Mixing in a Closed Room by the Action of Two Fans

The mixing induced by two constant flow rate fans, which vary periodically in direction, is studied as a function of the period of oscillation of the fans. The three-dimensional equations of motion are integrated to determine the particle trajectories. As first shown by Aref’s work on a two-dimensional map, mixing may be greatly enhanced by unsteadiness. It is found that trajectories can be trapped in a restricted region by surfaces which function similarly to KAM tori in two dimensions. Results are presented for the largest Lyapunov exponent and the correlation dimension as a function of oscillation period. These results may be used to determine the conditions for good mixing.