Velocity Fluctuations in a Particle-Laden Turbulent Flow over a Backward-Facing Step

Dilute gas-particle turbulent flow over a backward-facing step is numerically simulated. Large Eddy Simulation (LES) is used for the continuous phase and a Lagrangian trajectory method is adopted for the particle phase. Four typical locations in the flow field are chosen to investigate the two-phase velocity fluctuations. Time-series velocities of the gas phase with particles of different sizes are obtained. Velocity of the small particles is found to be similar to that of the gas phase, while high frequency noise exists in the velocity of the large particles. While the mean and rms velocities of the gas phase and small particles are correlated, the rms velocities of large particles have no correlation with the gas phase. The frequency spectrum of the velocity of the gas phase and the small particle phase show the -5/3 decay for higher wave number, as expected in a turbulent flow. However, there is a "rising tail' in the high frequency end of the spectrum for larger particles. It is shown that large particles behave differently in the flow field, while small particles behave similarly and dominated by the local gas phase flow.     

Application of particle tracking velocimetry for studying the dispersion of particles in a turbulent gas flow

A method for the determination of the dispersion of solid particles in a turbulent gas flow has been presented. This method is based on recording the particle trajectories with a high-speed video camera on separate regions of a flow, located at various distances from a point source of particles, and the subsequent processing of the frames. This method has been used to study the dispersion of solid particles under the conditions of turbulence in a horizontal channel with a rectangular cross section of 200 × 400 mm for a measuring region length of 2 m. Turbulence of the gas flow was generated by means of a grid with square meshes of the size of 16 mm. The average velocity of the gas flow in the measuring region was 5.1 m/s. The dispersion of 36-, 56- and 128-micron glass particles of spherical shape was studied in a region 450 mm long from the point source of particles. It has been shown that the dispersion of these particles in the direction of the action of the gravity force is larger than their dispersion in the perpendicular direction to the gravity force. The results of this study have shown that an increase in the size of particles leads to a decrease in the dispersion at small flight times of the particles (short-time dispersion).     

WALL DEPOSITION OF SMALL SUSPENDED PARTICLES IN A TURBULENT CHANNEL FLOW

The diffusion of small suspended particles in a turbulent channel flow is studied by solving the transport advection-diffusion equation. The mean flowfield in the channel is simulated using a two-equation k-ε turbulence model. Deposition velocity is evaluated at different sections in the channel for different particle sizes and flow Reynolds numbers. The effects of turbulence dispersion and Brownian diffusion on particle deposition velocity are discussed. The variation of particle deposition velocity with particle diameter, density and flow Reynolds number are analyzed. The wall deposition velocities for different size particles are compared with those obtained by other models.     

Hierarchical tree‐based finite element mesh generation

Hierarchical grid generation and its use as a basis for finite element mesh generation are considered in this paper. The hierarchical grids are generated by recursive subdivision using quadtrees in two dimensions and octrees in three dimensions. A numbering system for efficient storage of the quadtree grid information is examined, tree traversal techniques are devised for neighbour finding, and accurate boundary representation is considered. It is found that hierarchical grids are straightforward to generate from sets of seeding points which lie along domain boundaries. Quadtree grids are triangularized to provide finite element meshes in two dimensions. Three‐dimensional tetrahedral meshes are generated from octree grids. The meshes can be generated automatically to model complicated geometries with highly irregular boundaries and can be adapted readily at moving boundaries. Examples are given of two‐ and three‐dimensional hierarchical tree‐based finite element meshes and their application to modelling free surface waves. Copyright © 1999 John Wiley & Sons, Ltd.     

Direct numerical simulation of ellipsoidal particles in turbulent channel flow

This paper investigates the behaviour of elongated, axi-symmetric ellipsoidal particles, their interaction with turbulence, and the effects of the ellipsoids on turbulence in a turbulent channel flow with Re _τ = 150. The simulations are carried out with full four-way coupling using the point-source approach: the particles are affected by the fluid, the particles affect the fluid, and the particles can collide with each other or the wall using a realistic collision algorithm. The trajectories of the ellipsoids are tracked by solving the translational and rotational equations of motion in a Quaternion framework and are closed with hydrodynamic drag and torque laws. To specifically identify the effect of particle shape, simulations of single phase channel flow are compared to simulations with spherical particles and to simulations with ellipsoids. In all cases, the driving pressure drop, to establish a flow with Re _τ = 150, is kept constant. Both the spherical particles and the ellipsoidal particles have a Stokes number of 5. Although the volume fraction is very low, 0.00725 and 0.0219 % for the spheres and ellipsoids, respectively, there is some effect of the particles and the ellipsoids on the turbulence. Although the transport terms in the turbulent kinetic energy equation of the fluid are hardly affected, the turbulence kinetic energy itself decreases by 6.0 % for the flow laden with spherical particles and 4.8 % for the ellipsoidal particles. The homogeneous dissipation of turbulence kinetic energy by the fluid decreases due to the addition of particles, and the production also decreases. The particles dissipate turbulence kinetic energy of the fluid phase, predominantly in the near-wall region. Because there is a high average slip velocity in the stream-wise direction between the particles and the fluid in the near-wall region, the root mean square of the particle velocity is higher than that of the fluid velocity in this direction. In the other directions, the root mean square velocities of the particles are significantly lower than of the fluid. There is, however, a positive slip velocity between the particles and the fluid in the wall-normal direction, indicating that the particles move towards the wall with a higher momentum than that they return to the centre of the channel with. As a result, there is a 4–5 times higher concentration of particles near the wall than in the centre of the channel. As both the spherical and the ellipsoidal particles are very small, there is no major difference in their overall behaviour. However, in the near-wall region, there are some profound differences. The collision mechanism of ellipsoids with the walls is significantly different compared to spheres, the former predominantly inducing rotation resulting from a collision and the latter predominantly moving away from the wall after colliding. This is confirmed by the strong rotation as well as large root mean square of rotation of the ellipsoidal particles in the near-wall region. This results in a slight inward shift of the peak of the root mean square velocities of the fluid and the ellipsoidal particles as well as the peak in slip velocity, driving the momentum transfer, compared to the simulations with the spheres. Finally, the statistics of the orientation show that the ellipsoids align in the stream-wise direction in the near-wall region, because of the fluid boundary layer as well as the particle–wall collisions, but that there is no significant orientation of the ellipsoids outside of the near-wall region.     

Turbulence characteristics of open channel flow over non-equilibrium 3-D mobile dunes

This paper reports velocity measurements over mobile dunes using an acoustic Doppler velocimetry (ADV). Experiments were conducted with two different flow conditions resulting in the formation of two different size mobile dunes. Dunes height, wavelength and velocity of dunes found to be increasing with increase in average flow velocity for a constant flow depth. The quasi-stationary bed condition was assumed while measuring the velocity distribution along the depth. The effect of the non-equilibrium mobile dunes on the flow characteristics and turbulence is examined by computing turbulent intensities, turbulent kinetic energy and Reynolds shear stresses using time averaged and time–space averaged velocity measurements. The magnitudes of transverse velocities are approximately 1/10 of streamwise velocities and vertical velocities are approximately half of the transverse velocities. The considerable magnitudes of transverse velocities over mobile bedforms necessitate measurement of 3-D velocity components to analyze the flow field. Computed turbulence intensities are found to be maximum in the region consisting of the trough and the reattachment point of the dunes. It is observed that streamwise turbulence intensities near the bed are twice the transverse turbulence intensities, and transverse turbulence intensities are twice the vertical turbulence intensities. Reynolds stresses (transverse fluxes of streamwise and vertical momentum) are observed to be high on mobile bedforms which shows mobile dunes reinforce the secondary currents. Peak values of turbulent kinetic energy (TKE) and Reynolds stresses are also found in the region consisting of the trough and the reattachment point. It is visually observed in the present experiments that maximum erosion takes place at the reattachment point and eroded sediment is carried as total load and dropped on the lee slope of the subsequent downstream dune. This phenomenon is caused by flow expansion in the separation zone, and which is also the main reason for mobility of dunes and associated bedload transport. Most importantly, it is found that turbulence anisotropy increases with increase in size of mobile bedforms and anisotropy is extended up to the free surface in the flows over mobile bedforms, which proves the entire depth of flow is being disturbed by the mobile dunes.     

Deposition of solid particles in laminar boundary layer on a flat plate

Results are given of experimental and theoretical investigation of deposition of small solid particles on the surface of a flat plate under conditions of vertical laminar boundary layer. The present investigation is aimed at qualitatively and quantitatively estimating the effect made by the parameters of two-phase flow of the “gas—solid particles” type and by the adhesive properties of particles and surface on the deposition of particles on the plate surface. The flow velocity is 1.5 and 3 m/s. In so doing, the value of Reynolds number along the plate does not exceed 10⁵. Synthetic corundum powders with average sizes of 12, 23, and 32 μm are used as the dispersed phase of two-phase flow. The mass concentration of particles in the flow is 0.01 kg/m³. A flat plate of stainless steel is used as the object of investigation. The distributions of gas velocity and concentration of particles within the boundary layer are measured using laser optical diagnostics. The number of particles deposited along the plate surface is measured by the gravimetric method. The adhesive properties of the “particle-surface” pair are studied using the centrifugal method of detachment of particles from the surface. Logarithmic-normal dependences of the number of adhesion of particles on the force of detachment are obtained. The hydrodynamic parameters of two-phase flow in the vicinity of the plate surface are calculated using the model of two-phase laminar boundary layer. The mathematical expression is suggested for the calculation of the magnitude of deposition of solid particles along the surface of a flat plate, which includes the special features of hydrodynamics of flow, the adhesive properties of the particles and surface, and the probabilistic pattern of the process of entrapment of particles by the surface.     

基于大涡模拟方法的多层动网格技术识别平板气动参数

【摘要】从弱耦合的角度出发,对流体计算软件fluent进行二次开发,利用其用户自定义函数(UDFs)描述结构的运动状态并结合动网格技术实现流固耦合。在保证动网格运动速度符合空间守恒法则的条件下,针对固体模型在流场中运动受网格尺寸限制且易造成网格变形过大导致计算失败的问题提出了多层动网格的解决方法。流体动力计算时考虑湍流的作用,采用大涡模拟方法求解N-S方程。数值模拟了平板做单自由度强迫振动的断面绕流流场,通过最小二乘法拟合气动力时程曲线获得气动导数。仿真结果与通过Theodorsen理论导出的平板气动导数具有良好的一致性。     

The Influence of the Gravity Force on Longwave Marangoni Patterns in Two-Layer Films

An Euler–Euler two-fluid model based on the second-order-moment closure approach and the granular kinetic theory of dense gas-particle flows was presented. Anisotropy of gas-solid two-phase stress and the interaction between two-phase stresses are fully considered by two-phase Reynolds stress model and the transport equation of two-phase stress correlation. Under the microgravity space environments, hydrodynamic characters and particle dispersion behaviors of dense gas-particle turbulence flows are numerically simulated. Simulation results of particle concentration and particle velocity are in good agreement with measurement data under earth gravity environment. Decreased gravity can decrease the particle dispersion and can weaken the particle–particle collision as well as it is in favor of producing isotropic flow structures. Moreover, axial–axial fluctuation velocity correlation of gas and particle in earth gravity is approximately 3.0 times greater than those of microgravity and it is smaller than axial particle velocity fluctuation due to larger particle inertia and the larger particle turbulence diffusions.     

Simulated pulsed flow of gas and particles in a horizontal oppose-pulsed gas jets of bubbling fluidized bed

Flow behavior of gas and particles with a horizontal oppose-pulsed gas jets are simulated by means of a three dimensional Computational Fluid Dynamics (CFD) model with the kinetic theory of granular flow in a gas-particles bubbling fluidized bed. The effects of amplitudes and frequencies on the hydrodynamics of gas and particles are analyzed. The simulation results are presented in terms of phase velocity vector plot, volume fraction of phases, granular temperature, power spectrum and Reynolds stresses in the bed. Results show that the impingement caused by the oppose-pulsed gas jets oscillates with the variation of pulsed gas velocity. The impingement zone with the high solid volume fraction reciprocates from the left side to the right side through the bed center with the variation of pulsed jet gas velocities. The lateral velocity and gas turbulent kinetic energy, granular temperature and Reynolds stresses of gas and particles are larger near the pulsed gas jets than that at the center of the bed. The large dispersion coefficients of particles using the horizontal oppose-pulsed gas jets enhance the mixing of particles in gas-solid fluidized bed.     

Effect of the size of air bubbles on enhancement of heat transfer in an impinging liquid jet

The numerical modeling of heat transfer in a bubbly impinging jet is carried out. The axisymmetric system of RANS equations that take into account the two-phase nature of the flow is resolved based on the Euler approach. The turbulence of the liquid phase is described by the Reynolds stress transport model with taking into account the effect of bubbles on modification of the turbulence. The effect of the gas volumetric flow rate ratio and the bubble size on the flow structure and the heat transfer in a gas–liquid impact stream is studied. It is shown that the addition of the gas phase in a turbulent fluid causes an increase up to 1.5-fold in heat transfer. The comparison of the simulation results with experimental data showed that the developed model enables the simulation of turbulent bubbly impinging jet with heat transfer with the pipe wall in a wide range of gas fraction.     

Effect of intense turbulence on turbulent premixed V-flame

The influence of free stream turbulence on the statistics of turbulent premixed V-flame is numerically investigated in this paper. The flame front is tracked using the level-set algorithm with the effect of exothermicity and baroclinicity. Results indicate that free stream turbulence affects the statistics greatly including the conditioned and unconditioned mean axial and transverse velocities, fluctuation velocities and Reynolds stresses. The unconditioned and conditioned fluctuating velocities, unconditioned mean axial velocities and the flame brush thickness increase with increased free stream turbulence. The maximum unconditioned mean axial velocity along the centre line increases linearly with turbulence. The peaks of unconditioned transverse fluctuation velocity smoothens with the increase of free stream turbulence level, indicating that the effect of intermittency decreases with the increase of free stream turbulence. These results show that free stream turbulence is a major influence on turbulent statistics in premixed V-flame.     

基于POD的大涡模拟入流脉动合成方法研究

针对并行计算特点,发展适用于流体并行计算的大涡模拟(Large Eddy Simulation,LES)入流脉动直接合成方法。基于特征正交分解(Proper Orthogonal Decomposition, POD)型谱表示法合成入流面主要网格点脉动风速时程,采用有限元形函数空间插值获得入流面所有网格点风速时程,采用UDF(User Defined Functions)编程实现Fluent软件平台流体并行计算时合成的脉动风速时程读入及赋值。进行B类1:500缩尺比风场内宽高比1：6的单体方形截面高层建筑非定常绕流LES计算,将数值模拟所得风剖面、风速谱及结构风压系数统计值、自谱、相干性等,与刚性模型测压风洞试验及文献数值模拟结果比较。研究表明,该合成方法可较好模拟紊流风场,预测结构风荷载具有一定精度。     

Gas Flow and Particle Transport and Deposition in a Pilot-Scale Furnace

The present work describes a computer simulation study of gas flow and particle transport and deposition in a pilot-scale furnace with cooling system. The Gambit code is used to generate the geometry and the computational grid. An unstructured mesh is generated for the pilot-scale boiler. The FLUENT code is used for evaluating the gas mean velocity, turbulence fluctuation energy, and mean pressure, as well as temperature fields and chemical species concentrations. The particle equation of motion includes the nonlinear drag, gravity, Brownian, lift, and thermophoretic forces. The gas velocity and thermal conditions in the furnace are studied. Ensembles of particle trajectories are generated and statistically analyzed. Particle deposition rates on different walls are evaluated, and the effect of particle size is studied.     

Vortex Generation in Superfluid 3He by a Vibrating Grid

Recently we have found that a vibrating wire resonator produces turbulence in superfluid ³He-B at low temperatures when driven above its pair-breaking critical velocity. The vorticity is produced along with a beam of excitations from pair breaking. Here, we discuss preliminary measurements of turbulence generated from an oscillating grid at low temperatures. The grid oscillator is made from a goal-post shaped vibrating wire resonator supporting a fine copper mesh. While the dissipation by a conventional wire resonator is dominated by pair-breaking at the velocities required for turbulence generation, the dissipation of the grid oscillator appears to be dominated by turbulence. This allows us to generate turbulence without the unwanted effects of a quasiparticle beam. Preliminary measurements suggest that the grid turbulence has a rather different behaviour from that generated by conventional wire resonators.     

Grid deformation strategies for CFD analysis of screw compressors

Customized grid generation of twin screw machines for CFD analysis is widely used by the refrigeration and air-conditioning industry today, but is currently not suitable for topologies such as those of single screw, variable pitch or tri screw rotors. This paper investigates a technique called key-frame re-meshing that supplies pre-generated unstructured grids to the CFD solver at different time steps. To evaluate its accuracy, the results of an isentropic compression-expansion process in a reciprocating piston cylinder arrangement have been compared. Three strategies of grid deformation; diffusion equation mesh smoothing, user defined nodal displacement and key-frame remeshing have been assessed. There are many limitations to key-frame re-meshing. It requires time consuming pre-processing, has limited applicability to complex meshes and leads to inaccuracies in conservation of calculated variables. It was concluded that customized tools for generation of CFD grids are required for complex screw machines.     

Local Grid Refinement in Large-Eddy Simulation

A method for performing nested-grid calculations with a Large-Eddy Simulation (LES) code is described. The grid consists of a coarse mesh and a fine mesh which overlaps the coarse in some region. A standard finite-volume method is used on both meshes. By means of grid communication, the velocity and pressure at both meshes are matched. To check that large eddies which are already resolved on the coarse grid are not affected by the nesting procedure, a simple two-dimensional mixing layer is simulated. Several simulations of this flow have been carried out with a different number of grid points on the nested grid. It is found that, without much extra computational effort, the grid-nesting improves the turbulent statistics with respect to the results found on the coarse mesh. This improvement occurs first of all in the region where grid refinement is applied, but better results are also found on the coarse mesh outside the grid-refinement region. Furthermore, it is shown that the large-scale structures in this flow are not influenced by the boundary between the coarse and fine grid.     

Simulation and numerical investigations of the kinetics of atmospheric aerosol droplets in the wake behind a flat plate

Within the framework of the physicomathematical model of evolution of a polydisperse condensate, numerical investigations of the kinetics of atmospheric aerosol droplets in a supersonic two-phase flow past a flat plate were carried out. The gas flow was described by the Reynolds equations with the use of the two-parameter turbulence model. In view of the smallness of the condensate mass fraction in the incoming flow, the inverse effect of the dispersed phase on the gas was not considered. For various regimes of exposure to a flow, the characteristic features of the spatial distribution of the main parameters of the condensate fractions have been studied: the number densities, radii, temperatures, and averaged velocities of microdrops. The dependence of the dispersed phase dynamics on the Mach number and the incoming flow angle of attack has been investigated and the influence of the allowance for the processes of coagulation/fragmentation on the mass spectrum of droplets is shown. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 82, No. 2, pp. 331–341, March–April, 2009.     

A parametric study of dispersed laminar gas-particle flows through vertical and horizontal channels

Particle diameter, particle phase material density and inlet particle volume fraction are three important parameters governing the flow physics of dispersed gas-particle flows. In this work, an inhouse numerical solver is developed to investigate the effects of particle diameter (Stokes number), particle phase material density, inlet particle volume fraction and inlet phase velocities in the flow characteristics of gas-particle flows through vertical and horizontal channels and also in open domains. It is found that, for a constant inlet particle volume fraction, lower diameter particles attain a higher steady state velocity at any section inside the channel than the higher diameter particles; while the corresponding steady state gas velocity at any section increases with increase in particle diameter. On the other hand, for a constant particle diameter, the steady state gas phase velocity at any section decreases with increase in inlet particle volume fraction. Significant changes in both gas and particle velocity and volume fraction profiles have also been observed with inlet slip, i.e., when the velocities of both the phases at inlet are distinct as opposed to being equal, keeping all other flow and physical parameters invariant.