Actually, there is an abundance of information in the literature for 2-blade, flat-blade paddles in unbaffled reactors, if you just know where to look.  Look in Mixing, Principles and Applications, by Sinhi Nagata, Halsted Press, Kodansha Scientific Books, Tokyo, 1975 (which is in English).  Nagata has an empirical correlation relating dimensional ratios to power number in section 1.3.2, starting on page 27.  Figure 1.17 and Figure 1.18 show extensive data for power number as a function of Reynolds number in unbaffled tanks.  The plotted results do not exactly match your dimensional ratios, but your dimensional ratios can be interpolated on the graphs or estimated from the empirical correlation on page 30.

Nagata uses b for blade width, d for impeller diameter and D for tank diameter.  His plotted results include d = 0.8 D and d = 0.5 D and a couple of others for smaller impeller diameter ratios.  Your impeller is d = 0.633 D, for which you can interpolate.  He also has results for b/D = 0.05, 0.1, 0.2, 0.3, 0.5, 0.7, and 0.9.  Your impeller is b/D = 0.244.  What you did not provide, but can calculate, is sufficient information for the impeller Reynolds number of your impeller.  In addition to impeller diameter, you need rotational speed, fluid density and fluid viscosity to calculated Reynolds number.  Because your vessel is not baffled, the swirling motion and vortex depth affect the power number with respect to the rotational speed, even with the same fluid properties.

Impeller Reynolds number equals impeller diameter squared times rotational speed times density divided by viscosity in consistent units to make the Reynolds number dimensionless.  Probably the easiest conversion for you to use is to calculate Reynolds number using impeller diameter in meters, rotational speed in revolutions per second, density in kilograms per cubic meter, and viscosity in Pascals.  You can find your own conversion factors.

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