A novel extremum seeking scheme for closed-loop jet control

Abstract

Jet control is of great interest to a wide range of industrial and environmental applications. This work presents an investigation on the closed-loop control of a turbulent round jet for enhancing the jet mixing. The Reynolds number ReD range is 7333 to 9600 based on the jet exit diameter D and the exit velocity Ue. A single unsteady minijet is deployed upstream of the jet exit, which is produced through the on-off state of an electromagnetic valve. The open-loop control is investigated first. It has been found that, given the duty cycle a and volumetric flow rate ratio Cm of the minijet to that of the main jet, the decay rate K of jet centerline mean-velocity exhibits a maximum at the frequency ratio fe/f0  0.5, where fe and f0 are the excitation frequency of the minijet and the preferred mode frequency of the natural main jet, respectively. A novel extremum seeking closed-loop scheme is then investigated, with a view to achieving the optimal jet control performance automatically. The feedback signal is provided by the jet decay rate K1 of jet centerline running-mean velocity measured by a hot-wire, based on which the output voltage signal controls the frequency of the electromagnetic valve. Comparing with classical extremum seeking schemes, the present scheme introduces an input estimation error to adjust adaptively the excitation frequency, thus reducing greatly the steady-state oscillation and hence enhancing K1. Furthermore, this scheme is robust when ReD and initial fe are separately changed.