Calculations of edgetone flow with forced longitudinal oscillations

Abstract

Numerical calculations were carried out to study the effect of forced, symmetric, longitudinal flow oscillations on the inherent, strongly antisymmetrical oscillations of a previously studied edgetone flow at a Reynolds number of 450. The flow consists of a two-dimensional jet issuing from a nozzle and impinging on a body with a wedge-shaped leading edge. The flow is assumed to be incompressible, laminar and two-dimensional, and a finite-difference vorticity/stream-function formulation of the Navier-Stokes equations is employed. Three cases were considered with various combinations of forcing frequency and amplitude. It was found that for the two cases with large forcing amplitudes, the naturally dominant flow frequencies lock-in to the forcing frequency and its harmonics. In the third case the forcing amplitude was smaller and lock-in was not observed but the forced oscillations still had a significant impact on the flow. Mode competition between symmetric and antisymmetric modes is discussed for the three cases along with the manner in which the jet vortical structure is altered as a function of time and space. Results for all three cases are presented in the form of computer drawn equivorticity lines and plots of frequency spectra for the jet oscillations and for the pressure on the wedge.