Laminar-turbulent transition is an old yet unsolved problem. Notwithstanding the great effort made, there is an important question that seems not to have been addressed yet, that is, what is the inherent mechanism of ...Laminar-turbulent transition is an old yet unsolved problem. Notwithstanding the great effort made, there is an important question that seems not to have been addressed yet, that is, what is the inherent mechanism of breakdown that eventually leads to transition? The conventional idea is that the transition starts from the amplification of disturbances, and when the disturbances become larger, higher harmonics will be generated due to nonlinear effect, making the flow more and more complicated, and finally turbulent. Though the scenario seems clear, yet there is a missing link, that is, what happens in the breakdown process. Here we show by analyzing the results from direct numerical simulations that the change of stability characteristics of the mean flow profile plays a key role in the breakdown process.展开更多
Thermally-stratified shear turbulent channel flow with temperatureoscillation on the bottom wall of the channel was investigated with the Large Eddy Simulation (LES)approach coupled with dynamic Sub-Grid-Scale (SGS) m...Thermally-stratified shear turbulent channel flow with temperatureoscillation on the bottom wall of the channel was investigated with the Large Eddy Simulation (LES)approach coupled with dynamic Sub-Grid-Scale (SGS) models. The effect of temperature oscillation onthe turbulent channel flow behavior was examined. The phase-averaged velocities and temperature, andflow structures at different Richardson numbers and periods of the oscillation was analyzed.展开更多
This paper numerically investigates particle saltation in a turbulent channel flow having a rough bed consisting of 2–3 layers of densely packed spheres.In this study,we combined three the state-of-the-art technologi...This paper numerically investigates particle saltation in a turbulent channel flow having a rough bed consisting of 2–3 layers of densely packed spheres.In this study,we combined three the state-of-the-art technologies,i.e.,the direct numerical simulation of turbulent flow,the combined finite-discrete element modelling of the deformation,movement and collision of the particles,and the immersed boundary method for the fluid-solid interaction.Here we verify our code by comparing the flow and particle statistical features with the published data and then present the hydrodynamic forces acting on a particle together with the particle coordinates and velocities,during a typical saltation.We found strong correlation between the abruptly decreasing particle stream-wise velocity and the increasing vertical velocity at collision,which indicates that the continuous saltation of large grain-size particles is controlled by collision parameters such as particle incident angle,local rough bed packing arrangement,and particle density,etc.This physical process is different from that of particle entrainment in which turbulence coherence structures play an important role.Probability distribution functions of several important saltation parameters and the relationships between them are presented.The results show that the saltating particles hitting the windward side of the bed particles are more likely to bounce off the rough bed than those hitting the leeside.Based on the above findings,saltation mechanisms of large grain-size particles in turbulent channel flow are presented.展开更多
A three-dimensional Large Eddy Simulation (LES) has been performed ofhydrodynamic behavior of turbulent flow in open channel that the lower part of the domain isoccupied by a drag force layer to represent vegetation. ...A three-dimensional Large Eddy Simulation (LES) has been performed ofhydrodynamic behavior of turbulent flow in open channel that the lower part of the domain isoccupied by a drag force layer to represent vegetation. One equation model is used to closing theresolvable scale equations. The turbulent characteristic length is parameterized by a k-l model. Aphenomenal model is employed to express the performance of vegetation in the open channel. Theresult reveals that the present model has the capacity of describing three-dimensional structure oflarge eddy appearing in turbulent flow in open channel with vegetation region and has the capacityof tracing the development of large eddies.展开更多
When water flows through a multiple-orifice energy disspator, flow vibration and cavitation may become very important problems. A new kind of the energy dissipator has recieved much attention because of its effectiven...When water flows through a multiple-orifice energy disspator, flow vibration and cavitation may become very important problems. A new kind of the energy dissipator has recieved much attention because of its effectiveness in energy dissipation. In this paper numerical simulations of turbulent flows in a dissipator were presented. The flow was considered to be an asymmetric two-dimensional steady flow. K-Ε turbulent model was used and solution procedure was described. The calculation was performed with different flow conditions. Calculated results of the flow field are compared with experiments. The results demonstrate that turbulent flow through dissipator can be predicted.展开更多
Our previous study showed that the frictional drag decreases with increasing void fraction at Re〉1300, while it increases at Re 〈 1000. Decomposition of the Reynolds shear stress also implied that bubbles induce iso...Our previous study showed that the frictional drag decreases with increasing void fraction at Re〉1300, while it increases at Re 〈 1000. Decomposition of the Reynolds shear stress also implied that bubbles induce isotropy of turbulence. In order to confirm our previous analysis and to further investigate flow fields in the vicinity of bubbles, we analyze velocity fluctuations on the quadrant space in the streamwise and transverse directions (u′-v′ plane). Here, we focus on two specific Reynolds numbers (at Re≈900 and ≈1410, which are close to the laminar-to-turbulent transition regime) and discuss bubble effects on sweep (u′〉 0, v′〈 0 ) and ejection (u′〈 0, v′〉 0) events as a function of the Reynolds number. We also illustrate velocity fluctuations in the vicinity of an individual bubble and a swarm of bubbles on the u′- v′ coordinates. The results show that a bubble swarm suppresses the velocity fluctuations at Re≈1410.展开更多
Fully developed vertical turbulent channel flow with particle transport wasinvestigated by use of Large Eddy Simulation (LES) approach coupled with dynamic the Sub-Grid Scale(SGS) model. It was assumed that the motion...Fully developed vertical turbulent channel flow with particle transport wasinvestigated by use of Large Eddy Simulation (LES) approach coupled with dynamic the Sub-Grid Scale(SGS) model. It was assumed that the motion of each particle is followed in a Lagrangian frame ofreference driven by the forces exerted by fluid motion and gravity under the condition of one-waycoupling. The goal of this study is to investigate the effectiveness of the LES technique forpredicting particle transport in turbulent flow and the behavior of particle-laden turbulent channelflow for three kinds of particles at different Stokes numbers. To depict the behavior ofparticle-laden turbulent channel flow, statistical quantities including particle fluctuation andfluid-particle velocity correlation, and visualization of the particle number density field wereanalyzed.展开更多
Large Eddy Simulation (LES) of fully developed turbulent channel flow with heat transfer was performed to investigate the effects of the Reynolds number on the turbulence behavior. In the present study, the bottom wal...Large Eddy Simulation (LES) of fully developed turbulent channel flow with heat transfer was performed to investigate the effects of the Reynolds number on the turbulence behavior. In the present study, the bottom wall of the channel was cooled and the top wall was heated. The Reynolds numbers, based on the central mean-velocity and the half-width of the channel, were chosen as 4000, 6000, 10 4 and 2×10 4, and the Prandtl number as 1.0. To validate our calculations, the present results were compared with available data obtained by Direct Numerical Simulation (DNS), which proves to be in good agreement with each other. To reveal the effects of the Reynolds number, some typical quantities, including the velocity fluctuations, temperature fluctuation, heat fluxes and turbulent Prandtl number, were studied.展开更多
This study investigates turbulent particle-laden channel flows using direct numerical simulations employing the Eulerian-Lagrangian method.A two-way coupling approach is adopted to explore the mutual interaction betwe...This study investigates turbulent particle-laden channel flows using direct numerical simulations employing the Eulerian-Lagrangian method.A two-way coupling approach is adopted to explore the mutual interaction between particles and fluid flow.The considered cases include flow with particle Stokes number varying from St=2 up to St=100 while maintaining a constant Reynolds number of Reτ=180 across all cases.A novel vortex identification method,Liutex(Rortex),is employed to assess its efficacy in capturing near-wall turbulent coherent structures and their interactions with particles.The Liutex method provides valuable information on vortex strength and vectors at each location,enabling a detailed examination of the complex interaction between fluid and particulate phases.As widely acknowledged,the interplay between clockwise and counterclockwise vortices in the near-wall region gives rise to low-speed streaks along the wall.These low-speed streaks serve as preferential zones for particle concentration,depending upon the particle Stokes number.It is shown that the Liutex method can capture these vortices and identify the location of low-speed streaks.Additionally,it is observed that the particle Stokes number(size)significantly affects both the strength of these vortices and the streaky structure exhibited by particles.Furthermore,a quantitative analysis of particle behavior in the near-wall region and the formation of elongated particle lines was carried out.This involved examining the average fluid streamwise velocity fluctuations at particle locations,average particle concentration,and the normal velocity of particles for each set of particle Stokes numbers.The investigation reveals the intricate interplay between particles and near-wall structures and the significant influence of particles Stokes number.This study contributes to a deeper understanding of turbulent particle-laden channel flow dynamics.展开更多
The mechanical energy equation is a fundamental equation of a 1-D mathematical model in Hydraulics and Engineering Fluid Mechanics. This equation for the total flow used to be deduced by extending the Bernoulli's equ...The mechanical energy equation is a fundamental equation of a 1-D mathematical model in Hydraulics and Engineering Fluid Mechanics. This equation for the total flow used to be deduced by extending the Bernoulli's equation for the ideal fluid in the streamline to a stream tube, and then revised by considering the viscous effect and integrated on the cross section. This derivation is not rigorous and the effect of turbulence is not considered. In this paper, the energy equation for the total flow is derived by using the Navier-Stokes equations in Fluid Mechanics, the results are as follows:(1) A new energy equation for steady channel flows of incompressible homogeneous liquid is obtained, which includes the variation of the turbulent kinetic energy along the channel, the formula for the mechanical energy loss of the total flow can be determined directly in the deduction process.(2) The theoretical solution of the velocity field for laminar flows in a rectangular open channel is obtained and the mechanical energy loss in the energy equation is calculated. The variations of the coefficient of the mechanical energy loss against the Reynolds number and the width-depth ratio are obtained.(3) The turbulent flow in a rectangular open channel is simulated using 3-D Reynolds averaged equations closed by the Reynolds stress model(RSM), and the variations of the coefficient of the mechanical energy loss against the Reynolds number and the width-depth ratio are discussed.展开更多
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 su...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.展开更多
The concentration and orientation of fiber in a turbulent T-shaped branching channel flow are investi-gated numerically. The Reynolds averaged Navier-Stokes equations together with the Reynolds stress turbulent model ...The concentration and orientation of fiber in a turbulent T-shaped branching channel flow are investi-gated numerically. The Reynolds averaged Navier-Stokes equations together with the Reynolds stress turbulent model are solved for the mean flow field and the turbulent kinetic energy. The fluctuating velocities of the fluid are assumed as a random variable with Gaussian distribution whose variance is related to the turbulent kinetic energy. The slender-body theory is used to simulate the fiber motion based on the known mean and fluctuating velocities of the fluid. The results show that at low Reynolds number, fiber concentration is high in the flow separation regions, and fiber orientation throughout the channel is widely distributed with a slight preference of aligning along the horizontal axis. With increasing of Re, the high concentration region disappears, and fiber orientation becomes ho-mogeneous without any preferred direction. At high Reynolds number, fiber concentration increases gradually along the flow direction. The differences in the distribution of concentration and orientation between different fiber aspect ratio are evident only at low Re. Both Re and fiber aspect ratio have small effect on the variance of orientation angle.展开更多
Fully connected neural networks(FCNNs)have been developed for the closure of subgrid-scale(SGS)stress and SGS heat flux in large-eddy simulations of compressible turbulent channel flow.The FCNNbased SGS model trained ...Fully connected neural networks(FCNNs)have been developed for the closure of subgrid-scale(SGS)stress and SGS heat flux in large-eddy simulations of compressible turbulent channel flow.The FCNNbased SGS model trained using data with Mach number Ma=3.0 and Reynolds number Re=3000 was applied to situations with different Mach numbers and Reynolds numbers.The input variables of the neural network model were the filtered velocity gradients and temperature gradients at a single spatial grid point.The a priori test showed that the FCNN model had a correlation coefficient larger than 0.91 and a relative error smaller than 0.43,with much better reconstructions of SGS unclosed terms than the dynamic Smagorinsky model(DSM).In a posteriori test,the behavior of the FCNN model was marginally better than that of the DSM in predicting the mean velocity profiles,mean temperature profiles,turbulent intensities,total Reynolds stress,total Reynolds heat flux,and mean SGS flux of kinetic energy,and outperformed the Smagorinsky model.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant No.10232020)Liu-Hui Center of Applied Mathematics,Nankai and Tianjin University.
文摘Laminar-turbulent transition is an old yet unsolved problem. Notwithstanding the great effort made, there is an important question that seems not to have been addressed yet, that is, what is the inherent mechanism of breakdown that eventually leads to transition? The conventional idea is that the transition starts from the amplification of disturbances, and when the disturbances become larger, higher harmonics will be generated due to nonlinear effect, making the flow more and more complicated, and finally turbulent. Though the scenario seems clear, yet there is a missing link, that is, what happens in the breakdown process. Here we show by analyzing the results from direct numerical simulations that the change of stability characteristics of the mean flow profile plays a key role in the breakdown process.
文摘Thermally-stratified shear turbulent channel flow with temperatureoscillation on the bottom wall of the channel was investigated with the Large Eddy Simulation (LES)approach coupled with dynamic Sub-Grid-Scale (SGS) models. The effect of temperature oscillation onthe turbulent channel flow behavior was examined. The phase-averaged velocities and temperature, andflow structures at different Richardson numbers and periods of the oscillation was analyzed.
基金supported by a Marie Curie International Incoming Fellowship within the seventh European Community Framework Programme(Grant No.PIIF-GA-2009-236457)the financial support of the Science Fund for Creative Research Groups of the National Natural Science Foundation of China(Grant No.51321065)+2 种基金Programme of Introducing Talents of Discipline to Universities(Grant No.B14012)National Natural Science Foundation of China(Grant Nos.50809047 and 51009105)Natural Science Foundation of Tianjin(Grant No.12JCQNJC02600)
文摘This paper numerically investigates particle saltation in a turbulent channel flow having a rough bed consisting of 2–3 layers of densely packed spheres.In this study,we combined three the state-of-the-art technologies,i.e.,the direct numerical simulation of turbulent flow,the combined finite-discrete element modelling of the deformation,movement and collision of the particles,and the immersed boundary method for the fluid-solid interaction.Here we verify our code by comparing the flow and particle statistical features with the published data and then present the hydrodynamic forces acting on a particle together with the particle coordinates and velocities,during a typical saltation.We found strong correlation between the abruptly decreasing particle stream-wise velocity and the increasing vertical velocity at collision,which indicates that the continuous saltation of large grain-size particles is controlled by collision parameters such as particle incident angle,local rough bed packing arrangement,and particle density,etc.This physical process is different from that of particle entrainment in which turbulence coherence structures play an important role.Probability distribution functions of several important saltation parameters and the relationships between them are presented.The results show that the saltating particles hitting the windward side of the bed particles are more likely to bounce off the rough bed than those hitting the leeside.Based on the above findings,saltation mechanisms of large grain-size particles in turbulent channel flow are presented.
文摘A three-dimensional Large Eddy Simulation (LES) has been performed ofhydrodynamic behavior of turbulent flow in open channel that the lower part of the domain isoccupied by a drag force layer to represent vegetation. One equation model is used to closing theresolvable scale equations. The turbulent characteristic length is parameterized by a k-l model. Aphenomenal model is employed to express the performance of vegetation in the open channel. Theresult reveals that the present model has the capacity of describing three-dimensional structure oflarge eddy appearing in turbulent flow in open channel with vegetation region and has the capacityof tracing the development of large eddies.
文摘When water flows through a multiple-orifice energy disspator, flow vibration and cavitation may become very important problems. A new kind of the energy dissipator has recieved much attention because of its effectiveness in energy dissipation. In this paper numerical simulations of turbulent flows in a dissipator were presented. The flow was considered to be an asymmetric two-dimensional steady flow. K-Ε turbulent model was used and solution procedure was described. The calculation was performed with different flow conditions. Calculated results of the flow field are compared with experiments. The results demonstrate that turbulent flow through dissipator can be predicted.
文摘Our previous study showed that the frictional drag decreases with increasing void fraction at Re〉1300, while it increases at Re 〈 1000. Decomposition of the Reynolds shear stress also implied that bubbles induce isotropy of turbulence. In order to confirm our previous analysis and to further investigate flow fields in the vicinity of bubbles, we analyze velocity fluctuations on the quadrant space in the streamwise and transverse directions (u′-v′ plane). Here, we focus on two specific Reynolds numbers (at Re≈900 and ≈1410, which are close to the laminar-to-turbulent transition regime) and discuss bubble effects on sweep (u′〉 0, v′〈 0 ) and ejection (u′〈 0, v′〉 0) events as a function of the Reynolds number. We also illustrate velocity fluctuations in the vicinity of an individual bubble and a swarm of bubbles on the u′- v′ coordinates. The results show that a bubble swarm suppresses the velocity fluctuations at Re≈1410.
文摘Fully developed vertical turbulent channel flow with particle transport wasinvestigated by use of Large Eddy Simulation (LES) approach coupled with dynamic the Sub-Grid Scale(SGS) model. It was assumed that the motion of each particle is followed in a Lagrangian frame ofreference driven by the forces exerted by fluid motion and gravity under the condition of one-waycoupling. The goal of this study is to investigate the effectiveness of the LES technique forpredicting particle transport in turbulent flow and the behavior of particle-laden turbulent channelflow for three kinds of particles at different Stokes numbers. To depict the behavior ofparticle-laden turbulent channel flow, statistical quantities including particle fluctuation andfluid-particle velocity correlation, and visualization of the particle number density field wereanalyzed.
基金ThisstudywassupportedbytheNationalScienceFundforDistinguishedScholars (No :10 12 5 2 10 ),theChinaNKBRSFProject (No :2 0 0 1CB40 96 0 0 ),theProgramofHundredTalentsof (CAS) ,andtheProgramoftheTrans CenturyOutstandingYoungTrainingof(MOE)
文摘Large Eddy Simulation (LES) of fully developed turbulent channel flow with heat transfer was performed to investigate the effects of the Reynolds number on the turbulence behavior. In the present study, the bottom wall of the channel was cooled and the top wall was heated. The Reynolds numbers, based on the central mean-velocity and the half-width of the channel, were chosen as 4000, 6000, 10 4 and 2×10 4, and the Prandtl number as 1.0. To validate our calculations, the present results were compared with available data obtained by Direct Numerical Simulation (DNS), which proves to be in good agreement with each other. To reveal the effects of the Reynolds number, some typical quantities, including the velocity fluctuations, temperature fluctuation, heat fluxes and turbulent Prandtl number, were studied.
文摘This study investigates turbulent particle-laden channel flows using direct numerical simulations employing the Eulerian-Lagrangian method.A two-way coupling approach is adopted to explore the mutual interaction between particles and fluid flow.The considered cases include flow with particle Stokes number varying from St=2 up to St=100 while maintaining a constant Reynolds number of Reτ=180 across all cases.A novel vortex identification method,Liutex(Rortex),is employed to assess its efficacy in capturing near-wall turbulent coherent structures and their interactions with particles.The Liutex method provides valuable information on vortex strength and vectors at each location,enabling a detailed examination of the complex interaction between fluid and particulate phases.As widely acknowledged,the interplay between clockwise and counterclockwise vortices in the near-wall region gives rise to low-speed streaks along the wall.These low-speed streaks serve as preferential zones for particle concentration,depending upon the particle Stokes number.It is shown that the Liutex method can capture these vortices and identify the location of low-speed streaks.Additionally,it is observed that the particle Stokes number(size)significantly affects both the strength of these vortices and the streaky structure exhibited by particles.Furthermore,a quantitative analysis of particle behavior in the near-wall region and the formation of elongated particle lines was carried out.This involved examining the average fluid streamwise velocity fluctuations at particle locations,average particle concentration,and the normal velocity of particles for each set of particle Stokes numbers.The investigation reveals the intricate interplay between particles and near-wall structures and the significant influence of particles Stokes number.This study contributes to a deeper understanding of turbulent particle-laden channel flow dynamics.
文摘The mechanical energy equation is a fundamental equation of a 1-D mathematical model in Hydraulics and Engineering Fluid Mechanics. This equation for the total flow used to be deduced by extending the Bernoulli's equation for the ideal fluid in the streamline to a stream tube, and then revised by considering the viscous effect and integrated on the cross section. This derivation is not rigorous and the effect of turbulence is not considered. In this paper, the energy equation for the total flow is derived by using the Navier-Stokes equations in Fluid Mechanics, the results are as follows:(1) A new energy equation for steady channel flows of incompressible homogeneous liquid is obtained, which includes the variation of the turbulent kinetic energy along the channel, the formula for the mechanical energy loss of the total flow can be determined directly in the deduction process.(2) The theoretical solution of the velocity field for laminar flows in a rectangular open channel is obtained and the mechanical energy loss in the energy equation is calculated. The variations of the coefficient of the mechanical energy loss against the Reynolds number and the width-depth ratio are obtained.(3) The turbulent flow in a rectangular open channel is simulated using 3-D Reynolds averaged equations closed by the Reynolds stress model(RSM), and the variations of the coefficient of the mechanical energy loss against the Reynolds number and the width-depth ratio are discussed.
基金supported by the National Natural Science Foundation of China(Grant No.52131102)the National Key Research and Development Program of China(Grant No.2022YFC2806705)。
文摘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.
基金Supported by the Major Program of the National Natural Science Foundation of China (No.10632070).
文摘The concentration and orientation of fiber in a turbulent T-shaped branching channel flow are investi-gated numerically. The Reynolds averaged Navier-Stokes equations together with the Reynolds stress turbulent model are solved for the mean flow field and the turbulent kinetic energy. The fluctuating velocities of the fluid are assumed as a random variable with Gaussian distribution whose variance is related to the turbulent kinetic energy. The slender-body theory is used to simulate the fiber motion based on the known mean and fluctuating velocities of the fluid. The results show that at low Reynolds number, fiber concentration is high in the flow separation regions, and fiber orientation throughout the channel is widely distributed with a slight preference of aligning along the horizontal axis. With increasing of Re, the high concentration region disappears, and fiber orientation becomes ho-mogeneous without any preferred direction. At high Reynolds number, fiber concentration increases gradually along the flow direction. The differences in the distribution of concentration and orientation between different fiber aspect ratio are evident only at low Re. Both Re and fiber aspect ratio have small effect on the variance of orientation angle.
基金Financial support provided by the National Natural Science Foundation of China(Grant Nos.11702042 and 91952104)。
文摘Fully connected neural networks(FCNNs)have been developed for the closure of subgrid-scale(SGS)stress and SGS heat flux in large-eddy simulations of compressible turbulent channel flow.The FCNNbased SGS model trained using data with Mach number Ma=3.0 and Reynolds number Re=3000 was applied to situations with different Mach numbers and Reynolds numbers.The input variables of the neural network model were the filtered velocity gradients and temperature gradients at a single spatial grid point.The a priori test showed that the FCNN model had a correlation coefficient larger than 0.91 and a relative error smaller than 0.43,with much better reconstructions of SGS unclosed terms than the dynamic Smagorinsky model(DSM).In a posteriori test,the behavior of the FCNN model was marginally better than that of the DSM in predicting the mean velocity profiles,mean temperature profiles,turbulent intensities,total Reynolds stress,total Reynolds heat flux,and mean SGS flux of kinetic energy,and outperformed the Smagorinsky model.