Excitation and global calibration of duct modes with high orders and complex mixtures inside a cylindrical duct with flow

The spinning mode synthesizer is of great significance to the study of the propagation and radiation of aerodynamic noise in the cylindrical duct with flow as well as the evaluation of noise reduction with sound liners, working by controlling the array of loudspeakers and generating the specific distribution of the acoustical mode inside the duct. High-order circumferential modes, radial modes and their mixtures should be excited accurately with the manipulation of the multiple-rings array of loudspeakers. However, due to the systematic error of the loudspeaker, significant interference modes are generated simultaneously with the target mode, remarkably affecting the accuracy of mode excitation. A mode excitation method based on the least square and global calibration is proposed to motivate the target duct mode inside a flow duct and eliminate the influence of loudspeakers' system error on mode synthesizing. Through the global modeling of the system error of the loudspeaker sound source, the global calibration factor and flow field correction factor are introduced to convert the problem of solving the system error of each loudspeaker in the case of the flow field into the mode identification problem of a single loudspeaker in the case of no flow. The complex calibration factor of each loudspeaker is solved by matrix transformation and the least square method, after which the amplitude and phase excitation correction of the loudspeaker is realized. The presented method is applied to the spinning mode synthesizer in SJTU, whose experimental results indicate that the intensity of the interference modes is significantly suppressed, and the modal coefficient signal-to-noise ratio (SNRA) of the target excitation modes is greater than 15 dB within the operating frequency range.