ON THE DRAG COEFFICIENT AND THE CORRECT INTEGRATION OF THE EQUATION OF MOTION OF PARTICLES IN GASES

A great deal of work has been accomplished in the area of air particle flows during the last decade. The application of numerical techniques in fluid flows resulted in high activity on the subject of computational fluid mechanics with particles. Among the models developed for the treatment of particle flows in air is the Particle-Source-In Cell (PSI-CELL) model first introduced by Crowe and his coworkers. The techniques of this model were subsequently used by others, including the works in the references. In order to make the numerical calculations easier all the above use an integrated form of the equation of motion for the particles. The partile drag coefficient is the main input to this equation and is obtained by an empirical relation. This note aims at pointing out how an exact solution to the particle equation of motion can be obtained using the drag coefficient. It also shows the discrepancies in the obtained results stemming from other approximate solutions or from different drag coefficient expressions.