Turbulence energy dissipation rate

Mersmann and Geisler, R., 1991. DeteiTnination of the local turbulent energy dissipation rates in stirred vessels and its significance for different mixing tasks. In 4th World Congress of Chemical Engineering. Karlsruhe, Germany. 

The turbulent energy dissipation rate can be expressed in terms of the fluctuating rate-of-strain tensor ... 

For closed dissolution systems, it can be hypothesized that the hydrodynamics depends on the input of energy in a general way. The energy input may be characterized by the power input per unit mass of fluid or the turbulent energy dissipation rate per unit mass of fluid (/ ). Considering various paddle apparatus, the power input per unit mass of fluid (Fig. 3) can be calculated according to Plummer and Wigley [(12), Appendix B, nomenclature adapted] ... 

For a reactive process, the reactants must be brought into contact by mixing before a reaction can occur. In a motionless mixer in turbulent flow, the pressure drop defines the turbulent energy dissipation rate, which then determines the macro-, meso-, and micromixing rates. 

The mixer velocity is 1.5 ft/s the Reynolds number is 600 the calculated pressure drop is 3.1 psi the residence time is 0.0437 sec the turbulent energy dissipation rate is 1600HP/1000gal. The scale-up... 

For multiphase flow processes, turbulent effects will be much larger. Even operability will be controlled by the generated turbulence in some cases. For dispersed fluid-fluid flows (as in gas-liquid or liquid-liquid reactors), the local sizes of dispersed phase particles and local transport rates will be controlled by the turbulence energy dissipation rates and turbulence kinetic energy. The modeling of turbulent multiphase flows is discussed in the next chapter. 

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 ... 

Impeller size, shape and speed should ensure that the turbulence energy dissipation rates within the impeller zone are not excessive so as to avoid unwanted finer particles. 

In order to close the set of modeled transport equations, it is necessary to estimate turbulent viscosity or if the k-e model is used, the turbulent kinetic energy, k and turbulent energy dissipation rate, s. The modeled forms of the liquid phase k and s transport equations can be written in the following general format (subscript 1 denotes... 

FIGURE I IA.2 Predicted equilibrium bubble size distribution at three values of turbulent energy dissipation rates. Effect of energy dissipation rate on (a) group mass fraction and (b) total surface area. 

Turbulence kinetic energy k and turbulence energy dissipation rate s are then used to evaluate a velocity scale and a length scale ... 

Turbulent kinetic energy Turbulent energy dissipation rate Chemical species concentrations Local reaction rates... 

Davies J.T., Drop sizes of emulsions related to turbulent energy dissipation rates, Chem. Eng. Sa. 40 (1985) 5, p. 839-842... 

Zhou G., Kresta S.M., Impact of tank geometry on the maximum turbulence energy dissipation rate for impellers, AIChE ). 42 (1996) 9, p. 2476-2490... 

From the experimentally determined energy spectrum we can obtain the mean turbulent energy per unit mass of fluid MTKE t), the turbulent energy dissipation rate per unit mass of fluid e t), and the integral length scale... 

Accordingly, the wall boundary condition for the turbulent energy dissipation rate, e, is given by (1.429) ... 

Instead, the Kolmogorov micro-scales (1.328) to (1.330) characterize the dissipation scales of turbulence and might indicate the effectiveness of micromixing in the flow provided that the turbulent energy dissipation rate and the kinematic viscosity of the fluid is known. If the Kolmogorov micro length scale is much larger than the molecular scales, the molecules are not efficiently mixed by turbulent diffusion. 

Similar estimates of the turbulent energy dissipation rate per unit mass has been used by others as well [73, 68]. Nevertheless, the value of the energy dissipation rate has not been validated experimentally yet. For agitated vessels an analogous relation for the turbulent energy dissipation rate per unit mass has been reported by Prince and Blanch [92]. 

Fig. 9.5. A sketch of the breakage kernel of Luo and Svendsen [74]. An unequal daughter size distribution is predicted by this model. In this case the parent diameter size is, di = 0.006 (m), and the turbulent energy dissipation rate is set at, = 1 Reprinted with permission from [38], Copyright 2005 American Chemical...

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