Velocity friction

Eigure 20 compares the predictions of the k-Q, RSM, and ASM models and experimental data for the growth of the layer width 5 and the variation of the maximum turbulent kinetic energy k and turbulent shear stress normalized with respect to the friction velocity jp for a curved mixing layer... 

Vfjp is the friction velocity and =/pVV2 is the wall stress. The friction velocity is of the order of the root mean square velocity fluctuation perpendicular to the wall in the turbulent core. The dimensionless distance from the wall is y+ = yu p/. . The universal velocity profile is vahd in the wall region for any cross-sectional channel shape. For incompressible flow in constant diameter circular pipes, = AP/4L where AP is the pressure drop in length L. In circular pipes, Eq. (6-44) gives a surprisingly good fit to experimental results over the entire cross section of the pipe, even though it is based on assumptions which are vahd only near the pipe wall. 

For turbulent pipe flow, the friction velocity u, = used earlier... 

Turbulent flow near a wall, friction velocity = x/l Tp... 

When a coarse grid is used, wall functions are used for imposing boundary conditions near the walls (Section 11.2.3.3). The nondimensional wall distance should be 30 < y < ]Q0, where y = u,y/p. We cannot compute the friction velocity u. before doing the CFD simulation, because the friction velocity is dependent on the flow. However, we would like to have an estimation of y" to be able to locate the first grid node near the wall at 30 < y < 100. If we can estimate the maximum velocity in the boundary layer, the friction velocity can be estimated as n, — 0.04rj, . . After the computation has been carried out, we can verify that 30 nodes adjacent to the walls. 

R/p is known as the shearing stress velocity or friction velocity and is usually denoted by u. ... 

Longitudinal component of velocity rms velocity fluctuation Slip velocity Friction velocity... 

Figure 10 Friction velocity relationship Fk( o) in the Prandtl-Tomlinson model at...

Close to the ground, in the constant flux layer, u. is a measure of the turbulent transfer of momentum. The friction velocity is defined by... 

This latter result can be expressed in terms of the friction velocity u, and the Monin-Obukhov length L as... 

If relief is via a bursting disc, the flow capacity of the relief system will normally depend on friction and choke points in the relief system. The only exception is where friction is not important (LE/D less than about 40), where equation (A6.4) can be used.) Where friction is significant, an isometric sketch of the route of the relief system will be required to determine the capacity. If the system is to be of constant diameter, then using the sketch, the total equivalent length, LE, of the route, including the frictional resistance of bends and fittings can be determined111. This can also be expressed in terms of total frictional velocity head loss, K ... 

Recall our short discussion in Section 18.5 where we learned that turbulence is kind of an analytical trick introduced into the theory of fluid flow to separate the large-scale motion called advection from the small-scale fluctuations called turbulence. Since the turbulent velocities are deviations from the mean, their average size is zero, but not their kinetic energy. The kinetic energy is proportional to the mean value of the squared turbulent velocities, Mt2urb, that is, of the variance of the turbulent velocity (see Box 18.2). The square root of this quantity (the standard deviation of the turbulent velocities) has the dimension of a velocity. Thus, we can express the turbulent kinetic energy content of a fluid by a quantity with the dimension of a velocity. In the boundary layer theory, which is used to describe wind-induced turbulence, this quantity is called friction velocity and denoted by u. In contrast, in river hydraulics turbulence is mainly caused by the friction at the... 

The ratio between mean flow velocity, u, and friction velocity, u, is called a. According to Eqs. 24-4 and 24-5, a is related to the friction factor f ... 

Figure 24.8 Concentration of Xo estimate the dispersion coefficient Edjs we need the lateral turbulent diffusivity Ey measure t a)3 s a"ion°A (26 Tm (see Ecl- 24 45) which in tum is calculated from the friction velocity, u. Problem downstream of spill) and (b) 24.4 deals with the calculation of Edis. As it turns out, a realistic value which agrees...

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