Detection of the dominant acoustic modes emitted by turbomachinery using compressed sensing

Due to the aerodynamic interaction of turbomachinery components, as e.g. rotor and stator in axial turbomachinery or rotor and casing tongue in radial compressors, in a lot of cases only a small sub-set of acoustic modes is excited in the connected flow ducts. The knowledge of the dominant duct modes enables insight into the generating mechanisms and allows the calculation of the sound power emitted by the turbomachine. In this paper a method is presented, which allows the detection of the dominant modes with reduced efforts compared to standard methods. Typically, for the determination of the azimuthal mode orders Discrete Fourier Transformation or Least Squares Fit are used. For these methods, the amount of microphones needed for an exact reconstruction is based on the Nyquist criteria. The introduced method, compressed sensing, has the ability to reconstruct the dominant modes for underdetermined systems on the basis of non-equidistant microphone arrays. The reconstructed solutions of synthetic mode fields via compressed sensing are compared with Discrete Fourier Transformation and Least Squares Fit. Also, in practical applications microphone defects occur and is a circumstance that is accounted for in the presented study concluding the advantages and disadvantages of all three methods presented.