Kinematic eddy viscosity

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 universal velocity profile a dimensionless velocity + is plotted against lnyf, where y+ is a dimensionless distance from the surface. For the region where eddy transport dominates (eddy kinematic viscosity kinematic viscosity), the ratio of the mixing length (Ag) to the distance (>>) from the surface may be taken as approximately constant and equal to 0.4. Obtain an expression for d +/dy+ in terms of y+. 

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. 

Eddy kinematic viscosity, isotropic turbulence 702 penetration of laminar sub-layer 701... 

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. 

Estimate the value of the eddy kinematic viscosity s as a function of position for turbulent flow of water in a smooth pipe of internal diameter 100 mm. The centre-line velocity is 6.1 m/s and the pressure drop over a... 

Conditions in the fully turbulent outer part of the turbulent boundary layer are quite different. In a turbulent fluid, the shear stress f is given by equation 1.95. As illustrated in Example 1.10, outside the viscous sublayer and buffer zone the eddy kinematic viscosity e is much greater than the molecular kinematic viscosity v. Consequently equation 1.95 can be written as... 

Comparing equations 2.59 and 2.62, it follows that the eddy kinematic viscosity can be expressed in terms of the mixing length ... 

Calculation of eddy kinematic viscosity for turbulent flow 62... 

The eddy kinematic viscosity i/ is expressed according to the k e model as 1/ = where is the k-e model constant. 

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 ... 

The importance of the universal velocity profile is discussed in Section 12.4. From equation 12.18, for isotropic turbulence, the eddy kinematic viscosity, EaXEuE where XE is the mixing length and uE is some measure of the linear velocity of the fluid in the eddies. The momentum transfer rate per unit area in a direction perpendicular to the surface at position y is then ... 

Hence as y1 goes from 5 to 30, the ratio of the eddy kinematic viscosity to the kinematic viscosity goes from 0 to 5. 

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)... 

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