Shear-improved Smagorinsky Model Research Articles

Effect of inlet shear on turbulent flow past a wall-mounted finite-size square cylinder

The present study analyzes the effect of incoming shear flow on the wake behind a wall-mounted finite-length square cylinder of aspect ratio (AR=7) using large eddy simulation (LES). All the simulations were performed at a Reynolds number (Re) of 10000, based on cylinder width (d) and average inlet velocity (uavg), with different shear parameters, K=0.0,0.025,0.050 and 0.075. The shear-improved Smagorinsky model Lévêque et al. (2007) is used to account for the subgrid scale stress. It is found that the incoming flow shear has a profound effect on the modes of shedding. With increasing shear parameter anti-symmetric modes of shedding tends to dominate along the cylinder height, except close to the free-end where both symmetric and anti-symmetric modes of shedding co-exist. The incoming shear flow has also significant influence on the downwash flow from the free-end, the strength of which decreases with an increase in shear parameter. The resolved turbulent kinetic energy (TKE) associated with the cylinder wake is found to have maximum contribution from the transverse component of normal stress compared to the other components of normal stresses.

Evolution of the flow structures in an elevated jet in crossflow

The characteristic flow features of an elevated square jet in crossflow (EJICF) are studied numerically using large eddy simulation. The effect of jet to crossflow velocity ratio, also called velocity ratio (VR), on the flow field of an elevated jet in crossflow (EJICF) is investigated. All the computations are carried out at a Reynolds number (Re) of 20 000, based on the outer width of the stack (d) and free stream crossflow velocity (U∞), for four different velocity ratios (VR), namely, 0.5, 1.0, 1.5 and 2.0. The stack used in this study has an aspect ratio h/d = 7. The shear-improved Smagorinsky model has been used to account for the subgrid scale stress while solving the filtered three-dimensional unsteady Navier-Stokes equations. The modes of shedding in the stack wake are analyzed using both instantaneous and phase-averaged data. It is found that at a low jet to crossflow velocity ratio (VR = 0.5), the stack wake exhibits two different modes of shedding, symmetric and antisymmetric, similar to the wake of a wall mounted finite-size cylinder. At higher velocity ratios (VR ≥ 1), the stack wake shows the presence of only antisymmetric modes of shedding. It is also found that velocity ratio (VR) has a profound effect on the source of vorticity of the jet shear layer structures near the upwind side. At VR = 0.5, the upstream sides of the jet shear layer structures are found to draw their vortices from the outer surface of the stack boundary layer. At higher VR, they seem to be fed by the vorticity of the boundary layer developed on the inner wall surface of the stack. Both jet vortices and stack wake vortices are found to be present in the jet wake, and the shedding frequency of both the jet wake and the stack wake is found to be same. The spatial evolution of the counter-rotating vortex pair in the case of an EJICF is found to be similar to that of a JICF.

Study of fully-developed turbulent flow and heat transfer in a rotating wavy-walled duct

Finite volume based computations of fully developed flow and heat transfer through rotating wavy-walled ducts using large eddy simulation (LES) has been carried out. The shear improved Smagorinsky model (SISM) is employed to model the unresolved turbulent fluctuations. The wavy-walls of the duct are described by the sine function y=2asin2(πx/L). The geometrical ratios Hmin/Hmax and L/a are kept fixed to 0.2 and 8 respectively. The effect of rotation on the fluid flow and heat transfer characteristics are presented. All the computations are at a Reynolds number of 5000 and the rotation number is varied in the range, 0–0.5. It has been observed that the pressure drop across the wavy-walled duct varies with increasing rotation number. It is also found out that with rotation, the heat transfer increases on the trailing wall while the leading wall shows the opposite trend. Both Nusselt number and pressure drop for the wavy-walled duct is observed to be less than the corresponding values in ribbed duct geometry.

Large eddy simulation of rotating turbulent flows and heat transfer by the lattice Boltzmann method

Due to its advantage in parallel efficiency and wall treatment over conventional Navier-Stokes equation-based methods, the lattice Boltzmann method (LBM) has emerged as an efficient tool in simulating turbulent heat and fluid flows. To properly simulate the rotating turbulent flow and heat transfer, which plays a pivotal role in tremendous engineering devices such as gas turbines, wind turbines, centrifugal compressors, and rotary machines, the lattice Boltzmann equations must be reformulated in a rotating coordinate. In this study, a single-rotating reference frame (SRF) formulation of the Boltzmann equations is newly proposed combined with a subgrid scale model for the large eddy simulation of rotating turbulent flows and heat transfer. The subgrid scale closure is modeled by a shear-improved Smagorinsky model. Since the strain rates are also locally determined by the non-equilibrium part of the distribution function, the calculation process is entirely local. The pressure-driven turbulent channel flow with spanwise rotation and heat transfer is used for validating the approach. The Reynolds number characterized by the friction velocity and channel half height is fixed at 194, whereas the rotation number in terms of the friction velocity and channel height ranges from 0 to 3.0. A working fluid of air is chosen, which corresponds to a Prandtl number of 0.71. Calculated results are demonstrated in terms of mean velocity, Reynolds stress, root mean square (RMS) velocity fluctuations, mean temperature, RMS temperature fluctuations, and turbulent heat flux. Good agreement is found between the present LBM predictions and previous direct numerical simulation data obtained by solving the conventional Navier-Stokes equations, which confirms the capability of the proposed SRF LBM and subgrid scale relaxation time formulation for the computation of rotating turbulent flows and heat transfer.

Large Eddy Simulation of Self-Sustained Cavity Oscillation for Subsonic and Supersonic Flows

The primary objective is to perform a large eddy simulation (LES) using shear improved Smagorinsky model (SISM) to resolve the large-scale structures, which are primarily responsible for shear layer oscillations and acoustic loads in a cavity. The unsteady, three-dimensional (3D), compressible Navier–Stokes (N–S) equations have been solved following AUSM+-up algorithm in the finite-volume formulation for subsonic and supersonic flows, where the cavity length-to-depth ratio was 3.5 and the Reynolds number based on cavity depth was 42,000. The present LES resolves the formation of shear layer, its rollup resulting in large-scale structures apart from shock–shear layer interactions, and evolution of acoustic waves. It further indicates that hydrodynamic instability, rather than the acoustic waves, is the cause of self-sustained oscillation for subsonic flow, whereas the compressive and acoustic waves dictate the cavity oscillation, and thus the sound pressure level for supersonic flow. The present LES agrees well with the experimental data and is found to be accurate enough in resolving the shear layer growth, compressive wave structures, and radiated acoustic field.

Simulations of indoor airflow and particle dispersion and deposition by the lattice Boltzmann method using LES and RANS approaches

In this paper the Lattice Boltzmann method (LBM) in conjunction with the large eddy simulations (LES) and Reynolds Averaged Navier–Stokes (RANS) models was used to study the airflow and particle dispersion and deposition in indoor environments. The turbulent airflow was simulated first using the LES in framework of LBM, in which the sub-grid scale turbulence effects were simulated through a shear-improved Smagorinsky model (SISM). The airflow was also simulated using the k−ε turbulence model within the framework of LBM by the addition of two populations for the turbulence kinetic energy, k, and the dissipation rate, ε. The present simulation results for the airflow showed good agreement with the experimental data and the earlier numerical results.To simulate the particle dispersion and deposition in the room, particles with diameters of 10 nm–10 μm were investigated. For generating the instantaneous turbulence fluctuations for thek−ε model, the discrete random walk (DRW) method was used. Effects of SGS turbulence fluctuation on deposition rate of different size particles were also studied. It was shown that inclusion of the SGS turbulence fluctuations improves the model predictions. The simulated results for particle dispersion and deposition showed that the predictions of the present method are quite similar to the earlier finite volume method and are in good agreement with the experimental data.

Shear improved Smagorinsky model for large eddy simulation of flow in a stirred tank with a Rushton disk turbine

Large eddy simulation (LES) is a very attractive method for simulations of reactive flows for a wide range of Reynolds number. In this approach, the effects observed at the large scales (for velocity and concentrations) are directly computed using modelled interactions with the small subgrid scales. Small scales tend to be more isotropic than the large ones, so it is easier to predict their behaviour using simpler and more universal models than RANS ones and called subgrid-scale (SGS) models. In this work, computational fluid dynamics (CFD) and particle image velocimetry (PIV) techniques have been used to describe the flow field in standard stirred tank equipped with a Rushton disk turbine (RDT). A new efficient and cost effective SGS model called shear improved Smagorinsky model (SISM) for large eddy simulation (LES) has been successfully implemented and validated in the open source CFD code “OpenFOAM”. The shear improved Smagorinsky model is capable of predicting turbulent near wall region accurately without any wall function. The model is based on results concerning mean-shear effects in wall-bounded turbulence. It takes into account the mean shear arising due to anisotropy of the flow. The proposed model, in addition to being physically sound and consistent with the scale-by-scale energy budget of locally homogeneous shear turbulence, has a low computational cost when compared to the original Smagorinsky model and possesses a high potential for generalisation to complex non-homogeneous turbulent flows since no geometrical argument enters in the definition of the eddy-viscosity. However, an appropriate average must be specified in the absence of homogeneity directions. For this purpose we use an adaptive Kalman filter. There was good agreement between the CFD simulations and PIV experimental results.

Large-eddy simulation of 3-D corner separation in a linear compressor cascade

The increase of the thrust/weight ratio of aircraft engines is extremely restricted by different 3-D flow loss mechanisms. One of them is the corner separation that can form at the junction between a blade suction side and a hub or shroud. In this paper, in order to further investigate the turbulent characteristics of corner separation, large-eddy simulation (LES) is conducted on a compressor cascade configuration using NACA65 blade profiles (chord based Reynolds number: 3.82 × 105), in comparison with the previous obtained experimental data. Using the shear-improved Smagorinsky model as subgrid-scale model, the LES gives a good description of the mean aerodynamics of the corner separation, especially for the blade surface static pressure coefficient and the total pressure losses. The turbulent dynamics is then analyzed in detail, in consideration of the turbulent structures, the one-point velocity spectra, and the turbulence anisotropy. Within the recirculation region, the energy appears to concentrate around the largest turbulent eddies, with fairly isotropic characteristics. Concerning the dynamics, an aperiodic shedding of hairpin vortices seems to induce an unsteadiness of the separation envelope.

Unsteady behavior of corner separation in a compressor cascade: Large eddy simulation and experimental study

The present study carried out a pure large eddy simulation (LES) on a NACA65 linear compressor cascade (chord-based Reynolds number: 382 000), at an incidence angle of 4°. In this configuration, a corner separation at the juncture of the blade suction side and the end-wall is clearly observed experimentally. For the simulation, 852 CPUs are used in parallel and particular attention is paid to the inflow conditions, coupling LES with the calculation of the inlet boundary layer and associated velocity fluctuations. The shear-improved Smagorinsky model, which has been proved to be competent for turbomachines, is used in this study. Numerical results are carefully compared with pressure measurements, two-dimensional and stereo particle image velocimetry. LES is found to be superior to Reynolds-averaged Navier–Stokes approach in predicting the three-dimensional separated flows in the compressor cascade since pressure coefficients and losses are in very good agreement with the experiment. LES has been proven to simulate also the unsteady behavior of the separation. Finally, the experimental and numerical analysis of the inflow angle reveals high fluctuations of incidence upstream the leading edge of the blade near the end-wall, mostly associated with the incoming wall boundary layer.

Assessment of the shear-improved Smagorinsky model in laminar-turbulent transitional channel flow

In this paper, the shear-improved Smagorinsky model (SISM) is assessed in a K-type transitional channel flow. Our numerical simulation results show that the original SISM model is still too dissipative to predict the transitional channel flow. Two former reported empirical correction approaches, including a low-Reynolds-number correction and a shape-factor-based intermittency correction, are applied to further promote the capability of the SISM model in simulating the transition process. Numerical tests show that the shape-factor-based intermittency correction approach can correctly improve the transition-prediction capability of the SISM model, while the low-Reynolds-number correction approach fails. Furthermore, the shape-factor-based intermittency-corrected SISM model can capture the vortical structures during the transitional process very well and possesses the grid-insensitive characteristics.

Implementation of a roughness element to trip transition in large-eddy simulation

In aerodynamics, the laminar or turbulent regime of a boundary layer has a strong influence on friction or heat transfer. In practical applications, it is sometimes necessary to trip the transition to turbulent, and a common way is by use of a roughness element (e.g. a step) on the wall. The present paper is concerned with the numerical implementation of such a trip in large-eddy simulations. The study is carried out on a flat-plate boundary layer configuration, with Reynolds number Rex=1.3×106. First, this work brings the opportunity to introduce a practical methodology to assess convergence in large-eddy simulations. Second, concerning the trip implementation, a volume source term is proposed and is shown to yield a smoother and faster transition than a grid step. Moreover, it is easier to implement and more adaptable. Finally, two subgrid-scale models are tested: the WALE model of Nicoud and Ducros (Flow Turbul. Combust., vol. 62, 1999) and the shear-improved Smagorinsky model of Leveque et al. (J. Fluid Mech., vol. 570, 2007). Both models allow transition, but the former appears to yield a faster transition and a better prediction of friction in the turbulent regime.

Large Eddy Simulation of a Free Circular Jet

A large eddy simulation (LES) of an incompressible spatially developing circular jet at a Reynolds number of 10,000 is performed. The shear-improved Smagorinsky model (Lévêque et al., 2007, “A Shear-Improved Smagorinsky Model for the Large-Eddy Simulation of Wall-Bounded Turbulent Flows,” J. Fluid Mech., 570, pp. 491–502) is used for the resolution of the subgrid stress tensor within the filtered three-dimensional unsteady Navier–Stokes equations. Higher-order spatial and temporal discretization schemes are used for capturing the details of the turbulent flow field. With the help of instantaneous and time-averaged flow data, the spatial transition from the laminar state to the turbulent is analyzed. Flow structures are visualized using isosurfaces of the Q-criterion. Instantaneous flow patterns show single tearing and multiple pairing processes. Tracing individual vortex rings over a longer time period, a detailed understanding of the vortex interaction is revealed. The observed trends and the length of the potential core are in conformity with the findings of earlier experiments. The time-averaged axial velocity profile shows that the jet attains self-similarity and the computed profile matches well with the experimental results of Hussein et al. (1994, “Velocity Measurements in a High-Reynolds-Number, Momentum-Conserving, Axisymmetric, Turbulent Jet,” J. Fluid Mech., 258, pp. 31–75). The centerline decay of the velocity and entrainment rate are in agreement with published experiments. The Reynolds stress components u'u'¯, v'v'¯, and u'v'¯ and the third-order velocity moment are in good agreement with thr experimental results, thus confirming the validity of the present simulation.

Particle Tracking in Large Eddy Simulated Turbulent Channel Flow Using Generalized Lattice Boltzmann Method

The deposition of spherical solid particles with 0.00192 ≤ τ+ ≤ 160.56 in three-dimensional turbulent vertical and horizontal channel flows with friction Reynolds number was studied. A generalized lattice Boltzmann equation (GLBE) was used for computation of instantaneous turbulent flow field for which large eddy simulation (LES) was employed. The subgrid scale (SGS) turbulence effects were simulated through a shear-improved Smagorinsky model (SISM), which can predict turbulent near wall region without any wall function. The Lagrangian particle tracking approach was used, and qualitative distribution of particles in a vertical channel center plane and in a near wall region was presented. It was shown that, in horizontal channels, the rate of deposition is higher than in vertical channels since gravitational sedimentation is the dominant mechanism of deposition on the lower wall. Combination of SISM in GLBE with particle tracking analysis in turbulent channel flow is the novelty of the present work. Since the accuracy of the flow field is essential to correctly predict particles' behavior, a reliable method should be used to simulate the flow field. In the proposed method, the flow field equations are solved locally. The collaboration of this method and particle tracking can be considered a good candidate for simulation of particulate flow.

Simulation of turbulent duct flow by employing shear-improved Smagorinsky model accompanied by forced generalized lattice Boltzmann method

Purpose – The present work aims to deal with simulation of turbulent duct flow using generalized lattice Boltzmann equation (GLBE) in which large eddy simulation was employed. Design/methodology/approach – The sub-grid scale turbulence effects were simulated through a shear-improved Smagorinsky model (SISM) which is capable of predicting turbulent near wall region accurately without any wall function. Computations were done for fully developed turbulent square duct flow at Ret=300, based on duct width and average friction velocity. Findings – Results obtained for turbulent duct flow reveal that the GLBE in conjunction with SISM is able to correctly predict the existence of secondary flows and the computed detailed structure of first- and second-order statistics of main and secondary motions. The methodology is validated by comparing with previously published data. It is concluded that such framework is capable of predicting accurate results for turbulent duct flow. In addition, the operations in the present method are local; it can be easily programmed for parallel machines. Originality/value – The numerical method, including generalized lattice Boltzmann method with forcing term and implementation of SISM in GLBE, is used for the first time to simulate turbulent duct flow.

Direct and large-eddy simulation of turbulent flows on composite multi-resolution grids by the lattice Boltzmann method

In order to properly address the simulation of complex (weakly compressible) turbulent flows, the lattice Boltzmann method, originally designed for uniform structured grids, needs to be extended to composite multi-domain grids displaying various levels of spatial resolution. Therefore, physical conditions must be specified to determine the mapping of statistical information (about the populations of moving particles) at the interface between two domains of different resolutions. quite simply in terms of the probability distributions of the underlying discrete-velocity Boltzmann equation. Namely, the continuity of the mass density and fluid momentum is fulfilled by imposing the continuity of the equilibrium part of these distributions, whereas the discontinuity of the rate-of-strain tensor is ensured by applying a “spatial transformation” to the collision term of the discrete-velocity Boltzmann equation. The latter condition allows us to explicitly account for the subgrid-scale modeling in the treatment of resolution changes.Test computations of a turbulent plane-channel flow have been carried out. The lattice Boltzmann scheme relies on the standard D3Q19 lattice in a cell-vertex representation, and uses the BGK approximation for the collision term. A shear-improved variant of the Smagorinsky viscosity is used to account for possible subgrid-scale dynamics. In a quasi-direct numerical simulation at Reτ=180 with two levels of grid resolution, the results are found in excellent agreement with reference data obtained by a high-resolution pseudo-spectral simulation. In a Large-Eddy Simulation (LES) at Reτ=395 with three levels of grid resolution, the results compare reasonably well with high-resolution reference data. The accuracy is improved in comparison with a standard finite-volume LES performed with the same subgrid-scale viscosity and comparable grid resolution.By combining the simplicity and physical relevance of the shear-improved Smagorinsky model and the computational efficiency of the lattice Boltzmann scheme, here extended to composite multi-resolution grids, we believe that our proposal offers a high potential for the simulation of complex turbulent flows.

Three-dimensional numerical study of turbulent flow and heat transfer in a wavy-walled duct

The present study focuses on the computation of fully developed flow and heat transfer through a stationary wavy-walled duct using large eddy simulation (LES) in finite volume framework. Shear improved Smagorinsky model (SISM) has been used for the computation of eddy viscosity. The wavy-wall is described by the sine function y=2a sin2(πx/L). The geometrical ratios Hmin/Hmax and L/a are fixed to 0.2 and 8, respectively. The effect of Reynolds numbers (2053–10,000) on the flow field and heat transfer has been presented. Instantaneous, mean and turbulent quantities are reported. It has been observed that the flow is strongly three-dimensional. The friction factor is found to be insensitive to the Reynolds number. Normalized Nusselt number ratio shows significant Reynolds number dependency.

Preface for the special issue on computational heat transfer

The special issue reports the current advancements in the field of computational heat transfer. The area has witnessed rapid strides in the last four decades and the world has seen an explosive growth in the number, range of applicability and robustness of newer computational tools and their increasing application to problems of practical importance in thermal sciences. This issue carries articles that propose better than the state-of-the-art techniques for solving fluid flow and heat transfer problems, those that consider novel variants to existing techniques and demonstrate their use in engineering problems and also those that have employed well known techniques to very complex problems in fields ranging from chemical engineering to nuclear thermal hydraulics. The first paper in the issue by Yadav et al. reports the results of steady state simulations of a three dimensional model of a super critical CO2 based natural convection loop with end heat exchangers. The study shows that even for a small temperature difference of 18 K, buoyancy is powerful enough to result in high heat transfer rates. Nandakumar et al. in their paper studied the thermal hydraulics of sodium heated once through steam generator of a nuclear reactor by three dimensional simulations and used these results in a one dimensional analysis. The results from the study provide an estimate of a key engineering quantity, namely differential thermal expansion of shells and tubes in the steam generator. Amit Kumar and Malhotra formulated a two dimensional numerical model of downward flame over a thin solid fuel and solved it to study the effect of a gas phase heat sink (a wire mesh) on the flame spread and flame extinction. The numerical results were validated with experiments and both of them showed that the wire mesh was effective in reducing the flame spread when placed at a distance of 5 mm. Sengupta et al. carried out a three dimensional conjugate heat transfer analysis of the BeO reflector assemblies of a 2 W upgraded Apsara nuclear reactor. The key challenge here is the accomplishment of heat transfer purely by natural convection and the results indicate that the maximum air gap between the aluminium side and BeO blocks should not be more than 0.3 mm to keep the temperatures within safe limits. Biswas et al. considered a new sub-grid model pertaining to large eddy simulation (LES) methodology, namely shear improved Smagorinsky model that can take into account the mean shear arising out of the anisotropy of the flow. The model was tested for the lid driven cavity flow and the predictions were seen to agree well with the experiments as well as the LES model. Kalyana Raman et al. employed the immersed boundary method (IBM) under mixed convection at Re = 100 for an elliptic cylinder. The advantage of the IBM was the use of a simple Cartesian grid in the simulations. The critical Richardson number at which shedding gets suppressed was determined for different aspect ratios of the elliptic cylinder. Phongthanapanich and Dechaumpai proposed a new second order accurate characteristic based finite volume element method for analyzing time-dependent scalar convection–diffusionreaction equation in two dimensions. The method combined the finite volume and the finite element methods. It was seen that the method reduces spurious oscillations and does not require an artificial diffusion to improve the solution stability. Song and Tafti evaluated the use of a wall model for the LES of a rotating ribbed duct and compared the C. Balaji (&) Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, India e-mail: balaji@iitm.ac.in

Shear improved Smagorinsky model pertaining to large eddy simulation applied on lid- driven cavity flows

Recently, a new sub-grid-scale model pertaining to large eddy simulation methodology, namely shear improved-Smagorinsky model has been proposed. The model takes into account the mean shear arising due to anisotropy of the flow. In the present study, the model has been tested successfully on shear driven cavity flow to see its strength in predicting the complex flow features associated with separation or detached shear layer and analyze the associated numerical difficulties. The results have been compared with experimental data and findings from commonly used LES model. The model agrees well with the experimental counterpart and comparable with those due to other LES model.

Large Eddy Simulation of Turbulent Flow and Heat Transfer in a Ribbed Coolant Passage

Numerical simulations of hydrodynamic and thermally fully developed turbulent flow are presented for flow through a stationary duct with periodic array of inline transverse rib turbulators. The rib height to hydraulic diameter ratio (e/Dh) is 0.1 and the rib pitch to rib height ratio (P/e) is 10. The effect of secondary flow due to presence of rib turbulators on heat and mass transfer has been investigated. The present work reviews the use of a large eddy simulation (LES) turbulence model, known as shear‐improved Smagorinsky model (SISM), for predicting flow and heat transfer characteristics in the fully developed periodic flow region. The computations are performed for Reynolds number of 2,053 and the working fluid chosen to be air, the Prandtl number of which is 0.7. Instantaneous flow field, time‐mean, and turbulent quantities are reported together with heat transfer and a close match with experiments has been observed.

Dynamic Kalman filtering to separate low-frequency instabilities from turbulent fluctuations: Application to the Large-Eddy Simulation of unsteady turbulent flows

A dynamic method based on Kalman filtering is presented to isolate low-frequency unsteadiness from turbulent fluctuations in the large-eddy simulation (LES) of unsteady turbulent flows. The method can be viewed as an adaptive exponential smoothing, in which the smoothing factor adapts itself dynamically to the local behavior of the flow. Interestingly, the proposed method does not require any empirical tuning. In practice, it is used to estimate a shear-improved Smagorinsky viscosity, in which the low-frequency component of the velocity field is used to estimate a correction term to the Smagorinsky viscosity. The LES of the flow past a circular cylinder at Reynolds number ReD = 4.7 × 104 is examined as a challenging test case. Good comparisons are obtained with the experimental results, indicating the relevance of the shear-improved Smagorinsky model and the efficiency of the Kalman filtering. Finally, the adaptive cut-off of the Kalman filter is investigated, and shown to adapt locally and instantaneously to the complex flow around the cylinder.