Velocity, particle axial

The RTD quantifies the number of fluid particles which spend different durations in a reactor and is dependent upon the distribution of axial velocities and the reactor length [3]. The impact of advection field structures such as vortices on the molecular transit time in a reactor are manifest in the RTD [6, 33], MRM measurement of the propagator of the motion provides the velocity probability distribution over the experimental observation time A. The residence time is a primary means of characterizing the mixing in reactor flow systems and is provided directly by the propagator if the velocity distribution is invariant with respect to the observation time. In this case an exact relationship between the propagator and the RTD, N(t), exists... 

Figure 15.2(a). The membrane impedes further penetration of even smaller particles through the porous filter media. In many filtration applications, this filtration mechanism is valid for an axial velocity greater than about 4 to 6 m/s. 

Therefore, when operating in the filter cake mode, the axial velocity should be maintained at a level such that an adequate shear force exists along the filter media to prevent excessive caking of the catalyst that could cause a blockage in the down-comer circuit. For the separation of ultrafine catalyst particles from FT catalyst/wax slurry, the filter medium can easily become plugged using the dynamic membrane mode filtration. Also, small iron carbide particles (less than 3 nm) near the filter wall are easily taken into the pores of the medium due to their low mass and high surface area. Therefore, pure inertial filtration near the filter media surface is practically ineffective. 

Ideally, the axial velocity through the cross-flow unit should be greater than about 4-6 m/s to minimize the boundary layer of particles near the membrane surface. The wax permeate flow from the filter is limited by a control valve actuated by a reactor-level controller. Hence, a constant inventory of slurry is maintained within the SBCR system as long as the superficial gas velocity remains constant. Changes in the gas holdup due to a variable gas velocity are calculated... 

Cross-flow filtration systems utilize high liquid axial velocities to generate shear at the liquid-membrane interface. Shear is necessary to maintain acceptable permeate fluxes, especially with concentrated catalyst slurries. The degree of catalyst deposition on the filter membrane or membrane fouling is a function of the shear stress at the surface and particle convection with the permeate flow.16 Membrane surface fouling also depends on many application-specific variables, such as particle size in the retentate, viscosity of the permeate, axial velocity, and the transmembrane pressure. All of these variables can influence the degree of deposition of particles within the filter membrane, and thus decrease the effective pore size of the membrane. 

There is no radial velocity, and the axial velocity across the radius of the packed bed is uniform. Schwartz and Smith (1953) found that the velocity across the diameter of a packed bed is not uniform for radial aspect ratios (tube-to-particle diameter) less than about 30, due to the significant effect of the increased void space near the wall where the particles are locally ordered. This result has been verified by Hoiberg et al. (1971) for a packed bed reactor with radial aspect ratio about 50. They considered a radial velocity variation suggested by experimental observations with a sharp peak about 15% greater than the mean fluid velocity situated close to the wall. Simulations using their model showed results virtually identical to those obtained with a uniform velocity profile.3... 

Up Instantaneous axial velocity component of particle Greek Symbols... 

Tv i Particle temperature in front of the shock wave Wlk Axial velocity of phase 1 in region k... 

On the basis of the observations in the macroscale, the flow of a fast fluidized bed can be represented by the core-annulus flow structure in the radial direction, and coexistence of a bottom dense region and a top dilute region in the axial direction. Particle clusters are an indication of the heterogeneity in the mesoscale. A complete characterization of the hydrodynamics of a CFB requires the determination of the voidage and velocity profiles. There are a number of mathematical models accounting for the macro- or mesoaspects of the flow pattern in a CFB that are available. In the following, basic features of several types of models are discussed. 

Fig.22. Schematic presentation of a helical-Fl-FFF device (A), the generation of a helical flow in the annular space between a fixed and a constantly rotating cylinder (B) and the separation mechanism (C). The larger particles Y migrate faster towards the outer cylinder and are thus located in regions with lower axial velocity than the slower migrating ones...

Axial velocities of particles and effective diffusion coefficients of solids are constant throughout the reactor. 

FIGURE 4M (a) Left Measured and predicted tangential velocities in a 75-nun hydro-( lone right measured and predicted axial velocities in a 75-nun hydrocydone. (b) Predicted fluid streamlines and particle tirgectories in a 75-nim hydrocyclone. 

In fully developed laminar flow, each fluid particle moves at a constant axial velocity along a streamline and the velocity profile i/(r) remains unchanged in the flow direction. There is no motion in the radial direction, and thus the velocity component in the direction normal to flow is everywhere zero. There is no acceleration since the flow is steady and fully developed. 

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