Smagorinsky Subgrid Scale Research Articles

Wall-resolved large eddy simulation of turbulent mixed-convection heat transfer along a heated vertical flat plate

The present study aims to assess the predictive capabilities of wall-resolved large eddy simulation (LES) in computing the fluid flow and heat transfer characteristics in a mixed-convection turbulent boundary layer that developed along a large flat plate vertically mounted in air. The maximum Rayleigh number was approximately 3×1011, which resulted in fully developed turbulence conditions. To enhance the accuracy, computational efficiency, and numerical stability, the LES solved the low-Mach number compressible flow governing equations, which included fluctuating density effects and pressure-density decoupling. For the subgrid scale (SGS) closure, a locally dynamic Smagorinsky SGS model was implemented into the LES solver to enable the backscatter phenomenon intrinsic to transitioning boundary layer flows. The LES illustrated exceptional agreement with the statistics profiles in the boundary layer obtained with the experiments of previous studies, which showed sensitivity to freestream conditions. In particular, the LES correctly predicted the turbulent heat flux in the streamwise direction near the heated surface. Furthermore, the LES captured the rapid changes in spectra of fluctuating temperature and velocities due to the delay of transition with increasing freestream velocity.

Evaluation of the turbulent kinetic dissipation rate in an agitated vessel

The design of agitated tanks depends on operating conditions and processes for that are used for. An important parameter for the scale-up modelling is the dissipation rate of the turbulent kinetic energy. The dissipation rate is commonly assumed to be a function of the impeller power input. But this approach gives no information about distribution of the dissipation rate inside the agitated volume. In this paper the distributions of the dissipation rate inside the agitated vessels are estimated by evaluations of the CFD (Computational Fluid Dynamics). The results obtained from RANS (Reynolds Averaged Navier-Stokes equations) k-e turbulent model and LES (Large Eddy Simulations) with Smagorinsky SGS (Sub Grid Scale) model are compared. The agitated vessels with standard geometry equipped with four baffles and stirred by either a standard Rushton turbine or a high shear impeller were investigated. The results are compared with mean dissipation rate estimated from the total impeller power input.

Numerical investigation of the interaction of the turbulent dual-jet and acoustic propagation**Project supported by the Fundamental Research Funds for the Central Universities, China (Grant No. N150204003).

In order to study the interaction between two independent jets, a three-dimensional (3D) transient mathematical model is developed to investigate the flow field and acoustic properties of the two-stream jets. The results are compared with those of the single-stream jet at Mach number 0.9 and Reynolds number 3600. The large eddy simulation (LES) with dynamic Smagorinsky sub-grid scale (SGS) approach is used to simulate the turbulent jet flow structure. The acoustic field is evaluated by the Ffowcs Williams–Hawkings (FW-H) integral equation. Considering the compressibility of high-speed gas jets, the density-based explicit formulation is adopted to solve the governing equations. Meanwhile, the viscosity is approximated by using the Sutherland kinetic theory. The predicted flow characteristics as well as the acoustic properties show that they are in good agreement with the existing experimental and numerical results under the same flow conditions available in the literature. The results indicate that the merging phenomenon of the dual-jet is triggered by the deflection mechanism of the Coanda effect, which sequentially introduces additional complexity and instability of flow structure. One of the main factors affecting the dual-jet merging is the aperture ratio, which has a direct influence on the potential core and surrounding flow fluctuation. The analysis on the noise pollution reveals that the potential core plays a fundamental role in noise emission while the additional mixing noise makes less contribution than the single jet noise. The overall sound pressure level (OASPL) profiles have a directive property, suggesting an approximate 25° deflection from the streamwise direction, however, shifting toward lateral direction of about 10° to 15° in the dual-jet. The conclusion obtained in this study can provide valuable data to guide the development of manufacturing-green technology in the multi-jet applications.

Large eddy simulation of two isothermal and reacting turbulent separated oxy-fuel jets

In this work, a Large eddy simulation (LES) method and a tabulated chemistry approach according to the Flamelet Generated Manifold (FGM) strategy are coupled to numerically study the interactions of turbulent isothermal and reacting flows stemming from two aligned jets providing alternately fuel (natural gas) and oxidant (pure oxygen gas).The jets feature different geometries and deliver unequal momentums at the boundaries. The effect of oxygen in comparison to air environment on the FGM tabulation and results is pointed out. In addition, the impact of combustion on the flow and mixing field evolvement is analyzed. The LES relies on a dynamic Smagorinsky subgrid scale (SGS) model and a linear eddy diffusivity ansatz to close the SGS stresses and the SGS scalar fluxes for describing the turbulent flow field and the turbulent scalar field, respectively. For model assessment, available laser-based experimental data are used for model validation. In particular the numerical results are compared with available experimental data for the flow field. The latter are gained experimentally by the Particle Image Velocimetry (PIV) and laser tomography, respectively. In the first part of this paper, the jets interaction process is studied for the isothermal case while the oxy-fuel combustion in the reacting case is analyzed in the second part. The analysis is achieved in terms of statistical quantities for the flow velocity, mixture fraction, chemical species and temperature. An overall satisfactory agreement is reported.

Wall-resolved Large Eddy Simulation of a flow through a square-edged orifice in a round pipe at Re = 25,000

The orifice plate is a pressure differential device frequently used for flow measurements in pipes across different industries. The present study demonstrates the accuracy obtainable using a wall-resolved Large Eddy Simulation (LES) approach to predict the velocity, the Reynolds stresses, the pressure loss and the discharge coefficient for a flow through a square-edged orifice in a round pipe at a Reynolds number of 25,000. The ratio of the orifice diameter to the pipe diameter is β=0.62, and the ratio of the orifice thickness to the pipe diameter is 0.11. The mesh is sized using refinement criteria at the wall and preliminary RANS results to ensure that the solution is resolved beyond an estimated Taylor micro-scale. The inlet condition is simulated using a recycling method, and the LES is run with a dynamic Smagorinsky sub-grid scale (SGS) model. The sensitivity to the SGS model and to the pressure–velocity coupling is shown to be small in the present study. The LES is compared with the available experimental data and ISO 5167-2. In general, the LES shows good agreement with the velocity from the experimental data. The profiles of the Reynolds stresses are similar, but an offset is observed in the diagonal stresses. The pressure loss and discharge coefficients are shown to be in very good agreement with the predictions of ISO 5167-2. Therefore, the wall-resolved LES is shown to be highly accurate in simulating the flow across a square-edged orifice.

Large-eddy simulations of flow normal to a circular disk at Re=1.5×105

Abstract Numerical simulations of the flow normal to a circular disk have been carried out using the large-eddy simulation (LES) method with Smagorinsky subgrid scale model. The Reynolds number ( Re ) based on the free stream velocity and the diameter of the disk is 1.5 × 10 5 . The thickness to diameter ratio of the disk is 0.02. The instantaneous vortical structures in wake of the disk are revealed. Toroidal vortices are formed along the disk edges due to Kelvin–Helmholtz instability. The toroidal vortices break up as the flow goes downstream and then hairpin-like vortices are formed. Worm-like vortices parallel to the axis of the disk are observed in the center region of the medium wake. Two distinct vortex spreading modes in the far wake are observed: one has a main shedding plane; the other has not. Three dominant frequencies at the Strouhal number S t 1 = 0.01 , S t n = 0.148 (corresponding to the natural frequency) and St 3 ≈ 0.8–1.35, characterizing that the wake instability mechanisms are found through frequency analysis. The time and azimuth averaged statistics, e.g., streamlines, pressure, vorticity and profiles of velocity and kinetic energy, are also presented and discussed.

Modelling of pollutant dispersion with atmospheric instabilities in an industrial park

Large Eddy Simulation (LES) combined with a dynamic Smagorinsky subgrid scale model was used to simulate the wind field and particulate pollutant dispersion considering the effects of plant canopies and weather conditions. The model of the plant canopy was adopted to present the effects of drag force and buoyancy force and validated by bench mark results from previous reference. Then, using the model, four study cases in the Nanjing Sample Industrial Park were simulated under different weather conditions to consider the momentum effect of plant canopy, energy effect of plant canopy and the effect of atmospheric instabilities, respectively. The numerical results were also compared with those of idealized street canyon models, and it was proven that the accurate landform model was more practical to be applied in the study. The wind field and pollutant distribution were analyzed in each case to investigate the influence of plant canopy. It was shown that the wind velocity was lower near the canopy regions, especially in unstable conditions due to the entrainment effect of the buoyancy force. Meanwhile, the streamline could be changed by the buoyancy force in an upward trend. The distribution of the turbulent kinetic energy indicated that the turbulent flow in the atmosphere was weakened through the plant canopy, especially in unstable conditions. Considering the effect of buoyancy force, the direction of pollutant dispersion in horizontal profiles was different to the neutral condition, which proved that plant canopy can protect the downstream regions in unstable atmospheric conditions.

Numerical analysis of blood flow through an elliptic stenosis using large eddy simulation.

The presence of a stenosis caused by the abnormal narrowing of the lumen in the artery tree can cause significant variations in flow parameters of blood. The original flow, which is believed to be laminar in most situations, may turn out to turbulent by the geometric perturbation created by the stenosis. Flow may evolve to fully turbulent or it may relaminarise back according to the intensity of the perturbation. This article reports the numerical simulation of flow through an eccentrically located asymmetric stenosis having elliptical cross section using computational fluid dynamics. Large eddy simulation technique using dynamic Smagorinsky sub-grid scale model is applied to capture the turbulent features of flow. Analysis is carried out for two situations: steady inflow as ideal condition and pulsatile inflow corresponding to the actual physiological condition in common carotid artery. The spatially varying pulsatile inflow waveforms are mathematically derived from instantaneous mass flow measurements available in the literature. Carreau viscosity model is used to estimate the effect of non-Newtonian nature of blood. The present simulations for steady and pulsatile conditions show that post-stenotic flow field undergoes transition to turbulence in all cases. The characteristics of mean and turbulent flow fields have been presented and discussed in detail.

3D numerical simulation of the evolutionary process of aeolian downsized crescent-shaped dunes

Abstract A dune constitutive model was coupled with a large eddy simulation (LES) with the Smagorinsky subgrid-scale (SGS) model to accurately describe the evolutionary process of dunes from the macroscopic perspective of morphological dynamics. A 3D numerical simulation of the evolution of aeolian downsized crescent-shaped dunes was then performed. The evolution of the 3D structure of Gaussian-shaped dunes was simulated under the influence of gravity modulation, which was the same with the vertical oscillation of the sand bed to adjust the threshold of sand grain liftoff in wind tunnel experiments under the same wind speed. The influence of gravity modulation intensity on the characteristic scale parameter of the dune was discussed. Results indicated that the crescent shape of the dune was reproduced with the action of gravity during regulation of the saturation of wind-sand flow at specific times. The crescent shape was not dynamically maintained as time passed, and the dunes dwindled until they reached final decomposition because of wind erosion. The height of the dunes decreased over time, and the height–time curve converged as the intensity of modulation increased linearly. The results qualitatively agreed with those obtained from wind tunnel experiments.

Large Eddy Simulations of flow around a circular cylinder close to a flat seabed

Large Eddy Simulations (LES) with Smagorinsky subgrid scale model are used to study the turbulent flow and wake dynamics behind a circular cylinder close to a horizontal, plane wall at subcritical Reynolds number. The focus is on investigating the details of the flow around the cylinder placed at different distances from the wall and immersed in boundary layers of various thicknesses.The Reynolds number is Re = 13,100. The simulations with gap to diameter ratios (G/D) of 0.2, 0.6 and 1 are carried out in order to investigate the changes of the flow field and the vortex shedding due to the presence of the plane wall. The influence of the incoming boundary layer profile is investigated through simulations with logarithmic boundary layer inlet profile of thickness 0.48D and 1.6D, and compared with a uniform inlet flow profile. 2D and 3D simulations are performed for Re ranging from 100 to 13,100, to explore the importance of the flow three-dimensionality. The flow field in the cylinder wake, as well as the mean flow values, the spectral analysis and the pressure distribution on the cylinder surface are computed to study the flow physics due to the influences of the wall.

Large Eddy Simulation of isothermal cruciform jet flow: Preliminary results

Summary The present work is a numerical study of a turbulent isothermal jet issuing from cruciform nozzle into still air at a high Reynolds number of 1.7 × 10 5 . The numerical simulation was carried out by using open source CFD tool OpenFOAM ® . Three-dimensional cuboid shaped domain was used to simulate the unsteady turbulent flow field. The simulation was carried out by solving the filtered Navier–Stokes equations along with Smagorinsky sub-grid scale model. The Large Eddy Simulation (LES) solutions are compared with experimental data for validation of the jet flow physics. The flow field of turbulent jet from cruciform nozzle are described in terms of inverse mean axial velocity decay and visualizations. The vortical structures are visualized using iso-surface contours of vorticity magnitude. The vortical structures develop from the cruciform nozzle is significantly different from axisymmetric nozzles. The vortical structures show changes in shape as they move downstream from the nozzle. The cruciform jet shows complex vorticity dynamics in the near field region.

On the Influence of Polynomial De-aliasing on Subgrid Scale Models

In this work we investigate the interplay of polynomial de-aliasing and sub-grid scale models for large eddy simulations based on discontinuous Galerkin discretizations. It is known that stability is a major concern when simulating underresolved turbulent flows with high order nodal collocation type discretizations. By changing the interpolatory character of the nodal collocation type discretization to a projection based discretization by increasing the number of quadrature points (polynomial de-aliasing), one is able to remove the aliasing induced stability problems. We focus on this effect and on the consequence for large eddy simulations with explicit subgrid scale models. Often, subgrid scale models have to achieve two possibly conflicting tasks in a single simulation: firstly stabilizing the numerics and secondly modeling the physical effect of the missing scales. Within a discontinuous Galerkin approach, it is possible to use either a fast (but potentially aliasing afflicted) nodal collocation discretization or a projection-based (but computationally costly) variant in combination with an explicit subgrid scale model. We use this framework to investigate the effect on the appropriate model parameter of a standard Smagorinsky subgrid scale model and of a Variational Multiscale Smagorinsky formulation. For this we first consider the 3-D viscous Taylor-Green vortex example to investigate the impact on the stability of the method and second the turbulent flow past a circular cylinder to investigate and compare the accuracy of the results. We show that the aliasing instabilities of collocative discretizations severely limit the choice of the model constant, in particular for high order schemes, while for de-aliased DG schemes, the closure model parameters can be chosen independently from the numerical scheme. For the cylinder flow, we also find that for the same model settings, the projection-based results are in better agreement with the reference DNS than those of the collocative scheme.

Improvement of a stochastic backscatter model and application to large‐eddy simulation of street canyon flow

A stochastic backscatter (SB) subgrid‐scale (SGS) model is applied, for the first time, to large‐eddy simulation (LES) of street canyon flow. We model a ‘skimming flow’ regime under a neutrally stratified atmosphere, in which the approaching wind is perpendicular to the along‐street axis of a street canyon of unity aspect ratio. Previous LESs of this type have shown an under‐prediction of the intensity of the primary eddy (PE) that forms within the street canyon, indicating a lack of momentum transfer across the roof‐level shear layer. The SB model, however, acts to increase this momentum transfer, bringing the simulated PE intensity significantly closer towards that observed in a corresponding wind‐tunnel experiment. A metric for the PE intensity, ωPE, based on the two‐dimensional vorticity field, is increased from around 70% of the wind‐tunnel ωPE value (with the Smagorinsky SGS model) to as much as 90% (with the SB model). Calculation of the air exchange rate at roof‐level confirms that the rate of entrainment into the street canyon is increased with the inclusion of backscatter.We also outline an improvement to the SB model prior to its application. In its previous version, a constraint on the magnitude of the backscatter acceleration variances ensured a theoretically appropriate level of additional grid‐scale (backscattered) energy. Here, a further constraint on the magnitude of the main covariance term also facilitates a better representation of grid‐scale vertical momentum flux. This new constraint alone can help to increase the simulated ωPE value by as much as 10% of the wind‐tunnel ωPE value, and requires almost no additional computational effort. The effect of varying the magnitude and length‐scale of the imposed backscatter (via the backscatter coefficient and length of the filter used to generate the backscatter acceleration fields, respectively) is also investigated.

A full three dimensional numerical simulation of the sediment transport and the scouring at a rectangular obstacle

We employ a numerical simulation of the three-dimensional fluid flow and the simultaneous transport of sediment to reproduce current-driven sediment transport processes. In particular, the scouring at a rectangular obstacle is investigated. To solve the instationary incompressible Navier–Stokes equations we use the code NaSt3D. The morphological change of the sediment bed is modeled by Exner’s bed level equation, which is discretized and coupled to the discrete fluid model, i.e., to the NaSt3D code. A large eddy turbulence approach using a Smagorinsky subgrid scale tensor is applied. For our purposes, we only consider bed load transport under clear water conditions. Furthermore, we demonstrate mass conservation and convergence of our approach for a test case. We compare the results of our numerical simulations for a scour mark with those obtained in a laboratory flume. The typical sedimentary processes and the sedimentary form of a scour mark are well captured by our numerical simulation.

Large eddy simulation of a piston–cylinder assembly: The sensitivity of the in-cylinder flow field for residual intake and in-cylinder velocity structures

Large eddy simulation (LES) in an axisymmetric piston–cylinder geometry was carried out using three LES approaches: (1) Smagorinsky subgrid scale model, (2) implicit LES, and (3) scale selective discretisation (SSD). In addition to the LES subgrid scale model sensitivity study, two additional simulations were carried out in order to understand the roles of the intake and the in-cylinder residual turbulence to the flow statistics. Altogether 12 cycles were computed for each simulation on a grid with 5 million cells and requiring over a month of wall-clock time per simulation on a supercomputer. Analysis of velocity statistics revealed that the results were not very sensitive to the LES model type. However, the residual turbulence was noted to have a clear impact on the velocity statistics. In particular, the simulations revealed that removing the residual turbulence from the intake region at the top-dead-centre has a clear impact on the overall velocity statistics. In many cases the cycle-to-cycle variation (CCV) increased. In a respective numerical test, where only the in-cylinder turbulence was removed at top-dead-centre, weaker sensitivity was observed. In addition, the CCV relative to the mean velocity was in some cases as high as 30% even in such a non-reactive case. The present study complements previous studies on the same set-up by investigating the sensitivity of three LES models on flow statistics, quantifying CCV using three different LES approaches in the standard set-up, and assessing the role of residual turbulence on the flow statistics via modified flow cases.

A numerical dissipation rate and viscosity in flow simulations with realistic geometry using low-order compressible Navier–Stokes solvers

Recently it has become increasingly clear that the role of numerical dissipation, originating from the discretization of governing equations of fluid dynamics, rarely can be ignored regardless of the formal order of accuracy of a numerical scheme used in either explicit or implicit Large Eddy Simulations (LES). The numerical dissipation inhibits the predictive capabilities of LES whenever it is of the same order of magnitude or larger than the sub-grid-scale (SGS) dissipation. The need to estimate the numerical dissipation is most pressing for low-order methods employed by commercial CFD codes. Following the recent work of Schranner et al. (2015) the equations and procedure for estimating the numerical dissipation rate and the numerical viscosity in a commercial code are presented. The method allows to compute the numerical dissipation rate and numerical viscosity in the physical space for arbitrary sub-domains in a self-consistent way, using only information provided by the code in question. The procedure has been previously tested for a three-dimensional Taylor–Green vortex flow in a simple cubic domain and compared with benchmark results obtained using an accurate, incompressible spectral solver. In the present work the procedure is applied for the first time to a realistic flow configuration, specifically to a laminar separation bubble flow over a NACA 0012 airfoil at Ma=0.4 and Re=50,000. The method appears to be quite robust and its application reveals that for the code and the flow in question the numerical dissipation can be significantly larger than the viscous dissipation or the dissipation of the classical Smagorinsky SGS model.

Large eddy simulations of 45° inclined dense jets

Submerged inclined dense jets (negatively buoyant jets) occur in many engineering applications such as brine discharges from seawater desalination plants and de-cooling water discharges from liquefied natural gas plants, and their mixing behavior needs to be examined in details for the environmental impact analysis. In the present study, a detailed numerical investigation was performed using the large eddy simulation (LES) approach with both the Smagorinsky and Dynamic Smagorinsky sub-grid scale (SGS) models to simulate the characteristics of the inclined dense jet with 45° inclination. The numerical predictions included the jet trajectory, geometrical characteristics, jet spread and eddy structures. Experimental measurements were also obtained for the validation of the LES predictions, and data from existing studies in the literature were included for comparison. Overall, the LES predictions were able to reproduce the geometric characteristics of the inclined dense jet in a satisfactory manner in most aspects. The dilution was however generally underestimated, which was attributed primarily to the inability of the SGS models to reproduce the convective mixing induced by the buoyancy-induced instability using the adopted grid spacing in the bottom half of the inclined dense jet.

Evaluation of LES and RANS CFD modelling of multiple steady states in natural ventilation

This paper reports research carried out with the aim of evaluating and comparing the performance of Large Eddy Simulation (LES) and Unsteady Reynolds-Averaged Navier–Stokes (URANS) modelling for predicting the multiple steady states observed in experiments on a buoyancy-driven naturally ventilated enclosure. The sub-grid scales of the flow have been modelled using a Van Driest damped Smagorinsky sub-grid scale model in the case of LES and an RNG k-ε turbulence model has been used for URANS. A novel mesh design strategy was introduced to design the LES mesh to identify an optimum ‘well-resolved’ mesh, assuming that the flow investigated is free-shear dominated. It was found that the URANS solution eventually settled down into a permanent steady state, displaying no evidence of continuing instabilities or periodic unsteadiness. Both URANS and LES solutions captured the existence of three steady states as observed in experimental studies. However, LES was more accurate in predicting the temperatures inside the enclosure compared to URANS. In the URANS solutions, it was observed that for smaller lower opening areas the average indoor temperature had noticeable discrepancies when compared with experimental results. Unlike URANS, LES correctly predicted different steady state temperatures for different opening areas and the time to reach steady state agreed closely with theoretical predictions.

Experimental and numerical investigation of a three-dimensional vertical-axis wind turbine with variable-pitch

A combined experimental and numerical investigation is carried out to study the performance of a micro vertical-axis wind turbine (VAWT) with variable-pitch. Three-dimensional numerical simulations are essentially employed, for the VAWT involves a low aspect ratio (AR) three straight blades with struts. The performance of the VAWT is experimentally measured using a wind tunnel, while large eddy simulation (LES) with dynamic smagorinsky subgrid scale (SGS) model is employed to help understand the associated flow structure. The effects of wind speed, turbulence intensity, airfoil shape, and strut mechanism with and without variable-pitch on the performance of the turbine are carefully assessed, both experimentally and numerically. The accuracy of the SGS model in predicting the laminar–turbulent transition is also examined.

Large Eddy Simulation of Turbulent Channel Flow Using Smagorinsky Model and Effects of Smagorinsky Constants

A large eddy simulation (LES) of a turbulent channel flow is performed by using the Smagorinsky subgrid scale model and the effects of Smagorinsky constants in LES are discussed. The computation is performed in the domain of δ δ 2 δ 2 π × × π with 32 64 32 × × grid points at a Reynolds number Reτ = 590 based on the channel half width, δ and wall shear velocity, uτ. The performance of the Smagorinsky model is tested in LES for three values of Smagorinsky constant, CS = 0.065, 0.1 and 0.13, and for all three cases the computed essential turbulence statistics of the flow field are compared with Direct Numerical Simulation (DNS) data. Comparing the results with those from DNS data throughout the whole calculation domain we have found that turbulence statistics for CS = 0.065 show reasonable agreement with the DNS data. Agreements as well as discrepancies are discussed. The behavior of the flow structures in the computed flow field has also been discussed.