Turbulent resistance

Fig. 14. CFD predictions of turbulent flow (meshed REU geometry, air pathlines with spheres hidden for clarity, contours of turbulent kinetic energy k) for configuration B2. Copyright 2001 From Turbulent Resistance of Complex Bed Structures by J. Tobis. Reproduced by permission of Taylor and Francis, Inc., http //www.taylorandfrancis.com.

The pressure drop across the sparger for gas phase is due to viscous as well as turbulent resistance to the flow. It is expressed as... 

Due to the complex weave pattern for LAD screens, it is difficult to derive an exact solution for the flow through a LAD screen. An empirical solution from Armour and Cannon (1968) has been proposed, as well as basic computational fluid dynamics simulations from Zhang et al. (2009) for the flow through a LAD screen. Using the logic from Armour and Cannon (1968), the approximate solution is formulated as the sum of the pressure drop due to viscous (laminar) and inertial (turbulent) resistance. 

Measurement by Thermal Effects. When a fine wire heated electrically is exposed to a flowing gas, it is cooled and its resistance is changed. The hot-wire anemometer makes use of this principle to measure both the average velocity and the turbulent fluctuations in the flowing stream. The fluid velocity, L, is related to the current, /, and the resistances, R, of the wire at wire, and gas, g, temperatures via... 

Drop breakage occurs when surrounding fluid stresses exceed the surface resistance of drops. Drops are first elongated as a result of pressure fluctuations and then spHt into small drops with a possibiUty of additional smaller fragments (Fig. 19). Two types of fluid stresses cause dispersions, viscous shear and turbulence. In considering viscous shear effects, it is assumed that the drop size is smaller than the Kohnogoroff microscale, Tj. 

Early models used a value for that remained constant throughout the day. However, measurements show that the deposition velocity increases during the day as surface heating increases atmospheric turbulence and hence diffusion, and plant stomatal activity increases (50—52). More recent models take this variation of into account. In one approach, the first step is to estimate the upper limit for in terms of the transport processes alone. This value is then modified to account for surface interaction, because the earth s surface is not a perfect sink for all pollutants. This method has led to what is referred to as the resistance model (52,53) that represents as the analogue of an electrical conductance... 

For turbulent flow of a fluid past a solid, it has long been known that, in the immediate neighborhood of the surface, there exists a relatively quiet zone of fluid, commonly called the Him. As one approaches the wall from the body of the flowing fluid, the flow tends to become less turbulent and develops into laminar flow immediately adjacent to the wall. The film consists of that portion of the flow which is essentially in laminar motion (the laminar sublayer) and through which heat is transferred by molecular conduction. The resistance of the laminar layer to heat flow will vaiy according to its thickness and can range from 95 percent of the total resistance for some fluids to about I percent for other fluids (liquid metals). The turbulent core and the buffer layer between the laminar sublayer and turbulent core each offer a resistance to beat transfer which is a function of the turbulence and the thermal properties of the flowing fluid. The relative temperature difference across each of the layers is dependent upon their resistance to heat flow. 

D. Rectification in vertical wetted wall column with turbulent vapor flow, Johnstone and Pigford correlation =0.0.328(Wi) Wi P>vP 3000 < NL < 40,000, 0.5 < Ns. < 3 N=, v,.gi = gas velocity relative to R. liquid film = — in film -1 2 " [E] Use logarithmic mean driving force at two ends of column. Based on four systems with gas-side resistance only, = logarithmic mean partial pressure of nondiffusing species B in binary mixture. p = total pressure Modified form is used for structured packings (See Table 5-28-H). 

For a trumpet-shaped rounded entrance, with a radius of rounding greater than about 15 percent of the pipe diameter (Fig. 6-13Z ), the turbulent flow loss coefficient K is only about 0.1 (Vennard and Street, Elementary Fluid Meehanies, 5th ed., Wiley, New York, 1975, pp. 420-421). Rounding of the inlet prevents formation of the vena eontraeta, thereby reducing the resistance to flow. 

Perforated Plates and Screens A nonuniform velocity profile in turbulent flow through channels or process equipment can be smoothed out to any desired degree by adding sufficient uniform resistance, such as perforated plates or screens across the flow channel, as shown in Fig. 6-38. Stoker Ind. Eng. Chem., 38, 622-624 [1946]) provides the following equation for the effect of a uniform resistance on velocity profile ... 

With good diy scrubbing sorbents, the controlling resistance for gas cleaning is external turbulent diffusion, which also depends on energy dissipated by viscous and by inertial mechanisms. It turns out to Be possible to correlate mass-transfer rate as a fimctiou of the fric tiou Factor. 

For inlet or outlet end erosion-corrosion, either extend tube ends 3 or 4 inches into the water box or install sleeves, inserts, or ferrules into the tube ends. These should be a minimum of 5 inches long. The ferrules may be nonmetallic or erosion-resistant metals, such as stainless steel, if galvanically compatible. The end of the ferrule should be feathered to prevent turbulence. 

For turbine mixers that the width of a baffle should not exceed more than one-twelfth of the tank diameter and, for propeller mixers, no more than one-eighteenth the tank diameter. With side-entering, inclined or off-center propellers, as shown in Figure 13, baffles are not required. Instead, shrouded impellers and diffuser rings may be used to suppress vortex formation. These devices contribute to flow resistance and reduce circulation by creating intense shear and abnormal turbulence... 

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