Laminar-turbulent transition flow regime

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. 

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. 

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). 

The evolution of the Poiseuille number f Re) as a function of the Reynolds number is shown on figure 12. It is observed that the classical value for the laminar regime is obtained if the Reynolds number is less than 2000. The laminar turbulent transition occurs for the conventional value. The authors [22] investigated the entrance effects. They conclude that the friction factor is insensitive to the channel height and that there was no sign of a faster transition to turbulence compared to conventional channel flows. 

To verify the flow regime and the laminar-turbulent transition, a bronze block was replaced by an transparent altuglas plate. Visualisation with dye revealed a very stable flow for Reynolds numbers up to 2500 for both smooth and rough channels. On the contrary, large eddies were visualised for Reynolds numbers over 3800. Between these two values a stable flow region following turbulent structures were observed. 

For a 125 mm wafer, the air flow at the very edge is no longer laminar once the rotation rate exceeds about 3700 rpm. At 6000 rpm, the transition occurs at a radial position of 49 mm the outer 14 mm is in the transition or turbulent flow regime on a 125 mm wafer at this speed. In the turbulent region, the evaporation rate depends on radial position and varies with the spin speed to a power other than one-haIf. The result is expected to be a non-uniform resist thickness. While this effect is probably not important for the wafers in use today, it may become important in the future. The critical speed for a 200 mm wafer is only 1430 rpm. Above this value, at least part of the wafer will be in the turbulent air flow regime. 

At low Reynolds numbers, inertial forces are small compared to viscous forces and the flow remains laminar. At high Reynolds numbers, viscous forces become dominant and disturb the flow, which thus becomes turbulent The transition from a laminar flow regime to a turbulent flow regime never occurs suddenly there is always a transition flow regime. For example, the laminar flow inside tubular pipes occurs at the Reynolds number around 2300. The turbulent flow in the same pipe occurs at the Reynolds number higher than around 3000. The flow between the Reynolds numbers 2300 and 3000 is thus considered the transition flow. 

Let us begin with the system of mass transfer for flow in a conduit Figure 11-2 illustrates the correlation for heat and mass transfer. Note that the additional parameter as L/D is used in the regimes of laminar and transition flow. Also note that the heat and mass transfer can be described by one correlation at high Reynolds numbers (i.e., 5000 or more). This means that the turbulent mass transfer Nusselt number (by analogy) to equation (6-21) is... 

In laminar flow there are no disturbances, and therefore all flow particles move in the same direction. Transitional flow is the flow regime that takes place during the change from streamline to turbulent flow. In the case of turbulent flow the particles move in a given flow direction, but the flow is erratic and random. 

Reynolds number A dimensionless parameter that represents the ratio of the inertia forces to the viscous forces in a flow. Its magnitude denotes the actual flow regime, such as streamline (laminar), transitional, or turbulent. 

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 ... 

For most medium- and large-scale micromanifold structures, where one passage feeds multiple parallel channels, flow traverses through turbulent and transition flows in the micromanifold region. This fluid in turbulent to transition flow also turns in the micromanifold region as it drops flow into parallel microchannels, which are primarily in the laminar flow regime. 

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). 

Mixing processes involved in the manufacture of disperse systems, whether suspensions or emulsions, are far more problematic than those employed in the blending of low-viscosity miscible liquids due to the multi-phasic character of the systems and deviations from Newtonian flow behavior. It is not uncommon for both laminar and turbulent flow to occur simultaneously in different regions of the system. In some regions, the flow regime may be in transition, i.e., neither laminar nor turbulent but somewhere in between. The implications of these flow regime variations for scale-up are considerable. Nonetheless, it should be noted that the mixing process is only completed when Brownian motion occurs sufficiently to achieve uniformity on a molecular scale. 

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