A reinterpretation of the Odar and Hamilton data on the unsteady equation of motion of particles

Abstract

The experimental data and correlations derived by Odar and Hamilton have been the basis of studies that included the history term in the expression of the unsteady drag. Recent studies have shown that the value of the added mass coefficient is constant and equal to ½ over a very large range of Reynolds numbers. Recent studies on the history term have proven that its form is not correct at high Re. However, the experimental data are accurate at low Re and, most probably, they represent the most reliable set of experimental data on the unsteady force on solid spheres. We conducted a study to re-calculate the functional form of the history term in the unsteady equation of motion at low Re and to derive a new correlation for the so-called “history force coefficient,” Δ_H. The new correlation is expressed in terms of the Reynolds and Strouhal numbers of the particle. © 2010 American Institute of Chemical Engineers AIChE J, 2011