Universal velocity distribution

Universal velocity distribution for turbulent flow in a pipe... 

The K-E turbulence model discussed above only applies when e v. This will not be true near the wall. The most common way of dealing with this problem is to assume that there is a universal velocity distribution adjacent to the wall and the K-E turbulence mo del is then only applied outside of the region in which this wall region velocity distribution applies. Alternatively, more refined versions of the K-E turbulence model have been developed that apply under all conditions, i.e., across the entire boundary layer. 

We use an universal velocity distribution obtained by Churchill (2001) to approximate the fully developed velocity profile u( l2) across the turbulent core,... 

According to the concept of the universal velocity distribution, the velocity profile in the laminar sublayer is given by... 

Fig. 3.17 Universal velocity distribution law in the turbulent boundary layer a Eq. (3.158) b Eq. (3.159). The abcissa is logarithmic.

The Universal Velocity Distribution Law refers to the correlation of many sets of experimental measurements of the time avereged velocity profile near a wall during turbulent flow in smooch cireular lubes or ducts.37 These data are normally represented in terms of a dimensionless velocity u aed distance from (he wall, v + ... 

The universal velocity distribution or any other measured or assumed velocity profile can he ured to obtain the eddy viscosity from Eq. (2.4-17). If various assumptions regaiding the relationship between E0 and Er and the relmive importance of molecular and eddy transport processes are utede. analogies between mass transfer and momentum transfer CBn he obtained. As more sophisticated information becomes available on the anture of [he flows near a phase boundary, refined theories can be developed. 

Equations relating u" " to y are called universal velocity-distribution laws. 

UNIVERSAL VELOCITY-DISTRIBUTION EQUATIONS. Since the viscous sublayer is very thin, r r , and Eq. (5.10) can be written, with the substitution of —dy for dr, as... 

Universal velocity distribution turbulent flow of newtonian fluid in smooth pipe. 

UMITATIONS OF UNIVERSAL VELOCITY-DISTRIBUTION LAWS. The universal velocity equations have a number of limitations. It is certain that the buffer zone has no independent existence and that there is no discontinuity between the buffer zone and the turbulent core. Also, there is doubt as to the reality of the existence of a truly viscous sublayer. The equations do not apply well for Reynolds numbers from the critical to approximately 10,000, and it is known that a simple y -M relationship is not adequate for the turbulent core near the buffer zone or in the buffer zone itself. Finally, Eq. (5.31) calls for a finite velocity gradient at the centerline of the pipe, although it is known that the gradient at this point must be zero. 

It is possible to find more complex correlations for the velocity distribution in a pipe which do not have the limitations of Prandtl s power rule. In Fig. 11.7 the Reynolds number appears as a parameter in the velocity distribution plot. In trying to produce a universal velocity distribution rule, it seems logical to change the coordinates in Fig. 11.7 so that the Reynolds number enters either explicitly or implicitly in one of the coordinates, in the hope of getting all the data onto one curve. 

Figure 11.8 shows that in making up the universal velocity distribution it was necessary to introduce two combinations of variables which are in common use in the fluid mechanics literature. The ratio of the local velocity to the friction velocity is called (spoken of as m plus ). This is also the ratio of (the local time-average velocity/the average velocity in the entire flow) times the square root df (2//). The combination of the distance from the pipe wall and the friction velocity divided by the kinematic viscosity is called y. This is the product of a kind of Reynolds number based on distance from the wall rather than on, pipe diameter and y/fl2. 

Universal velocity distribution for turbulent flow in smooth tubes. [After Deissler reproduced from R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, Wiley, New York, 1960. Reproduced by permission of the publisher.]... 

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