Reynolds influence

Reynolds also discussed transpiration under the Influence of a pressure difference alone and gave an account of the phenomenon of Impulsion In a Crookes radiometer, an effect of great Interest to 19ch century scientists. 

Characterization and influence of electrohydro dynamic secondary flows on convective flows of polar gases is lacking for most simple as well as complex flow geometries. Such investigations should lead to an understanding of flow control, manipulation of separating, and accurate computation of local heat-transfer coefficients in confined, complex geometries. The typical Reynolds number of the bulk flow does not exceed 5000. 

Both effects can produce coarser atomization. However, the influence of Hquid viscosity on atomization appears to diminish for high Reynolds or Weber numbers. Liquid surface tension appears to be the only parameter independent of the mode of atomization. Mean droplet size increases with increasing surface tension in twin-fluid atomizers (34). is proportional to CJ, where the exponent n varies between 0.25 and 0.5. At high values of Weber number, however, drop size is nearly proportional to surface tension. 

It follows that since the addition of metal oxides has such a profound effect on the properties of liquid silicates such as the viscosity, that the Reynolds number of liquid silicates in metal-silicate liquid two-phase systems will influence the boundary layer thickness to a greater extent than in the liquid metals and alloys, mainly because of the higher viscosity of the silicate. 

Figure 3.2.1 illustrates the mixing in packed beds (Wilhelm 1962). As Reynolds number approaches the industrial range Rep > 100, the Peclet numbers approach a constant value. This means that dispersion is influenced by turbulence and the effect of molecular diffusion is negligible. 

Work done by Wiesner [6] is a much more accurate approach. The subject has also been reported on more recently by Simon and Bulskamper [71. They generally agree with Wiesner that the variance of performance with Reynolds number was more true at low value that at high values. The additional influence above a Reynolds number of 10 is not much. It would appear that if a very close guarantee depended on the Reynolds number to get the compressor within the acceptance range (if the Reynolds number was high to begin with), the vendor would be rather desperate. 

The criteria K is similar to the Archimedes number introduced in 19.30 liy Baturin and Shcpelev to characterize air jets influenced by buoyancy, or to ihe Richardson criteria used in meteorology to characterize rhe ratio of the mrbu-lence suppression by rhe buoyancy forces over the turbulence generation by the Reynolds tension, In the case of displacement ventilation, the Richardson criteria can be defined by rhe relationship -... 

A reduced scale of the model requires an increased velocity level in the experiments to obtain the correct Reynolds number if Re < Re for the prob lem considered, but the experiment can be carried out at any velocity if Re > RCj.. The influence of the turbulence level is shown in Fig. 12.40. A velocity u is measured at a location in front of the opening and divided by the exhaust flow rate in order to obtain a normalized velocity. The figure show s that the normalized velocity is constant for Reynolds numbers larger than 10 000, which means that the flow around the measuring point has a fully developed turbulent structure at that velocity level. The flow may be described as a potential flow with a normalized velocity independent of the exhaust flow rate at large distances from the exhaust opening— and far away from surfaces. 

The shape, size, and baffling of a specific mixing vessel significantly influences the Reynolds number, flow, and power numbers. 

As indicated earlier, non-Newtonian characteristics have a much stronger influence on flow in the streamline flow region where viscous effects dominate than in turbulent flow where inertial forces are of prime importance. Furthermore, there is substantial evidence to the effect that for shear-thinning fluids, the standard friction chart tends to over-predict pressure drop if the Metzner and Reed Reynolds number Re R is used. Furthermore, laminar flow can persist for slightly higher Reynolds numbers than for Newtonian fluids. Overall, therefore, there is a factor of safety involved in treating the fluid as Newtonian when flow is expected to be turbulent. 

The relation between c and / and X (defined by equation 5.1) is shown in Figure 5.4, where it is seen that separate curves are given according to the nature of the flow of the two phases. This relation was developed from studies on the flow in small tubes of up to 25 mm diameter with water, oils, and hydrocarbons using air at a pressure of up to 400 kN/m . For mass flowrates per unit area of U and G for the liquid and gas, respectively, Reynolds numbers Rei L d/fii ) and Rec(G d/fia) may be used as criteria for defining the flow regime values less than 1000 to 2000, however, do not necessarily imply that the fluid is in truly laminar flow. Later experimental work showed that the total pressure has an influence and data presented by Gr1H ITH(i9) may be consulted where... 

SHERWOOD and Pigford(7) found that the effect of the Schmidt group was also influenced by the Reynolds group and that the available data were, fairly well correlated as shown in Figure 10.16, in which (hod )/D is plotted against Re Sc0-67. 

Garner and Keey(52 53) dissolved pelleted spheres of organic acids in water in a low-speed water tunnel at particle Reynolds numbers between 2.3 and 255 and compared their results with other data available at Reynolds numbers up to 900. Natural convection was found to exert some influence at Reynolds numbers up to 750. At Reynolds numbers greater than 250, the results are correlated by equation 10.230 ... 

Experimental results for fixed packed beds are very sensitive to the structure of the bed which may be strongly influenced by its method of formation. GUPTA and Thodos157 have studied both heat transfer and mass transfer in fixed beds and have shown that the results for both processes may be correlated by similar equations based on. / -factors (see Section 10.8.1). Re-arrangement of the terms in the mass transfer equation, permits the results for the Sherwood number (Sh1) to be expressed as a function of the Reynolds (Re,) and Schmidt numbers (Sc) ... 

The paper by Davies et al. (2006) reports results of a numerical investigation of the laminar, periodically repeating flow in a parallel-plate micro-channel with superhydrophobic walls. In particular, the influence of the Reynolds number and the vapor cavity size on the overall flow dynamics was explored. A schematic of the near-wall and cavity regions is shown in Fig. 3.18. 

The results presented in Fig. 5.41 clearly show that two-phase mean heat transfer coefficients are strongly influenced by the liquid superficial Reynolds number (Rcls). As shown in Fig. 5.41, the heat transfer coefficient increases proportionally as Rcls increases. 

The influence of inlet conditions on stability of flow boiling in micro-channels was analyzed by Brutin and Tadrist (2004). The set-up with rectangular micro-channel 500 X 4,000 jm was used to study flow boiling at two kinds of upstream conditions, which corresponded to constant liquid velocity at channel entrance (confinement condition) and constant velocity at the syringe outlet. The flow characteristics corresponding to steady and unsteady regimes were studied and the Reynolds number that subdivided these states was found. 

There are two causes for oscillations of the heat flux, with 7 = const. (1) fluctuations of the heat transfer coefficient due to velocity fluctuations, and (2) fluctuations of the fluid temperature. At small enough Reynolds numbers the heat transfer coefficient is constant (Bejan 1993), whereas at moderate Re (Re 10 ) it is a weak function of velocity (Peng and Peterson 1995 Incropera 1999 Sobhan and Garimella 2001). Bearing this in mind, it is possible to neglect the influence of velocity fluctuations on the heat transfer coefficient and assume that heat flux flucmations are expressed as follows ... 

To avoid gas-liquid mass transfer Hmitation, which would have a negative influence on productivity, in correctly operated bioreactors there are turbulent flow conditions with more or less pronounced turbulence, for which the Reynolds stress formula (Eq. (2)) can be used. Whereas, as a rule there is fully developed turbulent flow in technical apparatuses (see condition (6) and explanations in Sect. 8), this is frequently not the case in laboratory fermenters. Equations (3) and (4) are then only valid to a limited extent. 

Walter et al. studied the flow distribution in simple multichannel geometries by means of the finite-element method [112]. In order to reduce the computational effort, a 2-D model was set up to mimic the 3-D multichannel geometry. Even at a comparatively small Reynolds number of 30 they found recirculation zones in the flow distribution chamber and corresponding deviations from the mean flow rate inside the channels of about 20%. They also investigated the influence of contact time variation on a simple two-step reaction. 

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