A Modeling Study on Particle Dispersion in Wall-Bounded Turbulent Flows

Three physical mechanisms which may affect dispersion of particle's motion in wall-bounded turbulent flows, including the effects of turbulence, wall roughness in particle-wall collisions, and inter-particle collisions, are numerically investigated in this study. Parametric studies with different wall roughness extents and with different mass loading ratios of particles are performed in fully developed channel flows with the Eulerian-Lagrangian approach. A low-Reynolds-number $k-\epsilon$ turbulence model is applied for the solution of the carrier-flow field, while the deterministic Lagrangian method together with binary-collision hard-sphere model is applied for the solution of particle motion. It is shown that the mechanism of inter-particle collisions should be taken into account in the modeling except for the flows laden with sufficiently low mass loading ratios of particles. Influences of wall roughness on particle dispersion due to particle-wall collisions are found to be considerable in the bounded particle-laden flow. Since the investigated particles are associated with large Stokes numbers, i.e., larger than $\mathcal{O}(1)$, in the test problem, the effects of turbulence on particle dispersion are much less considerable, as expected, in comparison with another two physical mechanisms investigated in the study.     

The effects of flow structure and particle mass loading on particle dispersion in particle-laden swirling jets

A direct numerical simulation of particle dispersion in particle-laden swirling jets issued into a rectangular container through a round nozzle is carried out. The swirl number is S=1.42 when the bubble vortex breakdown takes place. Two cases are simulated for comparison, i.e. five types of particles with Stokes numbers St=0.01, 0.1, 1, 10 and 100 respectively under the same flow rate, and four types of particles with St=0.5, 1, 5 and 10 respectively under the same mass loading. After simulation, it is found that the rectangular flow domain induces an important modification to the flow structure. It influences the dispersion characteristics in the peripheral cross area, forming a centrosymmetric dispersion of particles in the cross-sectional area. A quantitative analysis of the non-uniform particle dispersion is carried out. Moreover, the effect of mass loading on particle dispersion is explored and explained. It indicates the correlation between the inter-phase moment coupling and particle mass loading via the change of probability density function of the inter-phase velocity difference. Heavy mass loading causes an insufficient inter-phase momentum transport and the worse dispersion of large particles than that of small mass loading.     

Coupled radiation and turbulent multiphase flow in an aluminised solid propellant rocket engine

We present in this paper numerical simulations of coupled radiative transfer and turbulent flows at high temperature and pressure, typical of multiphase flows encountered in aluminised solid propellant rocket engines. The radiating medium is constituted of gases and of liquid or solid particles of oxidised aluminum. The turbulent flow of the gaseous phase is treated by using a four equation, low Reynolds number, boundary-layer-type turbulence model. The distributions of concentrations, temperatures, and temperature fluctuation variances of particles are calculated from a Lagrangian approach and a turbulence dispersion model. Thermal and mechanical non-equilibrium between the gas and different classes of particles is allowed. A locally one dimensional, iteratively based, radiative transfer solver is developed to compute wall fluxes and radiative source terms. It is shown that the thermal boundary layer attenuates significantly the radiative fluxes coming from the outer regions. Particle radiation is found to be much more important than gas radiation. Turbulent dispersion of particles in the boundary layer induces a decrease of particle concentration in the region of maximum turbulent kinetic energy, and then, decreases the attenuation effect of wall fluxes due to the boundary layer. The effects of turbulent temperature fluctuations are found to be small in the problem under consideration.     

旋流泵无叶腔内盐析颗粒湍流脉动特性研究

盐析晶体颗粒脉动特性是研究湍流输运状态下盐析过程的重要问题之一.为探索泵内盐析晶体颗粒湍流脉动规律及其对液相流场的影响,采用相位多普勒粒子速度场仪对旋流式输送泵无叶腔内的盐析湍流流场进行了测量,通过对改变泵运行工况、运行介质温度后颗粒脉动速度分布情况的分析,初步掌握了无叶腔中盐析晶体颗粒的湍流脉动特性;同时,讨论了晶体颗粒存在对液相湍流结构的影响。实验结果表明,随着流量的增加,颗粒的周向、径向及轴向脉动速度相应提高;盐析颗粒脉动速度值随温度发生变化,较高温度时速度脉动也较大;在一定条件下,盐析晶体颗粒表现出抑制湍流的行为。     

Statistics of particle pair relative velocity in the homogeneous shear flow

Small scale clustering of inertial particles and relative velocity of particle pairs have been fully characterized for statistically steady homogeneous isotropic flows. Depending on the particle Stokes relaxation time, the spatial distribution of the disperse phase results in a multi-scale manifold characterized by local particle concentration and voids and, because of finite inertia, the two nearby particles have high probability to exhibit large relative velocities. Both effects might explain the speed-up of particle collision rate in turbulent flows. Recently it has been shown that the large scale geometry of the flow plays a crucial role in organizing small scale particle clusters. For instance, a mean shear preferentially orients particle patterns. In this case, depending on the Stokes time, anisotropic clustering may occur even in the inertial range of scales where the turbulent fluctuations which drive the particles have already recovered isotropy. Here we consider the statistics of particle pair relative velocity in the homogeneous shear flow, the prototypical flow which manifests anisotropic clustering at small scales. We show that the mean shear, by imprinting anisotropy on the large scale velocity fluctuations, dramatically affects the particle relative velocity distribution even in the range of small scales where the anisotropic mechanisms of turbulent kinetic energy production are sub-dominant with respect to the inertial energy transfer which drives the carrier fluid velocity towards isotropy. We find that the particles’ populations which manifest strong anisotropy in their relative velocities are the same which exhibit small scale clustering. In contrast to any Kolmogorov-like picture of turbulent transport these phenomena may persist even below the smallest dissipative scales where the residual level of anisotropy may eventually blow-up. The observed anisotropy of particle relative velocity and spatial configuration is suggested to influence the directionality of the collision probability, as inferred on the basis of the so-called “ghost collision” model.     

湍流边界层中重粒子弥散的随机模型

在重粒子轨道模型的基础上,引入了Saffman力,并考虑了粒子-固壁碰撞和粒子-粒子碰撞的影响,建立了重粒子运动方程,耦合湍流脉动的随机方程,发展了重粒子弥散的随机模型,并在湍流边界层中考察该模型.将数值计算结果与实验结果进行比较,同时考察了Saffman力和粒子碰撞对计算结果的影响.     

Numerical simulation of the electrostatic powder coating process with a corona spray gun

In this paper results of investigations are described aiming to numerically simulate the electrostatic powder coating process using an extended commercial computational fluid dynamics (CFD) code. The fully three-dimensional turbulent flow was calculated. Based on the Lagrangian approach the trajectories of the powder particles were modelled considering electric and aerodynamic forces. In the calculations of the particle propagation both the particle size distribution and the particle charge distribution obtained through experiments have been applied. The model accounts for the space charge effect of the charged particles and the turbulence dispersion on the particle trajectories. It was found that the space charge plays an important role for the final spray pattern shape, also increasing the transfer efficiency. The numerical results, such as velocity profiles, static and dynamic film thickness on the target were in good agreement with experiment.     

Impact of trailing wake drag on the statistical properties and dynamics of finite-sized particle in turbulence

We study by means of an Eulerian-Lagrangian model the statistical properties of velocity and acceleration of a neutrally-buoyant finite-sized particle in a turbulent flow statistically homogeneous and isotropic. The particle equation of motion, besides added mass and steady Stokes drag, keeps into account the unsteady Stokes drag force-known as Basset-Boussinesq history force-and the non-Stokesian drag based on Schiller-Naumann parametrization, together with the finite-size Faxén corrections. We focus on the case of flow at low Taylor-Reynolds number, Re_λ?31, for which fully resolved numerical data which can be taken as a reference are available [Homann H., Bec J. Finite-size effects in the dynamics of neutrally buoyant particles in turbulent flow. J Fluid Mech 651 (2010) 81-91]. Remarkably, we show that while drag forces have always minor effects on the acceleration statistics, their role is important on the velocity behavior. We propose also that the scaling relations for the particle velocity variance as a function of its size, which have been first detected in fully resolved simulations, does not originate from inertial-scale properties of the background turbulent flow but it is likely to arise from the non-Stokesian component of the drag produced by the wake behind the particle. Furthermore, by means of comparison with fully resolved simulations, we show that the Faxén correction to the added mass has a dominant role in the particle acceleration statistics even for particles whose size attains the integral scale.     

Consistent theory of turbulent transport in two-dimensional magnetohydrodynamics

A theory of turbulent transport is presented in two-dimensional magnetohydrodynamics with background shear and magnetic fields. We provide theoretical predictions for the transport of magnetic flux, momentum, and particles and turbulent intensities, which show stronger reduction compared with the hydrodynamic case, with different dependences on shearing rate, magnetic field, and values of viscosity, Ohmic diffusion, and particle diffusivity. In particular, particle transport is more severely suppressed than momentum transport, effectively leading to a more efficient momentum transport. The role of magnetic fields in quenching transport without altering the amplitude of flow velocity and in inhibiting the generation of shear flows is elucidated. Implications of the results are discussed.     

Visualizations of the transitional flow patterns at the mid-span between shrouded co-rotating disks

Transitional air flow patterns at the mid-plane of gap between co-rotating disks in a stationary cylindrical enclosure are visualized under the acceleration condition of disks. The flow visualization is performed using olive oil particles with a laser sheet and CCD camera. On disk spinning-up, the transition flow patterns are clearly observed. The affect of magnitude of acceleration on the onset of transition and the relations of the number of vortex cells in fully turbulent regime of the flow in an outer region of the flow field to the rotating speed are also investigated. The centrifugal effect of particle is evaluated from the comparison with visualization results using hollow glass spheres.     

Effect of impact breakup of solid and liquid particles on two-phase supersonic flow about solids

Experimental modeling of processes occurring when a supersonic gaseous suspension containing solid or liquid particles flows about a freely flying body is carried out. Considered is the situation when the particles reach the surface of the body intact and are not entrained by the flow. It is found that, after the particles break into pieces and disperse, exchange between the phases intensifies, causing a change in the position of the bow shock wave and the formation of a layer with an increased concentration of the particles. Collisions of solid and liquid particles with the solid surface are modeled. The observation of the particle dispersion pattern after impact breakup and measurement of the particle velocity shed light upon a mechanism behind the formation and movement of a finely dispersed particle cloud that arises when initial particles experience impact breakup. It is found that the postcollision dispersion of the particles generates two shock waves originating from the interaction zone.     

Development and application of a diffusion-inertia model for calculating aerosol particle deposition from turbulent flows

Three-dimensional simulation of experiments on aerosol particle deposition in a turbulent flow is carried out. The k — ɛ turbulence model and the diffusion inertia model of particle transport and deposition were used in the simulation. The range of flow velocities and particle sizes is typical for the diffusion and turbophoresis deposition mechanisms. Deposition of particles in a turbulent flow is considered for cases of a direct vertical pipe and for a 90° bend in which the turbophoresis is coupled with centrifugal forces. The calculation results are in good agreement with experimental data. Deviations of results are comparable with those of discrete particle modeling.     

A numerical method for fully resolved simulation (FRS) of rigid particle–flow interactions in complex flows

A fictitious-domain based formulation for fully resolved simulations of arbitrary shaped, freely moving rigid particles in unsteady flows is presented. The entire fluid–particle domain is assumed to be an incompressible, but variable density, fluid. The numerical method is based on a finite-volume approach on a co-located, Cartesian grid together with a fractional step method for variable density, low-Mach number flows. The flow inside the fluid region is constrained to be divergence-free for an incompressible fluid, whereas the flow inside the particle domain is constrained to undergo rigid body motion. In this approach, the rigid body motion constraint is imposed by avoiding the explicit calculation of distributed Lagrange multipliers and is based upon the formulation developed by Patankar [N. Patankar, A formulation for fast computations of rigid particulate flows, Center for Turbulence Research Annual Research Briefs 2001 (2001) 185–196]. The rigidity constraint is imposed and the rigid body motion (translation and rotational velocity fields) is obtained directly in the context of a two-stage fractional step scheme. The numerical approach is applied to both imposed particle motion and fluid–particle interaction problems involving freely moving particles. Grid and time-step convergence studies are performed to evaluate the accuracy of the approach. Finally, simulation of rigid particles in a decaying isotropic turbulent flow is performed to study the feasibility of simulations of particle-laden turbulent flows.     

Large eddy simulation of orientation and rotation of ellipsoidal particles in isotropic turbulent flows

The rotational motion and orientational distribution of ellipsoidal particles in turbulent flows are of significance in environmental and engineering applications. Whereas the translational motion of an ellipsoidal particle is controlled by the turbulent motions at large scales, its rotational motion is determined by the fluid velocity gradient tensor at small scales, which raises a challenge when predicting the rotational dispersion of ellipsoidal particles using large eddy simulation (LES) method due to the lack of subgrid scale (SGS) fluid motions. We report the effects of the SGS fluid motions on the orientational and rotational statistics, such as the alignment between the long axis of ellipsoidal particles and the vorticity, the mean rotational energy at various aspect ratios against those obtained with direct numerical simulation (DNS) and filtered DNS. The performances of a stochastic differential equation (SDE) model for the SGS velocity gradient seen by the particles and the approximate deconvolution method (ADM) for LES are investigated. It is found that the missing SGS fluid motions in LES flow fields have significant effects on the rotational statistics of ellipsoidal particles. Alignment between the particles and the vorticity is weakened; and the rotational energy of the particles is reduced in LES. The SGS-SDE model leads to a large error in predicting the alignment between the particles and the vorticity and over-predicts the rotational energy of rod-like particles. The ADM significantly improves the rotational energy prediction of particles in LES.     

Heavy particle concentration in turbulence at dissipative and inertial scales

Spatial distributions of heavy particles suspended in an incompressible isotropic and homogeneous turbulent flow are investigated by means of high resolution direct numerical simulations. In the dissipative range, it is shown that particles form fractal clusters with properties independent of the Reynolds number. Clustering is there optimal when the particle response time is of the order of the Kolmogorov time scale tau(eta). In the inertial range, the particle distribution is no longer scale invariant. It is, however, shown that deviations from uniformity depend on a rescaled contraction rate, which is different from the local Stokes number given by dimensional analysis. Particle distribution is characterized by voids spanning all scales of the turbulent flow; their signature in the coarse-grained mass probability distribution is an algebraic behavior at small densities.     

3-D numerical analysis of EHD turbulent flow and mono-disperse charged particle transport and collection in a wire-plate ESP

The present study attempts to develop a detailed numerical approach and a simulation procedure to predict the motion of gas, ions and particles inside a simple parallel plate channel containing a single corona wire. A hybrid Finite Element (FEM)-Flux Corrected Transport (FCT)-Finite Volume (FVM) method is used: the FEM–FCT numerical algorithm is applied for modeling the steady-state corona discharge, while the turbulent gas flow and the particle motion under electrostatic forces are modeled using the commercial CFD code FLUENT. Calculations for the gas flow are carried out by solving the Reynolds-averaged Navier–Stokes equations and turbulence is modeled using the k–? turbulence model. An additional source term is added to the gas flow equation to include the effect of the electric field, obtained by solving a coupled system of the electric field and charge transport equations using User-Defined Functions (UDFs). The particle phase is simulated based on the Lagrangian approach, where a large number of particles is traced with their motion affected by the gas flow and electrostatic forces using the Discrete Phase Model (DPM) in FLUENT. The developed model is useful to gain insight into the particle collection phenomena that take place inside an ESP.     

Deposition of inertial particles from turbulent flow in channels at high Reynolds numbers

On the basis of the previously developed asymptotic theory of turbulent particle-laden flow with particle deposition in channels coupled with the transport model for the particle Reynolds stress, an asymptotic solution to the problem on the deposition of particles in the limit of high Reynolds numbers was obtained. The numerical calculations confirmed the presence, in the region of the transition from the diffusion-impaction regime of particle sedimentation to the inertia-moderated regime, bifurcation phenomenon of a solution found previously in earlier studies. Features of particle accumulation in the viscous sublayer are analyzed. On the basis of the numerical solution, correlations for particle deposition velocity were obtained. Boundary conditions of the wall-function type for particle concentration whose use allows widening the applicability limits of the equilibrium Eulerian models in terms of particle inertia are proposed.     

颗粒湍流扩散的数值模拟

1引言颗粒湍流扩散是气固两相流中的一个重要的研究课题,近年来,国外有大量文献报道这方面的工作。因为颗粒的湍流扩散的研究的一个基本问题就是湍流的描述,它一方面可以来检验湍流描述的正确性;另一方面,该问题是气固两相流理论中,特别是颗粒群轨道模型中一个难点。描述湍流大体上可分为两种方法。一是直接数值模拟方法（DNS）,J．B．Mclaughlin对管流内颗粒沉降的研究就基于直接数值模拟山,K．D．squires和J．K．Eaton对颗粒扩散的研究也基于DNS［2］,DNS一般只适用于低Reynolds数。另一方面,用随机方法来模拟湍流,该…     

Modulation of homogeneous shear turbulence laden with finite-size particles

The dynamics of homogeneous shear turbulence laden with spherical finite-size particles is investigated using fully resolved numerical simulations to understand how the presence of particles modulates turbulent shear flows. We focus on a dilute flow laden with non-sedimenting particles whose diameter is slightly smaller than or comparable with those of vortex cores in turbulence. An immersed boundary method is adopted to represent a spherical finite-size particle. Numerical results show that the presence of particles augments the viscous dissipation of turbulence kinetic energy, which leads to a slower increase in the turbulence energy. Although the augmentation of energy dissipation occurs predominantly inside viscous layers surrounding particles in an initial period, the contribution from their outside becomes more significant due to the modification of turbulence structures as turbulence develops. It is found that the particles exhibit weak tendency to accumulate in vortex layers. The particles approaching and colliding with vortex layers induce large velocity fluctuations, which leads to the generation and shedding of thin vortex tubes. Newly generated vortex tubes interact with developed vortex tubes and layers, and modify the entire structure of the vorticity field.