Turbulent transition regime

Nuc, applies to the conduction and the turbulent transition regime, Nu, to the laminar boundary layer regime, and Nu, to the turbulent boundary layer regime. Equation 4.92 fits the data with a maximum deviation of about 10 percent and mean deviation of about 4 percent. It compares well with computer simulations [177]. A more accurate but also more complex set of equations is also available in [84, 85]. Equation 4.92 has been validated up to Ra (HIL)3 = 1.5 x 1010 for HIL = 5,20, and 40. Equation 4.92 is based on data for perfectly conducting walls, but for HIL s 10 the effect of wall properties is not expected to be important (see Table 4.6, entry 9). 

Turbulent flow occurs when the Reynolds number exceeds a critical value above which laminar flow is unstable the critical Reynolds number depends on the flow geometry. There is generally a transition regime between the critical Reynolds number and the Reynolds number at which the flow may be considered fully turbulent. The transition regime is very wide for some geometries. In turbulent flow, variables such as velocity and pressure fluctuate chaotically statistical methods are used to quantify turbulence. 

Those particles with sizes d > d" at a given set of conditions (v, p, Pp, and a ) will settle only in the turbulent flow regime. For particles with sizes d < d, d" will settle only when the flow around the object is in the transitional regime. Recall that the transitional zone occurs in the Reynolds number range of 0.2 to 500. The sedimentation numbers corresponding to this zone are 3.6 < S, < 82,500 and 0.0022 < S2 < 1,515. 

For the same case of n = 1200 rpm and r = 0.5, we obtain u,/Ug = 800, whereas for the turbulent regime the ratio was only 28. This example demonstrates that the centrifugal process is more effective in the separation of small particles than of large ones. Note that after the radial velocity u, is determined, it is necessary to check whether the laminar condition. Re < 2, is fulfilled. For the transition regime, 2 < Re < 500, the sedimentation velocity in the gravity field is ... 

This ratio represents an average between similar ratios for the laminar and turbulent regimes. In the most general case, u, = f(D, Pp, p, /r, r, w), and hence we may ignore whether the particle displacement is laminar, turbulent or within the transition regime. This enables us to apply the dimensionless Archimedes number (recall the derivation back in Chapter 5) ... 

Pierce proposes and illustrates good agreement between the test data and the correlation for a smooth continuous curve for the Colburn factor over the entire range of Reynolds numbers for the laminar, transition, and turbulent flow regimes inside smooth tubes ... 

A summary of the nine batch reactor emulsion polymerizations and fifteen tubular reactor emulsion polymerizations are presented in Tables III IV. Also, many tubular reactor pressure drop measurements were performed at different Reynolds numbers using distilled water to determined the laminar-turbulent transitional flow regime. 

Figure 9. Monomer conversion vs. polymerization time in the helical tubular reactor transition and turbulent flow regimes...

However, several flow transition regimes have been identified between laminar and fully turbulent flow. The cessation of laminar Couette flow is marked by the appearance of Taylor vortices in the gap between the two cylinders. For the case of stationary outer cylinder, the critical angular velocity, C0crit> of inner cylinder at which these flow instabilities first appear can be estimated by using the following equations [102] ... 

The transition from laminar to turbulent flow on a rotating sphere occurs approximately at Re = 1.5 4.0 x 104. Experimental work by Kohama and Kobayashi [39] revealed that at a suitable rotational speed, the laminar, transitional, and turbulent flow conditions can simultaneously exist on the spherical surface. The regime near the pole of rotation is laminar whereas that near the equator is turbulent. Between the laminar and turbulent flow regimes is a transition regime, where spiral vortices stationary relative to the surface have been observed. The direction of these spiral vortices is about 4 14° from the negative direction of the azimuthal angle,. The phenomenon is similar to the flow transition on a rotating disk [19]. 

Metzner, A.B. and Reed, J.C., Flow of non-Newtonian fluids - correlation of the laminar, transition, and turbulent-flow regimes, AIChE Journal, 1, pp. 434-40 (1955). 

Henderson 575 presented a set of new correlations for drag coefficient of a single sphere in continuum and rarefied flows (Table 5.1). These correlations simplify in the limit to certain equations derived from theory and offer significantly improved agreement with experimental data. The flow regimes covered include continuum, slip, transition, and molecular flows at Mach numbers up to 6 and at Reynolds numbers up to the laminar-turbulent transition. The effect on drag of temperature difference between a sphere and gas is also incorporated. 

Clearly, the solution of this equation at forced-convection electrodes will depend on whether the fluid flow is laminar, in the transition regime, or turbulent. Since virtually all kinetic investigations have been performed in the laminar flow region, no further mention will be made of turbulent flow. The reader interested in mass transport under turbulent flow is recommended to consult refs. 14 and 15. 

It is clear that the flow regime is a complicated but predictable function of the physical properties of the liquid, the flow rate, and the slope of the channel. It has been shown that, for water films, gravity waves first appear in the region NrT = 1-2, capillary surface effects become important in the neighborhood of JVw = I, and the laminar-turbulent transition occurs in the zone ArRe = 250-500 (F7). 

Churchill also provided a single equation that may be used for Reynolds numbers in laminar, transitional, and turbulent flow, closely fitting/= 16/Re in the laminar regime, and the Colebrook formula, Eq. (6-38), in the turbulent regime. It also gives unique, reasonable values in the transition regime, where the friction factor is uncertain. 

The Reynolds number of the gas flow is usually in the transitional or turbulent flow regime. Therefore, a proper choice of the turbulence model is required, with a grid accurate enough for resolving details of the mixing layers and the generation of turbulence there. 

They observed eg to be reduced by the presence of solids, although this reduction is less pronounced in the churn-turbulent regime than in the transition regime. The relationships of Koida et al. [37] are... 

Taguchi and Miyamoto (1966) showed that for non-Newtonian fermentation broth, the power requirement in the turbulent flow regime was well correlated by the above correlation of Michel and Miller (1962). Broth from the production of gluco-amylase by Endomyces species and carboxymethyl-cellulose solutions were used as non-Newtonian fluids. For non-Newtonian fluids in laminar and transition regions, particularly for fluids with apparent viscosities greater than 300 cP, the impeller diameter and impeller blade width had considerable effects on power consumption in a non-gassed system. They proposed... 

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