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.     

Swirling-strength based large eddy simulation of turbulent flow around single square cylinder at low Reynolds numbers

In view of the fact that large scale vortices play the substantial role of momentum transport in turbulent flows, large eddy simulation(LES) is considered as a better simulation model. However, the sub-grid scale(SGS) models reported so far have not ascertained under what flow conditions the LES can lapse into the direct numerical simulation. To overcome this discrepancy, this paper develops a swirling strength based the SGS model to properly model the turbulence intermittency, with the primary characteristics that when the local swirling strength is zero, the local sub-grid viscosity will be vanished. In this paper, the model is used to investigate the flow characteristics of zero-incident incompressible turbulent flows around a single square cylinder(SC)at a low Reynolds number range Re ∈ [103, 104]. The flow characteristics investigated include the Reynolds number dependence of lift and drag coefficients, the distributions of time-spanwise averaged variables such as the sub-grid viscosity and the logarithm of Kolmogorov micro-scale to the base of 10 at Re = 2 500 and 104, the contours of spanwise and streamwise vorticity components at t = 170. It is revealed that the peak value of sub-grid viscosity ratio and its root mean square(RMS) values grow with the Reynolds number. The dissipation rate of turbulent kinetic energy is larger near the SC solid walls.The instantaneous factor of swirling strength intermittency(FSI) exhibits some laminated structure involved with vortex shedding.     

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.     

On Fokker–Planck Equations for Turbulent Reacting Flows. Part 2. Filter Density Function for Large Eddy Simulation

The application of large eddy simulation (LES) to turbulent reacting flow calculations is faced with several closure problems. Suitable parametrizations for filtered reaction rates for instance are hardly available in general. A way to overcome these problems is investigated here. This is done by extending LES equations for filtered velocities and scalars (mass fractions of species and temperature) to equations that involve subgrid scale (SGS) fluctuations. Such equations are called filter density function (FDF) methods because they determine the FDF, which is essentially the probability density function of SGS variables. The FDF model considered involves only three parameters: C ₀ that controls the generation of velocity fluctuations and two parameters which determine the relaxation of velocity and scalar fluctuations. The consideration of this model may be seen as the analysis of a limiting case: the implications of the most simple equations for the dynamics of SGS fluctuations are investigated in this way. These equations were proved recently by various simulations. Here, the FDF model is used analytically to improve simpler methods. Existing models for the SGS stress tensor in velocity LES equations and the diffusion coefficient in scalar FDF equations are generalized in this way. The advantages of these models compared to existing ones are pointed out. These investigations provide further evidence for the suitability of the FDF model considered and they provide its parameters. A theoretical value C ₀ = 19/12 is derived, which agrees very well with the results of direct numerical simulation. This estimate implies the same value for the universal Kolmogorov constant of the energy spectrum, which is consistent with the results of many measurements. The other two model parameters can be obtained then by dynamic procedures. Therefore, the closure problems of LES equations are overcome in this way such that adjustable parameters are not involved.     

Multi-scale analysis of subgrid stress and energy dissipation in turbulent channel flow

In present study, the subgrid scale （SGS） stress and dissipation for multiscale formulation of large eddy simulation are analyzed using the data of turbulent channel flow at Ret = 180 obtained by direct numerical simulation. It is found that the small scale SGS stress is much smaller than the large scale SGS stress for all the stress components. The dominant contributor to large scale SGS stress is the cross stress between small scale and subgrid scale motions, while the cross stress between large scale and subgrid scale motions make major contributions to small scale SGS stress. The energy transfer from resolved large scales to subgrid scales is mainly caused by SGS Reynolds stress, while that between resolved small scales and subgrid scales are mainly due to the cross stress. The multiscale formulation of SGS models are evaluated a priori, and it is found that the small- small model is superior to other variants in terms of SGS dissipation.     

On Near-Wall Treatment in (U)RANS-Based Closure Models

The present work is concerned with computational evaluation of a recently formulated near-wall relationship providing the value of the dissipation rate ε of the kinetic energy of turbulence k through its exact dependence on the Taylor microscale λ: ε = 10νk/λ ², (Jakirli? and Jovanovi?, J. Fluid Mech. 656:530–539, 2010). Dissipation rate determination benefits from the asymptotic behavior of the Taylor microscale resulting in its linear variation in terms of the wall distance (λ?∝?y) being valid throughout entire viscous sublayer. Accordingly, it can be applied as a unified near-wall treatment in all computational frameworks relying on a RANS-based model of turbulence (including also hybrid LES/RANS schemes) independent of modeling level—both main modeling concepts eddy-viscosity and Reynolds stress models can be employed. Presently, the feasibility of the proposed formulation was demonstrated by applying a conventional near-wall second-moment closure model based on the homogeneous dissipation rate ε _h ( ${\varepsilon_h =\varepsilon -0.5\partial \left( {{\nu \partial k}/ {\partial x_j }} \right)} / {\partial x_j }$ ; Jakirli? and Hanjali?, J. Fluid Mech. 539:139–166, 2002) and its instability-sensitive version, modeled in terms of the inverse turbulent time scale ω _h (ω _h ?=?ε _h /k; Maduta and Jakirli?, 2011), to a fully-developed channel flow with both flat walls and periodic hill-shaped constrictions mounted on the bottom wall in a Reynolds number range. The latter configuration is subjected to boundary layer separation from a continuous curved wall. The influence of the near-wall resolution lowering with respect to the location of the wall-closest computational node, coarsened even up to the viscous sublayer edge situated at $y_P^+ \approx 5$ in equilibrium flows, is analyzed. The results obtained follow closely those pertinent to the conventional near-wall integration with the wall-next node positioned at $y_P^+ \le 0.5$ .     

A mixed-timescale SGS model for thermal field at various Prandtl numbers

A new subgrid-scale (SGS) model for the thermal field is proposed. The model is an extended version of the mixed-timescale (MTS) SGS model for velocity field by Inagaki et al. (2005), which has been confirmed to be a refined SGS model for velocity field suited to engineering-relevant practical large eddy simulation (LES). In the proposed model for the thermal field, a hybrid timescale between the timescales of the velocity and thermal fields is introduced in a manner similar to velocity-field modeling. Thus, the present model dispenses with an ambiguous SGS turbulent Prandtl number, like the dynamic SGS model. In addition, the wall-limiting behavior of turbulence is satisfied, which is not in the original MTS model, by incorporating the wall-damping function for LES based on the Kolmogorov velocity scale proposed by Inagaki et al. (2010). The model performance is tested in plane channel flows at various Prandtl numbers, and the results show that this model gives the ratio of the timescales between the velocity and thermal fields similar to that obtained using the dynamic Smagorinsky model with locally calculated model parameters. It is also shown that the proposed model predicts better mean and fluctuating temperature profiles in cooperation with the revised MTS model for the velocity field, than the Smagorinsky model and the dynamic Smagorinsky model. The present model is constructed with fixed model parameters, so that it does not suffer from computational instability with the dynamic model. Thus, it is expected to be a refined and versatile SGS model suited for practical LES of the thermal field.     

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.     

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.     

Development of Gas-Particle Euler-Euler LES Approach: A Priori Analysis of Particle Sub-Grid Models in Homogeneous Isotropic Turbulence

A new large eddy simulation (LES) approach for particle-laden turbulent flows in the framework of the Eulerian formalism for inertial particle statistical modelling is developed. Local instantaneous Eulerian equations for the particle cloud are first written using the mesoscopic Eulerian formalism (MEF) proposed by Février et al. (J Fluid Mech 533:1–46, 2005), which accounts for the contribution of an uncorrelated velocity component for inertial particles with relaxation time larger than the Kolmogorov time scale. Second, particle LES equations are obtained by volume filtering the mesoscopic Eulerian ones. In such an approach, the particulate flow at larger scales than the filter width is recovered while sub-grid effects need to be modelled. Particle eddy-viscosity, scale similarity and mixed sub-grid stress (SGS) models derived from fluid compressible turbulence SGS models are presented. Evaluation of such models is performed using three sets of particle Lagrangian results computed from discrete particle simulation (DPS) coupled with fluid direct numerical simulation (DNS) of homogeneous isotropic decaying turbulence. The two phase flow regime corresponds to the dilute one where two-way coupling and inter-particle collisions are not considered. The different particle Stokes number (based on Kolmogorov time scale) are initially equal to 1, 2.2 and 5.1. The mesoscopic field properties are analysed in detail by considering the particle velocity probability function (PDF), correlated velocity power spectra and random uncorrelated velocity moments. The mesoscopic fields measured from DPS+DNS are then filtered to obtain large scale fields. A priori evaluation of particle sub-grid stress models gives comparable agreement than for fluid compressible turbulence models. It has been found that the standard Smagorinsky eddy-viscosity model exhibits the smaller correlation coefficients, the scale similarity model shows very good correlation coefficient but strongly underestimates the sub-grid dissipation and the mixed model is on the whole superior to pure eddy-viscosity model.     

Numerical Simulation of Single-Stream Jets from a Serrated Nozzle

Hybrid large-eddy type simulations for cold jet flows from a serrated nozzle are performed at an acoustic Mach number Ma _ac ?=?0.9 and Re?=?1.03×10⁶. Since the solver being used tends towards having dissipative qualities, the subgrid scale (SGS) model is omitted, giving a numerical type LES (NLES) or implicit LES (ILES) reminiscent procedure. To overcome near wall streak resolution problems a near wall RANS (Reynolds averaged Navier-Stokes) model is smoothly blended to the LES making a hybrid RANS-ILES. The geometric complexity of the serrated nozzle is fully considered without simplification or emulation. An improved but still modest hexahedral multi-block grid with circa 20 million grid points (with respect to 12.5 million in Xia et al., Int J Heat Fluid Flow 30:1067–1079, 2009) is used. Despite the modest grid size, encouraging and improved results are obtained. Directly resolved mean and second-order fluctuating quantities along the jet centerline and in the jet shear layer compare favorably with measurements. The radiated far-field sound predicted using the Ffowcs Williams and Hawkings (FW-H) surface integral method shows good agreement with the measurements in directivity and sound spectra.     

基于人工神经网络的亚格子应力建模

亚格子(SGS)应力建模在湍流大涡模拟(LES)中有着极为重要的作用. 传统亚格子应力模型存在相对误差较大、耗散过强等问题. 近年来, 计算机技术的发展使得人工神经网络(ANN)等机器学习方法逐渐成为亚格子应力建模型的新研究范式. 本文着重考虑滤波宽度及雷诺数影响, 在不可压缩槽道湍流中建立了亚格子应力的ANN模型. 该模型以滤波后的直接数值模拟(fDNS)流场物理量及滤波尺度为输入信息, 相应滤波尺度下的亚格子应力为输出量. 通过对不同滤波尺度及不同雷诺数数据的训练, ANN模型能够给出与直接数值模拟(DNS)高度吻合的亚格子应力. 此外, 模型在亚格子耗散等非ANN建模量上也有着优异的预测性能, 与基于DNS获得的对应物理量的相关系数大都在0.9以上, 较梯度模型及Smagorinsky模型有明显提升. 在后验测试中, ANN模型对流向平均速度剖面的预测同样优于梯度模型、Smagorinsky模型及隐式大涡模拟(ILES)等传统LES模型. 在脉动速度均方根预测方面, 除了某些法向位置外ANN模型的性能整体上相对其他3个模型有所提升. 然而, 随着网格尺度的增大ANN模型预测的结果与fDNS结果的偏差逐渐增大. 总之, ANN方法在发展高精度亚格子应力模型上具有很大的潜力.      

Assessment of Five SGS Models for Low-Rem MHD Turbulence

Assessment of three regularization-based and two eddy-viscosity-based subgrid-scale (SGS) turbulence models for large eddy simulations (LES) are carried out in the context of magnetohydrodynamic (MHD) decaying homogeneous turbulence (DHT) with a Taylor scale Reynolds number (Re_λ) of 120 and a MHD transition-to-turbulence Taylor-Green vortex (TGV) problems with a Reynolds number of 3000, through direct comparisons to direct numerical simulations (DNS). Simulations are conducted using the low-magnetic Reynolds number approximation (Re_m<<1). LES predictions using the regularization-based Leray- α,LANS- α, and Clark- α SGS models, along with the eddy viscosity-based non-dynamic Smagorinsky and the dynamic Smagorinsky models are compared to in-house DNS for DHT and previous results for TGV. With regard to the regularization models, this work represents their first application to MHD turbulence. Analyses of turbulent kinetic energy decay rates, energy spectra, and vorticity fields made between the varying magnetic field cases demonstrated that the regularization models performed poorly compared to the eddy-viscosity models for all MHD cases, but the comparisons improved with increase in magnitude of magnetic field, due to a decrease in the population of SGS eddies within the flow field.     

Effect of Particle Clusters on Carrier Flow Turbulence: A Direct Numerical Simulation Study

Experiments indicate that particle clusters that form in fluidized–bed risers can enhance gas-phase velocity fluctuations. Direct numerical simulations (DNS) of turbulent flow past uniform and clustered configurations of fixed particle assemblies at the same solid volume fraction are performed to gain insight into particle clustering effects on gas-phase turbulence, and to guide model development. The DNS approach is based on a discrete-time, direct-forcing immersed boundary method (IBM) that imposes no-slip and no-penetration boundary conditions on each particle’s surface. Results are reported for mean flow Reynolds number Re _p ?=?50 and the ratio of the particle diameter d _p to Kolmogorov scale is 5.5. The DNS confirm experimental observations that the clustered configurations enhance the level of fluid-phase turbulent kinetic energy (TKE) more than the uniform configurations, and this increase is found to arise from a lower dissipation rate in the clustered particle configuration. The simulations also reveal that the particle-fluid interaction results in significantly anisotropic fluid-phase turbulence, the source of which is traced to the anisotropic nature of the interphase TKE transfer and dissipation tensors. This study indicates that when particles are larger than the Kolmogorov scale (d _p ?>?η), modeling the fluid-phase TKE alone may not be adequate to capture the underlying physics in multiphase turbulence because the Reynolds stress is anisotropic. It also shows that multiphase turbulence models should consider the effect of particle clustering in the dissipation model.     

DNS of turbulent heat transfer in a channel flow with a high spatial resolution

Direct numerical simulations of turbulent heat transfer in a channel flow are performed to investigate the effects of Reynolds and Prandtl numbers on higher-order turbulence statistics such as a turbulent Prandtl number and the budget for the dissipation rate of the temperature variance. The Reynolds numbers based on the friction velocity and the channel half width are 180 and 395, and the molecular Prandtl numbers Pr’s 0.71–10.0. Careful attention is paid to ensure accuracy of the higher-order statistics through the use of a high spatial resolution comparable to Batchelor length scale. The wall-asymptotic value of the turbulent Prandtl number is mostly independent of Reynolds number for the current range of Pr’s. The budget for the dissipation rate of the temperature variance has been computed, and the negligible effect of a Reynolds number on the sum of all source and sink terms in near-wall region in the current computational range is found. This result is quite similar to the one in the budget for the dissipation rate of turbulent energy. In addition, a priori test for existing models is also performed to assess the Pr dependence on the individual terms and their summations in the budget.     

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     

A low Reynolds number variant of partially-averaged Navier-Stokes model for turbulence

A low Reynolds number (LRN) formulation based on the Partially Averaged Navier-Stokes (PANS) modelling method is presented, which incorporates improved asymptotic representation in near-wall turbulence modelling. The effect of near-wall viscous damping can thus be better accounted for in simulations of wall-bounded turbulent flows. The proposed LRN PANS model uses an LRN k-ε model as the base model and introduces directly its model functions into the PANS formulation. As a result, the inappropriate wall-limiting behavior inherent in the original PANS model is corrected. An interesting feature of the PANS model is that the turbulent Prandtl numbers in the k and ε equations are modified compared to the base model. It is found that this modification has a significant effect on the modelled turbulence. The proposed LRN PANS model is scrutinized in computations of decaying grid turbulence, turbulent channel flow and periodic hill flow, of which the latter has been computed at two different Reynolds numbers of Re = 10,600 and 37,000. In comparison with available DNS, LES or experimental data, the LRN PANS model produces improved predictions over the standard PANS model, particularly in the near-wall region and for resolved turbulence statistics. Furthermore, the LRN PANS model gives similar or better results - at a reduced CPU time - as compared to the Dynamic Smagorinsky 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.     

Superiority of PANS compared to LES in predicting a rudimentary landing gear flow with affordable meshes

Results of simulations of the flow around a rudimentary landing gear are presented in the paper. A newly proposed improved Partially-Averaged Navier–Stokes (PANS) method using k − ε − ζ − f turbulence model is used for prediction of the flow. The results are compared with the experimental data but also with the results of two LES simulations performed using the PANS computational grids. PANS simulations predicted the flow in good agreement with the experimental data. LES predicted a non-physical creation of separation over the front wheels that does not exist in the PANS prediction and was not observed in the experimental oil film. PANS simulations showed low sensitivity to the grid refinement. They show clear advantage compared with the LES simulations when the computational grid is inadequate for resolution of the near-wall flow structures.