Numerical simulation of slurry jets using mixture model

Slurry jets in a static uniform environment were simulated with a two-phase mixture model in which flow-particle interactions were considered. A standard k-ε turbulence model was chosen to close the governing equations. The computational results were in agreement with previous laboratory measurements. The characteristics of the two-phase flow field and the influences of hydraulic and geometric parameters on the distribution of the slurry jets were analyzed on the basis of the computational results. The calculated results reveal that if the initial velocity of the slurry jet is high, the jet spreads less in the radial direction. When the slurry jet is less influenced by the ambient fluid (when the Stokes number St is relatively large), the turbulent kinetic energy k and turbulent dissipation rate ε, which are relatively concentrated around the jet axis, decrease more rapidly after the slurry jet passes through the nozzle. For different values of St, the radial distributions of streamwise velocity and particle volume fraction are both self-similar and fit a Gaussian profile after the slurry jet fully develops. The decay rate of the particle velocity is lower than that of water velocity along the jet axis, and the axial distributions of the centerline particle streamwise velocity are self-similar along the jet axis. The pattern of particle dispersion depends on the Stokes number St. When St = 0.39, the particle dispersion along the radial direction is considerable, and the relative velocity is very low due to the low dynamic response time. When St = 3.08, the dispersion of particles along the radial direction is very little, and most of the particles have high relative velocities along the streamwise direction.     

基于大涡模拟的悬板径向坡度对排沙漏斗流场特性影响数值模拟

为了解悬板径向坡度改变对排沙漏斗流场的影响,文章采用了大涡模拟和VOF相结合的方法对悬板径向坡度i=0、0. 083、0. 173、0. 259时的排沙漏斗水气两相三维流场进行了数值模拟,并采用离散相颗粒轨道模型(DPM)模拟了悬板径向坡度不同时排沙漏斗对粒径0. 001～0. 1 mm颗粒的截除率。模拟结果表明:随着径向坡度增加,切向流速先增大后减小或趋于恒定,说明室内涡流强度并不是随着悬板径向坡度的增大而单调增加,存在一临界的坡度使室内涡流强度达到最大值;坡度i=0. 173时悬板上方区域(除溢流表层外)径向和垂向的合速度方向平行于悬板径向底坡且指向漏斗中心,使该区内的泥沙被再次输运至漏斗室而不易随溢出水流流出,减少了泥沙进入下游和沉降落淤于悬板的机率。颗粒截除率模拟结果也表明i=0. 173时的漏斗对各级粒径颗粒截除率最大,也表明悬板径向坡度存在一临界值使漏斗截除率达到最大值。     

Simulation of fine sediment transport in oscillatory boundary layer

Sediment transport and resulting morphodynamics take place at vastly different spatial and temporal scales. Bottom boundary layer dynamics is one of the most critical small-scale processes controlling sediment transport. However, it is very challenging as it involves highly nonlinear turbulent flow phenomenon that occurs at a scale as small as Kolmogorov scales. The unsteady nature of the flow forcing in the coastal environment, such as waves, is another important factor that further complicates the process. This paper aims to take a step to better understand wave-driven turbulent boundary layer and corresponding transport process. The problem of wave-driven sediment transport is simplified into fully developed oscillatory channel flow. Particles are assumed to be fine and dilute and hence they can be approximately considered as passive except gravitational settling with its settling velocity estimated from Stokes' law. Highly accurate pseudo-spectral flow solver has been employed and Direct Numerical Simulation (DNS) is carried out to resolve all scales of flow turbulence without sub-grid closure. Sediment concentration is then updated via mass conservation. Clear fluid simulation for intermittently turbulent condition (i.e., Stokes Reynolds number Re_Δ = 1000) is validated with earlier DNS results reported by Spalart and Baldwin [1989. Direct simulation of a turbulent oscillating boundary layer. Turbulent Shear Flows 6. Springer]. Fine sediment with dilute concentration is then added in the numerical simulation to study sediment suspension events under oscillatory flow. Suspension events are evaluated both qualitatively, by observing vortex structures, and quantitatively by the statistics of vertical fluxes. For fine particles and dilute concentration considered here, it is observed that particle phase is well-mixed in the boundary layer. Suspension is highly dependent on turbulent vortical structures at different wave phases.     

Numerical study of high-order Lagrangian structure functions in a turbulent channel flow with low Reynolds number

The scaling exponents of Lagrangian velocity structure functions from orders 1 to 10 in a low Reynolds number turbulent channel flow are investigated by using direct numerical simulation. The Reynolds number Re_τ is 80 (based on friction velocity on the wall). The Lagrangian velocity structure functions are shown to obey the scaling relations <Δv^q(τ)>∼τ^ζL(q). The scaling exponents are normalized by ζ_L(2) (so-called ESS procedure). The coincidence between the theoretical predictions and numerical calculations is very good for the longitudinal scaling exponent in the channel center. It is also found that the high-order longitudinal scaling exponents agree with theoretical values better than those for the transverse direction.

     

Effects of finite-size heavy particles on the turbulent flows in a square duct

A parallel direct-forcing fictitious domain method is applied in fully-resolved numerical simulations of particle-laden turbulent flows in a square duct. The effects of finite-size heavy particles on the mean secondary flow, the mean streamwise velocity, the root-mean-square velocity fluctuation, and the particle concentration distribution are investigated at the friction Reynolds number of 150, the particle volume fraction of 2.36%, the particle diameter of 0.1 duct width, and the Shields number ranging from 1.0 to 0.2. Our results show that the particle sedimentation breaks the up-down symmetry of the mean secondary vortices, and results in a stronger secondary-flow circulation which transports the fluids downward in the bulk center region and upward along the side walls at a low Shields number. This circulation has a significant impact on the distribution of the mean streamwise velocity, whose maximum value occurs in the lower half duct, unlike in the plane channel case. The flow resistance is increased and the turbulence intensity is reduced, as the Shields number is decreased. The particles accumulate preferentially at the face center of the bottom wall, due to the effect of the mean secondary flow. It is observed that the collision model has an important effect on the results, but does not change the results qualitatively.     

Velocity and concentration measurements in initial region of submerged round jets in stagnant environment and in coflow

Velocity and concentration fields are measured in submerged round jets in a stagnant environment and in coflow using laser Doppler anemometry and laser-induced fluorescence. Measurements are made in the initial region within distances of 40 jet exit diameter at jet Reynolds number between 1000 and 5000 and coflow-to-jet velocity ratio from 0 to 0.43. Different behaviors of jet spreading and dilution are found in jets at three different ranges of Reynolds number in which the jets are classified as initially laminar, transitional or turbulent. In the zone of established flow, the jet centerline velocity and concentration decay with downstream distance at different rates in the three groups of jets. For jets in coflow, axial development of normalized forms of centerline mean excess velocity and mean concentration at different velocity ratios can be reasonably well collapsed onto universal trends through the use of momentum length scale. Turbulence properties inside a jet are increased by the presence of a strong coflow. Inside the zone of flow establishment, some strange features are observed on jet turbulence properties. The length of zone of flow establishment increases from the turbulent jets, to the transition jets and to the laminar jets. The zone lengths for concentration are shorter than those for velocity by one to two jet exit diameters. Both lengths are shortened further in the presence of a coflow. For jets a stagnant environment and in the strong jet flow region of jets in coflow, jet widths increase linearly with downstream distance in transitional and turbulent jets. Self-similarity of radial profiles of mean velocity or excess velocity, mean concentration, turbulence intensities and concentration fluctuation level is explored in the zone of established flow.     

A SECOND-ORDER MOMENT TURBULENCE MODEL FOR POWER LAW FLUID WITH PARTICLES

The USM-θ model of power law fluid for dense two-phase turbulent flow was developed, which combines the unified second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. This model was used to simulate the turbulent flow of power law fluid single-phase in pipe. It is shown that the USM ? θ model has better prediction result than the k f ? ε f?kp?εp?θ model. The USM ? θ model was then used to simulate the dense two-phase turbulent up flow of power law fluid with particles. With the increase of the flow exponent, the velocities of power law fluid and particles increase near the pipe centre. Comparison between the two-phase flow of power law fluid-particle and of liquid-particle indicates that the axial fluctuation velocity of fluid phase and particle phase in liquid-particle two-phase flow is smaller than that in the power law fluid two-phase flow, but the two-phase velocities of power law fluid-particle and liquid-particle are close to each other.     

Effects of Rigid Unsubmerged Vegetation on Flow Field Structure and Turbulent Kinetic Energy of Gradually Varied Flow

The influence of rigid unsubmerged vegetation on flow structure and turbulent kinetic energy of gradually varied flow are experimentally investigated in this research. Natural reed stems of different densities are employed to examine the effects of the rigid unsubmerged vegetation on the flow in rivers. The results reveal that the vegetation existence significantly changes the gradually varied flow state from type M1 to type M2 in the vegetation section. The traditional power law describing the vertical flow velocity profile is evidently invalid when the vegetation density becomes high. With the irregularity index proposed in the research, the irregularity of vertical flow velocity profile in vegetated reach can be exponentially described in relation to the vegetation density. Furthermore, the turbulent kinetic energy is found to increase and reach a maximum value near the end of the vegetation section that is a potential localized erosion area. The results of the research have significances in river ecological restoration applications utilizing aquatic vegetation. Copyright © 2014 John Wiley & Sons, Ltd.     

DIRECT NUMERICAL SIMULATION OF TURBULENT FLOW IN A STRAIGHT SQUARE DUCT AT REYNOLDS NUMBER 600

This article presents the direct numerical simulation results of the turbulent flow in a straight square duct at a Reynolds number of 600, based on the duct width and the mean wall-shear velocity. The turbulence statistics along the wall bisector is examined with the turbulent flow field properties given by streamwise velocity and vorticity fields in the duct cross section. It was found that the solutions of the turbulent duct flow obtained in a spatial resolution with 1.2×10⁶ grid points are satisfactory as compared to the existing numerical and experimental results. The results indicate that it is reasonable to neglect the sub-grid scale models in this spatial resolution level for the duct flow at the particular friction Reynolds number.     

Energy gradient method for turbulent transition with consideration of effect of disturbance frequency

The energy gradient theory for flow instability and turbulent transition was proposed in our previous work. It was shown that the disturbance amplitude required for turbulent transition is inversely proportional to Re, which is in agreement with the experiments. In present study, the energy gradient theory is extended to include the effect of disturbance frequency on turbulent transition. The theoretical result obtained accords well with the experimental data in literature.

     

Artificial Neural Network and Grey Wolf Optimizer Based Surrogate Simulation-Optimization Model for Groundwater Remediation

We herein propose a simulation-optimization model for groundwater remediation, using PAT (pump and treat), by coupling artificial neural network (ANN) with the grey wolf optimizer (GWO). The input and output datasets to train and validate the ANN model are generated by repetitively simulating the groundwater flow and solute transport processes using the analytic element method (AEM) and random walk particle tracking (RWPT). The input dataset is the different realization of the pumping strategy and output dataset are hydraulic head and contaminant concentration at predefined locations. The ANN model is used to approximate the flow and transport processes of two unconfined aquifer case studies. The performance evaluation of the ANN model showed that the value of mean squared error (MSE) is close to zero and the value of the correlation coefficient (R) is close to 0.99. These results certainly depict high accuracy of the ANN model in approximating the AEM-RWPT model. Further, the ANN model is coupled with the GWO and it is used for remediation design using PAT. A comparison of the results of the ANN-GWO model with solutions of ANN-PSO (ANN-Particle Swarm Optimization) and ANN-DE (ANN-Differential Evolution) models illustrates the better stability and convergence behaviour of the proposed methodology for groundwater remediation.

     

Numerical investigation of a swirling flow under the optimal perturbation

The nonlinear evolution of 3-D instability of a viscous swirling flow, namely, the Oseen vortex, is addressed by direct numerical simulation with a Reynolds number equal to 5000. The global optimal perturbation is considered as the initial perturbation. In axisymmetric cases, three flow regimes are found: (1) the linear growth; (2) the decay of perturbation energy; (3) secondary energy growth. The linear energy growth, which is characterized by the amplification of radial perturbations, is arrested by the interaction between the vortex ring and the Oseen vortex core. The development of the vortex structure is also investigated for non-symmetric flows.

     

Role of Local Flow Conditions in River Biofilm Colonization and Early Growth

Direct numerical simulations of a turbulent boundary layer flow over a bed of hemispheres of height h are performed using an immersed boundary method for comparison with river biofilm growth experiments performed in a hydraulic flume. Flow statistics above the substrates are shown to be in agreement with measurements performed by laser Doppler velocimetry and particle image velocimetry in the experiments. Numerical simulations give access to flow components inside the roughness sublayer, and biofilm colonization patterns found in the experiments are shown to be associated with low shear stress regions on the hemisphere surface. Two bed configurations, namely staggered and aligned configurations, lead to different colonization patterns because of differences in the local flow topology. Dependence with the Reynolds number of the biofilm distribution and accrual 7 days after inoculum is shown to be associated to local flow topology change and shear stress intensity. In particular, the shear stress τ on the surface of the hemispheres is found to scale as , where Re_t = u^*h/ν, with u^* as the log law friction velocity and ν as the fluid kinematic viscosity. This scaling is due to the development of boundary layers along the hemisphere surface. Associated with a critical shear stress for colonization and early growth, it explains the increasing delay in biomass accrual for increasing flow velocities in the experiments. Copyright © 2014 John Wiley & Sons, Ltd.     

Numerical study on flow structure near two impermeable trapezoid submerged breakwaters on slop bottoms

Studying on hydrodynamic characteristics in water waves propagating over two impermeable trapezoid submerged breakwaters is of great significance to research design and construction of this type of submerged breakwaters. The turbulent characteristics are discussed with cnoidal waves in the wave flume with 1:20 smooth slope.The governing equations of the vertical 2D model are the Reynolds-averaged Navier-Stokes equations. The Reynolds stress terms are closed by a nonlinear (anisotropic) k − ε turbulence transportation model. Using a VOF method for tracking the free surface and source function wave generating method. Furthermore, the supplementary discussion is made by means of numerical results.

     

LARGE EDDY SIMULATION OF PARTICLE TRANSPORT IN FULLY DEVELOPED VERTICAL TURBULENT CHANNEL FLOW

Fully developed vertical turbulent channel flow with particle transport was investigated by use of Large Eddy Simulation (LES) approach coupled with dynamic the SubGrid Scale (SGS) model. It was assumed that the motion of each particle is followed in a Lagrangian frame of reference driven by the forces exerted by fluid motion and gravity under the condition of one-way coupling. The goal of this study is to investigate the effectiveness of the I.ES technique for predicting particle transport in turbulent flow and the behavior of particle-laden turbulent channel flow for three kinds of particles at different Stokes numbers. To depict the behavior of particle-laden turbulent channel flow, statistical quantities including particle fluctuation and fluid-particle velocity correlation, and visualization of the particle number density field were analyzed.     

辐流式沉淀池液固两相流力学特性三维数值模拟

采用两相流混合模型,选取RNG k-ε湍流模型封闭两相流时均方程,对辐流式二次沉淀池液固两相流力学特性进行三维数值模拟。采用有限体积法求解微分方程;紊动能、紊流耗散均采用Quick离散格式;速度与压力耦合求解时使用了压力隐式算子分裂PISO(Pressure-Implicit with Splitting of Operators)算法。通过模拟获得了速度场、紊动能和污泥质量浓度等参量在空间的分布规律,对沉淀池的设计有一定的参考价值。     

低含沙水流紊动结构的实验研究

本文用MicroADV对低含沙水流的紊动结构进行了较为系统的研究，在不同的粒径下，泥沙颗粒对流体流动结构的改变不一致；同样地，相同的粒径在不同的水流条件下，对流动结构的改变也不一样。     

Numerical simulations of viscous flows around surface ship by level set method

Numerical simulations of viscous flows around surface ships by coupling the 3D incompressible RANS equations with level set method are presented in this paper. The finite difference method is used to discretize the RANS equations with turbulent model SST k − ω. The fully nonlinear boundary condition at the free surface is satisfied at each time step and the evolution of the free surface is achieved by using the level set method. The coupled solver is applied to a benchmark case of viscous flows around an advancing Wigley ship with various Froude numbers. The computational results are in excellent agreement with experimental data. The simulations reveal clearly the generation and evolution of bow and stern waves.

     

A Partially-Averaged Navier-Stokes model for hill and curved duct flow

Turbulent flows past hill and curved ducts exist in many engineering applications. Simulations of the turbulent flow are carried out based on a newly developed technique, the Partially-Averaged Navier-Stokes (PANS) model, including separation, recirculation, reattachment, turbulent vortex mechanism. The focus is on how to accurately predict typical separating, reattaching and secondary motion at a reasonable computational expense. The effect of the parameter, the unresolved-to-total ratio of kinetic energy (f_k), is examined with a given unresolved-to-total ratio of dissipation (f_?) for the hill flow with a much coarser grid system than required by the LES. An optimal value of f_k can be obtained to predict the separation and reattachment locations and for more accurate simulation of the resolved turbulence. In addition, the turbulent secondary motions are captured by a smaller f_k as compared with the RANS method with the same grid.     

PARTICLE SIZE DISTRIBUTION IN A PLANAR JET FLOW UNDERGOING SHEAR-INDUCED COAGULATION AND BREAKAGE

A CFD simulation is performed for a particle-laden planar jet flow.The Reynolds number is 8300,and the initial particle diameter is 1 μm.Large Eddy Simulation(LES) is employed to calculate the flow field,and the Taylor-series expansion moment method(TEMOM) is adopted to deal with the balance equation of particle coagulation and breakage.The shear-induced coagulation kernel,power-law breakage kernel and symmetric fragment distribution function are involved.The prediction of the distribution of the mean streamwise velocity of the jet is in good agreement with experimental data.The evolution of particle number concentration,volume concentration,polydispersity,particle diameter and standard geometric deviation is discussed in detail.The results show that as the jet travels downstream,the particle number concentration and volume concentration decrease,while their spans become wider.The polydispersity and particle diameter are very large in the shear layers at the upstream and in the core of vortex structures at the downstream.The particle standard geometric deviation changes within the range of 1.32 ≤σg≤ 1.96,and increases sharply in the shear layers.All variables approach the steady-state as time progresses.