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.     

椭圆颗粒在剪切流中旋转特性的数值研究

研究颗粒在流体剪切作用下的运动特性是理解和预测颗粒悬浮流流动行为的关键.当流体的惯性不能忽略时,颗粒的运动往往变得非常复杂.本文采用格子Boltzmann方法对中等雷诺数下椭圆颗粒在剪切流中的旋转运动进行了模拟.首先,研究了雷诺数(0Re 170)的影响,结果表明当雷诺数低于临界值时,颗粒以周期性的方式旋转,角速度最小时对应的长轴方向随着雷诺数的增大而逐渐远离水平方向,而且这一倾角与雷诺数呈分段线性关系;当雷诺数大于临界值时,椭圆形颗粒最终保持静止状态,且静止时的转角与雷诺数呈幂函数关系,雷诺数越大,转角越小,椭圆的长轴越远离水平位置.其次,研究了椭圆颗粒的长短轴之比α(1α10)的影响,结果表明颗粒旋转的周期与α呈幂函数关系,α越大,颗粒旋转周期越小.此外,当α超过临界值时,颗粒也在水平位置附近保持静止状态,此时的转角与α也呈幂函数关系,α越大,转角越小.研究还发现,当雷诺数较大时椭圆颗粒在旋转过程中会产生过冲现象.     

Dynamics of dual-particles settling under gravity

As a first step towards understanding particle–particle interaction in fluid flows, the motion of two spherical particles settling in close proximity under gravity in Newtonian fluids was investigated experimentally for particle Reynolds numbers ranging from 0.01 to 2000. It was observed that particles repel each other for Re>0.1 and that the separation distance of settling particles is Reynolds number dependent. At lower Reynolds numbers, i.e. for Re<0.1, particles settling under gravity do not separate.The orientation preference of two spherical particles was found to be Reynolds number dependent. At higher Reynolds numbers, the line connecting the centres of the two particles is always horizontal, regardless of the way the two particles are launched. At lower Reynolds numbers, however, the particle centreline tends to tilt to an arbitrary angle, even of the two particles are launched in the horizontal plane. Because of the tilt, a side migration of the two particles was found to exist. A linear theory was developed to estimate the side migration velocity. It was found that the maximum side migration velocity is approximately 6% of the vertical settling velocity, in good agreement with the experimental results.Counter-rotating spinning of the two particles was observed and measured in the range of Re=0–10. Using the linear model, it is possible to estimate the influence of the tilt angle on the rate of rotation at low Reynolds numbers. Dual particles settle faster than a single particle at small Reynolds numbers but not at higher Reynolds numbers, because of particle separation. The variation of particle settling velocity with Reynolds number is presented. An equation which can be used to estimate the influence of tilt angle on particle settling velocity at low Reynolds number is also derived.     

Inertial Particles in Homogeneous Shear Turbulence: Experiments and Direct Numerical Simulation

The properties of the transport of heavy inertial particles in a uniformly sheared turbulent flow have been investigated by combining experimental and numerical data at particle Stokes number St?≈?0.3?÷?0.5 respectively. As in isotropic turbulence, particles are observed to avoid zones of intense enstrophy and to cluster in strain-dominated regions, resulting in highly intermittent spatial distributions. Moreover, the anisotropy of the mean flow is found to imprint a clear preferential orientation of the particle clusters in the direction of the maximum mean strain. These features are observed both in the numerics and in the experiments, and have been consistently quantified by a number of complementary statistical tools, such as the Voronoï tessellations and the pair correlation function. The latter quantity has been generalized in the form of the Angular Distribution Function and has allowed to evaluate the anisotropy content of the particle field at each scale. The behavior of this observable exhibits the same trend in the two datasets and suggests that, owing to increased inertia, the particle distribution starts to recover isotropy at scales smaller than the carrier velocity field. A proper rescaling of the two datasets in terms of their respective values of the shear scale allows to account for differences in the Reynolds number of experiments and numerics in the range of scales dominated by the mean shear.     

A numerical study of pulsatile laminar flows in a pipe with a ring-type constriction

Numerical simulations have been carried out to study pulsatile laminar flows in a pipe with an axisymmetric ringtype constriction. Three types of pulsatile flows were investigated, namely a physiological flow, a pure sinusoidal flow and a non-zero mean velocity sinusoidal flow. The laminar flow governing equations were solved by the SIMPLE algorithm on a non-staggered grid and a modified Crank-Nicolson approximation was used to discretrize the momentum equations with respect to time. The maximum flow Reynolds numer (Re) is 100. The Womersley number (N_w) ranges from 0 to 50, with the corresponding Strouhal number (St) ranging from 0 to 3·98. The constriction opening ratio (d/D) and thickness ratio (h/D) are fixed at 0·5 and 0·1 respectively. Within the time period investigated, all these pulsatile flows include both forward and backward flows. The unsteady recirculation region and the recirculation points change in size and location with time. For N_w ≤ 1 and St≤ 1·56 x 10^?3 the three pulsatile flows have the same simple relation between the instantaneous flow rate and pressure loss (Δp) across the constriction and the pressure gradient in the axial direction (dp/dz) in the fully developed flow region. The phase angles between the flow rate and pressure loss and the pressure gradient are equal to zero. With increasing N_w and St, the phase angle between the flow rate and the dp/dz becomes larger and has its maximum value of 90° at N_w = 50 and St = 3·98. The three pulsatile flows also show different relations between the flow rate and the pressure gradient. The pure sinusoidal flow has the largest maximum pressure gradient and the non-zero mean velocity sinusoidal flow has the smallest. For larger N_w and St the fully developed velocity profiles in the fully developed flow region have a smaller velocity gradient along the radial direction in the central region. The maximum recirculation length increases for N_w ranging from 0 to 4·2, while this length becomes very small at N_w = 50 and St = 3·98. The deceleration tends to enlarge the recirculation region and this effect appears for N_w ≥ 3 and St ≥ 1·43×10^?2. Linear relations exist between the flow rate and the instantaneous maximum values of velocity, vorticity and shear stress.     

Überlegungen zur Scherviskosität von Suspensionen aufgrund einer Dimensionsanalyse

Dimensional analysis of the motion of solid particles suspended in a fluid phase shows that the macroscopic relative shear viscosity of suspensions generally depends not only on the volume concentration and particle shape but also on two Reynolds numbers and a dimensionless sedimentation number. These dimensionless numbers are formed using parameters characterizing the structure and motion of the suspension at the microscopic level. The analysis was based on the assumptions that the dispersed particles are rigid and sufficiently large that Brownian motion may be neglected, that the continuous fluid phase is Newtonian and that the interactions between particles and between particles and fluid phase are only hydrodynamic. The Reynolds numbers describe the influence of the inertial forces at the microscopic level, and the sedimentation number the influence of gravity. The dimensionless numbers can be neglected if their values are much smaller than one. For each of the dimensionless numbers both the shear rate and the particle size influence the shear viscosity. Thus sedimentation number is large for low shear rates, whereas the Reynolds numbers are large for high shear rates. The viscosity function for one suspension can be transformed into the viscosity function for another suspension with geometrically similar particles but of a different size. The scale-up rules are derived from the requirement that the relevant dimensionless numbers must be constant. The influence of non-hydrodynamic effects at the microscopic level on the shear viscosity can be detected by deviations from the derived scale-up rules.     

Turbulent transport dissimilarity with modulated turbulence structure in channel flow of viscoelastic fluid

This experimental study investigated the turbulent transport dissimilarity with a modulated turbulence structure in a channel flow of a viscoelastic fluid using simultaneous particle image velocimetry and planar laser-induced fluorescence measurements. An instantaneous dye concentration field with fluctuating velocity vectors showed that mass was transferred by hierarchically large-scale wavy motions with inclination. A co-spectral analysis showed that the spatial phase modulation of the streamwise velocity and dye concentration fluctuations for the wall-normal velocity fluctuation corresponded to the relaxation time. The occurrence of intense dye concentration fluctuation and small streamwise velocity fluctuation in a thin boundary layer caused dissimilar turbulent transport because of the non-zero negative correlation of the streamwise velocity and dye concentration fluctuations for the wall-normal velocity fluctuation only on large scales. This explains the turbulent transport dissimilarity which leads to the zero averaged Reynolds shear stress and non-zero wall-normal turbulent mass flux.     

Numerical simulation of sedimentation of rectangular particle in Newtonian fluid

The sedimentation of a rectangular particle falling in a two-dimensional channel filled with Newtonian fluid was simulated with finite element arbitrary Lagrangian–Eulerian domain method. The numerical procedure was validated by comparison of the simulation results with existing numerical work. Moreover, good agreement was obtained between the simulation results and experimental measurements performed in the current study. The equilibrium position, stable orientation and drag coefficient of a rectangular particle for different particle Reynolds numbers (Re_p) were studied. The results show that there is a critical particle Reynolds number for the preferred orientation of a rectangular particle falling in a Newtonian fluid. When Re_p is smaller than the critical value, the particle falls with its long side parallel to gravity; otherwise the particle falls with its long side perpendicular to gravity. The critical particle Reynolds number is a decreasing function of the blockage ratio and aspect ratio. The distributions of pressure and shear stress on rectangular particle surface were analyzed. Moreover, the drag coefficient of the rectangular particle decreases as Re_p or the blockage ratio increases; however, it appears to be independent of aspect ratio.     

Direct numerical simulation of particle behaviour in the wall region of turbulent flows in horizontal channels

The motion of small particles in the wall region of turbulent channel flows has been investigated using direct numerical simulation. It is assumed that the particle concentration is low enough to allow the use of one-way coupling in the calculations, i.e. the fluid moves the particles but there is no feedback from the particles on the fluid motion. The velocity of the fluid is calculated by using a pseudospectral, direct solution of the Navier-Stokes equations. The calculations indicate that particles tend to segregate into the low-speed regions of the fluid motion near the wall. The segregation tendency depends on the time constant of the particle made non-dimensional with the wall shear velocity and kinematic viscosity. For very small and very large time constants, the particles are distributed more uniformly. For intermediate time constants (of the order 3), the segregation into the low-speed fluid regions is the highest. The finding that segregation occurs for a range of particle time constants is supported by experimental results. The findings regarding the more uniform distributions, however, still remain to be verified against experimental data which is not yet available. For horizontal channel flows, it is also found that particles are resuspended by ejections (of portions of the low-speed streaks) from the wall and are, therefore, primarily associated with low-speed fluid. The smaller particles are flung further upwards and, as they fall back towards the wall, they tend to be accelerated close to the fluid velocity. The larger particles have greater inertia and, consequently, accelerate to lower velocities giving higher relative velocities. This velocity difference, as a function of wall-normal distance, follows the same trend as in experiments but is always somewhat smaller in the calculations. This appears to be due to the Reynolds number for the numerical simulation being smaller than that in the experiment. It is concluded that the average particle velocity depends not only on the wall variables for scaling, but also on outer variables associated with the mean fluid velocity and fluid depth in the channel. This is because fluid depth in combination with the wall shear velocity determines how much time a particle, of a given size and density, spends in the outer flow and, hence, how close it gets to the local fluid velocity.     

Experimental Investigation of Three-Dimensional Vortex Structures Downstream of Vortex Generators Over a Backward-Facing Step

An experimental investigation of vortex generators has been carried out in turbulent backward-facing step (BFS) flow. The Reynolds number, based on a freestream velocity U₀ = 10 m/s and a step height h = 30 mm, was Re_h = 2.0 × 10⁴. Low-profile wedge-type vortex generators (VGs) were implemented on the horizontal surface upstream of the step. High-resolution planar particle image velocimetry (2D-2C PIV) was used to measure the separated shear layer, recirculation region and reattachment area downstream of the BFS in a single field of view. Besides, time-resolved tomographic particle image velocimetry (TR-Tomo-PIV) was also employed to measure the flow flied of the turbulent shear layer downstream of the BFS within a three-dimensional volume of 50 × 50 × 10 mm³ at a sampling frequency of 1 kHz. The flow control result shows that time-averaged reattachment length downstream of the BFS is reduced by 29.1 % due to the application of the VGs. Meanwhile, the Reynolds shear stress downstream of the VGs is considerably increased. Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) have been applied to the 3D velocity vector fields to analyze the complex vortex structures in the spatial and temporal approaches, respectively. A coherent bandwidth of Strouhal number 0.3 < St_h < 0.6 is found in the VG-induced vortices, and moreover, Λ-shaped three-dimensional vortex structures at St_h = 0.37 are revealed in the energy and dynamic approaches complementarily.     

The influence of the periodic disturbance on the local heat transfer in separated and reattached flow

A numerical study based on the large eddy simulation methodology was made of heat transfer in locally disturbed turbulent separated and reattached flow over a backward facing step. The local disturbance was given to the flow by a sinusoidally blowing/suction of the fluid into a separated shear layer. The Reynolds number was fixed at 33,000 and Richardson number at 0.5. The disturbance frequency was varied in the range 0 ≤ St ≤ 2, where St is the Strouhal number of disturbance. The obtained results revealed the existence of an optimum perturbation frequency value, St = 0.25, in terms of the reduced reattachment length. At this frequency the heat transfer is significantly enhanced in the recirculation zone. The influence of the frequency and the amplitude of disturbance, in the maximum heat transfer positions and the maximum local Nusselt number, is analysed.     

Numerical solution for the flow of viscoelastic fluids around an inclined circular cylinder.

Finite difference solutions have been obtained by the perturbation method to investigate the influence of shear thinning and elasticity on the flow around an inclined circular cylinder of finite length in a uniform flow. In this numerical analysis a generalized upper-convected Maxwell model, in which the viscosity changes according to the Cross model, has been used.The local flow over the cylinder is only slightly deflected. However, in the wake flow behind the cylinder the particle path is remarkably influenced by the axial flow and rapidly flows up parallel to the cylinder's axis. Then it gradually rejoins direction of the incoming flow. It is found that viscoelastic fluids are prone to flow axially in the vicinity of the cylinder. The numerical predictions generally agree with the flow visualization results.The numerical solutions also demonstrate that elasticity has a strong effect on the velocity profile especially around both ends of the cylinder; elasticity increases the asymmetric profiles of both circumferential velocity and axial velocity with respect to equal to 90° and decreases a difference in the circumferential velocity between the windward end and the leeward end.For non-Newtonian fluids, the length of the wake flow is influenced by not only the Reynolds number but also the cylinder diameter and it is larger for the cylinder with the smaller diameter at the same Reynolds number.Partly presented at the 9th Australasian Fluid Mechanics Conference, University of Auckland, New Zealand, 8–12 December, 1986     

The influence of flow-induced non-Newtonian fluid properties on turbulent drag reduction

Friction factors and velocity profiles in turbulent drag reduction can be compared to Newtonian fluid turbulence when the shear viscosity at the wall shear rate is used for the Reynolds number and the local shear viscosity is used for the non-dimensional wall distance. On this basis, an apparent maximum drag reduction asymptote is found which is independent of Reynolds number and type of drag reducing additive. However, no shear viscosity is able to account for the difference between the measured Reynolds stress and the Reynolds stress calculated from the mean velocity profile (the Reynolds stress deficit). If the appropriate local viscosity to use with the velocity fluctuation correlations includes an elongational component, the problem can be resolved. Taking the maximum drag reduction asymptote as a non-Newtonian flow, with this effective viscosity, leads to agreement with the concept of an asymptote only when the solvent viscosity is used in the non-dimensional wall distance.     

Large Scale Accumulation Patterns of Inertial Particles in Wall-Bounded Turbulent Flow

Turbulent internal flow in channel and pipe geometry with a diluted second phase of inertial particles is studied numerically. Direct numerical simulations (DNS) are performed at moderate Reynolds number (Re _?? ????200) in pipe and two channels??a smaller one similar in size to previous studies and a 3?×?3-times larger one??and Eulerian statistics pertaining to the particle concentration are evaluated. This simulation box constitutes the largest domain used for particle-laden flows so far. The resulting two-point correlations of the particle concentration show that in the smaller channel the particles organize in thin, streamwise elongated patterns which are very regular and long. The spanwise spacing of these structures is 120 and 160 plus units for the channel and pipe, respectively. Only in the larger box, the streamwise extent is long enough for the particle streaks to decorrelate, thus allowing the particles to move more freely. The influence of the box size on the characteristics of the turbophoresis is clearly shown; a 10% increase of the near-wall correlation is observed for particles with Stokes number St ^?+??=?50. It is thus shown that the box dimensions are an important factor in correctly assessing the motion of inertial particles, and their relation to the underlying velocity field. In addition the binning size effects on the correlation statistics of particle concentration are exploited. In particular the spanwise correlation peak values appear very sensitive to the adopted binning size, although the position of these peaks is found almost independent. Hence to allow a significant comparison between data of different configurations it is necessary to adopt the same binning spacing in inner variable.     

Particle behavior in homogeneous isotropic turbulence

Direct numerical simulations were conducted to investigate the behavior of heavy particles in homogeneous isotropic turbulence. The present study focused on the effect of particle inertia and drift on the autocorrelations of the particle velocity and the fluid seen by particles and the dispersion characteristics of particles. The Lagrangian integral time scale of particles monotonically increased as the magnitude of the particle response time increased, while that of the fluid seen by particles remained relatively constant; it reached a maximum when the particle response time was close to the Kolmolgorov time scale of the flow. Particle dispersion increased as the particle inertia increased for small particles, while for larger particles, it decreased as particle inertia increased; particle eddy diffusion coefficient was maximal, and greater than that of the fluid by about 30%, at the preferential concentration. The concentration field of the particles with τp/τk≈1.0 showed that particles tend to collect in regions of low vorticity (high strain) due to preferential concentration. As the drift velocity of a particle is increased it crosses the paths of fluid elements more rapidly and will tend to lose correlation with its previous velocity faster than a fluid element will. And the correlation of particle velocities along the drift direction is more persistent than that perpendicular to the direction of drift. Simulations also showed that the continuity effect and the crossing-trajectory effect are weakened for particles with infinite inertia.     

湍流两相流的脉动速度联合PDF输运方程

概率密度函数（PDF）的方法是构造两相湍流模型的一种重要的方法.构建气体-颗粒速度联合PDF输运方程的关键是颗粒所见气体微团速度的Langevin方程.首先由N-S方程出发,精确推导出颗粒所见气体微团脉动速度的Langevin方程,进而通过理论分析表明,对比通常采用的颗粒所见气体微团瞬时速度的Langevin方程而言,采用前者能有效地减少关联量的统计偏差.最后,给出了颗粒-气体脉动速度的联合PDF输运方程.     

Resolution sensitivity of momentum‐exchange and immersed boundary methods for solid–fluid interaction in the lattice Boltzmann method

In the lattice Boltzmann method (LBM), the mechanism of fluid–solid interaction can be effectively captured by appropriately enforcing the no‐slip conditions in shear direction, and bounce‐back of the non‐equilibrium distribution portion in the normal direction at fluid–solid interfaces. Among various solid–fluid interaction schemes being proposed for LBM in recent decades, two simple fluid–solid interaction methods—the momentum exchange algorithm (MEA) and the immersed boundary scheme (IBS)—were developed based on the above concept. In this paper, MEA and IBS are implemented in a D2Q9 LBGK system and applied to measure the wall correction factors of drag force upon a stationary circular particle midway in the Poiseuille channel flow at very low Reynolds number and drag coefficients at low to moderate Reynolds numbers. MEA and IBS are also employed to compare the fluid‐induced torque over the cylinder in the Taylor–Couette flow, and the steady velocity of a particle settling under the influence of gravity inside a tube. The above experiments show that IBS seems to be more accurate and less demanding on lattice resolution. Copyright © 2010 John Wiley & Sons, Ltd.     

Parametric study of separation and transition characteristics over an airfoil at low Reynolds numbers

Time-resolved surface pressure measurements are used to experimentally investigate characteristics of separation and transition over a NACA 0018 airfoil for the relatively wide range of chord Reynolds numbers from 50,000 to 250,000 and angles of attack from 0° to 21°. The results provide a comprehensive data set of characteristic parameters for separated shear layer development and reveal important dependencies of these quantities on flow conditions. Mean surface pressure measurements are used to explore the variation in separation bubble position, edge velocity in the separated shear layer, and lift coefficients with angle of attack and Reynolds number. Consistent with previous studies, the separation bubble is found to move upstream and decrease in length as the Reynolds number and angle of attack increase. Above a certain angle of attack, the proximity of the separation bubble to the location of the suction peak results in a reduced lift slope compared to that observed at lower angles. Simultaneous measurements of the time-varying component of surface pressure at various spatial locations on the model are used to estimate the frequency of shear layer instability, maximum root-mean-square (RMS) surface pressure, spatial amplification rates of RMS surface pressure, and convection speeds of the pressure fluctuations in the separation bubble. A power-law correlation between the shear layer instability frequency and Reynolds number is shown to provide an order of magnitude estimate of the central frequency of disturbance amplification for various airfoil geometries at low Reynolds numbers. Maximum RMS surface pressures are found to agree with values measured in separation bubbles over geometries other than airfoils, when normalized by the dynamic pressure based on edge velocity. Spatial amplification rates in the separation bubble increase with both Reynolds number and angle of attack, causing the accompanying decrease in separation bubble length. Values of the convection speed of pressure fluctuations in the separated shear layer are measured to be between 35 and 50% of the edge velocity, consistent with predictions of linear stability theory for separated shear layers.     

Influence of the orientation of a square cylinder on the wake properties

An experimental investigation of flow around a square cylinder placed at various angles with respect to the approach fluid velocity is reported. The focus of the study is toward examining the sensitivity of the wake properties to the cylinder orientation and Reynolds number. Angles of incidence in the range of 0-60° and Reynolds numbers of 1340, 4990, and 9980 have been considered. Velocity measurements have been carried out using an X-wire hotwire anemometer. The Strouhal number and the drag coefficient of the cylinder have been computed from the wake measurements. Utilizing the velocity traces at distinct probe locations in the near and the far wake, statistical properties such as the RMS velocities and the spectra have been obtained. Results obtained in the present work revealed that for a cylinder with zero inclination, flow separates from the corners on the face exposed to the incoming flow. For inclinations greater than zero, the points of separation on the cylinder move downstream and the wake size increases, but the separated shear layer rolls up over a shorter distance. These factors lead to a reduced drag coefficient and a higher Strouhal number. The center-line recovery of the time-averaged velocity and the decay rates of velocity fluctuations depend on the Reynolds number. A marginal effect of the cylinder orientation is also seen.     

固体颗粒对沟槽湍流边界层影响的实验研究

本文采用粒子图像测速技术(particles image velocimetry, PIV)研究固体颗粒对放置在平板湍流边界层中的平壁和沟槽壁面减阻效果的影响. 实验对清水和加入粒径为155 μm聚苯乙烯颗粒的流法向二维速度场信息进行采集, 对不同工况下的平均速度剖面、雷诺应力和湍流度等统计量进行对比, 分析流体在边界层中的行为. 运用空间局部平均结构函数提取了不同工况湍流边界层喷射?扫掠行为的空间拓扑结构并进行比较. 结果发现, 在不同的壁面条件下, 粒子加入后的对数律区中无量纲速度均略大于清水组, 雷诺切应力有所降低, 湍流度有所减弱. 对于不同流场速度下的沟槽而言, 颗粒的加入均降低了壁面附近的阻力, 而颗粒单独作用于光滑壁面的减阻效果并不明显. 加入粒子后的相干结构数目有所增加, 法向脉动速度下降. 沟槽壁面附近的相干结构数目有所增加, 法向脉动速度在自由来流速度较大时有所上升, 在速度较小时有所下降. 这表明不同减阻状况下的沟槽均能将大涡破碎成更多的涡, 并且粒子的加入强化了这种破碎作用.