Kinetic eddy dispersion

For conventional packings and linear isotherms Van Deemter et al. [10] developed the well-known equation for HETP including contributions from eddy dispersion (A-term), molecular diffusion (B-term) and intraparticle kinetics (C-term). 

This response time should be compared to the turbulent eddy lifetime to estimate whether the drops will follow the turbulent flow. The timescale for the large turbulent eddies can be estimated from the turbulent kinetic energy k and the rate of dissipation e, Xc = 30-50 ms, for most chemical reactors. The Stokes number is an estimation of the effect of external flow on the particle movement, St = r /tc. If the Stokes number is above 1, the particles will have some random movement that increases the probability for coalescence. If St 1, the drops move with the turbulent eddies, and the rates of collisions and coalescence are very small. Coalescence will mainly be seen in shear layers at a high volume fraction of the dispersed phase. 

Subscript 1 indicates continuous phase and 2 indicates dispersed phase. Cd is a parameter of the standard k-s model (0.09), k is turbulent kinetic energy and si is turbulent energy dissipation rate. The eddy lifetime seen by dispersed phase particles will in general be different from that for continuous phase fluid particles due to the so-called crossing-trajectory effect (Csnady, 1963). This can be expressed in the form ... 

In contrast to the equilibrium-dispersive model, which is based upon the assumptions that constant thermod3mamic equilibrium is achieved between stationary and mobile phases and that the influence of axial dispersion and of the various contributions to band broadening of kinetic origin can be accounted for by using an apparent dispersion coefficient of appropriate magnitude, the lumped kinetic model of chromatography is based upon the use of a kinetic equation, so the diffusion coefficient in Eq. 6.22 accounts merely for axial dispersion (i.e., axial and eddy diffusions). The mass balance equation is then written... 

Equation 6.84 shows that the column HETP is the sum of the independent contributions of the axial dispersion (molecular diffusion and eddy diffusion), the film mass transfer resistance, the pore diffusion, and slow kinetics of adsorption-desorption. By comparing Eqs. 6.84 and 6.57a, we obtain ... 

Droplet disintegration is caused by the kinetic energy of the turbulence eddies. Eddies whose size 2 corresponds approximately to the droplet diameter d32) be. z as 32, have the strongest dispersing action. For 2 > d32 the droplet is carried along by the flow and thereby is hardly deformed, whereas for 2 <132 the eddies... 

Since m 2 is proportional to the total turbulent kinetic energy, the total energy of the turbulence is important in the early dispersion. After long times the largest eddies will contribute to Ru and Ru will not go to zero until the particle can escape the influence of the largest eddies. From its definition, K,j has the dimensions of a diffusivity, since as t —> oo... 

To analyze the individual heat transfer kinetics of droplet clusters within the spray of twin-fluid atomizers, the local correlations between the droplet concentration and the heat and flow conditions are evaluated. Numerical simulations of the spray flow analyzed in this paper have been carried out with Large-Eddy-Simulation (LES) models with Lagrangian particle tracking (discrete particle method) for the droplet motion. A synthetic perturbation generator [30] for the inflow conditions for the gas flow and simple perturbations are added to the dispersed phase to induce realistic vortex patterns at the nozzle and in the consequent spray. 

---