Radial flow variation

All styles and designs of mixing impellers produce either an axial-flow or a radial-flow of the fluid during the impeller rotation. There are, of course, degrees of variation of each of these patterns, v. hich then become a pan of the selection and specifying process to achieve tire mixing objective. 

For electrolytes of low resistivity, it can be shown that the electrode potential distribution within cylindrical equipment is often very closely approximated to by neglecting the radial potential variation i.e. by assuming current flows only axially " . Astley has demonstrated that sea-water systems with diameters of up to at least 500 mm can be examined making a unidirectional current flow assumption. 

Taylor (T2) and Westhaver (W5, W6, W7) have discussed the relationship between dispersion models. For laminar flow in round empty tubes, they showed that dispersion due to molecular diffusion and radial velocity variations may be represented by flow with a flat velocity profile equal to the actual mean velocity, u, and with an effective axial dispersion coefficient Djf = However, in the analysis, Taylor... 

In addition to using different catalyst flow patterns in packed and slurry reactors, the flow can be varied to attain different catalyst contacting patterns. As shown in Figure 7-27, many flow patterns such as radial flow and fluid recirculation can be used. These allow variation of the flow velocity u for a given reactor size and residence time x. These recirculation flow patterns approach the flow of recycle reactors so the reactor performance approaches that of a CSTR at high recirculation. 

Clearly, in the absence of a radial temperature or velocity gradient, no radial mass transfer can exist unless, of course, a reaction occurs at the bed wall. When a system is adiabatic, a radial temperature and concentration gradient cannot exist unless a severe radial velocity variation is encountered (Carberry, 1976). Radial variations in fluid velocity can be due to the nature of flow, e.g. in laminar flow, and in the case of radial variations in void fraction. In general, an average radial velocity independent of radial position can be assumed, except from pathological cases such as in very low Reynolds numbers (laminar flow), where a parabolic profile might be anticipated. 

In the steady stagnation-flow formulation the thermodymanic pressure may be assumed to be constant and treated as a specified parameter. The small pressure variations in the axial direction, which may be determined from the axial momentum equaiton, become decoupled from the system of governing equations (Section 6.2). The small radial pressure variations associated with the pressure-curvature eigenvalue A are also presumed to be negligible. While this formulation works very well for the steady-state problem, it can lead to significant numerical difficulties in the transient case. A compressible formulation that retains the pressure as a dependent variable (not a fixed parameter) relieves the problem [323],... 

Spiral vortex. If a radial flow is superimposed upon the concentric flow previously described, the path lines will then be spirals. If the flow goes out through a circular hole in the bottom of a shallow vessel, the surface of liquid takes the form of an empty hole, with an air core sucked down the hole. If an outlet symmetrical with the axis is provided, as in a pump impeller, we might have a flow either radially inward or radially outward. If the two plates are a constant distance B apart, the radial flow with a velocity Vr is then across a series of concentric cylindrical surfaces whose area is 0.2nrB. Thus Q = 2nrBVr is a constant, from which it is seen that rVr is a constant. Thus the radial velocity varies in the same way with r that the circumferential velocity did in the preceding discussion. Hence the pressure variation with the radial velocity is just the same as for pure rotation. Therefore the pressure gradient of flow applies exactly to the case of spiral flow, as well as to pure rotation. 

The assumption of plug flow is valid as long as radial transport processes occur more rapidly than those processes that create radial concentration variations. A more detailed discussion of the implications of this assumption has been given by Edwards and Newman (381. 

An ideal stirred bioreactor is assumed to be well mixed so that the contents are uniform in composition at all times. The plug-flow bioreactor (PFB) is an ideal tubular-flow bioreactor without radial concentration variations. The nutrient concentration of an ideal batch bioreactor after time t will be the same as that of a steady-state PFB at the longitudinal location of the residence time. Therefore, the following analysis applies for both the ideal batch bioreactor and the steady-state PFB. 

Kubec el al. (1974) developed a model for a radial flow quench type converter. Kjaer (1985) and Michael and Filippo (1982) formulated model equations accounting for radial as well as axial variation of temperature and concentration. They found that radial variations have insignificant influence on the model predictions. 

Solutions for the Flow with Re < 400. It has been found that the effects of axial momentum diffusion and radial pressure variation are significant only in the duct inlet of x < 0.005. Chen [11] obtained the dimensionless hydrodynamic entrance length L y and the fully developed incremental pressure drop number K(< >), which are given by... 

Stone, H.A. and Brenner, H., Dispersion in flows with streamwise variations of mean velocity Radial flow. Ind. Eng. Chem. Res., 1999, 38 851-854. 

Without Thermal End Effects Neglecting the flow effect and considering only the steady-state radial temperature variation reduce Eq. 1 to... 

DT and FBT. These relatively high values of a indicate that radial flow impellers are more affected by variations in CIT as compared to the axial/mixed flow impellers. For CIT>02, the double 8 pattern exists. Chapman etal. (1983)measured for C/T>0.2 and found that increasing the clearance results in higher values of but no explicit relationship was reported. These authors suggest that large DT impellers located at relatively low clearance yield solid suspension at relatively low power input The empirical constant a was found to be a weak function of DIT. 

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