Invariant analysis of the Reynolds stress tensor for a nuclear fuel assembly with spacer grid and split type vanes

Invariant analysis of the Reynolds stress tensor anisotropy can give an accurate and deep intuitive understanding of the turbulent structure of a turbulent flow. Lumley's triangle has proven to be a powerful representation of the invariant analysis of the second-order statistics collection provided by the Reynolds stress tensor. In the present work the spectral element code Nek5000 has been used to investigate the turbulent structure of the flow across a pressurized water reactor spacer grid with split type mixing vanes. Wall-resolved large eddy simulation of the flow in a prototypical rod bundle geometry at Re = 14,000 and P/D = 1.32 are performed and validated against particle image velocimetry data. The results are then used to perform an in-depth invariant analysis. The results show a reorganization of the Reynolds stresses components in the downstream region of the spacer grid. The mixing vanes orientation produces a symmetric behavior between sub-channels. The turbulent structure in the fully developed region has the typical behavior of fully-developed channel flow turbulence. When averaging the state across regions of the sub-channels, we observed a transition from disk-like turbulence in the mixing vanes region to rod-like turbulence in the fully developed region.     

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.     

Large eddy simulation in a turbulent channel flow using exit boundary conditions

The influence of the exit boundary conditions on the vanishing first derivative of the velocity components and constant pressure on the large eddy simulation of the fully developed turbulent channel flow has been investigated for equidistant and stretched grids at the channel exit. Results show that the chosen exit boundary conditions introduce some small disturbances that are mostly damped by the grid stretching. The difference of rms values between the fully developed turbulent channel flow with periodicity conditions and the fully developed channel flow using inlet and the exit boundary conditions is less than 10% for the equidistant grids and less than 5% for the stretched grids. The chosen boundary conditions are of interest because they may be used in complex problems with back flow at the exit. Copyright © 1999 John Wiley & Sons, Ltd.     

Application of the PITM Method Using Inlet Synthetic Turbulence Generation for the Simulation of the Turbulent Flow in a Small Axisymmetric Contraction

We investigate the turbulence modeling of second moment closure used both in RANS and PITM methodologies from a fundamental point of view and its capacity to predict the flow in a low turbulence wind tunnel of small axisymmetric contraction designed by Uberoi and Wallis. This flow presents a complex phenomenon in physics of fluid turbulence. The anisotropy ratio of the turbulent stresses τ ₁₁/τ ₂₂ initially close to 1.4 returns to unity through the contraction, but surprisingly, this ratio gradually increases to its pre-contraction value in the uniform section downstream the contraction. This point constitutes the interesting paradox of the Uberoi and Wallis experiment. We perform numerical simulations of the turbulent flow in this wind tunnel using both a Reynolds stress model developed in RANS modeling and a subfilter scale stress model derived from the partially integrated transport modeling method. With the aim of reproducing the experimental grid turbulence resulting from the effects of the square-mesh biplane grid on the uniform wind tunnel stream, we develop a new analytical spectral method of generation of pseudo-random velocity fields in a cubic box. These velocity fields are then introduced in the channel using a matching numerical technique. Both RANS and PITM simulations are performed on several meshes to study the effects of the contraction on the mean velocity and turbulence. As a result, it is found that the RANS computation using the Reynolds stress model fails to reproduce the increase of anisotropy in the centerline of the channel after passing the contraction. In the contrary, the PITM simulation predicts fairly well this turbulent flow according to the experimental data, and especially, the “return to anisotropy” in the straight section of the channel downstream the contraction. This work shows that the PITM method used in conjunction with an analytical synthetic turbulence generation as inflow is well suited for simulating this flow, while allowing a drastic reduction of the computational resources.     

充分发展圆管湍流的实验研究

采用粒子数字图像测速（digital particle image velocimetry,DPIV)和定量流动显示技术（quantitative flow visualization,QFA)对充分发展的圆管湍流进行了研究。测量结果和直接数值模拟（direct numerical simulation,DNS)结果进行了比较，结果表明作者开发的DPIV技术取得了满意的精度。在此基础上对圆管湍流的动力学机理进行了研究，分析了上抛和下扫在湍流生成中的贡献以及流动显示结构内的脉动速度分布，测量结果显示在圆管湍流的近壁区存在横向强脉冲现象和流动显示所能观察到的结构为上抛占主导地位的结构。     

Analysis of high-order velocity moments in a strained channel flow

In the current study, model expressions for fifth-order velocity moments obtained from the truncated Gram-Charlier series expansions model for a turbulent flow field probability density function are validated using data from direct numerical simulation (DNS) of a planar turbulent flow in a strained channel. Simplicity of the model expressions, the lack of unknown coefficients, and their applicability to non-Gaussian turbulent flows make this approach attractive to use for closing turbulent models based on the Reynolds-averaged Navier-Stokes equations. The study confirms validity of the model expressions. It also shows that the imposed flow deformation improves an agreement between the model and DNS profiles for the fifth-order moments in the flow buffer zone including when the flow reverses its direction. The study reveals sensitivity of particularly odd velocity moments to the grid resolution. A new length scale is proposed as a criterion for the grid generation near the wall and in the other flow areas dominated by high mean velocity gradients when higher-order statistics have to be collected from DNS.     

Turbulent Energy Scale-Budget Equations for nearly Homogeneous Sheared Turbulence

For moderate Reynolds numbers, the isotropic relation between second-order and third-order moments for velocity increments (Kolmogorov's equation) is not respected, reflecting a non-negligible correlation between the scales responsible for the injection, transfer and dissipation of the turbulent energy. For (shearless) grid turbulence, there is only one dominant large-scale phenomenon, which is the non-stationarity of statistical moments resulting from the decay of energy downstream of the grid. In this case, the extension of Kolmogorov's analysis, as carried out by Danaila, Anselmet, Zhou and Antonia, J. Fluid Mech. 391, 1999 359-369) is quite straightforward. For shear flows, several large-scale phenomena generally coexist with similar amplitudes. This is particularly the case for wall-bounded flows, where turbulent diffusion and shear effects can present comparable amplitudes. The objective of this work is to quantify, in a fully developed turbulent channel flow and far from the wall, the influence of these two effects on the scale-by-scale energy budget equation. A generalized Kolmogorov equation is derived. Relatively good agreement between the new equation and hot-wire measurements is obtained in the outer region (40 < x ⁺ ₃ < 150) of the channel flow, for which the turbulent Reynolds number is R _λ≈ 36.     

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.     

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.     

Numerical analysis of turbulent structure in compound meandering open channel by algebraic Reynolds stress model

The turbulent flow in a compound meandering channel with a rectangular cross section is one of the most complicated turbulent flows, because the flow behaviour is influenced by several kinds of forces, including centrifugal forces, pressure‐driven forces and shear stresses generated by momentum transfer between the main channel and the flood plain. Numerical analysis has been performed for the fully developed turbulent flow in a compound meandering open‐channel flow using an algebraic Reynolds stress model. The boundary‐fitted coordinate system is introduced as a method for coordinate transformation in order to set the boundary conditions along the complicated shape of the meandering open channel. The turbulence model consists of transport equations for turbulent energy and dissipation, in conjunction with an algebraic stress model based on the Reynolds stress transport equations. With reference to the pressure–strain term, we have made use of a modified pressure–strain term. The boundary condition of the fluctuating vertical velocity is set to zero not only for the free surface, but also for computational grid points next to the free surface, because experimental results have shown that the fluctuating vertical velocity approaches zero near the free surface. In order to examine the validity of the present numerical method and the turbulent model, the calculated results are compared with experimental data measured by laser Doppler anemometer. In addition, the compound meandering open channel is clarified somewhat based on the calculated results. As a result of the analysis, the present algebraic Reynolds stress model is shown to be able to reasonably predict the turbulent flow in a compound meandering open channel. Copyright © 2005 John Wiley & Sons, Ltd.     

Turbulent flow around a wall-mounted cube: A direct numerical simulation

An immersed-boundary method was employed to perform a direct numerical simulation (DNS) of flow around a wall-mounted cube in a fully developed turbulent channel for a Reynolds number Re = 5610, based on the bulk velocity and the channel height. Instantaneous results of the DNS of a plain channel flow were used as a fully developed inflow condition for the main channel. The results confirm the unsteadiness of the considered flow caused by the unstable interaction of a horseshoe vortex formed in front of the cube and on both its sides with an arch-type vortex behind the cube. The time-averaged data of the turbulence mean-square intensities, Reynolds shear stresses, kinetic energy and dissipation rate are presented. The negative turbulence production is predicted in the region in front of the cube where the main horseshoe vortex originates.     

射流元件控制通道流动的三维数值模拟

针对一种射流元件控制通道的复杂结构 ,采用分块对接技术和网格“融合”技术生成计算网格 ,并运用五步显式格式的 Runge-Kutta法和多重网格法对含全 N-S方程、RNG k-ε湍流模型和两层分区壁面模型的流动模型进行数值求解。通过对控制通道内部流动的数值模拟和流场特性分析 ,提出了改进方案     

大涡模拟研究展向旋转槽道湍流流动

本文用大涡模拟预测了以不同转速做展向旋转的槽道湍流流动,统计平均的流向速度型在壁面附近与已有实验数据符合很好,在通道中部的预测差异也能给出合理解释,对比不同转速的计算结果,表明展向旋转通道的湍流应力和壁面摩擦力在压力面附近提高、在吸力面附近降低,这些高阶湍流统计量的变化规律可以结合湍流应力输运方程加以解释,漩涡识别技术显示了近壁条带结构,其形态和猝发率受旋转附加力的影响发生改变,进而影响壁面摩擦速度的数值和分布,进一步考察垂直流动方向的截面内速度分布,发现旋转引起了垂直壁面方向的流动,形成正负相间排列的流向涡对,并随着转速的增加向压力面靠近。      

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 fully developed turbulent flow in a curved channel

In this paper large eddy simulation of the fully developed turbulent flow in a curved channel is carried out. The computational results are presented and compared with the experimental results of Eskinazi and Yeh^[1]. It is shown that the numerical results of the present LES are reliable and the influence of the curvature on the turbulence feature is correctly revealed.     

Parallel large eddy simulation of turbulent flow around MIRA model using linear equal‐order finite element method

A parallel large eddy simulation code that adopts domain decomposition method has been developed for large‐scale computation of turbulent flows around an arbitrarily shaped body. For the temporal integration of the unsteady incompressible Navier–Stokes equation, fractional 4‐step splitting algorithm is adopted, and for the modelling of small eddies in turbulent flows, the Smagorinsky model is used. For the parallelization of the code, METIS and Message Passing Interface Libraries are used, respectively, to partition the computational domain and to communicate data between processors. To validate the parallel architecture and to estimate its performance, a three‐dimensional laminar driven cavity flow inside a cubical enclosure has been solved. To validate the turbulence calculation, the turbulent channel flows at Re_τ = 180 and 1050 are simulated and compared with previous results. Then, a backward facing step flow is solved and compared with a DNS result for overall code validation. Finally, the turbulent flow around MIRA model at Re = 2.6 × 10⁶ is simulated by using approximately 6.7 million nodes. Scalability curve obtained from this simulation shows that scalable results are obtained. The calculated drag coefficient agrees better with the experimental result than those previously obtained by using two‐equation turbulence models. Copyright © 2007 John Wiley & Sons, Ltd.     

The Relevance of a Back-Scatter Model for Depth-Averaged Flow Simulation

This study demonstrates the importance of a sophisticated sub-grid model when performing a depth-averaged unsteady RANS simulation of a shallow flow. The reduction of resolution and the spatial dimensions exclude important physical processes as present in three-dimensional turbulence. Especially the effect of the bottom turbulence on the formation of horizontal eddies appears of key importance. A method is proposed to incorporate these effects by means of a kinematic simulation that mimics the residual turbulent fluctuations in a straight channel flow after depth-averaging. This method is developed in the context of the evolution of large eddies in a shallow mixing layer. A comparison with experiments shows that the proposed method works satisfactory. Naturally, it does not fully account for the omission of all 3D-effects.     

A ghost-cell immersed boundary method for large-eddy simulations of compressible turbulent flows

A methodology to perform a ghost-cell-based immersed boundary method (GCIBM) is presented for simulating compressible turbulent flows around complex geometries. In this method, the boundary condition on the immersed boundary is enforced through the use of ‘ghost cells’ that are located inside the solid body. The computations of variables on these ghost cells are achieved using linear interpolation schemes. The validity and applicability of the proposed method is verified using a three-dimensional (3D) flow over a circular cylinder, and a large-eddy simulation of fully developed 3D turbulent flow in a channel with a wavy surface. The results agree well with the previous numerical and experimental results, given that the grid resolution is reasonably fine. To demonstrate the capability of the method for higher Mach numbers, supersonic turbulent flow over a circular cylinder is presented. While more work still needs to be done to demonstrate higher robustness and accuracy, the present work provides interesting insights using the GCIBM for the compressible flows.     

Novel Implementation and Assessment of a Digital Filter Based Approach for the Generation of LES Inlet Conditions

A novel implementation of a digital filter based inlet condition generator for Large Eddy Simulation (LES) is presented. The effect of using spatially varying turbulence scales as inputs is investigated; it is found that this has impact on both accuracy and affordability, and has prompted the algorithm implementation changes described in the paper. LES of a channel flow with a periodically repeating constriction was used as a test case. The accuracy of the present simulation using a streamwise periodic boundary condition (PBC) was first established by comparison with a previously published highly resolved LES study. Post-processed statistics from the PBC simulation were then input into a Digital Filter Generator (DFG) algorithm. Three time series were created using the DFG for subsequent use as LES inlet conditions. In the first, as well as inputting the spatially varying first and second moments of the velocity field over the inlet plane from the PBC simulation, the turbulence scales input into the DFG were chosen to be spatially uniform with values specified by an area weighted average across the channel inlet height. In the second and third time-series, the turbulence scales were allowed to change in the wall normal direction, their variation again being deduced from the PBC simulation. These various time series were then used as inlet boundary conditions for LES prediction of the same flow case. Analysis of the results and comparison to the PBC predictions showed that the use of spatially varying turbulence scales increased the accuracy of the simulation in some important areas. However, the cost of generating unsteady inlet conditions using the DFG approach increased significantly with the use of spatially varying turbulence scales. Consequently, a new technique applied as part of the DFG approach is described (used as an ‘on the fly’ method), which significantly reduces the cost of generating LES inlet conditions, even when spatially non-uniform turbulent scales are used.     

Turbulence structure of polymer turbulent channel flow with and without macromolecular polymer structures

The presence of macromolecular polymer structures in a fully developed turbulent channel flow has been shown to substantially increase the drag reduction compared to non-structured polymer flows. This study presents a detailed analysis of experimental data obtained using laser Doppler velocimetry (LDV) to develop insights into the effects of the presence of macromolecular polymer structures on the turbulence characteristics of a channel flow. It is argued that polymer structures could contribute to minimizing the interaction between the inner and outer regions of the flow, which, in turn, can contribute to the modification of the coherent structure of the turbulence.