Terminal-tube velocity effect

Figure 19.5 Effect of terminal-tube velocity on exchanger performance.

The effects of excessively low tube-side velocity will be to damage the tube bundle due to terminal tube velocity problems. 

The walls of the vessel containing the liquid exert an extra retarding effect on the terminal falling velocity of the particle. The upward flow of the displaced liquid, not only influences the relative velocity, but also sets up a velocity profile in the confined geometry of the tube. This effect may be quantified by introducing a wall factor, /, which is defined as the ratio of the terminal falling velocity of a sphere in a tube, V, to that in an imconfined liquid, V, viz.. 

To perform accurate viscosity measurements with the falling-body technique, various corrections (fall-tube dimensions, effect of fall-tube ends, terminal velocity, falling-body shape, position of the fall-tube) ought to still to be considered (Wakeham et ai, 1991). 

Here Kjj is obtained from Fig. 9.5. Equation (9-27) and the equations of Chapter 5 can be used to determine the decrease in Sh for a rigid sphere with fixed settling on the axis of a cylindrical tube. For example, for a settling sphere with 2 = 0.4 and = 200, Uj/Uj = 0.76 and UJUj = 0.85. Since the Sherwood number is roughly proportional to the square root of Re, the Sherwood number for the settling particle is reduced only 8%, while its terminal velocity is reduced 24%. As in creeping flow, the effect of container walls on mass and heat transfer is much smaller than on terminal velocity. 

For large bubbles where inertia effects are dominant, enclosed vertical tubes lead to bubble elongation and increased terminal velocities (G7). The bubble shape tends towards that of a prolate spheroid and the terminal velocity may be predicted using the Davies and Taylor assumptions discussed in Chapter 8, but with the shape at the nose ellipsoidal rather than spherical. The maximum increase in terminal velocity is about 16% for the case where 2 is small (G6) and 25% for a bubble confined between parallel plates (G6, G7) and occurs for the enclosed tube relatively close to the bubble axis. 

Support the anemometer sensor probe with a suitable stand so that optimum control of test positions can be maintained. Orient the probe perpendicular to the velocity flow vector being measured. Measure and record the velocity at the approximate center of each filter area of 0.37 m (4 ft ). The probe should be positioned at a distance of no more than 15 cm (6 in.) from the filter face. The effect of nonuniform velocity across the filter face can be minimized by taking more readings per unit area or by using a tube array sensor. Air flow volume test The supply air flow volume is measured by using a flow hood in a manner that includes all of the air issuing from each terminal filter or supply diffuser. The air flow volume test should be performed as follows ... 

There is a crucial difference between the two situations however and this can be seen from the sign of the reflection coefficient. In the closed termination case, the tube ends in a solid wall and the reflection coefficient is -1. From Equation 11.16b we can see that in such a case the volume velocity will be 0. If we find the equivalent pressure expressions for Equation 11.16b, we see that the pressure terms add, and hence the pressure at this point is (pc)/.4i. Intuitively, we can explain this as follows. The solid wall prevents any particle movement and so the volume velocity at this point must be 0. The pressure however is at its maximum, as the wall stopping the motion is in effect an infinite impedance, meaning no matter how much pressure is applied, no movement will occur. In the open end situation, when the reflection coefficient is 1, we see from Equation 11.16b that the volume velocity is at a maximum and now the pressure is 0. Intuitively, this can be explained by the fact that now the impedance is 0, and hence no pressure is needed to move the air particles. Hence the pressure p L, t) is 0, and the volume velocity is at its maximum. 

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