Energy dissipation rate, average

Turbulent velocity fluctuations ultimately dissipate their kinetic energy through viscous effects. MacroscopicaUy, this energy dissipation requires pressure drop, or velocity decrease. The ener dissipation rate per unit mass is usually denoted . For steady ffow in a pipe, the average energy dissipation rate per unit mass is given by... 

In all of the above equations, is assumed to be constant and uniform throughout the flow field. In most items of bioprocess equipment, however, there is a spatial distribution of energy dissipation. The definition of an average or a maximum energy dissipation rate is notoriously difficult in the case of bioprocess equipment such as high pressure homogenisers, centrifuges, pumps and microfiltration units which all have complex flow fields. 

Fig. 7. Variation in cell death rates with average energy dissipation rate for capillary and jet flows. From reference [59], redrawn with permission. 1998, Wiley-Liss, Inc, a subsidiary of John Wiley Sons, Inc...

Fig. 4. Energy dissipation rate G and Work of Fracture iV/asa function of time to crack initiation u with eveiy point represaiting the average of three measurements...

Energy dissipation rate (or power draw) per mass of mixture (W/kg) Average energy dissipation rate (or power draw) per mass of mixture per mass (W/kg)... 

The shear stress is easily estimated. Let the shock pressure be P(x,y,z,t) = Pq sin(2 rx/A) u(z-vt,y) where Pq is the shock wave pressure and A is the wave length. The shear stress is then i(x,y,z,t) = grad P(x,y,z,t) dr = (2. /A)PoCos(2nx/A)/where /is the average crystal particle size. Determination of the local energy dissipation rate can be obtained from Equation (14). It is predicted that initiation will first occur where the shear stress and the energy dissipation rate are greatest so that initiation will first occur at x = mA/2, where m = 0, 1,2, etc. On the x,y plane first initiation... 

The initial turbulence length and time scale are calculated using average quantities for the turbulent kinetic energy and energy dissipation rate as ... 

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