS adds to the transport of turbulent kinetic energy from the core region towards the moving wall where the energy production is negligible. Energy is supplied to this particular flow only by the driving pressure gradient and the wall motion enhances this energy input from the mean flow. About half of the supplied mechanical energy is directly lost by viscous dissipation whereas the other half is first converted from mean-flow energy to turbulent kinetic energy and thereafter dissipated.     

Validation of a novel very large eddy simulation method for simulation of turbulent separated flow

The paper describes the validation of a newly developed very LES (VLES) method for the simulation of turbulent separated flow. The new VLES method is a unified simulation approach that can change seamlessly from Reynolds‐averaged Navier–Stokes to DNS depending on the numerical resolution. Four complex test cases are selected to validate the performance of the new method, that is, the flow past a square cylinder at Re = 3000 confined in a channel (with a blockage ratio of 20%), the turbulent flow over a circular cylinder at Re = 3900 as well as Re = 140,000, and a turbulent backward‐facing step flow with a thick incoming boundary layer at Re = 40,000. The simulation results are compared with available experimental, LES, and detached eddy simulation‐type results. The new VLES model performs well overall, and the predictions are satisfactory compared with previous experimental and numerical results. It is observed that the new VLES method is quite efficient for the turbulent flow simulations; that is, good predictions can be obtained using a quite coarse mesh compared with the previous LES method. Discussions of the implementation of the present VLES modeling are also conducted on the basis of the simulations of turbulent channel flow up to high Reynolds number of Re_τ = 4000. The efficiency of the present VLES modeling is also observed in the channel flow simulation. From a practical point of view, this new method has considerable potential for more complex turbulent flow simulations at relative high Reynolds numbers. Copyright © 2013 John Wiley & Sons, Ltd.     

Large Eddy Simulations: How to evaluate resolution

The present paper gives an analysis of fully developed channel flow at Reynolds number of Re=u_τδ/ν=4000 based on the friction velocity, u_τ, and half the channel height, δ. Since the Reynolds number is high, the LES is coupled to a URANS model near the wall (hybrid LES–RANS) which acts as a wall model. It it found that the energy spectra is not a good measure of LES resolution; neither is the ratio of the resolved turbulent kinetic energy to the total one (i.e. resolved plus modelled turbulent kinetic energy). It is suggested that two-point correlations are the best measures for estimating LES resolution. It is commonly assumed that SGS dissipation takes place at high wavenumbers. Energy spectra of the fluctuating velocity gradients show that this is not true; the major part of the SGS dissipation takes place at low to midrange wavenumbers. Furthermore, the energy spectra of the fluctuating velocity gradients reveals that the accuracy of the predicted velocity gradients at the highest resolved wavenumbers is very poor.     

LES of the adverse-pressure gradient turbulent boundary layer

We describe large-eddy simulations (LES) of the flat-plate turbulent boundary layer in the presence of an adverse pressure gradient. The stretched-vortex subgrid-scale model is used in the domain of the flow coupled to a wall model that explicitly accounts for the presence of a finite pressure gradient. The LES are designed to match recent experiments conducted at the University of Melbourne wind tunnel where a plate section with zero pressure gradient is followed by section with constant adverse pressure gradient. First, LES are described at Reynolds numbers based on the local free-stream velocity and the local momentum thickness in the range 6560–13,900 chosen to match the experimental conditions. This is followed by a discussion of further LES at Reynolds numbers at approximately 10 times and 100 times these values, which are well out of range of present day direct numerical simulation and wall-resolved LES. For the lower Reynolds number runs, mean velocity profiles, one-point turbulent statistics of the velocity fluctuations, skin friction and the Clauser and acceleration parameters along the streamwise, adverse pressure-gradient domain are compared to the experimental measurements. For the full range of LES, the relationship of the skin-friction coefficient, in the form of the ratio of the local free-stream velocity to the local friction velocity, to both Reynolds number and the Clauser parameter is explored. At large Reynolds numbers, a region of collapse is found that is well described by a simple log-like empirical relationship over two orders of magnitude. This is expected to be useful for constant adverse-pressure gradient flows. It is concluded that the present adverse pressure gradient boundary layers are far from an equilibrium state.