Duct spinning mode's particle velocity imaging with in-duct circular microphone array

Nowadays, the measurements within a duct have to be conducted using in-duct microphone array, which is unable to provide information of complete acoustic solutions across the test section. In this work, an imaging method of acoustic spinning modes propagating within a circular duct simply with surface pressure informa- tion is introduced. The proposed method is developed in a theoretical way and is demonstrated by a numerical simulation case. The fundamental idea behind the testing method was originally developed in control theory for ordinary differential equations. Spinning mode propagation, however, is formulated in partial differential equations. A finite difference technique is used to reduce the associated partial differential equations to a clas- sical form in control theory. The observer method can thereafter be applied straightforwardly. The algorithm is recursive and thus could be operated in real-time. The observer error of the method is analyzed then. A numerical simulation for a straight circular duct is conducted. The acoustic solutions on the test section can be reconstructed with a good agreement to analytical solutions. The results suggest the potential and applications of the proposed method.