Effective Reynolds number

The RNG theory as applied to turbulence reduces the Reynolds number to an effective Reynolds number (Reeff) by increasing an effective viscosity (/small-scale eddies are eliminated, which reduces computational demand considerably. The new equation for the variation of the effective viscosity is as follows ... 

The differential form of this equation is used in calculating the effective viscosity in the RNG k-s model. This method allows varying the effective viscosity with the effective Reynolds number to accurately extend the model to low-Reynolds-number and near-wall flows. 

Assuming a tetrahedral packing model, Heath developed expressions for an effective Reynolds number and a modified Jd factor which extended Eqs. (20) and (21) to his packed bed data. He also showed that his information on natural crystals of fairly soluble materials correlated well with the literature data previously cited. 

An effective Reynolds number Ree(f is then calculated from... 

Reynolds number (Re) A measure of the state of turbulence in a fluid system. It is calculated as the ratio of inertia effects to viscous effects. Reynolds number is dimensionless. Flow systems with Re values <2200... 

In thin film hydrodynamic lubrication theory, the importance of inertia forces in the fluid film depends on the magnitude of the effective Reynolds number Re ( Re = where U... 

Comparing with equation (2.9) for flow system with single length scale, we can conclude that the effective Reynolds number Re fi for this two-length-scale problem is... 

Note that at small value of Re g, the left-hand side of equation (2.26) is equal to zero. This effective Reynolds number can therefore be arbitrarily small compared to the conventional Reynolds number (Re = pYph/n) given a sufficiently long channel. Thus, microchannel flows easily satisfy the Poiseuille flow assumption leading to (V V)V = 0 compared to the conventional channels. 

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. 

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. 

A = 4.05 X lO " cm/(s-kPa)(4.1 X 10 cm/(s-atm)) and = 1.3 x 10 cm/s (4)//= 1 mPa-s(=cP), NaCl diffusivity in water = 1.6 x 10 cm /s, and solution density = 1 g/cm . Figure 4 shows typical results of this type of simulation of salt water permeation through an RO membrane. Increasing the Reynolds number in Figure 4a decreases the effect of concentration polarization. The effect of feed flow rate on NaCl rejection is shown in Figure 4b. Because the intrinsic rejection, R = 1 — Cp / defined in terms of the wall concentration, theoretically R should be independent of the Reynolds... 

Entrance and Exit Effects In the entrance region of a pipe, some distance is required for the flow to adjust from upstream conditions to the fuUy developed flow pattern. This distance depends on the Reynolds number and on the flow conditions upstream. For a uniform velocity profile at the pipe entrance, the computed length in laminar flow required for the centerline velocity to reach 99 percent of its fully developed value is (Dombrowski, Foumeny, Ookawara and Riza, Can. J. Chem. Engr, 71, 472 76 [1993])... 

Curved Pipes and Coils For flow through curved pipe or coil, a secondary circiilation perpendicular to the main flow called the Dean effect occurs. This circulation increases the friction relative to straight pipe flow and stabilizes laminar flow, delaying the transition Reynolds number to about... 

The drag coefficients for disks (flat side perpendicular to the direction of motion) and for cylinders (infinite length with axis perpendicular to the direclion of motion) are given in Fig. 6-57 as a Function of Reynolds number. The effect of length-to-diameter ratio for cylinders in the Newton s law region is reported by Knudsen and Katz Fluid Mechanics and Heat Transfer, McGraw-Hill, New York, 1958). 

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. 

A turbine flowmeter consists of a straight flow tube containing a turbine which is free to rotate on a shaft supported by one or more bearings and located on the centerline of the tube. Means are provided for magnetic detection of the rotational speed, which is proportional to the volumetric flow rate. Its use is generally restric ted to clean, noncorrosive fluids. Additional information on construction, operation, range, and accuracy can be obtained from Holzbock (Instruments for Measurement and Control, 2d ed., Reinhold, New York, 1962, pp. 155-162). For performance characteristics of these meters with liquids, see Shafer,y. Basic Eng., 84,471-485 (December 1962) or May, Chem. Eng., 78(5), 105-108 (1971) and for the effect of density and Reynolds number when used in gas flowmetering, see Lee and Evans, y. Basic Eng., 82, 1043-1057 (December 1965). 

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