Turbulent region

A low Reynolds number indicates laminar flow and a paraboHc velocity profile of the type shown in Figure la. In this case, the velocity of flow in the center of the conduit is much greater than that near the wall. If the operating Reynolds number is increased, a transition point is reached (somewhere over Re = 2000) where the flow becomes turbulent and the velocity profile more evenly distributed over the interior of the conduit as shown in Figure lb. This tendency to a uniform fluid velocity profile continues as the pipe Reynolds number is increased further into the turbulent region. 

The transition from laminar to turbulent flow occurs at Reynolds numbers varying from ca 2000 for n > 1 to ca 5000 for n = 0.2. In the laminar region the Fanning friction factor (Fig. 2) is identical to that for Newtonian fluids. In the turbulent region the friction factor drops significantly with decreasing values of producing a family of curves. 

Often, a pilot plant will operate in the viscous region while the commercial unit will operate in the transition region, or alternatively, the pilot plant may be in the transition region and the commercial unit in the turbulent region. Some experience is required to estimate the difference in performance to be expected upon scale-up. 

Bearing designs are also affeeted by the transition of the film from a laminar to a turbulent region. The transition speed Nt) ean be eomputed using the following relationship ... 

Studies on various turbine agitators have shown that geometrie ratios that vary from the standard design ean eause different effeets on the Power number Np in the turbulent regions [24]. 

Consider the mixing in both small and large-seale systems to oeeur in the turbulent region, designated as S and L respeetively. Using the Norwood and Metzner s eorrelation [26], the mixing time for both systems is... 

Figure 7-21. B-faotor versus Reynolds number in the turbulent regions. (Source Chen, S. J., Kenics technical data KTEK-2, 1978.)...

The flow pattern in Fig. 10.55 has a violent turbulent region, characterized by a vortex street and two free vortices rotating in opposite directions... 

For flow in a pipe, a Reynolds nmiiber above 2100 is an indication of turbulent flow. Thus, witli a Reynolds number of 9769.23, Uie flow is in the turbulent region. 

Although the outside coefficient of a vertical coil is some 13% higher than for a helical coil, the inside coefficient is quite often lower due to the physical arrangement and the lower coefficient if gases are evolved and venting is required. The over-all coefficient may end up about the same as the helical coil. The outside film coefficient for a system varies with in the turbulent region. Thus... 

The tube-side inlet to an exchanger, i.e. the tube ends, is a highly turbulent region and nylon ferrules in the tube ends of the inlet pass have been used in cupro-nickel-tubed condensers to prevent erosion. Where the flow is two phase the same rules will apply except that an erosion velocity limit is more difficult to specify. 

We recall from our earlier discussion of chaos in one-dimensional continuous systems (see section 4.1) that period-doubling is not the only mechanism by which chaos can be generated. Another frequently occurring route to chaos is intermittency. But while intermittency in low dimensional dynamical systems appears to be constrained to purely temporal behavior [pomeau80], CMLs exhibit a spatio-temporal intermittency in which laminar eddies are intermixed with turbulent regions in a complex pattern in space-time. 

Read power number versus Reynolds number in turbulent region is based on geometry of the impellers. The lowest power number is less than l,for marine propellers. For flat bladed turbines in a turbulent region, the power number is equal to 6. The power graph is illustrated in Figure 6.6. 

Thus, the pipe friction chart for a Newtonian fluid (Figure 3.3) may be used for shearthinning power-law fluids if Remit is used in place of Re. In the turbulent region, the ordinate is equal to (R/pu2)n 0 fn5. For the streamline region the ordinate remains simply R/pu2, because Reme has been defined so that it shall be so (see equation 3.140). More recently, Irvine(25j has proposed an improved form of the modified Blasius equation which predicts the friction factor for inelastic shear-thinning polymer-solutions to within 7 per cent. 

For purposes of scale-up, it is generally most satisfactory in the laminar region to maintain a constant speed for the tip of the impeller, and mixing time will generally increase with scale. The most satisfactory basis for scale-up in the turbulent region is to maintain a constant power input per unit volume. 

That tire existence of the buffer layer may be neglected and that in turbulent flow the boundary layer may be considered as consisting of a turbulent region adjacent to a laminar sub-layer which separates it from the surface. 

It may be noted that no assumptions have been made concerning the nature of the flow within the boundary layer and therefore this relation is applicable to both the streamline and the turbulent regions. The relation between ux and y is derived for streamline and turbulent flow over a plane surface and the integral in equation 11.9 is evaluated. 

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. 

The velocity at the inner edge of the turbulent region must also be given by the equation for the velocity distribution in the turbulent region. 

Finally, over the greater part of the fluid, the turbulent region in which eddy motion is large compared with molecular diffusion. 

Approximate form of velocity profile In turbulent region... 

Tf auH and b8s are the velocity and temperature, respectively, at the edge of the laminar sub-layer (see Figure 12.5), applying the Reynolds analogy (equation 12,99) for transfer across the turbulent region ... 

The method is based on the calculation of the total temperature difference between the fluid and the surface, by adding the components attributable to the laminar sub-layer, the buffer layer and the turbulent region. In the steady state, the heat flux (<70) normal to the surface will be constant if the effects of curvature are neglected. 

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