Acoustic Impedance of Outlet of a Hard-Walled Unbaffled Cylindrical Duct for Multimode Incident Wave

J. Jurkiewicza, A. Snakowskab and D. Smolikc aFaculty of Electrical Engineering, Automatics, Computer Science and Electronicsand Electronics, AGH, al. A. Mickiewicza 30, 30-059 Cracow, Poland bFaculty of Mechanical Engineering and Robotics, AGH, al. A. Mickiewicza 30, 30-059 Cracow, Poland cFaculty of Physics and Applied Computer Science, AGH, al. A. Mickiewicza 30, 30-059 Cracow, Poland

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In the paper, the specific acoustic impedance of outlet of an unbaffled duct for incident wave composed of one or many circumferential cut-on duct modes has been derived and presented on graphs. When considering the multimode excitation the equal energy per mode principle and random phases have been assumed. Experimentally verified assumption on equal energy per mode allows for quantitative analysis of the sound field and thus provides more physical insight into the in-duct and out-duct phenomena. The assumption of random phase was implemented by means of the Monte Carlo method and so the expected value, the standard deviation and the percentile curves of the impedance were presented. Numerical data obtained according to the derived theoretical formulae for single and multimode incident wave manifest strong modal character and dependence on the modes phases. The assumption of multimode incident wave has brought the theoretical model closer to what is being observed in practice, especially when ducts of large radius, such as heating and air conditioning systems or turbojet engines, are considered.

DOI: 10.12693/APhysPolA.119.1061 PACS numbers: 43.20.Mv, 43.20.Rz