Near-bottom flow velocity

The axial impeller discharges fluid mainly axially, parallel to the impeller shaft. The fluid is pumped through the impeller, normally towards the bottom of the tank. Since the flow make a turn at the bottom, the velocity vectors fan out radially at approximately D/2 beneath the impeller. Then, the flow moves along the bottom and rises near the tank wall. Analyzing the flow pattern, one can see that a back-flow eddy region is formed directly under the impeller. Upon examining the flow around the axial impeller one can also observe that a large contribution to the inlet flow enters radially at the tip of the impeller blade. This pattern is shown in Fig 7.1. 

Movement of a soluble chemical throughout a water body such as a lake or river is governed by thermal, gravitational, or wind-induced convection currents that set up laminar, or nearly frictionless, flows, and also by turbulent effects caused by inhomogeneities at the boundaries of the aqueous phase. In a river, for example, convective flows transport solutes in a nearly uniform, constant-velocity manner near the center of the stream due to the mass motion of the current, but the friction between the water and the bottom also sets up eddies that move parcels of water about in more randomized and less precisely describable patterns where the instantaneous velocity of the fluid fluctuates rapidly over a relatively short spatial distance. The dissolved constituents of the water parcel move with them in a process called eddy diffusion, or eddy dispersion. Horizontal eddy diffusion is often many times faster than vertical diffusion, so that chemicals spread sideways from a point of discharge much faster than perpendicular to it (Thomas, 1990). In a temperature- and density-stratified water body such as a lake or the ocean, movement of water parcels and their associated solutes will be restricted by currents confined to the stratified layers, and rates of exchange of materials between the layers will be slow. 

The gas moves in plug flow with an axial velocity of along the duct length the spherical particles have the same axial velocity. However, near the bottom surface of tbe chamber, tbe wall region, the gas flow velocity is significantly reduced. The wall region thickness is 3g. 

Figure 6.4 uses the same simulation result as that shown in Fig. 6.2, with the fluid flow velocity profiles, where the flow in the porous package is defined by the Brinkman equation, but at different cross-section lines along the package. The solid line is the same as that in Fig. 6.2, i.e. the middle of the package (Plate I, y=0), the dotted line is near the top of the package (y=0.06) and the dashed line is near the bottom of the package (y=-0.06). 

Figure 6-32, taken from Govier and Aziz, schematically indicates four flow pattern regions superimposed on a plot of pressure gradient vs. mixture velocity = Vl -t- V5 = Qj + ( s)/A where and Vs are the superficial liquid and solid velocities, Qi, and ( 5 are liquid and solid volumetric flow rates, and A is the pipe cross-sectional area. is the transition velocity above which a bed exists in the bottom of the pipe, part of which is stationary and part of which moves by saltation, with the upper particles tumbling and bouncing over one another, often with Formation of dunes. With a broad particle-size distribution, the finer particles may be fully suspended. Near V 4, the pressure gra-... 

Fig.2 and Fig.3 show the typical liquid velocity and gas hold up distribution in the ALR. From the figures, one notices that the cyclohexane circulates in the ALR under the density difference between the riser and the downcomer. An apparent large vortex appears near the air sparger when the circulating liquid flows fi om the downcomer to the riser at the bottom. In the riser, liquid velocity near the draft-tube is much larger than that near the reactor wall, the latter moved somewhat downward. The gas holdup is nonuniform in the reactor, most gas exists in the riser while only a little appears in the dowmcomer. 

Where there is a wide range of particle sizes in the powder, fluidisation will be more even in a bed that is tapered so as to provide the minimum cross-section at the bottom. If the pressure gradient is low and the gas does not therefore expand significantly, the velocity will decrease in the direction of flow. Coarse particles which will then tend to become fluidised near the bottom of the bed assist in the dispersion of the fluidising gas. At the same time, the carry-over of fines from the top will be reduced because of the lower velocity at the exit. 

---