各向同性湍流内颗粒碰撞率的直接模拟研究

对 Re_{\lambda } 约为51均匀各向同性湍流内 St_{k}(=\tau_{p}/\tau_{k}) 为 0 ~10.0 的 有限惯性颗粒的碰撞行为进行了直接数值模拟，以研究湍流对有限惯性 颗粒碰撞的影响. 结果表明，具有一定惯性颗粒的湍流碰撞率完全不同于零惯性的轻颗粒 (St_{k}=0) 和可忽略湍流作用的重颗粒 (St{k} \to \infty) , 其变化趋势极其复杂： 在Stk为 0~1.0 之间，颗粒的碰撞率随 St 的增加而近乎线性地剧烈增长，在 Stk≈1.0 3.0(对应的StE=τp/Te≈0.5)附近，颗粒碰撞率出现两个峰值，在Stk>3.0以后，颗粒的碰撞率随惯性增 大而逐渐趋向于重颗粒极限；在峰值处，有限惯性颗粒的平均碰撞率的峰值较轻颗粒增强了 30倍左右. 为进一步分析湍流作用下颗粒碰撞率的影响因素，分别使用可能发生碰撞 的颗粒对的径向分布函数和径向相对速度来量化颗粒的局部富集效应和湍流掺混效应，表明 St_{k} \approx 1.0 时局部富集效应最为强烈，使得颗粒的碰撞率出现第1个峰值； 湍流掺混效应则随着颗粒Stk的增大而渐近增大；局部富集和湍流掺混联合作用的结果， 使得颗粒碰撞率在 St_{k} \approx 3.0 附近出现另一个峰值.     

Turbulent collision of inertial particles: Point-particle based,hybrid simulations and beyond

Point-particle based direct numerical simulation (PPDNS) has been a productive research tool for studying both single-particle and particle-pair statistics of inertial particles suspended in a turbulent carrier flow. Here we focus on its use in addressing particle-pair statistics relevant to the quantification of turbulent collision rate of inertial particles. PPDNS is particularly useful as the interaction of particles with small-scale (dissipative) turbulent motion of the carrier flow is mostly relevant. Furthermore, since the particle size may be much smaller than the Kolmogorov length of the background fluid turbulence, a large number of particles are needed to accumulate meaningful pair statistics. Starting from the relative simple Lagrangian tracking of so-called ghost particles, PPDNS has significantly advanced our theoretical understanding of the kinematic formulation of the turbulent geometric collision kernel by providing essential data on dynamic collision kernel, radial relative velocity, and radial distribution function. A recent extension of PPDNS is a hybrid direct numerical simulation (HDNS) approach in which the effect of local hydrodynamic interactions of particles is considered, allowing quantitative assessment of the enhancement of collision efficiency by fluid turbulence. Limitations and open issues in PPDNS and HDNS are discussed. Finally, on-going studies of turbulent collision of inertial particles using large-eddy simulations and particle-resolved simulations are briefly discussed.     

The influence of sub-grid scale motions on particle collision in homogeneous isotropic turbulence

The absence of sub-grid scale (SGS) motions leads to severe errors in particle pair dynamics, which represents a great challenge to the large eddy simulation of particle-laden turbulent flow. In order to address this issue, data from direct numerical simulation (DNS) of homogenous isotropic turbulence coupled with Lagrangian particle tracking are used as a benchmark to evaluate the corresponding results of filtered DNS (FDNS). It is found that the filtering process in FDNS will lead to a non-monotonic variation of the particle collision statistics, including radial distribution function, radial relative velocity, and the collision kernel. The peak of radial distribution function shifts to the large-inertia region due to the lack of SGS motions, and the analysis of the local flowstructure characteristic variable at particle position indicates that the most effective interaction scale between particles and fluid eddies is increased in FDNS. Moreover, this scale shifting has an obvious effect on the odd-order moments of the probability density function of radial relative velocity, i.e. the skewness, which exhibits a strong correlation to the variance of radial distribution function in FDNS. As a whole, the radial distribution function, together with radial relative velocity, can compensate the SGS effects for the collision kernel in FDNS when the Stokes number based on the Kolmogorov time scale is greater than 3.0. However, it still leaves considerable errors for \({ St}_\mathrm{k }<3.0\).     

Direct numerical simulation of modulation of isotropic turbulence by poly‐dispersed particles

A direct numerical simulation technique based on two‐way coupling is presented to study a particle‐laden, decaying isotropic turbulent flow. Physical characteristics of turbulence modulation because of the mono‐dispersed (i.e., particles with single Stokes number) and poly‐dispersed particles (i.e., particles with more than one Stokes number) were investigated. A scale dependent effective viscosity that summarizes the aspects of the interaction between the velocity field and particles is defined in the study. Particles of Stokes number (St) 3.2,6.4 and 12.8 were used in performing the simulations. Poly‐dispersed particles were acquired by mixing particles of two different Stokes numbers at a time. As a whole, decay of turbulence because of the poly‐dispersed particles is observed to be larger than that of the decay of turbulence because of the mono‐dispersed particles. Simulations of poly‐dispersed particle indicate nonlinear characteristics in the modification of the temporal evolution of turbulence energy and dissipation. The scale dependent effective viscosity, which correlates with the energy spectrum plot, indicates that the decay of turbulence is mostly observed at the intermediate scales of turbulence. The effective viscosity for the simulations of the poly‐dispersed particles was calculated to be higher than that of the simulations of the mono‐dispersed particles. Copyright © 2011 John Wiley & Sons, Ltd.     

Particle response in a planar sudden expansion flow

Particle velocity and concentration statistics were measured in a vertically downward planar sudden expansion flow for large-eddy particle Stokes numbers (τ_pU_o/5H) ranging from 0.5 to 7.4. Particles with Stokes numbers greater than 3 did not enter the recirculation zone, exhibited substantial attenuation of cross-stream velocity fluctuations, and had large streamwise velocity fluctuations in regions of strong velocity gradient. The smallest particles filled the recirculation zone and showed strong response to the large eddies in the flow. Phase-locked particle concentration measurements showed that these particles were centrifuged away from vortex cores and concentrated between vortices. Intermediate-size particles with Stokes numbers of 1.4 were injected intermittently into the recirculation zone as tongues of particles moving down between vortices. Particle Reynolds number was found to have negligible effect on the particle velocity statistics.     

Simulation of particles released near the wall in a turbulent boundary layer

A direct numerical simulation was used along with a Lagrangian particle tracking technique to study particle motion in a horizontal, spatially developing turbulent boundary layer along an upper-wall (with terminal velocity directed away from the wall). The objective of the research was to study particle diffusion, dispersion, reflection, and mean velocity in the context of two parametric studies: one investigated the effect of the drift parameter (the ratio of particle terminal velocity to fluid friction velocity) for a fixed and finite particle inertia, and the second varied the drift parameter and particle inertia by the same amount (i.e. for a constant Froude number). A range of drift parameters from 10⁻⁴ to 10⁰ were considered for both cases. The particles were injected into the simulation at a height of four wall units for several evenly distributed points across the span and a perfectly elastic wall collision was specified at one wall unit.Statistics collected along the particle trajectories demonstrated a transition in particle movement from one that is dominated by diffusion to one that is dominated by gravity. For small and intermediate sized particles (i.e. ones with outer Stokes numbers and drift parameters much less than unity) transverse diffusion away from the wall dominated particle motion. However, preferential concentration is seen near the wall for intermediate-sized particles due to inhomogeneous turbulence effects (turbophoresis), consistent with previous channel flow studies. Particle–wall collision statistics indicated that impact velocities tended to increase with increasing terminal velocity for small and moderate inertias, after which initial conditions become important. Finally, high relative velocity fluctuations (compared to terminal velocity) were found as particle inertia increased, and were well described with a quasi-one-dimensional fluctuation model.     

Acceleration of heavy particles in isotropic turbulence

The paper concerns the effect of particle inertia on acceleration statistics. A simple analytical model for predicting the acceleration of heavy particles suspended in an isotropic homogeneous turbulent flow field is developed. This model is capable of describing the influence of both Stokes and Reynolds numbers on the particle acceleration variance. Comparisons of model predictions with numerical simulations are presented.     

Relative particle velocity in a turbulent flow

On the basis of a statistical approach using a probability density function for the coordinates of two particles in a turbulent flow, the parameters of the relative particle motion are investigated. For the functions describing particle entrainment in the turbulence, rigorous results are obtained using a 3D turbulence spectrum. A method of calculating the particle relative-velocity rate with account for particle trajectory correlation is presented. The effects of particle inertia and velocity slip on the parameters of the relative particle motion are studied. Simple approximating formulas for calculating the relative particle motion in a turbulent flow are proposed. The calculation results are compared with the data of direct numerical simulation of stochastic particle trajectories in an isotropic turbulent field.     

蒙特卡洛方法数值研究大气颗粒物动力学效应和辐射传输性质

爆发性增强的雾天,空气污染严重能见度低,这与大气边界层湍流性质、悬浮颗粒的动力学及散射性质密切相关.文中基于颗粒群平衡方程和Mie理论,采取加权蒙特卡洛方法,自行开发了Fortran程序.文中计算所得的颗粒尺度分布函数、颗粒散射性质与实验值、理论解一致,验证了数值模型和方法的正确性.此外,数值研究了雾爆发性增强阶段雾滴谱拓宽、能见度降低的机理,讨论湍流输运和颗粒局部聚集效应下颗粒间的碰并过程,并耦合颗粒散射性质,数值分析雾发展中湍流耗散率对颗粒对径向相对速度、系统透过率的影响;以及颗粒对径向相对速度与系统透过率、颗粒尺度的关系.研究结果表明:随着湍流耗散率的增大,颗粒的径向相对速度呈现先缓慢而后快速增大的变化趋势.1000s时刻,湍流的耗散率为1.0×10-2m2/s3,颗粒径向相对速度(无量纲)为0.0969;对于0.6μm的可见光,雾环境颗粒系统的透过率为0.47.此外,雾发展中雾滴易与气溶胶碰并,系统的散射性质与水组成的雾滴系统不同,天气的能见度明显降低.      

Stochastic modeling of particle diffusion in a turbulent boundary layer

Several Continuous Random Walk (CRW) models were constructed to predict turbulent particle diffusion based on Eulerian statistics that can be obtained with Reynolds-Averaged Navier Stokes (RANS) solutions. The test conditions included a wide range of particle inertias (Stokes numbers) with a near-wall injection (y⁺ = 4) in a turbulent boundary layer that is strongly anisotropic and inhomogeneous. To assess the performance of the models, the CRW results were compared to particle diffusion statistics gathered from a Direct Numerical Simulation (DNS). In particular, comparisons were made with transverse concentration profiles, root-mean-square of particle trajectory coordinates, and mean transverse particle velocity away from the wall.The results showed that accurate simulation required a modified (non-dimensionalized) Markov chain to handle the large gradients in turbulence near the wall as shown by simulations with fluid-tracer particles. For finite-inertia particles, an incremental drift correction for the Markov chain developed herein to account for Stokes number effects was critical to avoiding non-physical particle collection in low-turbulence regions. In both cases, inclusion of anisotropy in the turbulence model was found to be important, but the influence of off-diagonal terms was found to be weak. The results were generally good, especially for long-time and large inertia particles.     

Modeling droplet dispersion and interphase turbulent kinetic energy transfer using a new dual-timescale Langevin model

Dispersion of spray droplets and the modulation of turbulence in the ambient gas by the dispersing droplets are two coupled phenomena that are closely linked to the evolution of global spray characteristics, such as the spreading rate of the spray and the spray cone angle. Direct numerical simulations (DNS) of turbulent gas flows laden with sub-Kolmogorov size particles, in the absence of gravity, report that dispersion statistics and turbulent kinetic energy (TKE) evolve on different timescales. Furthermore, each timescale behaves differently with Stokes number, a non-dimensional flow parameter (defined in this context as the ratio of the particle response time to the Kolmogorov timescale of turbulence) that characterizes how quickly a particle responds to turbulent fluctuations in the carrier or gas phase. A new dual-timescale Langevin model (DLM) composed of two coupled Langevin equations for the fluctuating velocities, one for each phase, is proposed. This model possesses a unique feature that the implied TKE and velocity autocorrelation in each phase evolve on different timescales. Consequently, this model has the capability of simultaneously predicting the disparate Stokes number trends in the evolution of dispersion statistics, such as velocity autocorrelations, and TKE in each phase. Predictions of dispersion statistics and TKE from the new model show good agreement with published DNS of non-evaporating and evaporating droplet-laden turbulent flow.     

Statistics of particle dispersion in direct numerical simulations of wall-bounded turbulence: Results of an international collaborative benchmark test

In this paper the results of an international collaborative test case relative to the production of a direct numerical simulation and Lagrangian particle tracking database for turbulent particle dispersion in channel flow at low Reynolds number are presented. The objective of this test case is to establish a homogeneous source of data relevant to the general problem of particle dispersion in wall-bounded turbulence. Different numerical approaches and computational codes have been used to simulate the particle-laden flow and calculations have been carried on long enough to achieve a statistically steady condition for particle distribution. In such stationary regime, a comprehensive database including both post-processed statistics and raw data for the fluid and for the particles has been obtained. The complete datasets can be downloaded from the web at http://cfd.cineca.it/cfd/repository/. In this paper the most relevant velocity statistics (for both phases) and particle distribution statistics are discussed and benchmarked by direct comparison between the different numerical predictions.     

Agglomeration of inertial particles in a random rotating symmetric straining flow

This paper is concerned with the development and validation of a simple Lagrangian model for particle agglomeration in a turbulent flow involving the collision of particles in a sequence of correlated straining and vortical structures which simulate the Kolmogorov small scales of motion of the turbulence responsible for particle pair dispersion and collision. In this particular study we consider the collision rate of monodisperse spherical particles in a symmetric (pure) straining flow which is randomly rotated to create an isotropic flow. The model is similar to the classical model of Saffman and Turner (S&T) (1956) for the collision (agglomeration) of tracer particles suspended in a turbulent flow. However unlike S&T, the straining flow is not frozen in time persisting only for timescales ∼Kolmogorov timescale. Furthermore, we consider the collision of inertial particles as well as tracer particles, and study their behavior not only at the collision boundary but also in its vicinity. In the simulation, particles are injected continuously at the boundaries of the straining flow, the size of the straining region being typical of the Kolmogorov length scale η_K of the turbulence. For steady state conditions, we calculate the flux of particles colliding with a test particle at the centre of the straining flow and consider its dependence on the inertia of the colliding particles (characterized by the particle Stokes number, St). The model replicates the segregation and accumulation observed in DNS and in particular the maximum segregation for St ∼ 1 (where St is the ratio of the particle response time to the Kolmogorov timescale). We also calculate the contributions of the various turbulent forces in the momentum balance equation for satellite particles and show for instance that for small Stokes number, there is a balance between turbulent diffusion and turbophoresis (gradient of kinetic stresses) which in turn is responsible for the build-up of concentration at the collision boundary. As found in previous studies, for the case of inertialess tracer particles, the collision rate turns out to be significantly smaller than the S&T prediction due to a lowering of the concentration at the collision boundary compared to the fully mixed value. The increase in collision rate for St ∼ 0.5 is shown to be a combination of particle segregation (build-up of concentration near the collision boundary) and the decorrelation of the relative velocity between the local fluid and a colliding particle. The difference from the S&T value for the agglomeration kernel is shown to be a consequence of the choice of perfectly absorbing boundary conditions at collision and the influence of the time scale of the turbulence (eddy lifetime). We draw the analogy between turbulent agglomeration and particle deposition in a fully developed turbulent boundary layer.     

Dispersion and clustering of bidisperse particles in isotropic turbulence

A statistical kinetic model describing the dispersion and clustering of particles with different inertia in homogeneous turbulence is presented. The model developed is used for calculating the relative velocity, the radial distribution function, and the particle collision kernel in a stationary bidisperse suspension. The results obtained are compared with the data of a direct numerical simulation.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 94–107. Original Russian Text Copyright © 2005 by Alipchenkov and Zaichik.     

Direct numerical simulation of a particle-laden low Reynolds number turbulent round jet

Direct numerical simulation method is used for the investigating of particle-laden turbulent flows in a spatially evolution of low Reynolds number axisymmetric jet, and the Eulerian–Lagrangian point-particle approach is employed in the simulation. The simulation uses an explicit coupling scheme between particles and the fluid, which considers two-way coupling between the particle and the fluid. The DNS results are compared well with experimental data with equal Reynolds number (R_e = 1700). Our objects are: (i) to investigate the correlation between the particle number density and the fluctuating of fluid streamwise velocity; (ii) to examine whether the three-dimensional vortex structures in the particle-laden jet are the same as that in the free-air jet and how the particles modulate the thee-dimensional vortex structures and turbulence properties with different Stokes number particles; (iii) to discover the particle circumferential dispersion with different Stokes number particles. Our findings: (i) all the particles, regardless of their particle size, tend to preferentially accumulate in the region with large-than-mean fluid streamwise velocity; (ii) the small Stokes number particles take an important part in the modulation of three-dimensional vortex structures, but for the intermediate and larger sized particles, this modulation effect seems not so apparent; (iii) the particle circumferential dispersion is more effective for the smaller and intermediate sized particles, especially for the intermediate sized particles.     

Gas turbulence modulation in the pneumatic conveying of massive particles in vertical tubes

The present work is concerned with the interaction between large particles and gas phase turbulence. Gas turbulence modulation in these systems is considered to be dominated by a generation mechanism which arises due to the presence of wakes behind particles. Following a recent proposal, a closure for gas turbulence modulation accounting for the effect of wakes is employed within the context of a mathematical model for particle-laden, turbulent flows. The model accounts for particle particle and particle-wall interactions associated with larger particles based on concepts from gas kinetic theory. It is shown that due to the significant flattening of the mean gas velocity profile with the addition of particles, and the corresponding decrease in turbulent energy production, a generation mechanism must be present in order to produce gas velocity fluctuation predictions which are consistent with the experimental measurements, even in the case where the experimental results indicate a net suppression of gas phase turbulence in the presence of particles.     

Statistical models for predicting the effect of bidisperse particle collisions on particle velocities and stresses in homogeneous anisotropic turbulent flows

The purpose of this paper is to present and compare two statistical models for predicting the effect of collisions on particle velocities and stresses in bidisperse turbulent flows. These models start from a kinetic equation for the probability density function (PDF) of the particle velocity distribution in a homogeneous anisotropic turbulent flow. The kinetic equation describes simultaneously particle–turbulence and particle–particle interactions. The paper is focused on deriving the collision terms in the governing equations of the PDF moments. One of the collision models is based on a Grad-like expansion for the PDF of the velocity distributions of two particles. The other model stems from a Grad-like expansion for the joint fluid–particle PDF. The validity of these models is explored by comparing with Lagrangian simulations of particle tracking in uniformly sheared and isotropic turbulent flows generated by LES. Notwithstanding the fact that the fluid turbulence may be isotropic, the particle velocity fluctuations are anisotropic due to the impact of gravitational settling. Comparisons of the model predictions and the numerical simulations show encouraging agreement.     

Dynamics of PIV seeding particles in turbulent premixed flames

Particle image velocimetry (PIV) estimates the fluid velocity field measuring the displacement of small dispersed particles between two successive instants separated by a small time interval. The accuracy of the measurements depends on the ability of the particles to accommodate their velocity to the fluid fluctuations. When the fluid is subjected to extreme accelerations, the small but finite inertia prevents the particles from following the fluid, originating a substantial relative velocity. This effect is shown to be crucial for applications of PIV to turbulent premixed combustion, particularly in the product region at locations just behind the instantaneous flame front. The issuing inaccuracy may easily spoil the estimate of certain statistical observables which are of crucial importance in the theory of turbulent premixed combustion. By exploiting the direct numerical simulation of a model air/methane flame, a suitable criterion for proper particle seeding is validated and compared with the corresponding experiments with a combined PIV/OH-LIF (laser-induced fluorescence) system. The proposed parameter, the flamelet Stokes number, depends on particle properties and thermochemical conditions of the flame and substantially restricts the particle dimensions required for a reliable estimate of the relevant flow statistics.     

Bichromatic particle streak velocimetry bPSV

We propose a novel technique for three-dimensional three-component (3D3C) interfacial flow measurement. It is based on the particle streak velocimetry principle. A relatively long integration time of the camera is used for capturing the movement of tracer particles as streaks on the sensor. The velocity along these streaks is extracted by periodically changing the illumination using a known pattern. A dye with different absorption characteristics in two distinct wavelengths is used to color the fluid. The depth of particles relative to the fluid interface can then be computed from their intensities when illuminated with light sources at those two different wavelengths. Hence, from our approach, a bichromatic, periodical illumination together with an image processing routine for precisely extracting particle streak features is used for measuring 3D3C fluid flow with a single camera. The technique is applied to measuring turbulent Rayleigh–Bénard convection at the free air--water interface. Using Lagrangian statistics, we are able to demonstrate a clear transition from the Batchelor regime to the Richardson regime, both of which were postulated for isotropic turbulence. The relative error of the velocity extraction of our new technique was found to be below 0.5?%.     

Comparison of the RANS and PDF methods for air-particle flows

Two simulation methods, namely Reynolds-Averaged Navier–Stokes (RANS) equations, and Probability Distribution Function (PDF) are currently widely used for the modeling of multiphase flows. These two approaches are supplemented with appropriate closure equations that take into account all the pertinent forces and interaction effects on the solid particles, such as: particle–turbulence interactions; turbulence modulation; particle–particle interactions; particle–wall interactions; gravitation, drag and lift forces. The two methods have been used in order to simulate the turbulent particulate flow in upward pipes. The flow domain in all cases was a cylindrical pipe and the computations were carried for upward pipe flow. Monodisperse as well as polydisperse mixtures of particles have been considered. In general, the average velocity results obtained from the two methods are in close agreement, because the methods predict well the average velocity distribution of the carrier fluid as well as the solids. Thus, the differences in the average axial velocities predicted by the methods are not substantial. Differences in the turbulence intensity are more significant. A comparison of the numerical results obtained shows the relative importance of retaining the diffusion terms in both the axial and radial directions in the RANS method. Also the comparisons of the results show the relative effect of the lift forces in the distribution of solid particles.