Evaluation of Subgrid-scale Models in Large-eddy Simulations of Turbulent Flow in a Centrifugal Pump Impeller

The current research of large eddy simulation （LES） of turbulent flow in pumps mainly concentrates in applying conventional subgrid-scale （SGS） model to simulate turbulent flow, which aims at obtaining the flow field in pump. The selection of SGS model is usually not considered seriously, so the accuracy and efficiency of the simulation cannot be ensured. Three SGS models including Smagorinsky-Lilly model, dynamic Smagorinsky model and dynamic mixed model are comparably studied by using the commercial CFD code Fluent combined with its user define function. The simulations are performed for the turbulent flow in a centrifugal pump impeller. The simulation results indicate that the mean flows predicted by the three SGS models agree well with the experimental data obtained from the test that detailed measurements of the flow inside the rotating passages of a six-bladed shrouded centrifugal pump impeller performed using particle image velocimetry （PIV） and laser Doppler velocimetry （LDV）. The comparable results show that dynamic mixed model gives the most accurate results for mean flow in the centrifugal pump impeller. The SGS stress of dynamic mixed model is decompose into the scale similar part and the eddy viscous part. The scale similar part of SGS stress plays a significant role in high curvature regions, such as the leading edge and training edge of pump blade. It is also found that the dynamic mixed model is more adaptive to compute turbulence in the pump impeller. The research results presented is useful to improve the computational accuracy and efficiency of LES for centrifugal pumps, and provide important reference for carrying out simulation in similar fluid machineries.

Applying resolved-scale linearly forced isotropic turbulence in rational subgrid-scale modeling

In previous attempts of rational subgrid-scale (SGS) modeling by employing the Kolmogorov equation of filtered (KEF) quantities, it was necessary to assume that the resolved-scale second-order structure function is stationary. Forced isotropic turbulence is often used as a framework for establishing and validating such SGS models based on stationary restrictions, for it generates statistical stationary samples. However, traditional forcing method at low wavenumbers cannot provide an analytic form of forcing term for a complete KEF in physical space, which has been illustrated to be essential in the modeling of such SGS models. Thus, an alternative forcing method giving an analytic forcing term in physical space is needed for rational SGS modeling. Giving an analytic linear driving term in physical space, linearly forced isotropic turbulence should be considered an ideal theoretical framework for rational SGS modeling. In this paper, we demonstrate the feasibility of establishing a rational SGS model with stationary restriction based on linearly forced isotropic turbulence. The performance of this rational SGS model is validated. We, therefore, propose the use of linearly forced isotropic turbulence as a complement to free-decaying isotropic turbulence and low-wavenumber forced isotropic turbulence for SGS model validations.

Mathematical Constraints in Multiscale Subgrid-Scale Modeling of Nonlinear Systems

To shed light on the subgrid-seale （SGS） modeling methodology of nonlinear systems such as the Navier-Stokes turbulence, we define the concepts of assumption and restriction in the modeling procedure, which are shown by generalized derivation of three general mathematical constraints for different combinations of restrictions. These constraints are verified numerically in a one-dimensional nonlinear advection equation. This study is expected to inspire future research on the SGS modeling methodology of nonlinear systems.

A SECOND-ORDER DYNAMIC SUBGRID-SCALE STRESS MODEL

A second-order dynamic model based on the general relation between the subgrid-scale stress and the velocity gradient tensors was proposed. A priori test of the second-order model was made using moderate resolution direct numerical simulation date at high Reynolds number ( Taylor microscale Reynolds number R-lambda = 102 similar to 216) for homogeneous, isotropic forced flow, decaying flow, and homogeneous rotating flow. Numerical testing shows that the second-order dynamic model significantly improves the correlation coefficient when compared to the first-order dynamic models.

Stochastic modeling of subgrid-scale effects on particle motion in forced isotropic turbulence

The subgrid-scale effects on particle motion were investigated in forced isotropic turbulence by DNS and priorLES methods.In the DNS field,the importance of Kolmogorov scaling to preferential accumulation was validated by comparing the radial distribution functions under various particle Stokes numbers.The prior-LES fields were generated by filtering the DNS data.The subgrid-scale Stokes number(StSGS)is a useful tool for determining the effects of subgrid-scale eddies on particle motion.The subgrid-scale eddies tend to accumulate particles with StSGSb 1 and disperse particles with 1 b StSGSb 10.For particles with StSGS?1,the effects of subgrid-scale eddies on particle motion can be neglected.In order to restore the subgrid-scale effects,the Langevin-type stochastic model with optimized parameters was adopted in this study.This model is effective for the particles with StSGS N 1 while has an adverse impact on the particles with StSGSb 1.The results show that the Langevin-type stochastic model tends to smooth the particle distribution in the isotropic turbulence.

A new mixed subgrid-scale model for large eddy simulation of turbulent drag-reducing flows of viscoelastic fluids

A mixed subgrid-scale（SGS） model based on coherent structures and temporal approximate deconvolution（MCT） is proposed for turbulent drag-reducing flows of viscoelastic fluids. The main idea of the MCT SGS model is to perform spatial filtering for the momentum equation and temporal filtering for the conformation tensor transport equation of turbulent flow of viscoelastic fluid, respectively. The MCT model is suitable for large eddy simulation（LES） of turbulent dragreducing flows of viscoelastic fluids in engineering applications since the model parameters can be easily obtained. The LES of forced homogeneous isotropic turbulence（FHIT） with polymer additives and turbulent channel flow with surfactant additives based on MCT SGS model shows excellent agreements with direct numerical simulation（DNS） results. Compared with the LES results using the temporal approximate deconvolution model（TADM） for FHIT with polymer additives, this mixed SGS model MCT behaves better, regarding the enhancement of calculating parameters such as the Reynolds number.For scientific and engineering research, turbulent flows at high Reynolds numbers are expected, so the MCT model can be a more suitable model for the LES of turbulent drag-reducing flows of viscoelastic fluid with polymer or surfactant additives.

A new dynamic subgrid-scale model using artificial neural network for compressible flow

The subgrid-scale(SGS)kinetic energy has been used to predict the SGS stress in compressible flow and it was resolved through the SGS kinetic energy transport equation in past studies.In this paper,a new SGS eddy-viscosity model is proposed using artificial neural network to obtain the SGS kinetic energy precisely,instead of using the SGS kinetic energy equation.Using the infinite series expansion and reserving the first term of the expanded term,we obtain an approximated SGS kinetic energy,which has a high correlation with the real SGS kinetic energy.Then,the coefficient of the modelled SGS kinetic energy is resolved by the artificial neural network and the modelled SGS kinetic energy is more accurate through this method compared to the SGS kinetic energy obtained from the SGS kinetic energy equation.The coefficients of the SGS stress and SGS heat flux terms are determined by the dynamic procedure.The new model is tested in the compressible turbulent channel flow.From the a posterior tests,we know that the new model can precisely predict the mean velocity,the Reynolds stress,the mean temperature and turbulence intensities,etc.

Rational subgrid-scale modelling: a short survey

We review the previous attempts of rational subgrid-scale （SGS） modelling by employing theKolmogorov equation of filtered quantities. Aiming at explaining and solving the underlyingproblems in these models, we also introduce the recent methodological investigations for therational SGS modelling technique by defining the terms of assumption and restriction. Thesemethodological works are expected to provide instructive criterions for not only the rational SGSmodelling, but also other types of SGS modelling practices.

A new dynamic formula for determining the coefficient of Smagorinsky model

The most common method to determine the coefficient of Smagorinsky model now is to employ the Germano identity,however it is too complex and expensive in numerical calculation. In this letter we propose a new dynamic formula for determining the coefficient,which is based on the Kolmogorov equation of filtered velocity in physical space.The simplified formula is quite easy to implement in calculation.It is then verified in both homogeneous isotropic turbulence and wall-bounded turbulence by A Priori and A Posteriori tests.

基于Smagorinsky和Vreman模型的竖通道内旋转热流场大涡模拟

为了确定Vreman亚格子模型对于有侧开缝的竖通道内旋转火焰热流场模拟的适用性,基于一竖通道内旋转火焰实验场景,分别使用基于Smagorinsky和Vreman亚格子模型的大涡模拟技术进行了模拟。通过对所得结果比较确定基于Smagorinsky亚格子模型的大涡模拟技术可以得到与实验吻合的火焰状态,而使用Vreman亚格子模型会在一定程度上低估旋转火焰周围的粘性耗散,从而过高地估计旋转火焰周围的切向速度,使火焰不能保持相对稳定的旋转状态。

Modeling of Motion of Particle Clouds Formed by Dumping Dredged Material

The motion of particle clouds formed by dumping dredged material into quiescent waters is experimentally and numerically studied. In the numerical model, the particle phase is modeled by the dispersion model, and turbulence is calculated by the large eddy simulation. The governing equations, including the filtered Navier-Stokes equations and mass transport equation, are solved based on the operator-splitting algorithm and an implicit cubic spline interpolation scheme. The eddy viscosity is evaluated by the modified Smagorinsky model including the buoyancy term. Comparisons of main flow characteristics, including shape, size, average density excess, moving speed and the amount of particles deposited on the bed, between experimental and computational results show that the numerical model well predicts the motion of the cloud from the falling to spreading stage. The effects of silt-fence on the motion of the particle cloud are also investigated.

Applications of a Surface Runoff Model with Horton and Dunne Runoff for VIC

Surface runoff is mainly generated by two mechanisms, infiltration excess (Horton) runoff and saturation excess (Dunne) runoff; and the spatial variability of soil properties, antecedent soil moisture, topography, and rainfall will result in different surface runoff generation mechanisms. For a large area (e.g., a model grid size of a regional climate model or a general circulation model), these runoff generation mechanisms are commonly present at different portions of a grid cell simultaneously. Missing one of the two major runoff generation mechanisms and failing to consider spatial soil variability can result in significant under/over estimation of surface runoff which can directly introduce large errors in soil moisture states over each model grid cell. Therefore, proper modeling of surface runoff is essential to a reasonable representation of feedbacks in a land-atmosphere system. This paper presents a new surface runoff parameterization with the Philip infiltration formulation that dynamically represents both the Horton and Dunne runoff generation mechanisms within a model grid cell. The parameterization takes into account the effects of soil heterogeneity on Horton and Dunne runoff. The new parameterization is implemented into the current version of the hydrologically based Variable Infiltration Capacity (VIC) land surface model and tested over one watershed in Pennsylvania, USA and over the Shiguanhe Basin in the Huaihe Watershed in China. Results show that the new parameterization plays a very important role in partitioning the water budget between surface runoff and soil moisture in the atmosphere-land coupling system, and has potential applications on large hydrological simulations and land-atmospheric interactions. It is further found that the Horton runoff mechanism should be considered within the context of subgrid-scale spatial variability of soil properties and precipitation.

基于动态Smagorinsky-MRT-LBM的圆柱绕流湍流研究

采用多松弛格子玻尔兹曼与大涡模拟的动态Smagorinsky亚格子涡粘模型相结合的方法对圆柱绕流湍流进行模拟,研究300至10 000不同雷诺数下的单圆柱绕流湍流涡的周期性变化。研究结果表明:计算所得的斯考特数值和阻力系数值与文献中实验结果以及有限元仿真结果基本一致,说明该方法对于不同雷诺数的湍流模拟是合理的。

Assessment of the modulated gradient model in decaying isotropic turbulence

A recently introduced nonlinear model undergoes evaluations based on two isotropic turbulent cases:a University of Wiscosion-Madison case at a moderate Reynolds number and a Johns Hopkins University case at a high Reynolds number.The model uses an estimation of the subgrid-scale(SGS) kinetic energy to model the magnitude of the SGS stress tensor,and uses the normalized velocity gradient tensor to model the structure of the SGS stress tensor.Testing is performed for the first case through a comparison between direct numerical simulation(DNS) results and large eddy simulation(LES) results regarding resolved kinetic energy and energy spectrum.In the second case,we examine the resolved kinetic energy,the energy spectrum,as well as other key statistics including the probability density functions of velocities and velocity gradients,the skewness factors,and the flatness factors.Simulations using the model are numerically stable,and results are satisfactorily compared with DNS results and consistent with statistical theories of turbulence.

Smagorinsky模型的变分多尺度有限元方法

主要研究求解Smagorinsky模型的变分多尺度有限元方法.从理论上给出了有限元逼近解与真解之间的误差估计,并给出了大雷诺数Re=10 000时的数值算例,算例结果验证了所给方法的有效性.

具有非线性slip边界条件的Smagorinsky模型有限元误差估计

Smagorinsky模型是大涡模拟中常见的数学模型,研究求解了具有非线性slip边界条件的Smagorinsky模型有限元方法,并且根据理论所得的有限元误差估计,设计数值模拟实验,通过六个不同网格尺度下的有限元逼近解与真实解的相对误差验证理论所得结果的准确性.

Recent understanding on the subgrid-scale modeling of large-eddy simulation in physical space

In the last 50 years,the methodology of large-eddy simulation(LES)has been greatly developed,while lots of different subgridscale(SGS)models have appeared.However,the understanding of the procedure of SGS modeling is still not clear.The present contribution aims at reviewing the recent SGS models and,more importantly,expressing our recent understanding on the SGS modeling of LES in physical space.Taking the Kolmogorov equation for filtered quantities(KEF)as an example,it is argued that the KEF alone is not enough to be a closure method.Three physical laws are then introduced to complete this closure procedure and are expected to inspire the future researches of SGS modeling.

Subgrid-scale model based on the vorticity gradient tensor for rotating turbulent flows

A new subgrid-scale(SGS)stress model is proposed for rotating turbulent flows,and the new model is based on the traceless symmetric part of the square of the velocity gradient tensor and the symmetric part of the vorticity gradient tensor(or the so-called vorticity strain rate tensor).The new subgrid-scale stress model is taken into account the effect of the vortex motions in turbulence,which is reflected on the anti-symmetric part of the velocity gradient tensor.In addition,the eddy viscosity of the new model reproduces the proper scaling as O(y^3)near the wall.Then,the new SGS model is applied in large-eddy simulation of the spanwise rotating turbulent channel flow.Different simulating cases are selected to test the new model.The results demonstrate that the present model can well predict the mean velocity profiles,the turbulence intensities,and the rotating turbulence structures.In addition,it needs no a second filter,and is convenient to be used in the engineering rotational flows.

Assessment of subgrid-scale models in wall-modeled large-eddy simulations of turbulent channel flows

Considering the demanding of grid requirements for high-Reynolds-number wall-bounded flow,the wall-modeled large-eddy simulation(WMLES)is an attractive method to deal with near wall turbulence.However,the effect of subgrid-scale(SGS)models for wall-bounded turbulent flow in combination with wall stress models is still unclear.In this paper,turbulent channel flow at Reτ=1000 are numerically simulated by WMLES in conjunction with four different SGS models,i.e.,the wall-adapting local eddy-viscosity model,the dynamic Smagorinsky model,the dynamic SGS kinetic energy model and the dynamic Lagrangian model.The mean velocity profiles are compared with the law of the wall,and the velocity fluctuations are compared with direct numerical simulation data.The energy spectrum of velocity and wall pressure fluctuations are presented and the role of SGS models on predicting turbulent channel flow with WMLES is discussed.

An improved dynamic subgrid-scale model and its application to large eddy simulation of rotating channel flows

A new dynamic subgrid-scale (SGS) model, which is proved to satisfy the principle of asymptotic material frame indifference (AMFI) for rotating turbulence, is proposed based on physical and mathematical analysis. Comparison with direct numerical simulation (DNS) results verifies that the new SGS model is effective for large eddy simulation (LES) on rotating turbulent flow. The SGS model is then applied to the LES of the spanwise rotating turbulent channel flow to investigate the rotation effect on turbulence characteristics, budget terms in the transport equations of resolved Reynolds stresses, and flow structures near the wall regions of the rotating channel.