Kinetics turbulent energy

The kinetic energy responsible for breakup comes from eddies smaller than the drop diameter, since larger eddies would presumably only carry the drop along with them without breaking it. The kinetic turbulent energy is proportional to (7r/6)a p , where for drops of size within the inertial subrange of an isotropic turbulent flow ... 

Thus, the kinetic turbulent energy of drop of size a is given by... 

K" oc energy input per unit time/kinetic turbulence energy... 

If one supposes that turbulence diffusion coefficient Dt is equal to kinematic coefficient of turbulence viscosity Vt which in its turn can be expressed by specific kinetic turbulence energy K (mVsec ) and rate of dissipation of last one is e (mVsec ) then (1.16) will be as following ... 

Calculations have confirmed that the standard C-e model of turbulence gives oversized values, such as the values of kinetic turbulence energy, C. Much better results are obtained using the KECHEN and KERNG models (Figure 2.14), especially designed for detached flows with circulation zones. 

The balanced equation for turbulent kinetic energy in a reacting turbulent flow contains the terms that represent production as a result of mean flow shear, which can be influenced by combustion, and the terms that represent mean flow dilations, which can remove turbulent energy as a result of combustion. Some of the discrepancies between turbulent flame propagation speeds might be explained in terms of the balance between these competing effects. 

The source terms on the right-hand sides of Eqs. (25)-(29) are defined as follows. In the momentum balance, g represents gravity and p is the modified pressure. The latter is found by forcing the mean velocity field to be solenoidal (V (U) = 0). In the turbulent-kinetic-energy equation (Eq. 26), Pk is the source term due to mean shear and the final term is dissipation. In the dissipation equation (Eq. 27), the source terms are closures developed on the basis of the form of the turbulent energy spectrum (Pope, 2000). Finally, the source terms... 

In turbulent flow, there is direct viscous dissipation due to the mean flow this is given by the equivalent of equation 1.98 in terms of the mean values of the shear stress and the velocity gradient. Similarly, the Reynolds stresses do work but this represents the extraction of kinetic energy from the mean flow and its conversion into turbulent kinetic energy. Consequently this is known as the rate of turbulent energy production ... 

By definition, the turbulent kinetic energy k can be found directly from the turbulent energy spectrum by integrating over wavenumber space ... 

This transition has profound effects in all fluid dynamics, and certainly so in aerodynamics. The velocity profile in (he boundary layer becomes fuller neat the surface on account of Ihe higher average kinetic energy of the layer created by turbulent energy exchange from layer lo layer. The effective viscosity is therefore larger in turbulent than laminar flow, ihe turbulent boundary layer thickens more rapidly downstream, the skin friction increases. 

Equation 6-107 gives the total energy loss in fixed beds as the sum of viscous energy loss (the first term on the right side of the equation) and the kinetic or turbulent energy loss (the second term on the right side of the equation). For gas systems, approximately 80% of the energy loss depends on turbulence and can be represented by the second term of Equation 6-107. In liquid systems, the viscous term is the major factor. 

Kinetic energy of turbulent motion q - y Turbulent energy dissipation... 

This form is appealing because the first term in F.-,/2 can be interpreted as a gradient diffusion of turbulent kinetic energy, and the second is negative-definite (suggestive of dissipation of turbulence energy). However, the rate of entropy production is proportional to... 

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 ... 

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... 

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... 

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