Turbulent kinetic energy dissipation

Turbulent kinetic energy dissipation rate density (m s ) = Turbulent viscosity (kg m sec )... 

The source terms in the equation for the turbulent kinetic energy dissipation rate are implemented through the source terms Sp and Sc in the following way ... 

Pulsations of less scale possess significantly less energy and are not able to deform particles of disperse phase. Pulsations of big scale carry the elements of disperse phase and do not deform their surface. The fundamental problem under estimation of disperse inclusions of multiphase systems in tubular turbulent apparatus according to (1.23) is calculation of rate of turbulence kinetic energy dissipation e. It requires the development of model describing disperse processes in turbulent flows. 

Various models for bubble breakage and coalescence rates are presented in the literature. These rates usually depend on physical properties, such as densities, viscosities and surface tension, and on turbulence properties, most commonly the turbulent kinetic energy dissipation rate. To calculate local bubble size distributions, also local physical properties and turbulence level should be used. This can be done via CFD (Alopaeus et al. 1999,2002 Keskinen and Majander 2000). 

Variable e is the rate of turbulent kinetic energy dissipation per unit mass, which, based on [8.14], can be written as ... 

Let us first consider the case of steady-state turbulence (the case of unsustained turbulence is discussed later). An energy source has to inject some energy at a rate equal to the rate s of turbulent kinetic energy dissipation. That is what ideally occurs in a perfectly stirred reactor of volume V (Figure 11.3) in which a moving... 

The starting point of Kolmogorov s theory is eqnation [11.1], which stipnlates that the rate of turbulent kinetic energy dissipation is independent of viscosity and hence depends only on Ums and It ... 

So the turbulent kinetic energy dissipation rate at the end of the jet can be calculated from quantities that are known the jet velocity at the nozzle, the nozzle diameter, and the path length. 

The gas phase turbulent kinetic energy dissipation rate equation yields. 

---