Structural subgrid-scale modeling for large-eddy simulation: A review

Accurately modeling nonlinear interactions in turbulence is one of the key challenges for large-eddy simu-lation (LES) of turbulence. In this article, we review recent studies on structural subgrid scale modeling, focusing on evaluating how well these models predict the effects of small scales. The article discusses a priori and a posteriori test results. Other nonlinear models are briefly discussed, and future prospects are noted.     

Scaling law of resolved-scale isotropic turbulence and its application in large-eddy simulation

Eddy-damping quasinormal Markovian （EDQNM） theory is employed to calculate the resolved-scale spectrum and transfer spectrum, based on which we investigate the resolved-scale scaling law. Results show that the scaling law of the resolved-scale turbulence, which is affected by several factors, is far from that of the full-scale turbulence and should be corrected. These results are then applied to an existing subgrid model to improve its performance. A series of simulations are performed to verify the necessity of a fixed scaling law in the subgrid modeling.     

Invariant subgrid modelling in large-eddy simulation of heat convection turbulence

Symmetries have an important role in turbulence. To some extent, they contain the physics of the equations (conservation laws, etc.), and it is essential that turbulence models respect them. However, as observed by Oberlack (Annual Research Briefs. Stanford University, Stanford 1997) and next by Razafindralandy and Hamdouni (Direct and Large-Eddy Simulation 6: Proceedings of the 6th International ERCOFTAC Workshop on Direct and Large-Eddy Simulation. Springer, Heidelberg, 2006) in the case of an isothermal fluid, only few subgrid stress tensor models preserve the symmetries of the Navier–Stokes equations. In this communication, we present the symmetries of the equations of a non-isothermal fluid flow and analyze some common subgrid stress tensor and flux models under the point of view of these symmetries.      

A complete and irreducible dynamic SGS heat-flux modelling based on the strain rate tensor for large-eddy simulation of thermal convection

In this paper, a general family of explicit algebraic tensor diffusivity functions based on the resolved temperature gradient vector and strain rate tensor is studied and applied to the construction of new constitutive relations for modelling the subgrid-scale (SGS) heat flux (HF). Based on Noll’s formulation, dynamic linear and nonlinear tensor diffusivity models are proposed for large-eddy simulation of thermal convection. The constitutive relations for these two proposed models are complete and irreducible. These two new models include several existing dynamic SGS HF models as special cases. It is shown that in contrast to the conventional modelling approach, the proposed models embody more degrees of freedom, permit non-alignment between the SGS HF and resolved temperature gradient vectors, reflect near-wall flow physics at the subgrid scale, and therefore, allow for a more realistic geometrical representation of the SGS heat flux for large-eddy simulation of thermal convection. Numerical simulations have been performed using a benchmark test case of a combined forced and natural convective flow in a vertical channel with a Reynolds number of and a Grashof number of Gr = 9.6 × 10⁵. The results obtained using the two proposed SGS HF models are compared with reported direct numerical simulation (DNS) data as well as predictions obtained using several conventional dynamic SGS HF models.     

Geometrical properties of the vorticity vector derived using large-eddy simulation

In this paper, the geometrical properties of the resolved vorticity vector derived from large-eddy simulation are investigated using a statistical method. Numerical tests have been performed based on a turbulent Couette channel flow using three different dynamic linear and nonlinear subgrid-scale stress models. The geometrical properties of have a significant impact on various physical quantities and processes of the flow. To demonstrate, we examined helicity and helical structure, the attitude of with respect to the eigenframes of the resolved strain rate tensor and negative subgrid-scale stress tensor -τ_ij, enstrophy generation, and local vortex stretching and compression. It is observed that the presence of the wall has a strong anisotropic influence on the alignment patterns between and the eigenvectors of , and between and the resolved vortex stretching vector. Some interesting wall-limiting geometrical alignment patterns and probability density distributions in the form of Dirac delta functions associated with these alignment patterns are reported. To quantify the subgrid-scale modelling effects, the attitude of with respect to the eigenframe of -τ_ij is studied, and the geometrical alignment between and the Euler axis is also investigated. The Euler axis and angle for describing the relative rotation between the eigenframes of -τ_ij and are natural invariants of the rotation matrix, and are found to be effective for characterizing a subgrid-scale stress model and for quantifying the associated subgrid-scale modelling effects on the geometrical properties of .     

Temporal large-eddy simulation of unstratified and stably stratified turbulent channel flows

Recently, Pruett et al. [Pruett, C.D., Gatski, T.B., Grosch, C.E., Thacker, W.D., 2003. The temporally filtered Navier–Stokes equations: properties of the residual stress. Phys. Fluids 15, 2127–2140] proposed an approach to large-eddy simulation (LES) based on time-domain filtering; their approach was termed temporal large-eddy simulation or TLES. In a continuation of their work, Pruett and collaborators tested their methodology by successfully performing TLES of unstratified turbulent channel flow up to Reynolds number of 590 (based on channel half-height and friction velocity) [Pruett, C.D., Thomas, B.C., Grosch, C.E., Gatski, T.B., 2006. A temporal approximate deconvolution model for LES. Phys. Fluids 18, 028104, 4p]. Here, we carefully analyze the TLES methodology in order to understand the role of its key components and in the process compare TLES to more traditional approaches of spatial LES. Furthermore, we extend the methodology to stably stratified turbulent channel flow.     

Evaluation of subgrid-scale models in large-eddy simulation of flow past a two-dimensional block

Large-eddy simulations of flow past a two-dimensional (2D) block were performed to evaluate four subgrid-scale (SGS) models: (i) the traditional Smagorinsky model, (ii) the Lagrangian dynamic model, (iii) the Lagrangian scale-dependent dynamic model, and (iv) the modulated gradient model. An immersed boundary method was employed to simulate the 2D block boundaries on a uniform Cartesian grid. The sensitivity of the simulation results to grid refinement was investigated by using four different grid resolutions. The velocity streamlines and the vertical profiles of the mean velocities and variances were compared with experimental results. The modulated gradient model shows the best overall agreement with the experimental results among the four SGS models. In particular, the flow recirculation, the reattachment position and the vertical profiles are accurately reproduced with a relative coarse grid resolution of (N_x × N_y × N_z=) 160 × 40 × 160 (n_x × n_z = 13 × 16 covering the block). Besides the modulated gradient model, the Lagrangian scale-dependent dynamic model is also able to give reasonable prediction of the flow statistics with some discrepancies compared with the experimental results. Relatively poor performance by the Lagrangian dynamic model and the Smagorinsky model is observed, with simulated recirculating patterns that differ from the measured ones. Analysis of the turbulence kinetic energy (TKE) budget in this flow shows evidence of a strong production of TKE in the shear layer that forms as the flow is deflected around the block.     

A diagnostic tool for jet noise using a line-source approach and implicit large-eddy simulation data

In this work, we propose a cost-effective approach allowing one to evaluate the acoustic field generated by a turbulent jet. A turbulence-resolving simulation of an incompressible turbulent round jet is performed for a Reynolds number equal to $460,000$ thanks to the massively parallel high-order flow solver Incompact3d. Then a formulation of Lighthill's solution is derived, using an azimuthal Fourier series expansion and a compactness assumption in the radial direction. The formulation then reduces to a line source theory, which is cost-effective to implement and evaluate. The accuracy of the radial compactness assumption, however, depends on the Strouhal number, the Mach number, the observation elevation angle, and the radial extent of the source. Preliminary results are showing that the proposed method approaches the experimental overall sound pressure level by less than 4 dB for aft emission angles below 50°.     

Assessment of ghost-cell based cut-cell method for large-eddy simulations of compressible flows at high Reynolds number

Large-eddy simulations (LES) of high Reynolds number flows are performed using a non-body conformal method in conjunction with a wall model. We use a simple wall function to model the wall-shear stress and the truncation error of the numerical discretization to model the sub-grid scale turbulence (implicit LES), although these can be easily replaced if necessary. The validation cases are: turbulent flow through an inclined channel, turbulent flow over a wavy surface, and supersonic flow over a circular cylinder. Since the near-wall grids are naturally coarse, the key is to use a method that is capable of capturing the flow dynamics accurately in the vicinity of the interface. Towards the purpose, we develop a Cartesian cut-cell method, referred to as the ghost-cell based cut-cell method (GC-CCM), in the context of fully compressible solutions of Navier–Stokes equations. This method employs ghost-cells inside the solid interface such that the local spatial reconstruction remains consistent everywhere including in the vicinity of the boundary. In order to capture the near-wall flow behavior more accurately with coarse grids, this method decomposes cell faces of merged cells and computes fluxes through each decomposed segment separately. The objective of this work is to qualify whether the proposed method can accurately represent the high Reynolds number flows in the vicinity of immersed interfaces. To analyze the performance of the proposed method, we compare the results to the corresponding numerical results from the two other non-body conformal methods, namely the ghost-cell based immersed boundary method (GCIBM) and standard cut-cell method (S-CCM), that are implemented in the same numerical solver. The comparison demonstrates that the proposed method is capable of capturing near-wall flows relatively accurately with coarse grids.     

Large-eddy simulation of turbulent flow and heat transfer in plane and rib-roughened channels

Large-eddy simulation results are presented and discussed for turbulent flow and heat transfer in a plane channel with and without transverse square ribs on one of the walls. They were obtained with the finite-difference code Harwell-FLOW3D, Release 2, by using the PISOC pressure-velocity coupling algorithm, central differencing in space, and Crank-Nicolson time stepping. A simple Smagorinsky model, with van Driest damping near the walls, was implemented to model subgrid scale effects. Periodic boundary conditions were imposed in the streamwise and spanwise directions. The Reynolds number based on hydraulic diameter (twice the channel height) ranged from 10 000 to 40 000. Results are compared with experimental data, k-? predictions, and previous large-eddy simulations.     

High‐order filtering for control volume flow simulation

A general methodology is presented in order to obtain a hierarchy of high‐order filter functions, starting from the standard top‐hat filter, naturally linked to control volumes flow simulations. The goal is to have a new filtered variable better represented in its high resolved wavenumber components by using a suitable deconvolution. The proposed formulation is applied to the integral momentum equation, that is the evolution equation for the top‐hat filtered variable, by performing a spatial reconstruction based on the approximate inversion of the averaging operator. A theoretical analysis for the Burgers' model equation is presented, demonstrating that the local de‐averaging is an effective tool to obtain a higher‐order accuracy. It is also shown that the subgrid‐scale term, to be modeled in the deconvolved balance equation, has a smaller absolute importance in the resolved wavenumber range for increasing deconvolution order. A numerical analysis of the procedure is presented, based on high‐order upwind and central fluxes reconstruction, leading to congruent control volume schemes. Finally, the features of the present high‐order conservative formulation are tested in the numerical simulation of a sample turbulent flow: the flow behind a backward‐facing step. Copyright © 2001 John Wiley & Sons, Ltd.     

搅拌槽流场特性的大涡模拟研究

采用大涡模型结合气液两相流时均方程,对六直叶圆盘涡轮搅拌槽内的流场特性进行了数值模拟。自由水面的捕捉用VOF(Volume of Fluid)法,用Simplec方法求解控制方程。通过模拟得到了搅拌槽内复杂的双涡旋流场结构、转轮叶端尾涡的发展变化情况以及轴向流速的分布规律。通过对比大涡模拟与RNGκ-ε的计算结果,得知大涡模型能模拟出流场内瞬时旋涡的发展变化过程,反映出挡板的存在破坏了圆形搅拌槽的流通模式,提高了叶片附近的混合效率;桨叶区域湍流呈现明显的各向异性,时均流速存在明显的波动性。从而证明了用大涡模拟探讨搅拌槽内湍流现象及流场结构的可靠性。     

Large Eddy Simulation of Turbulent Reacting Shear Layers Including Finite-Rate Chemistry and Detailed Diffusion Processes

Large eddy simulations (LES) of turbulent temporal shear layers with hydrogen chemistry are performed. In these simulations, approximate deconvolution is applied as an implicit subgrid-scale modeling approach to a reacting flow in combination with a steady flamelet model for the filtered heat release term. No additional heuristical or physical subgrid models are used. The formulation of the flamelet equations in physical space does not only allow to consider a detailed reaction scheme and the extinguished phase but also to take into account detailed diffusion mechanisms (Soret and Dufour effects, multicomponent diffusion coefficients). Two different levels of diffusion approximations are investigated in this work, the aim of which is twofold: Firstly, to verify approximate deconvolution as a tool for convective transport of mass, momentum and energy in gas flow, by comparing the LES results with those of a direct numerical simulation and secondly, to investigate the influence of detailed diffusion on the laminar flamelets and the LES results.     

A hybrid dynamic Smagorinsky model for large eddy simulation

A hybrid dynamic subgrid-scale model (HDSM) pertaining to Large-eddy simulation (LES) has been developed. The coefficient obtained by German dynamic Smagorinsky model (DSM) was integrated with a new dynamic coefficient, based on the dynamic subgrid characteristic length and controlled by the subgrid-scale (SGS) motions. In HDSM, the characteristic wave number determining the characteristic length of the dynamic subgrid is calculated from a new energy weighted mean method when the subgrid scale turbulent kinetic energy and the dissipation wave number are known. The dissipation wave-number is derived from the SGS turbulent kinetic energy spectrum equation. The total dissipation rate spectrum equation is based on the Pao energy spectrum and local equilibrium assumption. The dynamic subgrid characteristic length could take into account the rapidly fluctuating small scale behaviours and the spatial variation of turbulent characteristics. HDSM was used to simulate the fully developed channel and turbulent flow past a circular cylinder, and to determine the impact of the dam-break flow on downstream structure. The HDSM is robust in respect to anisotropic mesh and is less sensitive to grid resolution, and would accurately describe the energy transfer from large-scale to SGS fluctuations and capture more fluctuations of turbulence with same meshes compared to the DSM.     

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.     

Large-eddy simulation of buoyancy-driven natural ventilation in an enclosure with a point heat source

Rising buoyant plumes from a point heat source in a naturally ventilated enclosure have been investigated using large-eddy simulation (LES). The aim of the work is to assess the performance and the accuracy of LES for modelling buoyancy-driven displacement ventilation of an enclosure and to shed more light on the transitional behaviour of the plume and the coherent structures involved. The Smagorinsky sub-grid scale model is used for the unresolved small-scale turbulence. The Rayleigh number, Ra is chosen to be in the range where spatial transition from laminar to turbulent flow takes place (Ra = 1.5 × 10⁹). The plume properties (source strength and rate of spread) as well as the ventilation properties (stratification height and temperature of stratified layer) estimated using the theory of Linden et al. are found to agree reasonably well with the LES results. The variation of the plume width with height indicates a linear variation of the entrainment coefficient rather than a constant value used by Linden et al. for a fully turbulent thermal plume. Flow visualisation revealed the nature of the large-scale coherent structures involved in the transition to turbulence in the plume. The most excited modes observed in the velocity, pressure and temperature fields spectra correspond to Strouhal number in the range 0.3 ≤ St ≤ 0.55 which is in agreement with those observed by Zhou et al. for a turbulent forced plume. Excited modes less than thisvalue (St = 0.2) were observed and may be due to low-frequency motions felt throughout the flow.