Turbulence turbulent boundary layer

CATALYSTS - REGENERATION - FLUID CATALYTIC CRAC KING UNITS] (Vol 5) Turbulent boundary layer model... 

Another concept sometimes used as a basis for comparison and correlation of mass transfer data in columns is the Clulton-Colbum analogy (35). This semi-empirical relationship was developed for correlating mass- and heat-transfer data in pipes and is based on the turbulent boundary layer model... 

For a turbulent boundary layer, the total drag may be roughly estimated using Eqs. (6-184) and (6-185) for finite cylinders. Measured forces by Kwon and Prevorsek ]. Eng. Jnd., 101, 73-79 [1979]) are greater than predicted this way. 

FIGURE 4.24 Laminar and turbulent boundary layers and temperature distribution inside the boundary layer. 

In a turbulent boundary layer, flow takes place in the direction perpendicular to the surface over which the flow occurs. 

Comparison of the velocity profiles for laminar and turbulent boundary layers. 

Fig. 9.4 A turbulent boundary layer forms behind a cylinder for TZ 10. ...

Equation 11.12 does not fit velocity profiles measured in a turbulent boundary layer and an alternative approach must be used. In the simplified treatment of the flow conditions within the turbulent boundary layer the existence of the buffer layer, shown in Figure 11.1, is neglected and it is assumed that the boundary layer consists of a laminar sub-layer, in which momentum transfer is by molecular motion alone, outside which there is a turbulent region in which transfer is effected entirely by eddy motion (Figure 11.7). The approach is based on the assumption that the shear stress at a plane surface can be calculated from the simple power law developed by Blasius, already referred to in Chapter 3. 

Putting the constant equal to zero, implies that <5 = 0 when x = 0, that is that the turbulent boundary layer extends to the leading edge of the surface. An error is introduced by this assumption, but it is found to be small except where the surface is only slightly longer than the critical distance xc for the laminar-turbulent transition. 

It is of interest to compare the rates of thickening of the streamline and turbulent boundary layers at the transition point. Taking a typical value of Rexc — 105, then ... 

Thus the turbulent boundary layer is thickening at about four times the rate of the streamline boundary layer at the transition point. 

The relations between ux and y have already been obtained for both streamline and turbulent flow. A relation between and y for streamline conditions in the boundary layer is now derived, although it is not possible to define the conditions in the turbulent boundary layer sufficiently precisely to derive a similar expression for that case. 

It is found that the velocity at a distance y from the surface may be expressed as a simple power function (u oc y" for the turbulent boundary layer at a plane surface. What is the value of n if the ratio of the momentum thickness to the displacement thickness is 1.78 ... 

For a very thin liquid film, the value of 3 cannot be evaluated, and it should be replaced by a new parameter 3, using the generalized turbulent boundary-layer profile in an adiabatic flow as in Reference (Levy and Healzer, 1980). GF can be solved stepwise along the pipe until the G value goes to zero, where dryout occurs. This analysis was performed to compare the calculated g"rit with Wurtz data (Wurtz, 1978) and also to compare with the predictions by the well-known Biasi et al. correlation (1968), as shown in Figure 5.90. For the limited data points compared, the agreement was good. 

Hacker, D. S., 1963, Comment on Velocity Defect Law for a Transpired Turbulent Boundary Layer, AIAA J. 7(11) 2676. (5)... 

Kutateladze, S. S., and A. I. Leont ev, 1964, Turbulent Boundary Layers in Compressible Gases, D. B. Spalding, trans., Academic Press, New York. (5)... 

For turbulent flow on a rotating sphere or hemisphere, Sawatzki [53] and Chin [22] have analyzed the governing equations using the Karman-Pohlhausen momentum integral method. The turbulent boundary layer was assumed to originate at the pole of rotation, and the meridional and azimuthal velocity profiles were approximated with the one-seventh power law. Their results can be summarized by the... 

Integrating Eq. (6-24) over the turbulent boundary layer (from jq, the edge of the buffer layer, to y) gives... 

Equation (6-31) applies to the laminar sublayer region in a Newtonian fluid, which has been found to correspond to 0 < y+ < 5. The intermediate region, or buffer zone, between the laminar sublayer and the turbulent boundary layer can be represented by the empirical equation... 

Derive the relation between the friction factor and Reynolds number in turbulent flow for smooth pipe [Eq. (6-34)], starting with the von Karman equation for the velocity distribution in the turbulent boundary layer [Eq. (6-26)]. 

Let us try to preserve convection. If we ignore Il6 but maintain the more correct turbulent boundary layer convection (Equation (12.24)), then... 

The boundary layer thickness gradually increases until a critical point is reached at which there is a sudden thickening of the boundary layer this reflects the transition from a laminar boundary layer to a turbulent boundary layer. For both types, the flow outside the boundary layer is completely turbulent. In that part of the boundary layer near the leading edge of the plate the flow is laminar and consequently this is known as a... 

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