A throttling mechanism sustaining a hole tone feedback system at very low Mach numbers

This study investigates the sound produced when a jet, issued from a circular nozzle or hole in a plate, goes through a similar hole in a second plate. The sound, known as a hole tone, is encountered in many practical engineering situations. Direct computations of a hole tone feedback system were conducted. The mean velocity of the air jet was 10 m s^-1. The nozzle and the end plate hole both had a diameter of 51 mm, and the impingement length between the nozzle and the end plate was 50 mm. The computational results agreed well with past experimental data in terms of qualitative vortical structures, the relationship between the most dominant hole tone peak frequency and the jet speed, and downstream growth of the mean jet profiles. Based on the computational results, the shear-layer impingement on the hole edge, the resulting propagation of pressure waves and the associated vortical structures are discussed. To extract dominant unsteady behaviours of the hole tone phenomena, a snapshot proper orthogonal decomposition (POD) analysis of pressure fluctuation fields was conducted. It was found that the pressure fluctuation fields and the time variation of mass flows through the end plate hole were dominantly expressed by the first and second POD modes, respectively. Integrating the computational results, an axisymmetric throttling mechanism linking mass flow rates through the hole, vortex impingement and global pressure propagation, is proposed.