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has been cited by the following article:

• 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.