Channel Reynolds number

An experimentally based rule-of-thumb is that laminar flow often occurs when the pipe Reynolds number, Vdjv, is less than 2,000, or when an open channel Reynolds number, Vhjv, is less than 500, where V is the cross-sectional mean velocity, d is the pipe diameter, v is the kinematic viscosity of the fluid, and h is the channel depth. The diameter or depth that would not be exceeded to have laminar flow by these experimental criteria is given in Table 5.1. 

The unexpected results of Sablani et al. [17] (i.e., less turbulence with smaller spacer thickness) may be best explained by an excellent paper by Schwinge et al. [82], The latter employed computational fluid dynamics (CFD) in a study of unsteady flow in narrow spacer-filled channels for spiral-wound membrane modules. The flow patterns were visualized for different filament configurations incorporating variations in mesh length and filament diameter and for channel Reynolds numbers, Re y, up to 1000. The simulated flow patterns revealed the dependence of the formation of... 

A numerical study of the effect of area ratio on the flow distribution in parallel flow manifolds used in a Hquid cooling module for electronic packaging demonstrate the useflilness of such a computational fluid dynamic code. The manifolds have rectangular headers and channels divided with thin baffles, as shown in Figure 12. Because the flow is laminar in small heat exchangers designed for electronic packaging or biochemical process, the inlet Reynolds numbers of 5, 50, and 250 were used for three different area ratio cases, ie, AR = 4, 8, and 16. 

The flow distribution in a manifold is highly dependent on the Reynolds number. Figure 14b shows the flow distribution curves for different Reynolds number cases in a manifold. When the Reynolds number is increased, the flow rates in the channels near the entrance, ie, channel no. 1—4, decrease. Those near the end of the dividing header, ie, channel no. 6—8, increase. This is because high inlet velocity tends to drive fluid toward the end of the dividing header, ie, inertia effect. 

Figure 15 shows the effect of the width ratio DJthe ratio of the combining header width to the dividing header width, on the flow distribution in manifolds for Reynolds number of 50. By increasing DJthe flow distribution in the manifold was significantly improved. The ratio of the maximum channel flow rate to the minimum channel flow rate is 1.2 for the case of D /= 4.0, whereas the ratio is 49.4 for the case oiDjD,=0.5. 

Noncircular Channels Calciilation of fric tional pressure drop in noncircular channels depends on whether the flow is laminar or tumu-lent, and on whether the channel is full or open. For turbulent flow in ducts running full, the hydraulic diameter shoiild be substituted for D in the friction factor and Reynolds number definitions, Eqs. (6-32) and (6-33). The hydraiilic diameter is defined as four times the channel cross-sectional area divided by the wetted perimeter. For example, the hydraiilic diameter for a circiilar pipe is = D, for an annulus of inner diameter d and outer diameter D, = D — d, for a rectangiilar duct of sides 7, h, Dij = ah/[2(a + h)].T ie hydraulic radius Rii is defined as one-fourth of the hydraiilic diameter. 

The critical Reynolds number for transition from laminar to turbulent flow in noncirciilar channels varies with channel shape. In rectangular ducts, 1,900 < Re < 2,800 (Hanks and Ruo, Ind. Eng. Chem. Fundam., 5, 558-561 [1966]). In triangular ducts, 1,600 < Re < 1,800 (Cope and Hanks, Ind. Eng. Chem. Fundam., II, 106-117 [1972] Bandopadhayay and Hinwood, j. Fluid Mech., 59, 775-783 [1973]). 

Reynolds number for gas S = length of corrugation side Uge = effective velocity of gas Ug = superficial velocity of gas Ui = superficial velocity of liquid Ap = pressure drop per unit packed height e = packing void fraction 0 = angle of flow channel (from horizontal) fi = viscosity p = density... 

For flow in an open channel, only turbulent flow is considered because streamline flow occurs in practice only when the liquid is flowing as a thin layer, as discussed in the previous section. The transition from streamline to turbulent flow occurs over the range of Reynolds numbers, updm/p = 4000 — 11,000, where dm is the hydraulic mean diameter discussed earlier under Flow in non-circular ducts. 

For developed laminar flow in smooth channels of t/h > 1 mm, the product ARe = const. Its value depends on the geometry of the channel. For a circular pipe ARe = 64, where Re = Gdh/v is the Reynolds number, and v is the kinematic viscosity. 

The heat transfer correlations are considered separately in the laminar and turbulent regimes in Figs. 2.21 and 2.22, respectively. The dependence of the Nusselt number on the Reynolds number is stronger in all the micro-channel predictions compared to conventional results, as indicated by the steeper slopes of the former Choi et al. (1991) predict the strongest variation of Nusselt number with Re. The predictions for all cases by Peng et al. (1996) also fall below those for a conventional channel. 

However, for flow in micro-channels, the wall thickness can be of the same order of channel diameter and will affect the heat transfer significantly. For example, Choi et al. (1991) reported that the average Nusselt numbers in micro-channels were much lower than for standard channels and increased with the Reynolds number. 

We consider the problem of liquid and gas flow in micro-channels under the conditions of small Knudsen and Mach numbers that correspond to the continuum model. Data from the literature on pressure drop in micro-channels of circular, rectangular, triangular and trapezoidal cross-sections are analyzed, whereas the hydraulic diameter ranges from 1.01 to 4,010 pm. The Reynolds number at the transition from laminar to turbulent flow is considered. Attention is paid to a comparison between predictions of the conventional theory and experimental data, obtained during the last decade, as well as to a discussion of possible sources of unexpected effects which were revealed by a number of previous investigations. 

Equation (3.4) reflects the dependence of the friction factor on the Reynolds number, whereas Eq. (3.5) shows conformity between actual and calculated shapes of a micro-channel. Condition (3.5) is the most general since it testifies to an identical form of the dependencies of the experimental and theoretical friction factor on the... 

Pfund et al. (2000) studied the friction factor and Poiseuille number for 128-521 pm rectangular channels with smooth bottom plate. Water moved in the channels at Re = 60—3,450. In all cases corresponding to Re < 2,000 the friction factor was inversely proportional to the Reynolds number. A deviation of Poiseuille number from the value corresponding to theoretical prediction was observed. The deviation increased with a decrease in the channel depth. The ratio of experimental to theoretical Poiseuille number was 1.08 0.06 and 1.12 zb 0.12 for micro-channels with depths 531 and 263 pm, respectively. 

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