The dynamics of vortex amplifiers. I - Analytical model. II - Dynamic measurements and comparison with model predictions

A semiempirical technique for the dynamic modeling of vortex amplifiers (VA) is demonstrated for a particular VA geometry. The model parameters are determined explicitly from the amplifier static characteristics except for two which are estimated from measurements of the VA dynamic response; the two are time constants associated with the chamber time delay and the vortex rotational inertia. The model is linearized about a working point and is given in terms of an admittance matrix. In addition, a general experimental procedure is described for determining the linearized transfer admittances of the VA. The flow response at the ports to a measured pressure perturbation applied to any one of them was determined with a hot-wire anemometer. Self and transfer admittances were determined with a dual-channel spectrum analyzer. Measurements at two working points compared well with those predicted by the theoretical model of Boucher and Kitsios (1985).