Blade linear velocity

In Figure 9, the upper line represents the viscous layer, which shows the progressive development of the linear velocity profile. The thickness at any position relative to the blade is given approximately as... 

Almost all flows in chemical reactors are turbulent and traditionally turbulence is seen as random fluctuations in velocity. A better view is to recognize the structure of turbulence. The large turbulent eddies are about the size of the width of the impeller blades in a stirred tank reactor and about 1/10 of the pipe diameter in pipe flows. These large turbulent eddies have a lifetime of some tens of milliseconds. Use of averaged turbulent properties is only valid for linear processes while all nonlinear phenomena are sensitive to the details in the process. Mixing coupled with fast chemical reactions, coalescence and breakup of bubbles and drops, and nucleation in crystallization is a phenomenon that is affected by the turbulent structure. Either a resolution of the turbulent fluctuations or some measure of the distribution of the turbulent properties is required in order to obtain accurate predictions. 

Note that the linear speed of the blades will increase steadily in the radial direction, from the root of the blade to its tip. Hence we have taken the blade velocity, cg, as the average velocity, i.e. the velocity at the midlength of the blade. 

The rotational speed of the rotor, or turbine, increases linearly with flow velocity within + 0.5% over a wide flow range from 10 1 to 20 1 [10]. The turbine speed is typically measured by detecting the pulse of each blade electrically, mechanically, or optically each pulse represents a certain volume of fluid. The flow rate of the fluid is determined by integrating the total number of pulses over a period of time. The accuracy of these meters is better than 1% over a wide range of flow rates [4]. Accuracy is compromised, however, with blade wear, bearing friction due to wear, and when a vapor enters the line for liquid flows [10]. 

By varying the impeller blade dimensions variations in power per unit volume were made at a constant impeller speed. At low power per unit volumes there was a linear increase in k a which correlated with P/V with an exponent of 0.9 to 1.2. yond the breakpoint the exponent relating the P/V dependence was 0.53. In both regions the k,a dependend on the superficial gas velocity to the 0.3 power. Tnese results are similar to those reported earlier by Blakebrough and Sambamurthy (1966) and Hamer and Blakebrough (1963) obtained in smaller scale vessels also using paper pulp suspensions. Other references on the aeration of viscous non-Newtonian fermentation broth are Banks (1977) and Blanch and Bhavaraju (1976). 

Once the material has entered region B it will be subject to an imsteady-state developing-flow situation in the full-developed form the velocity gradient is linear, changing uniformly from the blade velocity at the blade surface to zero at the vessel wall. 

It is noteworthy that the sharpness of the abrading blade does not appear in the theory. Clearly, it must be sufficiently sharp so that only one element of the abrasion pattern is deformed at any one time, but this should not be a severe limitation. This conclusion is broadly confirmed by experiment. The difference in abrasion between a new razor blade and one used for several thousand revolutions is negligible. Cutting thus plays little part in this abrasion measurement. Also, the normal load itself does not appear in the theory, being relevant only insofar as it controls the frictional force F. The rate of revolution used was equivalent to a linear abrading velocity of 3- 1 cm/sec. This velocity is not critical and changing it by a factor of 2 produces an inappreciable effect. 

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