Reynolds number importance

Pressure Drop. The prediction of pressure drop in fixed beds of adsorbent particles is important. When the pressure loss is too high, cosdy compression may be increased, adsorbent may be fluidized and subject to attrition, or the excessive force may cmsh the particles. As discussed previously, RPSA rehes on pressure drop for separation. Because of the cychc nature of adsorption processes, pressure drop must be calculated for each of the steps of the cycle. The most commonly used pressure drop equations for fixed beds of adsorbent are those of Ergun (143), Leva (144), and Brownell and co-workers (145). Each of these correlations uses a particle Reynolds number (Re = G///) and friction factor (f) to calculate the pressure drop (AP) per... 

Reynolds dumber. One important fluid consideration in meter selection is whether the flow is laminar or turbulent in nature. This can be deterrnined by calculating the pipe Reynolds number, Ke, a dimensionless number which represents the ratio of inertial to viscous forces within the flow. Because... 

Both wetted-sensor and clamp-on Doppler meters ate available for Hquid service. A straight mn of piping upstream of the meter and a Reynolds number of greater than 10,000 ate generally recommended to ensure a weU-developed flow profile. Doppler meters ate primarily used where stringent accuracy and repeatabiHty ate not requited. Slurry service is an important appHcation area. 

Flow Past Bodies. A fluid moving past a surface of a soHd exerts a drag force on the soHd. This force is usually manifested as a drop in pressure in the fluid. Locally, at the surface, the pressure loss stems from the stresses exerted by the fluid on the surface and the equal and opposite stresses exerted by the surface on the fluid. Both shear stresses and normal stresses can contribute their relative importance depends on the shape of the body and the relationship of fluid inertia to the viscous stresses, commonly expressed as a dimensionless number called the Reynolds number (R ), EHp/]1. The character of the flow affects the drag as well as the heat and mass transfer to the surface. Flows around bodies and their associated pressure changes are important. 

Flow Past Deformable Bodies. The flow of fluids past deformable surfaces is often important, eg, contact of Hquids with gas bubbles or with drops of another Hquid. Proper description of the flow must allow for both the deformation of these bodies from their shapes in the absence of flow and for the internal circulations that may be set up within the drops or bubbles in response to the external flow. DeformabiUty is related to the interfacial tension and density difference between the phases internal circulation is related to the drop viscosity. A proper description of the flow involves not only the Reynolds number, dFp/p., but also other dimensionless groups, eg, the viscosity ratio, 1 /p En tvos number (En ), Api5 /o and the Morton number (Mo),giJ.iAp/plG (6). 

In order to select the pipe size, the pressure loss is calculated and velocity limitations are estabHshed. The most important equations for calculation of pressure drop for single-phase (Hquid or vapor) Newtonian fluids (viscosity independent of the rate of shear) are those for the deterrnination of the Reynolds number, and the head loss, (16—18). 

Based on such analyses, the Reynolds and Weber numbers are considered the most important dimensionless groups describing the spray characteristics. The Reynolds number. Re, represents the ratio of inertial forces to viscous drag forces. 

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... 

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. 

Turboexpanders eurrently in operation range in size from about 1 hp to above 10,000 hp. In the small sizes, the problems are miniaturization, Reynolds Number effeets, heat transfer, seal, and meehanieal problems, and often inelude bearing and eritieal speed eoneerns. In intermediate sizes, these problems beeome less signifieant, but bearing rubbing speeds and vibration beeome inereasingly important. 

The relationship between adsorption capacity and surface area under conditions of optimum pore sizes is concentration dependent. It is very important that any evaluation of adsorption capacity be performed under actual concentration conditions. The dimensions and shape of particles affect both the pressure drop through the adsorbent bed and the rate of diffusion into the particles. Pressure drop is lowest when the adsorbent particles are spherical and uniform in size. External mass transfer increases inversely with d (where, d is particle diameter), and the internal adsorption rate varies inversely with d Pressure drop varies with the Reynolds number, and is roughly proportional to the gas velocity through the bed, and inversely proportional to the particle diameter. Assuming all other parameters being constant, adsorbent beds comprised of small particles tend to provide higher adsorption efficiencies, but at the sacrifice of higher pressure drop. This means that sharper and smaller mass-transfer zones will be achieved. 

Fully developed nonisothermal flow may also be similar at different Reynolds numbers, Prandtl numbers, and Schmidt numbers. The Archimedes number will, on the other hand, always be an important parameter. Figure 12.30 shows a number of model experiments performed in three geometrically identical models with the heights 0.53 m, 1.60 m, and 4.75 m." Sixteen experiments carried out in the rotxms at different Archimedes numbers and Reynolds numbers show that the general flow pattern (jet trajectory of a cold jet from a circular opening in the wall) is a function of the Archimedes number but independent of the Reynolds number. The characteristic length and velocity in Fig. 12.30 are defined as = 4WH/ 2W + IH) and u = where W is... 

The assumption of a self-similar flow (Reynolds number-independent flow) simplifies full-scale experiments and is also a useful tool in the formulation of simple measuring procedures. This section will show two examples of self-similar flow where the Archimedes number is the only important parameter. 

Nq is strongly dependent on the flow regime, Reynolds Number, N e, and installation geometi y of the impeller. The flow from an impeller is only that produced by the impeller and does not include the entrained flow, which can be a major part of the total motion flow from the impeller. The entrained flow refers to fluid set in motion by the turbulence of the impeller output stream [27]. To compare different impellers, it is important to define the t -pe of flows being considered. 

One particularly important feature of the plate heat exchanger is that the turbulence induced by the troughs reduces the Reynolds number at which the flow becomes laminar. If the characteristic length dimension in the Reynolds number is taken as twice the average gap between plates, the Re number at which the flow becomes laminar varies from about 100 to 400, according to the type of plate. 

This chapter is organized into two main parts. To give the reader an appreciation of real fluids, and the kinds of behaviors that it is hoped can be captured by CA models, the first part provides a mostly physical discussion of continuum fluid dynamics. The basic equations of fluid dynamics, the so-called Navier-Stokes equations, are derived, the Reynolds Number is defined and the different routes to turbulence are described. Part I also includes an important discussion of the role that conservation laws play in the kinetic theory approach to fluid dynamics, a role that will be exploited by the CA models introduced in Part II. 

What this transcription into dimensionless variables means physically is very interesting. It means that, if expressed in terms of the dimensionless variables v, x and t, any two fluid problems will have essentially the same flow solutions whenever their Reynolds numbers are equal. This is of considerable practical importance. of course, since it implies that the air flow past an airplane wing, for example,... 

The ratio u/d represents the velocity gradient in the fluid, and thus the group (pu/d) is proportional to the shear stress in the fluid, so that (pu2)/(pu/d) = (dup/p) = Re is proportional to the ratio of the inertia forces to the viscous forces. This is an important physical interpretation of the Reynolds number. 

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 effect of length to diameter ratio (l/d) on the value of the heat transfer coefficient may be seen in Figure 9.24. It is important at low Reynolds numbers but ceases to be significant at a Reynolds number of about 104. 

The film coefficients for the water jacket were in the range 635-1170 W/nr K for water rates of l. 44—9.23 1/s, respectively. It may be noted that 7.58 1/s corresponds to a vertical velocity of only 0.061 m/s and to a Reynolds number in the annulus of 5350. The thermal resistance of the wall of the pan was important, since with the sulphonator it accounted for 13 per cent of the total resistance at 32.3 K and 31 per cent at 403 K. The change in viscosity with temperature is important when considering these processes, since, for example, the viscosity of the sulphonation liquors ranged from 340 mN s/rn2 al 323 K to 22 mN s/m2 at 40.3 K. 

The relation of hydraulic diameter to channel length and the Reynolds number are important factors that determine the effect of the viscous energy dissipation on flow parameters. 

Under certain conditions the energy dissipation may lead to an oscillatory regime of laminar flow in micro-channels. The relation of hydraulic diameter to channel length and the Reynolds number are important factors that determine the effect of viscous energy dissipation on flow parameters. The oscillatory flow regime occurs in micro-channels at Reynolds numbers less than Recr- In this case the existence of velocity fluctuations does not indicate change from laminar to turbulent flow. 

One particular characteristic of conduction heat transfer in micro-channel heat sinks is the strong three-dimensional character of the phenomenon. The smaller the hydraulic diameter, the more important the coupling between wall and bulk fluid temperatures, because the heat transfer coefficient becomes high. Even though the thermal wall boundary conditions at the inlet and outlet of the solid wall are adiabatic, for small Reynolds numbers the heat flux can become strongly non-uniform most of the flux is transferred to the fluid at the entrance of the micro-channel. Maranzana et al. (2004) analyzed this type of problem and proposed the model of channel flow heat transfer between parallel plates. The geometry shown in Fig. 4.15 corresponds to a flow between parallel plates, the uniform heat flux is imposed on the upper face of block 1 the lower face of block 0 and the side faces of both blocks... 

In experiments of flow and heat transfer in micro-channels, some parameters, such as the Reynolds number, heat transfer coefficient, and Nusselt number, are difficult to obtain with high accuracy. The channel hydraulic diameter measurement error may play a very important role in the uncertainty of the friction factor (Hetsroni... 

At Reynolds number above 10-20, a new flow regime is established. While still laminar, it is obviously unsymmetrical. The inertial effects, therefore, are important but do not dominate to the extent of making the flow turbulent. In this region, a stable trailing vortex is set up behind each blade. 

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