Drag coefficient Schiller-Naumann

Fd was evaluated from the drag coefficient at bubble Reynolds number and the projected area of the bubble. As the Reynolds number varied from 2 to 700, the drag coefficient CD was evaluated by the Schiller and Naumann (S4) equation ... 

Schiller, L. and Naumann, A.Z., Uber die grundlegenden Berechnungen bei der Schwerkraftaufbereitung [A fundamental drag coefficient correlation], Z. Ver. Dent. Ing., 77 (1933) 318-320. 

The Schiller and Naumann equation was used for the estimation of the drag coefficient and the pressure drop of the air flowing through the curtain of the falling solids to that of air flowing through the free cross section of the drum for estimation of the effect of the particle shielding. 

This way, the intuitively anticipated diffusion of bubbles from a region with many bubbles to a dilute region is back into the theory not in the mass balances, but rather in the momentum balances, as it is after all a consequence of the drag force. The diffusion coefficient in Eq. (3.11) is estimated from the ratio of turbulence and bubble response times and the turbulent kinetic energy of the liquid phase. Finally, for the drag coefficient various relations are present, for example, based on Schiller and Naumann [47] ... 

Schiller, L., Naumann, A. (1933). A drag coefficient correlation. Zeitschrift des Vereins Deutscher Ingenieure, 77, 318-320. 

Fig. 10.21 Drag coefficient in dependence of agglomerate Reynolds number determined with AES and VES (closed line corresponds to the standard drag according to Schiller and Naumann 1933) [40]...

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