Investigation of gas-particle turbulent pipe flow with allowance for collisions with the wall and particle rotation

A model of gas-particle turbulent pipe flow which takes into account phase velocity slip, particle interaction with the wall and rotation of the particles is proposed. Allowance for the Magnus force makes it possible to describe the intense transverse skipping motion of the particles and to obtain good agreement between the calculation results and the experimental data over a broad range of flow conditions. The model is based on the use of the transport equations for the averaged flow parameters and the correlation moments describing the turbulent transfer of the momentum and angular momentum of the dispersed phase.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 56–64, January–February, 1990.     

Subgrid continuum modeling of particle motion in a turbulent flow

An Eulerian continuum approach to modeling the motion of dispersed particles within the framework of the large-eddy simulation method is developed. The approach is based on a kinetic equation for the filtered probability density function for the particle velocity in a turbulent flow. Models for the subgrid turbulent stresses of the dispersed phase are presented.     

A closed model of fluctuating particle motion in a turbulent flow

Random particle motion in a turbulent and molecular velocity fluctuation field is considered. Using a spectral representation of the carrier-phase Eulerian velocity fluctuation correlations, a closed system of integral equations for calculating the carrier-phase velocity correlation along the particle trajectory and the particle Lagrangian velocity fluctuation correlation is obtained. Based on this system, the fluctuations of the particle parameters are analyzed. In the limiting case of a passive admixture, an estimate is found for the ratio of the integral Lagrangian and Eulerian time scales and the Kolmogorov constant for the Lagrangian structure function of the carrier-phase velocity fluctuations.     

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.     

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.     

Effect of an unsteady swirled turbulent flow on the motion of a single solid particle

An unsteady swirled turbulent flow between two rotating flat disks is modeled. The flow is directed along the radius toward the rotation axis. A quasi-steady character of the turbulent flow, caused by oscillations of the radial velocity at the entrance to the gap between the disks with a period close to the time of dynamic relaxation of the particle, is studied with the use of the known two-equation Wilcox’s k-ω model of turbulence. The influence of the Stokes number and the frequency and amplitude of oscillations of the carrier medium on the motion of single particles in the field of centrifugal and aerodynamic forces is considered.     

Pulsating motions of a solid particle in turbulent flow

The relations governing the transverse pulsations of a spherical particle in a turbulent flow are examined. On the basis of the resulting relations an estimate is made of the effect of several factors on the intensity of the velocity pulsations of the solid component in dispersed flow through a conduit.     

Direct numerical simulation of particle dispersion in a turbulent jet considering inter-particle collisions

To investigate the behaviour of inter-particle collision and its effects on particle dispersion, direct numerical simulation of a three-dimensional two-phase turbulent jet was conducted. The finite volume method and the fractional-step projection algorithm were used to solve the governing equations of the gas phase fluid and the Lagrangian method was applied to trace the particles. The deterministic hard-sphere model was used to describe the inter-particle collision. In order to allow an analysis of inter-particle collisions independent of the effect of particles on the flow, two-way coupling was neglected. The inter-particle collision occurs frequently in the local regions with higher particle concentration of the flow field. Under the influence of the local accumulation and the turbulent transport effects, the variation of the average inter-particle collision number with the Stokes number takes on a complex non-linear relationship. The particle distribution is more uniform as a result of inter-particle collisions, and the lateral and the spanwise dispersion of the particles considering inter-particle collision also increase. Furthermore, for the case of particles with the Rosin–Rammler distribution (the medial particle size is set d₅₀ = 36.7 μm), the collision number is significantly larger than that of the particles at the Stokes number of 10, and their effects on calculated results are also more significant.     

Model of a gas of solid particles with allowance for inelastic collisions

A study is made of the structure of the interaction region of a flow of solid particles with a surface (or another flow) in the case when the width of this region is much greater than the mean free path of the particles between collisions. The disperse phase is described by means of a model of an ideal non-heat-conducting gas of imperfectly elastic spherical particles. For simplicity, the influence of the carrier medium on the motion of the particles is ignored.     

Measurements and simulations of particle dispersion in a turbulent flow

A particle imaging technique has been used to collect droplet displacement statistics in a round turbulent jet of air. Droplets are injected on the jet axis, and a laser sheet and position-sensitive photomultiplier tube are used to track their radial displacement and time-of-flight. Dispersion statistics can be computed which are Lagrangian or Eulerian in nature. The experiments have been simulated numerically using a second-order closure scheme for the jet and a stochastic simulation for the particle trajectories. Results are presented for non-vaporizing droplets of sizes from 35 to 160 μm. The simulations have underscored the importance of initial conditions and early droplet displacement history on the droplet trajectory for droplets with large inertia relative to the turbulence. Estimates of initial conditions have been made and their effect on dispersion is quantified.     

Modeling of the turbulent motion of particles in a vertical channel

The results of modeling of the statistical parameters of a turbulent particle motion in a vertical plane channel are presented. The model is based on a kinetic equation for the particle velocity probability density function. The results are compared with direct numerical simulation.     

Modeling plane turbulent Couette flow

Among the salient features of shear-driven plane Couette flow is the constancy of the total shear stress (viscous and turbulent) across the flow. This constancy gives rise to a quasi-homogenous core region, which makes the bulk of the flow substantially different from pressure-driven Poiseuille flow. The present second-moment closure study addresses the conflicting hypotheses relating to turbulent Couette flow. The inclusion of a new wall-proximity function in the wall-reflection part of the pressure-strain model seems mandatory, and the greement with recent experimental and direct numerical simulation (DNS) results is encouraging. Analysis of model computations in the range 750 ≤ Re ≤ 35,000 and comparisons with low-Re DNS data suggest that plane Couette flow exhibits a local-equilibrium core region, in which anisotropic, homogeneous turbulence prevails. However, the associated variation of the mean velocity in the core, as obtained by the model, conflicts with the intuitively appealing assumption of homogeneous mean shear. The constancy of the velocity gradient exhibited by the DNS therefore signals a deficiency in the modeled transport equation for the energy dissipation rate.     

Wake response of a stationary finite-sized particle in a turbulent channel flow

Here we consider the effect of a finite-sized stationary particle in a channel flow of modest turbulence at _Reτ=178.12${\mathit{Re}}_{\tau }=178.12$. The size of particle is varied such that the particle Reynolds number ranges from about 40 to 450. The location of the particle is chosen to be either in the buffer layer (_yp+=17.81)$(y_{p+}=17.81)$ or at the channel center. Fully resolved direct numerical simulations of the turbulent channel flow around the particles is performed. Here the ambient turbulence intensity relative to the mean velocity seen by the particle is large (I=23.16%)$(I=23.16\%)$ in the buffer region, while it is substantially lower (I=4.09%)$(I=4.09\%)$ at the channel center. We present results on turbulence modulation due to the particle in terms of wake dynamics and vortex shedding.     

Modeling of vertical turbulent exchange in a stratified near-wall flow

A modified model of turbulence is proposed to describe the processes of vertical transport in inhomogeneous turbulent flows. This model includes algebraic relations for the Reynolds stresses and turbulent-exchange coefficients. Using this model, the growth of the depth of a mixed layer under the action of the wind load in neutral and stable stratified near-wall flows has been predicted. The calculation results for a stable stratified flow that were obtained using the modified and standard two-parametric models of turbulence are compared with experimental data. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 57–64, November–December, 1998.