An analytical model of the dynamics of reattaching jets

Abstract

A jet that emerges from a nozzle and attaches to an inclined, setback wall is studied. The reattaching jet is the canonical element of most fluidic devices, and the aim of this paper is to improve the understanding of its dynamics. An analytical model is developed that describes the dynamic behavior of the jet position in response to acoustic excitation. A novel, unsteady jet curvature equation is derived from first principles, which forms the basis of the model. The Görtler velocity profile for a plane, turbulent jet is assumed, and an alternative approach to determining its virtual origin is used. A novel approach to modeling the momentum balance at the jet reattachment point is demonstrated to predict the observed behavior in response to acoustic excitation. The resulting model is linearized at a series of operating points informed by data from the literature at a range of flow rates, wall setback distances, and gas types. A Monte Carlo analysis is conducted to quantify the model sensitivity to parameter uncertainty. The bandwidth of the jet response to acoustic excitation is demonstrated to depend linearly on jet velocity.