Dynamic coupling of fluid and structural mechanics for simulating particle motion and interaction in high speed compressible gas particle laden flow

In this work, structural finite element analyses of particles moving and interacting within high speed compressible flow are directly coupled to computational fluid dynamics and heat transfer analyses to provide more detailed and improved simulations of particle laden flow under these operating conditions. For a given solid material model, stresses and displacements throughout the solid body are determined with the particle–particle contact following an element to element local spring force model and local fluid induced forces directly calculated from the finite volume flow solution. Plasticity and particle deformation common in such a flow regime can be incorporated in a more rigorous manner than typical discrete element models where structural conditions are not directly modeled. Using the developed techniques, simulations of normal collisions between two 1 mm radius particles with initial particle velocities of 50–150 m/s are conducted with different levels of pressure driven gas flow moving normal to the initial particle motion for elastic and elastic–plastic with strain hardening based solid material models. In this manner, the relationships between the collision velocity, the material behavior models, and the fluid flow and the particle motion and deformation can be investigated. The elastic–plastic material behavior results in post collision velocities 16–50% of their pre-collision values while the elastic-based particle collisions nearly regained their initial velocity upon rebound. The elastic–plastic material models produce contact forces less than half of those for elastic collisions, longer contact times, and greater particle deformation. Fluid flow forces affect the particle motion even at high collision speeds regardless of the solid material behavior model. With the elastic models, the collision force varied little with the strength of the gas flow driver. For the elastic–plastic models, the larger particle deformation and the resulting increasingly asymmetric loading lead to growing differences in the collision force magnitudes and directions as the gas flow strength increased. The coupled finite volume flow and finite element structural analyses provide a capability to capture the interdependencies between the interaction of the particles, the particle deformation, the fluid flow and the particle motion.     

An analytical approach for the closure equations of gas–solid flows with inter-particle collisions

This work examines the effect of inter-particle collisions on the motion of solid particles in two-phase turbulent pipe and channel flows. Two mechanisms for the particle–particle collisions are considered, with and without friction sliding. Based on these collision mechanisms, the correlations of the various velocity components of colliding particles are obtained analytically by using an averaging procedure. This takes into account three collision coordinates, two angles and the distance between the centers of colliding particles. The various stress tensor components are obtained and then introduced in the mass, linear momentum and angular momentum equations of the dispersed phase. The current approach applies to particle–particle collisions that result from both the average velocity difference and the turbulent velocity fluctuations. In order to close the governing equations of the dispersed phase, the pseudo-viscosity coefficients are defined and determined by the time of duration of the inter-particle collision process. The model is general enough to apply to both polydisperse and monodisperse particulate systems and has been validated by comparisons with experimental data.     

Differentially weighted direct simulation Monte Carlo method for particle collision in gas–solid flows

In gas–solid flows, particle–particle interaction (typical, particle collision) is highly significant, despite the small particles fractional volume. Widely distributed polydisperse particle population is a typical characteristic during dynamic evolution of particles (e.g., agglomeration and fragmentation) in spite of their initial monodisperse particle distribution. The conventional direct simulation Monte Carlo (DSMC) method for particle collision tracks equally weighted simulation particles, which results in high statistical noise for particle fields if there are insufficient simulation particles in less-populated regions. In this study, a new differentially weighted DSMC (DW-DSMC) method for collisions of particles with different number weight is proposed within the framework of the general Eulerian–Lagrangian models for hydrodynamics. Three schemes (mass, momentum and energy conservation) were developed to restore the numbers of simulation particle while keeping total mass, momentum or energy of the whole system unchanged respectively. A limiting case of high-inertia particle flow was numerically simulated to validate the DW-DSMC method in terms of computational precision and efficiency. The momentum conservation scheme which leads to little fluctuation around the mass and energy of the whole system performed best. Improved resolution in particle fields and dynamic behavior could be attained simultaneously using DW-DSMC, compared with the equally weighted DSMC. Meanwhile, computational cost can be largely reduced in contrast with direct numerical simulation.     

Modeling of the random packing of a loose layer of polydisperse spherical particles

A method for calculating the loose packing structure of polydisperse spherical particles with a predetermined size distribution function is proposed. The coordinates of the particle centers in the loose layer are determined as the result of random fall of single spheres on a substrate under the action of gravity, assuming the inelastic collision of the spheres and considering the force of their adhesive interaction, and also assuming that the motion of one sphere on the surface of the other is pure slip. Numerical simulation is used to obtain the pattern of arrangement of polydisperse spherical particles in the loose powder layer, whose porosity depends on the particle size distribution function. The results are compared with experimental data.     

Differentially weighted direct simulation Monte Carlo method for particle collision in gas-solid flows

In gas-solid flows,particle-particle interaction(typical,particle collision) is highly significant,despite the small particles fractional volume.Widely distributed polydisperse particle population is a typical characteristic during dynamic evolution of particles(e.g.,agglomeration and fragmentation) in spite of their initial monodisperse particle distribution.The conventional direct simulation Monte Carlo(DSMC)method for particle collision tracks equally weighted simulation particles,which results in high statistical noise for particle fields if there are insufficient simulation particles in less-populated regions.In this study,a new differentially weighted DSMC(DW-DSMC) method for collisions of particles with different number weight is proposed within the framework of the general Eulerian-Lagrangian models for hydrodynamics.Three schemes(mass,momentum and energy conservation) were developed to restore the numbers of simulation particle while keeping total mass,momentum or energy of the whole system unchanged respectively.A limiting case of high-inertia particle flow was numerically simulated to validate the DW-DSMC method in terms of computational precision and efficiency.The momentum conservation scheme which leads to little fluctuation around the mass and energy of the whole system performed best.Improved resolution in particle fields and dynamic behavior could be attained simultaneously using DW-DSMC,compared with the equally weighted DSMC.Meanwhile,computational cost can be largely reduced in contrast with direct numerical simulation.     

Modelling of gas–solid turbulent channel flow with non-spherical particles with large Stokes numbers

This paper describes a complete framework to predict the behaviour of interacting non-spherical particles with large Stokes numbers in a turbulent flow. A summary of the rigid body dynamics of particles and particle collisions is presented in the framework of Quaternions. A particle-rough wall interaction model to describe the collisions between non-spherical particles and a rough wall is put forward as well. The framework is coupled with a DNS-LES approach to simulate the behaviour of horizontal turbulent channel flow with 5 differently shaped particles: a sphere, two types of ellipsoids, a disc, and a fibre. The drag and lift forces and the torque on the particles are computed from correlations which are derived using true DNS.The simulation results show that non-spherical particles tend to locally maximise the drag force, by aligning their longest axis perpendicular to the local flow direction. This phenomenon is further explained by performing resolved direct numerical simulations of an ellipsoid in a flow. These simulations show that the high pressure region on the acute sides of a non-spherical particle result in a torque if an axis of the non-spherical particle is not aligned with the flow. This torque is only zero if the axis of the particle is perpendicular to the local direction of the flow. Moreover, the particle is most stable when the longest axis is aligned perpendicular to the flow.The alignment of the longest axis of a non-spherical particle perpendicular to the local flow leads to non-spherical particles having a larger average velocity compared to spherical particles with the same equivalent diameter. It is also shown that disc-shaped particles flow in a more steady trajectory compared to elongated particles, such as elongated ellipsoids and fibres. This is related to the magnitude of the pressure gradient on the acute side of the non-spherical particles. Finally, it is shown that the effect of wall roughness affects non-spherical particles differently than spherical particles. Particularly, a collision of a non-spherical particle with a rough wall induces a significant amount of rotational energy, whereas a corresponding collision with a spherical particle results in mostly a change in translational motion.     

高浓度固-液两相流紊流的动理学模型

采用分子动理学方法,基于固-液两相流液相分子或颗粒相颗粒的Boltzmann方程,对Boltzmann方程分别取零矩和一次矩,则得到高浓度固-液两相流紊流的连续方程和动量方程,再和较成熟的低浓度两相流连续方程和动量方程比较,取低浓度两相流控制方程中较成熟合理的有关项和高浓度时由动理学方法推导出的颗粒间碰撞项,则得到高浓度固-液两相流紊流的最终控制方程:连续方程和动量方程.     

稠密气固两相流各向异性颗粒相矩方法

基于气体分子动力学和颗粒动理学方法,考虑颗粒速度脉动各向异性,建立颗粒相二阶矩模型.应用初等输运理论,对三阶关联项进行模化和封闭.考虑颗粒与壁面之间的能量传递和交换,建立颗粒相边界条件模型.采用Koch等计算方法模拟气固脉动速度关联矩.考虑气体-颗粒间相互作用,建立稠密气体-颗粒流动模型.数值模拟提升管内气固两相流动特性,模拟结果表明提升管内颗粒相湍流脉动具有明显的各向异性.预测颗粒速度、浓度和颗粒脉动速度二阶矩与Tartan等实测结果相吻合.模拟结果表明轴向颗粒速度脉动强度约为平均颗粒相脉动强度的1.5倍,轴向颗粒脉动能大约是径向颗粒脉动能3.0倍.     

Modelling of particle-wall collisions in confined gas-particle flows

This paper demonstrates that numerical simulations of confined particulate two-phase flows require a detailed modelling of particle—wall collisions which includes the wall surface structure and the particle shape. These effects are taken into account by “irregular bouncing” models which are based on the statistical treatment of the collision process. In this study, results obtained using various “irregular bouncing” models based on the impulse equations for a particle—wall collision are considered and compared with experimental observations. The wall roughness is simulated by assuming that the particle collides with a virtual wall which has a randomly distributed inclination with respect to the plane, smooth wall. A Gaussian distribution for this random inclination showed the best agreement with experimental results. Numerical predictions of a turbulent two—phase flow in a vertical channel, where the particle phase is treated using a Lagrangian approach, showed that the different models applied for a particle-wall collision have a strong effect on the particle velocity fluctuations and the mass flux profiles in the region of fully developed flow. The numerical simulations using the irregular bouncing models yielded considerably higher values for the particle velocity fluctuations, which also agreed better with the experimental values. This effect was most pronounced for large particles, where the distance they need to respond to the fluid flow is larger than the characteristic dimension of the confinement. On the other hand, the motion of small particles is less affected by the choice of the wall-collision model. These effects of the wall roughness on the velocity fluctuations of the dispersed phase have not been considered in previous studies using irregular bouncing models.     

Particle collision theories applied to agglomeration in suspension

An experimental and theoretical investigation has been made of an agglomeration technique for small solid particles suspended in a liquid. In this technique the particles are agglomerated under the action of a binding liquid, which is added to the turbulently flowing suspension and wets the particles. Special attention was paid to the first part of the wetting period of the technique.Using existing particle collision theories it was found, that the collision efficiency for solid particles and binding liquid droplets during the first part of the wetting period is extremely low; only one out of every thousand to ten thousand collisions results in an adhesion of a particle to a droplet. The influence of the energy dissipation rate and of the viscosity of the suspension liquid on the collision process as predicted by one of the theories is in reasonably good agreement with the experimental results.     

湍流边界层中固体颗粒运动的数值模拟

根据Ｌａｇｒａｎｇｅ颗粒运动微分方程及不可压缩湍流边界层中流体的壁面速度分布规律，数值求解了颗粒在湍流边界层中的运动，考虑了Ｓａｆｆｍａｎ升为对颗粒运动的影响，壁面对运动阻力的影响，给出了固体颗粒沉积边壁，在边界层外缘上所需的最小速度和最小入射角，计算结果还表明边界层对固体颗粒撞击边壁的速度和入射角有较大影响，从数值结果可可以发现一个重要现象。     

Relaxation of a fluidized bed to the state of a continuous medium

The kinetic equation proposed in [1,2] for describing the behavior of a system of particles in a gas flow differs from the usual Boltzmann equation with respect to the additional terms that take into account random variations of the particle velocity under the influence of the flow. As shown in [2], the collision operator and the Brownian-type operator in the starting kinetic equation describe essentially different simultaneous physical processes of change of state of the particle system: equalization of the mean kinetic energy of the particles and change of energy due to the action of the viscous forces associated with the suspending flow. Therefore the method of solving the kinetic equation used in [2], a direct generalization of the Chapman-Enskog method of solving the kinetic equation it is necessary to investigate method of solving the kinetic equation it is necessar y to investigate the relaxation processes in the system. Moreover, the relaxation of systems of the fluidized-bed type to the continuum state is also of independent interest in connection with the analysis of fast processes in the system, i.e., processes with a characteristic duration of the order of the mean free time.     

Particle size distribution in CPFD modeling of gas–solid flows in a CFB riser

A computational particle fluid dynamics (CPFD) numerical method to model gas–solid flows in a circulating fluidized bed (CFB) riser was used to assess the effects of particle size distribution (PSD) on solids distribution and flow. We investigated a binary PSD and a polydisperse PSD case. Our simulations were compared with measured solids concentrations and velocity profiles from experiments, as well as with a published Eulerian-Eulerian simulation. Overall flow patterns were similar for both simulation cases, as confirmed by experimental measurements. However, our fine-mesh CPFD simulations failed to predict a dense bottom region in the riser, as seen in other numerical studies. Above this bottom region, distributions of particle volume fraction and particle vertical velocity were consistent with our experiments, and the simulated average particle diameter decreased as a power function with riser height. Interactions between particles and walls also were successfully modeled, with accurate predictions for the lateral profiles of particle vertical velocity. It was easy to implement PSD into the CPFD numerical model, and it required fewer computational resources compared with other models, especially when particles with a polydisperse PSD were present in the heterogeneous flow.     

Calculation of the momentum and heat transfer in turbulent gas-particle jet flows

The equations for the second moments of the dispersed-phase velocity and temperature fluctuations are used for calculating gas-suspension jet flows within the framework of the Euler approach. The advantages of introducing the equations for the second moments of the particle velocity fluctuations has previously been quite convincingly demonstrated with reference to the calculation of two-phase channel boundary flows [9–11]. The flows considered below have a low solid particle volume concentration, so that interparticle collisions can be neglected and, consequently, the stochastic motion of the particles is determined exclusively by their involvement in the fluctuating motion of the carrier flow. In addition to the equations for the turbulent energy of the gas and its dissipation, the calculation scheme includes the equations for the turbulent energy and turbulent heat transfer of the solid phase; however, the model constructed does not contain additional empirical constants associated with the presence of the particles in the flow.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 69–80, May–June, 1992.     

On the velocity of ghost particles and the bias errors in Tomographic-PIV

The paper discusses bias errors introduced in Tomographic-PIV velocity measurements by the coherent motion of ghost particles under some circumstances. It occurs when a ghost particle is formed from the same set of actual particles in both reconstructed volumes used in the cross-correlation analysis. The displacement of the resulting ghost particle pair is approximately the average displacement of the set of associated actual particles. The effect is further quantified in a theoretical analysis and in numerical simulations and illustrated in an actual experiment. It is shown that the bias error does not significantly affect the measured flow topology as deduced in an evaluation of the local velocity gradients. Instead, it leads to a systematic underestimation of the measured particle displacement gradient magnitude. This phenomenon is alleviated when the difference between particles displacement along the volume depth is increased beyond a particle image diameter, or when the reconstruction quality is increased or when the accuracy of the tomographic reconstruction is improved. Furthermore, guidelines to detect and avoid such bias errors are proposed.     

非球形固体颗粒对弯管内壁的磨损机制

为研究弯管内固体颗粒在液相夹带条件下的运动特性及颗粒对弯管内壁的磨损,采用计算流体动力学与离散元耦合的方法,建立数值模型,考虑固液两相之间的作用,对弯管内的固液两相流动进行数值模拟;通过软件的应用程序编程接口嵌入自编译磨损模型;借助试验结果,验证数值模型的有效性. 结果表明,所建立的数值模拟方案可以准确地模拟颗粒在管内的运动特征并能够预测弯管内壁的磨损位置以及磨损程度. 弯管内的二次流对颗粒运动有重要影响,弯管外侧壁面中心线附近的磨损较严重,磨损的形式以小角度划擦切削为主. 弯管磨损主要与颗粒对壁面的碰撞速度、碰撞角度及碰撞频率有关. 运动中的颗粒与壁面发生多次碰撞,碰撞角度逐渐减小. 随着颗粒球形度的增大,在相同碰撞条件下引起的磨损量变小,但是会降低颗粒的随流性. 颗粒形状影响颗粒在流场中的运动速度以及颗粒与壁面的碰撞. 随着颗粒球形度增大,严重磨损区域向弯管进口方向移动,壁面平均磨损量先减小后增大;当输送颗粒的球形度为0.91时,壁面磨损量最小.      

Particle collisions in a turbulent flow

An equation for the two-point probability density function of the two-particle the coordinate and velocity distribution is obtained. A closed system of equations for the first and second two-point moments of the velocity fluctuations of a pair of particles with allowance for the turbulent flow inhomogeneity is given. Boundary conditions for the equations of the particle concentration and the intensity of the relative random velocity during particle collision are obtained. A unified formula describing the interparticle collision process as a result of turbulent motion and the average relative particle velocity slip is obtained for the kernel of the coagulation equation. The effect of the average velocity slip of the particles and the carrier phase on the parameters of motion of the dispersed admixture and its coagulation is investigated on the basis of a two-point two-time velocity fluctuation autocorrelation function with two time and space scales representing the energy-bearing and small-scale motion of the fluid phase.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 104–116, March–April, 1996.     

A numerical study of the influence of the Basset force on the statistics of LDV velocity data sampled in a flow region with a large spatial velocity gradient

 The motion of small particles, such as those typically used as seeding particles for tracer particle flow velocity measurement techniques, is studied numerically for a flow region with a large spatial velocity gradient. The influence of the Basset history integral on the statistics of results of particle motion calculations which are based on multi-disperse particle size distributions is investigated. The biasing of the measured velocity data, with regard to the actual flow velocity, which results as a consequence of such particle size distributions is discussed. It is found that the net effect of the Basset integral on the calculations is indeed to reduce the maximum RMS deviation associated with the multi-disperse distribution and that the relative reduction increases with a decreasing particle density. The main result of this study is, thus, that it is desirable to use light tracer particles not only because they more readily adjust to a changed flow velocity but in particular also because they tend to contribute less to the overall RMS deviation of velocity data sampled in a region with a large spatial gradient of the flow velocity. Received: 9 August 1996/Accepted: 25 January 1997     

Statistical model of collisions of bidisperse particles in an anisotropic turbulent flow

A statistical model for describing the motion and collisions of a bidisperse mixture of particles in anisotropic turbulent flows is presented. The model is based on a kinetic equation for the particle velocity probability density function (PDF). The results are compared with the data of a direct numerical simulation of the sedimentation of a bidisperse mixture of particles under the action of the gravity force.