Particle-turbulence interaction

the condition for the minimum velocity for bubble formation or the minimum bubbling point can be obtained when 

One of the earliest models for turbulence modulation in homogeneous dilute particleladen flows is Hinze s model (1972), in which the assumption of vortex trapping of particles is employed. On the basis of this model, the particle turbulent kinetic energy, kp, is determined by the local gas turbulent kinetic energy k as 

On the bais of an extensive review of experimental results of turbulence modulation in dilute suspension pipe flows and jet flows, Gore and Crowe (1989) proposed a critical ratio of particle diameter to a characteristic integral length scale of turbulence by the following relation 

In general, at least six mechanisms, which are not independent of each other, contribute to turbulence modulation in gas-solid suspension flows  

To simplify the following calculation, the drag coefficient is expressed by 

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In addition, DNS of turbulent flow in a periodic box offer interesting opportunities for studying in a fully resolved mode the intimate details of the flow field, its interaction with particles and the mutual interaction between particles (including particle-particle collisions and coalescence). Such simulations may yield new insights see, e.g., Ten Cate et al. (2004) and Derksen (2006b). The same can be said about our understanding of particle-turbulence interactions in wall-bounded flows this has increased due to Portela and Oliemans (2003) exploiting both DNS and LES and due to Ten Cate et al. (2004). 

Y. Nino, M.H. Garcia, Experiments on particle-turbulence interactions in the near-wall region of an open channel flow Implications for sediment transport, J. Fluid Mech. 326 (1996) 285-319. 

Hetsroni, G. (1989). Particle-Turbulence Interaction. Int. J. Multiphase Flow, 15,735. 

However, in other cases the model predictions deviate much more from each other and were in poor agreement the experimental data considering the measurable quantities like phase velocities, gas volume fractions and bubble size distributions. An obvious reason for this discrepancy is that the breakage and coalescence kernels rely on ad-hoc empiricism determining the particle-particle and particle-turbulence interaction phenomena. The existing param-eterizations developed for turbulent flows are high order functions of the local... 

Hetsroni G (1989) Particles-turbulence interaction. Int J Multiphase Flow 15 735... 

McLaughlin, J.B. Numerical computation of particles-turbulence interaction. Int J. Multiphase Flow. 1994, 20(Suppl), 211-252. 

In the numerical integration of a particle trajectory, the selection of the integral time step is important. A typical way of choosing the integral time step is based on the interacting duration between the turbulent eddy and the particle. This interacting duration Tj may be determined by... 

Interactions of the particles with the fluctuating component of the gas velocity, which lead to particle turbulent diffusion and induce an exchange of the kinetic energy between the fluctuating components of the velocity of the two phases, which results in either damping the fluctuations of the gas velocity and enhancing fluctuations in particle velocity, or vice versa... 

For dilute suspensions, particle-particle interactions can be neglected. The extent of transfer of particles by the gradient in the particle phase density or volume fraction of particles is proportional to the diffusivity of particles Dp. Here Dp accounts for the random motion of particles in the flow field induced by various factors, including the diffusivity of the fluid whether laminar or turbulent, the wake of the particles in their relative motion to the fluid, the Brownian motion of particles, the particle-wall interaction, and the perturbation of the flow field by the particles. 

Huid-solid Reasonable Turbulence modeling + refined models for particle-particle and particle-wall interaction -L prediction of flow regime transition + interaction of hydrodynamics with chemical transformation processes... 

The limiting steps in the model development are the formulation of closure relations or closure laws determining turbulence effects, interfacial transfer fluxes and the bubble coalescence and breakage processes. When sufliciently dilute dispersions are considered, only particle - fluid interactions are significant and the two-fluid closures can be employed. In these particular cases, only the interaction between each of the dispersed gas phases (d) and the continuous liquid phase (c) is considered parameterizing the last term on the RHS of (8.12) ... 

Figure VI.1 gives the results of Schlichting [284] for the variation in the thickness of the boundary layer and the velocity at its boundary as functions of the axial velocity of the flow (vq). We see from Fig. VI.l under what conditions the particles may sink" and in what cases the particles will project outside the boundary of the laminar layer, i.e., experience laminar-turbulent interaction with the flow.

Turbulence interacts with both scalars (dye, reactants) and dispersed phases (bubbles, drops, and particles) according to the relative length and time... 

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