## Description of Oxygen Transfer Power Consumption and Efficiency by Surface Aerators Using Dimensionless Numbers

With the results from above, we return to the experimental results during surface aeration with an aeration turbine (see Fig. 5.6). Oxygen transfer rate OTR, power consumption P/V and efficiency E were measured in clean water and plotted in Fig. 5.7. Now we will describe these results for a series of aerators (Simplex, Type A), which are characterized by geometric similarity.

However, the problems to solve are more difficult than those in Section 5.5.2:

• The stirred tank is aerated and buoyancy forces must be considered. Dimensional analysis now yields a set of three dimensionless numbers:

with Froude number:

• A further number must be developed which gives information about the rate of oxygen transfer. The relevance list is:

Using the method described above, we obtain:

with:

I a* (dimensionless surface tension) (5.92)

Let us look at the system air/water and we can conclude that all material coefficients are constant, resulting in:

Therefore, the set of dimensionless numbers for air/water is:

If we do not consider aerators with small diameter d and low rotation speed n, Re > 104 is valid (turbulent region of the flow) and Re does not influence Ne and Y remarkably. We can conclude that it must be possible to describe the results using (Zlokarnik 1979, 1980):

and:

Both results obtained by experiments can be represented as straight lines if we use double-logarithmic plots (Figs. 5.14 and 5.15). But the author chose to use a larger region in Fr numbers (0.02 < Fr < 0.8) for power measurement (Fig. 5.13) compared with oxygen transfer measurements (0.08 < Fr < 0.35; Fig. 5.14).

The straight lines in both figures are given by:

and:

Y = 1.25 ■ 10-3 Fr089 (5.97) From these equations a dimensionless efficiency can be defined as:

E* = — (5.98) Ne and with Eqs. (5.96) and (5.97):

can be used together with Eq. (5.96) and Eq. (5.97) for scale-up calculations, if the dimensionless geometric numbers are (nearly) constant.

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