Eddy diffusion kinematic viscosity

Whereas the kinematic viscosity fx/p, the thermal diffusivity k/Cpp, and the diffusivity D are physical properties of the system and can therefore be taken as constant provided that physical conditions do not vary appreciably, the eddy coefficients E, Eh, and ED will be affected by the flow pattern and will vary throughout the fluid. Each of the eddy coefficients is proportional to the square of the mixing length. The mixing length will ... 

It has been shown that it is reasonable to assume that the eddy kinematic viscosity E and the eddy thermal diffusivity Eh are equal. The variation of E through the buffer zone is... 

In the buffer zone the value of d +/dy+ is twice this value. Obtain an expression for the eddy kinematic viscosity E in terms of the kinematic viscosity (pt/p) and y+. On the assumption that the eddy thermal diffusivity Eh and the eddy kinematic viscosity E are equal, calculate the value of the temperature gradient in a liquid flowing over the surface at y =15 (which lies within the buffer layer) for a surface heat flux of 1000 W/m The liquid has a Prandtl number of 7 and a thermal conductivity of 0.62 W/m K. 

It has been assumed that the density is constant in writing these equations, which are therefore strictly valid only for incompressible flow. ed is called the eddy diffusivity and eh the eddy thermal diffusivity. Although s can be interpreted as the eddy diffusivity of momentum, it is usually called the eddy viscosity and sometimes by the better name eddy kinematic viscosity. 

In the above equations, pi, Ejy, and v are eddy thermal diffusivity, eddy diffusivity, and eddy kinematic viscosity, respectively, all having the same dimensions (L- ). It should be noted that these are not properties of fluid or system, because... 

Transfer by molecular diffusion is discussed in Section 12.2 and the concept of the mixing length in Section 12.3.2. By analogy with kinetic theory, the eddy kinematic viscosity, E, is given by ... 

In the recirculation flow regime Eissa et al. (E6) have reported radial diffusivities Er of 1.21 cmVsec at Uq = 6.3 cm/sec and 1.26 cmVsec at 7.8 cm/sec for a 5-cm-diam bubble column equipped with a multiple-orifice-plate gas distributor. These diffusivities amount to 60% of the eddy kinematic viscosity i i = 2 cmVsec for = 5 cm (Fig. 31). Reith et al. (R3) have measured a radial diffusivity of 10 cmVsec at Uq = 9.3 cm/sec for a 14-cm-diam bubble column equipped with a perforated plate orifice having one 2-mm-diam hole per cm this is slightly lower than the average... 

Ed, Eh, Ey Eddy diffusivity, Eddy thermal diffusivity, and Eddy kinematic viscosity, respectively (m2 h-1 or cm2 s-1)... 

Quantity is analogous to fi, the absolute viscosity. Also, in analogy with the kinematic viscosity v the quantity called the eddy diffusivity of momentum, is defined as e,j = EJp. 

Although these eddy diffusivities act in the same manner as the kinematic viscosity and thermal diffusivity in laminar flow, the critical difference is that the eddy diffusivities are not properties of the fluid but are dependent largely on the dynamic behavior of the fluid motion. In this section the fluid dynamic bases for evaluating these eddy diffusivities are given. They will then be used in a variety of convective heating situations to yield formulas useful in engineering computations. 

The principal feature of turbulent flows is the presence of eddies which are large compared with the molecular scale and which aid the mixing process (turbulent dispersion). This mixing mechanism in liquids is often rapid compared with the other processes of bulk flow and molecular diffusion. The eddies vary in size, having a maximum scale, L, which is of the order of the scale of the equipment (i.e. impeller or baffles) down to a minimum value, /, which, according to Kolmogoroff, for isotropic turbulence depends only upon the power input per unit mass to the system and the kinematic viscosity of the liquid ... 

In lateral mixing, the horizontal diffusion written in Equation 16 is subjected to the eddy kinematic viscosity. Conventionally, the vertical diffusion coefficient v, which is related to the vertical velocity distribution is applied by simply multiplying a constant even in horizontal mixing as v,, and furthermore, the value given for flow on the area without vegetation, as follows ... 

In the vegetated area, the turbulence diffusivity exists only in the bed roughness boundary layer, and the kinematic eddy viscosity will be formulated as follows ... 

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