Intermediate Flow Regimes

For the intermediate flow regime, a correlation for CD has to be chosen. A correlation that covers much of the range of interest for fluidisation is due to Dallavalle 7... 

Multi-layer diffusion is developed when the molecule/surface interactions are strong. This mechanism is like to an intermediate flow regime between surface diffusion and capillary condensation [18]. 

In the intermediate flow regime, particles adopt preferred orientations. Particles will usually align themselves with their maximum cross section normal to the direction of relative motion. There is no appreciable secondary motion in the intermediate flow regime, so results for flow past fixed objects of the same shape can be used if the orientation corresponds to the preferred orientation. 

Equation (84) provides accurate quantitative predictions of particulate fluidized bed expansion characteristics in both laminar and turbulent flow regimes. For the intermediate flow regime, only a qualitative trend was observed. Equation (84) is slightly different in dependence of voidage from the drag coefficient suggested by Wen and Yu (1966) as shown here ... 

Copious experimentation has confirmed the validity of the above limiting forms, and led to correlations for the intermediate flow regime in terms of the particle Reynolds number. A compact form, which for most practical purposes adequately represents all the data, is attributed to Dallavalle (1948) ... 

From this point on, it s some very simple algebra. You can solve equation 5 for u, and then substitute an expression in for Cq for each of the three flow regimes (laminar, turbulent and intermediate). 

Note that the abscissa in Figure 2.4 starts at a value of 0.4, which corresponds to the voidage of a randomly packed bed. Equation 2.44 is valid for the extremes of flow regimes but strictly requires correction for the intermediate case (Khan and Richardson, 1990 Di Felice, 1994). 

Figure 14.3 shows results from flow reactor experiments on NO sensitized oxidation of methane in the 800 to 1200 K temperature range. In the absence of NO, temperatures of about 1100 K are required to initiate rapid oxidation of CH4 [31], but in the presence of NO, reaction occurs at temperatures as low as 850 K. The results indicate three different temperature regimes a low-temperature region (900-1000 K) with partial oxidation of methane, an intermediate-temperature regime with little reaction (1000-1150 K), and a high-temperature regime (>1150 K) with complete oxidation. 

Based on these experiments, a kind of flow-pattern map was proposed describing a region of laminar flow where viscous losses dominate, an intermediate region with secondary flow where inertial losses dominate (albeit still not turbulent) and a region of fully developed turbulent flow (see Figure 1.142) [151]. The transitional Reynolds number from the pure laminar to the secondary-flow regime increases with the ratio of bend length to hydraulic diameter. 

Siggia (18) predicted the same equation from the percolation approach by taking into consideration the hydrodynamic flow, but with

initial growth regime and

intermediate flow stage. 

It is common for industrial pumping and processing equipment to use shear rates that fall in the intermediate shear regime from about 10 to 1000 s 1 as illustrated in Table I. A convenient way to summarize the flow properties of fluids is by plotting flow curves of shear stress versus shear rate (r vs 7). These curves can be categorized into several rheological classifications (Figure 3). Suspensions are frequently pseudoplastic as shear rate increases viscosity decreases. This is also termed... 

Answer For boundary layer mass transfer across gas-liquid interfaces, X = and y =. In the laminar flow regime, 2 = 5. This problem is analogous to one where the bubble is stationary and a liquid flows past the submerged object at intermediate Reynolds numbers. 

According with response curves (Fig. 3.8) tubular turbulent apparatus relate to apparatus of intermediate type, i.e. there is a deviation from plug-flow regime firstly at the expense of reverse current. The degree of the last one is determined by longitudinal mixing coefficient E. 

Dimensionless numbers are pure numbers that are expressed as ratios of physical properties and are used to classify or understand a system. Already, in Chapter 6, we defined the Reynolds number as the ratio of the fluid s inertial forces, pud, to its viscous force and used it to differentiate between the laminar, intermediate, and turbulent flow regimes. In the laminar flow regime, viscous forces dominate but, as the velocity increases, the Reynolds number increases and inertial forces predominate in the turbulent regime. 

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