LES of incompressible heat and fluid flows past a square cylinder at high Reynolds numbers

This paper presents large eddy simulation (LES) results of incompressible heat and fluid flows around a square cylinder (SC) at zero incident angle at high Reynolds numbers (Re) in the range from 1.25×10⁵ to 3.5×10⁵. LES results are obtained on the basis of swirling strength based sub-grid model, and a higher order upwind scheme developed with respect to the Taylor expansion. It was found that, for the zero incident SC wake flows at a Reynolds number in the range {Re₅ = Re/10⁵ ∈ [1.25, 3.5]}, the Strouhal number equals to 0.1079, completely independent of the Reynolds number; the coefficient of drag is around 1.835 with an uncertainty of about 1.9%, almost non-sensitive to the Re. When Re is beyond 3.0×10⁵, the time-averaged peak value of sub-grid viscosity is over 340, implying that the role of sub-grid model is crucial in some regions where vortex motion is active and vortex interaction is intense. The time–spanwise (t-z) averaged sub-grid viscosity ratio profiles and the profiles of fluctuations of the sub-grid viscosity ratio and velocity components at four locations downstream of the SC are presented. The fields of the t-z averaged sub-grid viscosity ratio, and the instantaneous fields of streamwise and spanwise vorticities are also reported and discussed. The predicted mean Nusselt number is compared with empirical correlations, revealing that swirling strength based LES has its potential in predicting natural and industrial flows.     

Wall modeling for implicit large-eddy simulation and immersed-interface methods

We propose and analyze a wall model based on the turbulent boundary layer equations (TBLE) for implicit large-eddy simulation (LES) of high Reynolds number wall-bounded flows in conjunction with a conservative immersed-interface method for mapping complex boundaries onto Cartesian meshes. Both implicit subgrid-scale model and immersed-interface treatment of boundaries offer high computational efficiency for complex flow configurations. The wall model operates directly on the Cartesian computational mesh without the need for a dual boundary-conforming mesh. The combination of wall model and implicit LES is investigated in detail for turbulent channel flow at friction Reynolds numbers from Re _τ  = 395 up to Re _τ =100,000 on very coarse meshes. The TBLE wall model with implicit LES gives results of better quality than current explicit LES based on eddy viscosity subgrid-scale models with similar wall models. A straightforward formulation of the wall model performs well at moderately large Reynolds numbers. A logarithmic-layer mismatch, observed only at very large Reynolds numbers, is removed by introducing a new structure-based damping function. The performance of the overall approach is assessed for two generic configurations with flow separation: the backward-facing step at Re _h = 5,000 and the periodic hill at Re _H = 10,595 and Re _H = 37,000 on very coarse meshes. The results confirm the observations made for the channel flow with respect to the good prediction quality and indicate that the combination of implicit LES, immersed-interface method, and TBLE-based wall modeling is a viable approach for simulating complex aerodynamic flows at high Reynolds numbers. They also reflect the limitations of TBLE-based wall models.     

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.     

Vortices for computing: the engines of turbulence simulation

Vortices have been described as the “sinews of turbulence”. They are also, increasingly, the computational engines driving numerical simulations of turbulence. In this paper, I review some recent advances in vortex-based numerical methods for simulating high Reynolds number turbulent flows. I focus on coherent vortex simulation, where nonlinear wavelet filtering is used to identify and track the few high energy multiscale vortices that dominate the flow dynamics. This filtering drastically reduces the computational complexity for high Reynolds number simulations, e.g. by a factor of 1000 for fluid–structure interaction calculations (Kevlahan and Vasilyevvon in SIAM J Sci Comput 26(6):1894–1915, 2005). It also has the advantage of decomposing the flow into two physically important components: coherent vortices and background noise. In addition to its computational efficiency, this decomposition provides a way of directly estimating how space and space–time intermittency scales with Reynolds number, Re ^α . Comparing α to its non-intermittent values gives a realistic Reynolds number upper bound for adaptive direct numerical simulation of turbulent flows. This direct measure of intermittency also guides the development of new mathematical theories for the structure of high Reynolds number turbulence.     

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.     

Large Eddy Simulations Using an Unstructured Grid Compressible Navier - Stokes Algorithm

Large Eddy Simulation (LES) of the decay of isotropic turbulence and of channel flow has been performed using an explicit second-order unstructured grid algorithm for tetrahedral cells. The algorithm solves for cell-averaged values using the finite volume form of the unsteady compressible Jittered Navier-Stokes equations. The inviscid fluxes are obtained from Godunov's exact Riemann solver. Reconstruction of the flow variables to the left and right sides of each face is performed using least squares or Frink's method. The viscous fluxes and heat transfer are obtained by application of Gauss' theorem. LES of the decay of nearly incompressible isotropic turbulence has been performed using two models for the SGS stresses: the Monotone Integrated Large Eddy Simulation (MILES) approach, wherein the inherent numerical dissipation models the sub-grid scale (SGS) dissipation, and the Smagorinsky SGS model. The results using the MILES approach with least squares reconstruction show good agreement with incompressible experimental data. The contribution of the Smagorinsky SGS model is negligible. LES of turbulent channel flow was performed at a Reynolds number (based on channel height and bulk velocity) of 5600 and Mach number of 0.5 (at which compressibility effects are minimal) using Smagorinsky's SGS model with van Driest damping. The results show good agreement with experimental data and direct numerical simulations for incompressible channel flow. The SGS eddy viscosity is less than 10% of the molecular viscosity, and therefore the LES is effectively MILES with molecular viscosity.     

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.      

Large-eddy simulation of circular cylinder flow at subcritical Reynolds number: Turbulent wake and sound radiation

The flows past a circular cylinder at Reynolds number 3900 are simulated using large-eddy simulation(LES) and the far-field sound is calculated from the LES results. A low dissipation energy-conserving finite volume scheme is used to discretize the incompressible Navier–Stokes equations. The dynamic global coefficient version of the Vreman's subgrid scale(SGS) model is used to compute the sub-grid stresses. Curle's integral of Lighthill's acoustic analogy is used to extract the sound radiated from the cylinder. The profiles of mean velocity and turbulent fluctuations obtained are consistent with the previous experimental and computational results. The sound radiation at far field exhibits the characteristic of a dipole and directivity. The sound spectra display the-5/3 power law. It is shown that Vreman's SGS model in company with dynamic procedure is suitable for LES of turbulence generated noise.     

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.     

LES prediction of space-time correlations in turbulent shear flows

We compare the space-time correlations calculated from direct numerical simulation(DNS) and large-eddy simulation(LES) of turbulent channel flows.It is found from the comparisons that the LES with an eddy-viscosity subgrid scale(SGS) model over-predicts the space-time correlations than the DNS.The overpredictions are further quantified by the integral scales of directional correlations and convection velocities.A physical argument for the overprediction is provided that the eddy-viscosity SGS model alone does not includes the backscatter effects although it correctly represents the energy dissipations of SGS motions.This argument is confirmed by the recently developed elliptic model for space-time correlations in turbulent shear flows.It suggests that enstrophy is crucial to the LES prediction of spacetime correlations.The random forcing models and stochastic SGS models are proposed to overcome the overpredictions on space-time correlations.     

Coherent Structures and their Frequency Signature in the Separated Shear Layer on the Sides of a Square Cylinder

The purpose of the present work is to study the various specific time scales of the turbulent separating flow around a square cylinder, in order to determine the Reynolds number effect on the separating shear layer, where occurs a transition to turbulence. Unsteady analysis based on large eddy simulation (LES) at intermediate Reynolds numbers and laser doppler velocimetry (LDV) measurements at high Reynolds numbers are carried out. The Reynolds number, based on the cylinder diameter D and the inflow velocity U _o , is ranging from Re?=?50 to Re?=?300,000. A special focus is performed on the coherent structures developing on the sides and in the wake of a square cylinder. For a large Reynolds number range above Re?≈?1,000, both signatures of Von Karman (VK) and Kelvin–Helmholtz (KH) type vortical structures are found on velocity time samples. The combination of their frequency signature is studied based on Fourier and wavelet analysis. In the present study, We observe the occurrence of KH pairings in the separating shear layer on the side of the cylinder, and confirm the intermittency nature of such a shear flow. These issues concerning the structure of the near wake shear layer which were addressed for the round cylinder case in a recent experimental publication (Rajagopalan and Antonia, Exp Fluids 38:393–402, 2005) are of interest in the present flow configuration as well.     

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.     

Large-eddy structures of turbulent swirling flows and methane-air swirling diffusion combustion

Turbulent swirling flows and methane-air swirling diffusion combustion are studied by large-eddy simulation (LES) using a Smagorinsky-Lilly subgrid scale turbulence model and a second-order moment (SOM) SGS combustion model, and also by RANS modeling using the Reynolds Stress equation model with the IPCM+wall and IPCM pressure-strain models and SOM combustion model. The LES statistical results for swirling flows give good agreement with the experimental results, indicating that the adopted subgrid-scale turbulence model is suitable for swirling flows. The LES instantaneous results show the complex vortex shedding pattern in swirling flows. The initially formed large vortex structures soon break up in swirling flows. The LES statistical results of combustion modeling are near the experimental results and are as good as the RANS-SOM modeling results. The LES results show that the size and range of large vortex structures in swirling combustion are different from those of isothermal swirling flows, and the chemical reaction is intensified by the large-eddy vortex structures. The project supported by the Special Funds for Major State Basic Research (G-1999-0222-07). The English text was polished by Keren Wang.     

Transient growth and bypass transition in stenotic flow with a physiological waveform

A direct analysis method is applied to compute optimal transient growth initial conditions for physiologically relevant pulsatile flows in a smooth axisymmetric stenosis with 75% occlusion. The flow waveform employed represents phase-average measurements obtained in the human common carotid artery. Floquet analysis shows that the periodic flow is stable to infinitesimal eigenmodal-type perturbations that would grow from one cycle to the next at the Reynolds numbers considered. However, the same flows display explosive transient growth of optimal disturbances, with our analysis predicting disturbance energy growths of order 10²⁵ within half a pulse period at a mean bulk flow Reynolds number Re = 300, which is significantly lower than the physiological value of Re = 450 at this location. Direct numerical simulation at Re = 300 shows that when the base flow is perturbed a small amount with the optimal growth initial condition, the disturbance grows rapidly in time in agreement with the linear analysis, and saturates to provide a locally turbulent state within half a pulse period. This transition resulting from non-normal growth mechanisms shows the flow exhibits bypass transition to turbulence. Our analysis suggests that this route to localized turbulent states could be relatively common in human arterial flows.     

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.     

LES Study of Turbulent Boundary Layer Over a Smooth and a Rough 2D Hill Model

Large eddy simulation (LES) is carried out to investigate the turbulent boundary-layer flows over a hill-shaped model with a steep or relatively moderate slope at moderately high Reynolds numbers (Re = O(10³)) defined by the hill height and the velocity at the hill height. The study focuses on the effects of surface roughness and curvature. For Sub-grid Scale (SGS) modeling of LES, both the dynamic Smagorinsky model (DSM) and the dynamic mixed model (DMM) are applied. The behavior of the separated shear layer and the vortex motion are affected by the oncoming turbulence, such that the shear layer comes close to the ground surface, or the size of a separation region becomes small because of the earlier instability of the separated shear layer. Appropriate measures are required to generate the inflow turbulence. The methods of Lund et al. (J. Comput. Phys., 140:233–258, 1998) and Nozawa and Tamura (J. Wind Eng. Ind. Aerodyn., 90:1151–1162, 2002; The 4th European and African Conference on Wind Engineering, 1–6, 2005) are employed to simulate the smooth- and rough-wall turbulent boundary layers in order to generate time-sequential data of inflow turbulence. This paper discusses the unsteady phenomena of the wake flows over the smooth and rough 2D hill-shaped obstacles and aims to clarify the roughness effects on the flow patterns and the turbulence statistics distorted by the hill. Numerical validation is conducted by comparing the simulation results with wind tunnel experiment data for the same hill shape at almost the same Re. The applicability of DSM and DMM are discussed, focusing on the recirculation region behind a steep hill.     

External Intermittency Simulation in Turbulent Round Jets

Direct numerical and large eddy simulation (DNS and LES) are applied to study passive scalar mixing and intermittency in turbulent round jets. Both simulation techniques are applied to the case of a low Reynolds number jet with Re = 2,400, whilst LES is also used to predict a high Re = 68,000 flow. Comparison between time-averaged results for the scalar field of the low Re case demonstrate reasonable agreement between the DNS and LES, and with experimental data and the predictions of other authors. Scalar probability density functions (pdfs) for this jet derived from the simulations are also in reasonable accord, although the DNS results demonstrate the more rapid influence of scalar intermittency with radial distance in the jet. This is reflected in derived intermittency profiles, with LES generally giving profiles that are too broad compared to equivalent DNS results, with too low a rate of decay with radial distance. In contrast, good agreement is in general found between LES predictions and experimental data for the mixing field, scalar pdfs and external intermittency in the high Reynolds number jet. Overall, the work described indicates that improved sub-grid scale modelling for use with LES may be beneficial in improving the accuracy of external intermittency predictions by this technique over the wide range of Reynolds numbers of practical interest.     

A Non-Linear SGS Model Based On The Spatial Velocity Increment

A new subgrid scale (SGS) modelling concept for large-eddy simulation (LES) of incompressible flow is proposed based on the three-dimensional spatial velocity increment δ u _i . The new model is inspired by the structure function formulation developed by Métais and Lesieur [39] and applied in the context of the scale similarity type formulation. First, the similarity between the SGS stress tensor τ _ij and the velocity increment tensor Q _ij = δ u _i δ u _j is analyzed analytically and numerically using a priori tests of fully developed pipe flow at Re _τ = 180. Both forward and backward energy transfers between resolved and unresolved scales of the flow are well predicted with a SGS model based on Q _ij . Secondly, a posteriori tests are performed for two families of turbulent shear flows. LES of fully developed pipe flow up to Re _τ = 520 and LES of round turbulent jet at Re _D = 25000 carried out with a dynamic version of the model provide promising results that confirm the power of this approach for wall-bounded and free shear flows.     

A parametric study of LES on laminar-turbulent transitional flows past an airfoil

Low-Reynolds-number aerodynamic performance of small-sized air vehicles is an area of increasing interest. In this study, low-Reynolds-number flows past an SD7003 airfoil are investigated to understand important viscous features of laminar separation and transitional flow followed by the complicated behavior of the flow reattachment process. In order to satisfy the three-dimensional (3D) requirement of the code, a simple “3D wing” is constructed from a two-dimensional (2D) airfoil. A parametric study of large eddy simulation (LES) on the airfoil flows at Re = 60,000 is performed. Effects of grid resolution and sub-grid scale (SGS) models are investigated. Although 3D effects cannot be accurately captured owing to the limitation of the grid resolution in the spanwise direction, the preliminary LES calculations do reveal some important flow characteristics such as leading-edge laminar separation and vortex shedding from the primary laminar separation bubble on the low-Reynolds-number airfoil.