The methodology to excite acoustic modes in the cylindrical duct with small axial gradients of diameter and temperature

The Spinning Mode Synthesizer (SMS) is an effective test rig for studying noise propagation and radiation in aeroengines and gas turbines for investigating the mechanism of combustion oscillation, where specific acoustic modes are generated through precise amplitude modulation and phase shifting of an artificial sound source system. Conventional SMSs neglect the variation of cross-sections and work at room temperature, and fail to correctly characterize the propagation of acoustic modes in combustors. A methodology is proposed to excite duct modes in cylindrical ducts with small axial gradients of diameter and temperature. The variation of axial wavenumber and sound velocity separately influenced by varying diameter and temperature gradients is theoretically investigated and considered in the process of mode excitation. The coefficients of the observation matrix for acoustic field propagation are derived as functions corresponding to the axial coordinate by solving the three-dimensional wave equations using the Wentzel–Kramers– Brillouin (WKB) approximation. Moreover, the transition of cut-on modes into cut-off modes at some special wavenumber dependent on the diameter and temperature of the duct is theoretically investigated. Through the input of target modes and inversion of the obtained observation matrix, the amplitude and phase angles of the loudspeaker array required by mode excitation are determined. A spinning mode synthesizer is established on a cylindrical duct with a varying diameter to validate the proposed method of mode excitation, equipped with 24 loudspeakers distributed in 3 rings, and both azimuthal modes and radial modes are successfully generated in the experiments. The amplitude of target modes stimulated by the facility is 10 dB higher than any other cut-on modes across the operating frequency range, demonstrating a great signal-tonoise ratio and robustness of the proposed method.