Near field phased array model of injector system scattering in annular combustors

A common geometry used in energy and propulsion systems is a circular or annular duct with periodic arrays of discrete injectors. Full three dimensional modeling of the wave dynamics of these systems is computationally expensive. Moreover, in many cases, it is the features of the wave field, such as dominant wave propagation directions, that are of primary interest. This paper presents a reduced order model for such complex geometries focused on capturing these dominant wave features, utilizing a near-field, phased array model. A spinning disturbance interacting with a periodic injector array leads to scattered waves generated at each injector. These scattered waves have regular and discrete phase differences, analogous to acoustic phased arrays, and lead to dominant wave scattering in preferential directions. Net azimuthal flow of the gas also influences this dominant scattering direction through convection. This paper maps out the dependence of wave scattering directions, particularly forward and backward scattering, upon number of injectors, wave speed, flow Mach number, and number of waves.