TITLE:
Predicting the Two-Phase Liquid-Solid Drag Model Using the Calculus of Variation
AUTHORS:
Hamid Reza Nazif, Amir Hossein Javadi, Neda Fallahnezhad
KEYWORDS:
Calculus of Variations, Drag Coefficient, Ergun Pressure Drop, Fluidization
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.1,
January
11,
2018
ABSTRACT: The simplified momentum equations of the two-phase
flow have been adopted as the basic assumptions in this study. For vessels of
small diameter, the shear stress becomes important and the friction pressure
drop proposed by Ergun considers this effect by involving the wall effect. By
replacing the Ergun pressure drop and the first order velocity term for
particles drag model in the momentum equations, the relation for the drag
coefficient versus the volume fraction is obtained. The calculus of variations
is used with certain restriction for extremization of this drag coefficient. An
analytical correlation for the drag coefficient is obtained depending on the
volume fraction of “fluid particles”. The drag function obtained in previous
studies does not match with the empirical data in the bed volume fraction range of [0.45 to 0.59]. Therefore, the function is
modified and the results are better adjusted with the empirical data.