AGE method simulations of a turbulent far‐wake compared to spectral DNS

Turbulent flow simulation methods based on finite differences are attractive for their simplicity, flexibility and efficiency, but not always for accuracy or stability. This paper demonstrates that a good compromise is possible with the advected grid explicit (AGE) method. Starting from the same initial field as a previous spectral DNS, AGE method simulations of a planar turbulent wake were carried out as DNS, and then at three levels of reduced resolution. The latter cases were in a sense large‐eddy simulations (LES), although no specific sub‐grid‐scale model was used. Results for the two DNS methods, including variances and power spectra, were very similar, but the AGE simulation required much less computational effort. Small‐scale information was lost in the reduced resolution runs, but large‐scale mean and instantaneous properties were reproduced quite well, with further large reductions in computational effort. Quality of results becomes more sensitive to the value chosen for one of the AGE method parameters as resolution is reduced, from which it is inferred that the numerical stability procedure controlled by the parameter is acting in part as a sub‐grid‐scale model. Copyright © 2002 John Wiley & Sons, Ltd.     

Shear‐improved Smagorinsky modeling of turbulent channel flow using generalized Lattice Boltzmann equation

Generalized Lattice Boltzmann equation (GLBE) was used for computation of turbulent channel flow for which large eddy simulation (LES) was employed as a turbulence model. The subgrid‐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 a relatively coarse grid with shear Reynolds number of 180 in a parallelized code. Good numerical stability was observed for this computational framework. The results of mean velocity distribution across the channel showed good correspondence with direct numerical simulation (DNS) data. Negligible discrepancies were observed between the present computations and those reported from DNS for the computed turbulent statistics. Three‐dimensional instantaneous vorticity contours showed complex vortical structures that appeared in such flow geometries. It was concluded that such a framework is capable of predicting accurate results for turbulent channel flow without adding significant complications and the computational cost to the standard Smagorinsky model. As this modeling was entirely local in space it was therefore adapted for parallelization. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Influence of mesh deformation on the quality of large eddy simulations

The influence of mesh motion on the quality of large eddy simulation (LES) was studied in the present article. A three‐dimensional, turbulent pipe flow (Re_τ=360) was considered as a test case. Simulations with both stretching and static meshes were carried out in order to understand how mesh motion affects the turbulence statistics. The spatial filtering of static and moving mesh direct numerical simulation (DNS) data showed how an ideal LES would perform, while the comparison of DNS cases with static and moving meshes revealed that no significant numerical errors arise from the mesh motion when the simulation is fully resolved. The comparison of the filtered fields of the DNS with a moving mesh with the corresponding LES fields revealed different responses to mesh motion from different numerical approaches. A straightforward test was applied in order to verify that the moving mesh works consistently in LES: when the mesh is stretched in the streamwise direction, the moving mesh results should be in between the two extremal resolutions between which the mesh is stretched. Numerical investigations using four different LES approaches were carried out. In addition to the Smagorinsky model, three implicit LES approaches were used: linear interpolation (non‐dissipative), the Gamma limiter (dissipative), and the scale‐selective discretisation (slightly dissipative). The results indicate that while the Smagorinsky and the scale‐selective discretisation approaches produce results consistent with the resolution of the non‐static mesh, the implicit LES with linear interpolation or the Gamma scheme do not. Copyright © 2016 John Wiley & Sons, Ltd.     

Implicit LES of free and wall‐bounded turbulent flows based on the discontinuous Galerkin/symmetric interior penalty method

This paper presents the second validation step of a compressible discontinuous Galerkin solver with symmetric interior penalty (DGM/SIP) for the direct numerical simulation (DNS) and the large eddy simulation (LES) of complex flows. The method has already been successfully validated for DNS of an academic flow and has been applied to flows around complex geometries (e.g. airfoils and turbomachinery blades). During these studies, the advantages of the dissipation properties of the method have been highlighted, showing a natural tendency to dissipate only the under‐resolved scales (i.e the smallest scales present on the mesh), leaving the larger scales unaffected. This phenomenon is further enhanced as the polynomial order is increased. Indeed, the order increases the dissipation at the largest wave numbers, while its range of impact is reduced. These properties are spectrally compatible with a subgrid‐scale model, and hence DGM may be well suited to be used for an implicit LES (ILES) approach. A validation of this DGM/ILES approach is here investigated on canonical flows, allowing to study the impact of the discretisation on the turbulence for under‐resolved computations. The first test case is the LES of decaying homogeneous isotropic turbulence (HIT) at very high Reynolds number. This benchmark allows to assess the spectral behaviour of the method for implicit LES. The results are in agreement with theory and are even slightly more accurate than other numerical results from literature, obtained using a pseudo‐spectral (PS) method with a state‐of‐the‐art subgrid‐scale model. The second benchmark is the LES of the channel flow. Three Reynolds numbers are considered: Re_τ=395, 590 and 950. The results are compared with DNS of Moser et al. and Hoyas et al., also using PS methods. Both averaged velocity and fluctuations are globally in good agreement with the reference, showing the ability of the method to predict equilibrium wall‐bounded flow turbulence. To show that the method is able to perform accurate DNS, a DNS of HIT at Re_λ=64 and a DNS of the channel flow at Re_τ=180 are also performed. The effects of the grid refinement are investigated on the channel flow at Re_τ=395, highlighting the improvement of the results when refining the mesh in the spanwise direction. Finally, the modification of the ILES parameters, that is the Riemann solver and of the SIP coefficient, is studied on both cases, showing a significant influence on the choice of the Riemann solver. Copyright © 2015 John Wiley & Sons, Ltd.     

Surface‐sampled simulations of turbulent flow at high Reynolds number

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

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.     

Large eddy simulation of free surface shallow‐water flow

Shallow‐water flow with free surface frequently occurs in ambient water bodies, in which the horizontal scale of motion is generally two orders of magnitude greater than the water depth. To accurately predict this flow phenomenon in more detail, a three‐dimensional numerical model incorporating the method of large eddy simulation (LES) has been developed and assessed. The governing equations are split into three parts in the finite difference solution: advection, dispersion and propagation. The advection part is solved by the QUICKEST scheme. The dispersion part is solved by the central difference method and the propagation part is solved implicitly using the Gauss–Seidel iteration method. The model has been applied to free surface channel flow for which ample experimental data are available for verification. The inflow boundary condition for turbulence is generated by a spectral line processor. The computed results compare favourably with the experimental data and those results obtained by using a periodic boundary condition. The performance of the model is also assessed for the case in which anisotropic grids and filters with horizontal grid size of the order of the water depth are used for computational efficiency. The coarse horizontal grid was found to cause a significant reduction in the large‐scale turbulent motion generated by the bottom turbulence, and the turbulent motion is predominately described by the sub‐grid scale (SGS) terms. The use of the Smagorinsky model for SGS turbulence in this situation is found inappropriate. A parabolic mixing length model, which accounts for the filtered turbulence, is then proposed. The new model can reproduce more accurately the flow quantities. Copyright © 2000 John Wiley & Sons, Ltd.     

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 stretched vortex subgrid‐scale models for LES of incompressible inhomogeneous turbulent flow

The physical space version of the stretched vortex subgrid scale model is tested in LES of the turbulent lid‐driven cubic cavity flow. LES is carried out by using a higher order finite‐difference method. The effects of different vortex orientation models and subgrid turbulence spectrums are assessed through comparisons of the LES predictions against DNS. Three Reynolds numbers 12000, 18000, and 22000 are studied. Good agreement with the DNS data for the mean and fluctuating quantities is observed. Copyright © 2013 John Wiley & Sons, Ltd.     

The effect of inflow conditions on the transition to turbulence in large eddy simulations of spatially developing mixing layers

Large Eddy Simulations (LES) of spatially developing turbulent mixing layers have been performed for flows of uniform density and Reynolds numbers of up to 50,000 based on the visual thickness of the layer and the velocity difference across it. On a fine LES grid, a validation simulation performed with a hyperbolic tangent inflow profile produces flow statistics that compare extremely well with reference Direct Numerical Simulation (DNS) data. An inflow profile derived from laminar Blasius profiles produces a flow that is significantly different to the reference DNS, particularly with respect to the initial development of the flow. When compared with experimental data, however, it is the boundary layer-type inflow simulation produces the better prediction of the flow statistics, including the mean transition location. It is found that the boundary layer inflow condition is more unstable than the hyperbolic tangent inlet profile. A suitably designed coarse LES grid produces good predictions of the mean transition location with boundary layer inflow conditions at a low computational cost. The results suggest that hyperbolic tangent functions may produce unreliable DNS data when used as the initial condition for studies of the transition in the mixing layer flow.     

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

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

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.     

旋转圆管湍流的大涡模拟数值研究

采用大涡模拟（LES）方法,并结合动力学亚格子尺度应力（SGS）模型,通过数值求解柱坐标系下的滤波Navier-Stokes方程,研究了绕管轴旋转圆管内的湍流流动特性.为验证计算的可靠性,以及动力学SGS模型对于旋转湍流的适用性,将大涡模拟计算所得的结果,与相应的直接模拟（DNS）结果和实验数据进行了对比验证,吻合良好.进一步对旋转圆管湍流的物理机理进行了探讨,研究了湍流特性随旋转速率的变化规律.当旋转速率增加时,湍流流动有层流化的发展趋势.基于湍动能变化的关系,分析了旋转效应对湍流脉动生成的抑制作用.     

Error of large-eddy simulation in the wall pressure fluctuation of a turbulent channel flow

We analyze the error of large-eddy simulation(LES) in wall pressure fluctuation of a turbulent channel flow. To separate different sources of the error, we conduct both direct numerical simulations(DNS)and LES, and apply an explicit filter on DNS data to obtain filtered DNS(FDNS) data. The error of LES is consequently decomposed into two parts: The first part is the error of FDNS with respect to DNS,which quantifies the influence of the filter operation. The second part is the difference between LES and FDNS induced by the error of LES in velocity field. By comparing the root-mean-square value and the wavenumber-frequency spectrum of the wall pressure fluctuation, it is found that the inaccuracy of the velocity fluctuations is the dominant source that induces the error of LES in the wall pressure fluctuation.The present study provides a basis on future LES studies of the wall pressure fluctuation.     

Numerical simulations of non‐equilibrium turbulent boundary layer flowing over a bump

Large‐eddy simulation (LES) and Reynolds‐averaged Navier–Stokes simulation (RANS) with different turbulence models (including the standard k?ε, the standard k?ω, the shear stress transport k?ω (SST k?ω), and Spalart–Allmaras (S–A) turbulence models) have been employed to compute the turbulent flow of a two‐dimensional turbulent boundary layer over an unswept bump. The predictions of the simulations were compared with available experimental measurements in the literature. The comparisons of the LES and the SST k?ω model including the mean flow and turbulence stresses are in satisfied agreements with the available measurements. Although the flow experiences a strong adverse pressure gradient along the rear surface, the boundary layer is unique in that intermittent detachment occurring near the wall. The numerical results indicate that the boundary layer is not followed by mean‐flow separation or incipient separation as shown from the numerical results. The resolved turbulent shear stress is in a reasonable agreement with the experimental data, though the computational result of LES shows that its peak is overpredicted near the trailing edge of the bump, while the other used turbulence models, except the standard k?ε, underpredicts it. Analysis of the numerical results from LES confirms the experimental data, in which the existence of internal layers over the bump surface upstream of the summit and along the downstream flat plate. It also demonstrates that the quasi‐step increase in skin friction is due to perturbations in pressure gradient. The surface curvature enhances the near‐wall shear production of turbulent stresses, and is responsible for the formation of the internal layers. The aim of the present work is to examine the response and prediction capability of LES with the dynamic eddy viscosity model as a sub‐grid scale to the complex turbulence structure with the presence of streamline curvature generated by a bumpy surface. Aiming to reduce the computational costs with focus on the mean behavior of the non‐equilibrium turbulent boundary layer of flow over the bump surface, the present investigation also explains the best capability of one of the used RANS turbulence models to capture the driving mechanism for the surprisingly rapid return to equilibrium over the trailing flat plate found in the measurements. Copyright © 2010 John Wiley & Sons, Ltd.     

Investigation of a Dynamic Hybrid RANS/LES Modelling Methodology for Finite-Volume CFD Simulations

This paper investigates a recently proposed dynamic hybrid RANS-LES framework using a general-purpose finite-volume flow solver. The new method is highly generalized, allowing coupling of any selected RANS model with any selected LES model and containing no explicit grid dependence in its formulation. Selected results are presented for three test cases: two-dimensional channel flow, backward facing step, and a nozzle flow relevant to biomedical applications. Comparison with experimental and DNS data, and with other hybrid RANS-LES approaches, highlights the advantages of the new method and suggests that further investigation is warranted.     

Large-Eddy and Direct Numerical Simulations of the Bachalo-Johnson Flow with Shock-Induced Separation

The Bachalo-Johnson experiment on an axisymmetric bump has been a primary validation case for turbulence models in shock-boundary-layer interactions since the 1980’s. In the present work, Wall-Modelled Large-Eddy Simulations (WMLES) of this flow were conducted using Improved Delayed Detached-Eddy Simulation (IDDES) as the sub-grid-scale (SGS) and wall model, with a synthetic turbulence generator, expecting close enough agreement with experiment. However, the WMLES results are disappointing, even in terms of the shock position, even though the results from two grids with 4.7 × 10⁸ and 1.6 × 10⁹ cells respectively agree well with each other. This failure of grid refinement to warn of an inaccurate simulation is of great concern, and the reasons for it are explored. We then conducted a Direct Numerical Simulation (DNS) embedded in the LES over a reduced domain, with 8 × 10⁹ grid cells. The DNS has a far more accurate shock position and overall pressure distribution. The skin friction in the favourable pressure gradient is also much higher than in the LES; thus, wide differences appear upstream of the shock wave, most probably caused by the rapid acceleration which leads to atypical shear-stress profiles. Other SGS models were tried, and performed worse than IDDES. The DNS essentially fulfils the initial expectations although in a reduced domain and provides data for turbulence-modelling studies, for instance by extracting an effective eddy viscosity from it. The most noticeable remaining disagreement with experiment is over the Reynolds shear stress.     

Large eddy simulation of gas-particle turbulent channel flow with momentum exchange between the phases

This paper presents results of a large eddy simulation (LES) combined with Lagrangian particle tracking and a point-force approximation for the feedback effect of particles on the downward turbulent gaseous flow in a vertical channel. The LES predictions are compared with the results obtained by direct numerical simulation (DNS) of a finer computational mesh. A parametric study is conducted for particles with two response times in simulations with and without streamwise gravitational settling and elastic, binary interparticle collisions. It is shown that the classical and the dynamic Smagorinsky turbulence models adequately predict the particle-induced changes in the mean streamwise velocity and the Reynolds stresses of the carrier phase for the range of parameters studied. However, the largest discrepancies between the LES and DNS results are found in the cases of particle-laden flows. Conditional sampling of the instantaneous resolved flow fields indicates that the mechanisms by which particles directly oppose the production of momentum and vorticity of the organized fluid motions are also observed in the LES results. However, the geometric features of the near-wall quasistreamwise vortices are overestimated by the use of both turbulence models compared to the DNS predictions.     

Large Eddy Simulation of Scalar Mixing in a Coaxial Confined Jet

The highly turbulent flow occurring inside gas-turbine combustors requires accurate simulation of scalar mixing if CFD methods are to be used with confidence in design. This has motivated the present paper, which describes the implementation of a passive scalar transport equation into an LES code, including assessment/testing of alternative discretisation schemes to avoid over/undershoots and excessive smoothing. Both second order accurate TVD and higher order accurate DRP schemes are assessed. The best performance is displayed by a DRP method, but this is only true on fine meshes; it produces similar (or larger) errors to a TVD scheme on coarser meshes, and the TVD approach has been retained for LES applications. The unsteady scalar mixing performance of the LES code is validated against published DNS data for a slightly heated channel flow. Excellent agreement between the current LES predictions and DNS data is obtained, for both velocity and scalar statistics. Finally, the developed methodology is applied to scalar transport in a confined co-axial jet mixing flow, for which experimental data are available. Agreement with statistically averaged fields for both velocity and scalar, is demonstrated to be very good, and a considerable improvement over the standard eddy viscosity RANS approach. Illustrations are presented of predicted time-resolved information e.g. time histories, and scalar pdf predictions. The LES results are shown, even using a simple Smagorinsky SGS model, to predict (correctly) lower values of the turbulent Prandtl number in the free shear regions of the flow, compared to higher values in the wall-affected regions. The ability to predict turbulent Prandtl number variations (rather than input these as in combustor RANS CFD models) is an important and promising feature of the LES approach for combustor flow simulation since it is known to be important in determining combustor exit temperature traverse.