Numerical Simulation of the Hole-Tone Feedback Cycle Based on the Discrete Vortex Method and the Acoustic Analogy

An axisymmetric numerical simulation approach to the holetone feedback problem is developed. It is based on the discrete vortex method and an ‘acoustic analogy’ representation of flow noise sources. The shear layer of the jet is represented by ‘free’ discrete vortex rings, and the jet nozzle and the end plate by bound vortex rings. A vortex ring is released from the nozzle at each time step in the simulation. The newly released vortex rings are disturbed by acoustic feedback. The simulated frequencies f follow the criterion L/u_c + L/c₀ = n/f where L is the gap length, u_c is the shear layer convection velocity, c₀ is the speed of sound, and n is a mode number (n = 1/2, 1, 3/2, ...). This is in agreement with experimental observations. The numerical model also display mode shifts (jumps in the chosen value of n), as seen in experiments.