Low Reynolds number

At low particle Reynolds numbers for a bubbling bed, the Ergun expression can be simplified using only the first term in Eq. (31). 

At the same limit, the minimum fluidization velocity can be written as, 

This will be referred to as the simplified scaling relationship. At low Reynolds numbers, this still includes the gas-to-particle density ratio. 

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The convection term in the equation of motion is kept for completeness of the derivations. In the majority of low Reynolds number polymer flow models this term can be neglected. 

The majority of polymer flow processes are characterized as low Reynolds number Stokes (i.e. creeping) flow regimes. Therefore in the formulation of finite element models for polymeric flow systems the inertia terms in the equation of motion are usually neglected. In addition, highly viscous polymer flow systems are, in general, dominated by stress and pressure variations and in comparison the body forces acting upon them are small and can be safely ignored. 

For hquid systems v is approximately independent of velocity, so that a plot of JT versus v provides a convenient method of determining both the axial dispersion and mass transfer resistance. For vapor-phase systems at low Reynolds numbers is approximately constant since dispersion is determined mainly by molecular diffusion. It is therefore more convenient to plot H./v versus 1/, which yields as the slope and the mass transfer resistance as the intercept. Examples of such plots are shown in Figure 16. 

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. 

Eurther research on convective transport under low Reynolds number, quasicontinuum conditions is needed before the optimal design of such a micro heat exchanger is possible. The cooling heat exchanger is usually thermally linked to a relatively massive substrate. The effects of this linkage need to be explored and accurate methods of predicting the heat-transfer and pressure-drop performance need to be developed. 

TurbulentPremixedFlames. Combustion processes and flow phenomena are closely coimected and the fluid mechanics of a burning mixture play an important role in forming the stmcture of the flame. Laminar combusting flows can occur only at low Reynolds numbers, defined as... 

Porous Media Packed beds of granular solids are one type of the general class referred to as porous media, which include geological formations such as petroleum reservoirs and aquifers, manufactured materials such as sintered metals and porous catalysts, burning coal or char particles, and textile fabrics, to name a few. Pressure drop for incompressible flow across a porous medium has the same quahtative behavior as that given by Leva s correlation in the preceding. At low Reynolds numbers, viscous forces dominate and pressure drop is proportional to fluid viscosity and superficial velocity, and at high Reynolds numbers, pressure drop is proportional to fluid density and to the square of superficial velocity. 

The drag coefficient for rigid spherical particles is a function of particle Reynolds number, Re = d pii/ where [L = fluid viscosity, as shown in Fig. 6-57. At low Reynolds number, Stokes Law gives 24... 

With liquids at low velocities, the effect of the Reynolds number upon the coefficient is important. The coefficients are appreciably less than unity for Reynolds numbers less than 500 for pitot tubes and for Reynolds numbers less than 2300 for pitot-static tubes [see Folsom, Trans. Am. Soc. Mech. Eng., 78, 1447-1460 (1956)]. Reynolds numbers here are based on the probe outside diameter. Operation at low Reynolds numbers requires prior calibration of the probe. 

Find the correction factor for adverse temperature-gradient buildup at low Reynolds number J/. 

Even the good heat transfer conditions turned out to be false, however, if the correlation derived for single cylinders by McAdams (1954) were extrapolated to Rep < 100. Nelson and Galloway (1975) pointed out that at low Reynolds numbers the real heat transfer coefficient could be four... 

Turbulence, which prevails in the great majority of fluid-flow situations, poses special problems. Due to the wide range of space and time scales in turbulence flow, its exact numerical simulation is possible only at relatively low Reynolds number (around 100 or below) and if the geometry is simple. 

Oosthuizen, P. H. 1983. An Experimental Study of Low Reynolds Number Circular jet Flott. ASME Preprint 83-FE-36. 

In ref. 38 the k-co model was used to predict low-Reynolds-number, recirculating flow. 

For very low Reynolds numbers, 7 . << 1, the flow lines wrap smoothly around the cylinder, as shown in figure 9.1. 

If the surface over which the fluid is flowing contains a series of relatively large projections, turbulence may arise at a very low Reynolds number. Under these conditions, the frictional force will be increased but so will the coefficients for heat transfer and mass transfer, and therefore turbulence is often purposely induced by this method. 

Many materials of practical interest (such as polymer solutions and melts, foodstuffs, and biological fluids) exhibit viscoelastic characteristics they have some ability to store and recover shear energy and therefore show some of the properties of both a solid and a liquid. Thus a solid may be subject to creep and a fluid may exhibit elastic properties. Several phenomena ascribed to fluid elasticity including die swell, rod climbing (Weissenberg effect), the tubeless siphon, bouncing of a sphere, and the development of secondary flow patterns at low Reynolds numbers, have recently been illustrated in an excellent photographic study(18). Two common and easily observable examples of viscoelastic behaviour in a liquid are ... 

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