NUMERICAL INVESTIGATION OF SPINNING MODE TRANSMISSION THROUGH VARIABLE AREA ANNULAR DUCTS WITH FLOW

Understanding sound propagation through variable area ducts continues to be important for controlling turbomachinery noise. In analytical treatment of the problem it is usually assumed that duct cross sections vary slowly and no mode scattering takes place. It is the purpose of this work to investigate numerically the effects of cross-sectional changes of varying degree on transmission of acoustic modes typical to turbomachinery. First, sound fields of interest through such ducts are obtained numerically by solving the linearized Euler equations in frequency domain. Then, the acoustic fields are analyzed by an eigenmode decomposition approach applied to the whole length of the duct. This approach is based on linearized Euler equations, and hence enables identification of both the pressure and velocity fields associated with each of the downstream and upstream propagating waves. In this way a power balance between all relevant wave components is easily established revealing the details of the acoustic processes through the duct. Results indicate that modal scattering out of an incident mode into other propagating modes is observed mostly for the mid-cut-on range of radial orders for the plane to mid-cut-on range of azimuthal order modes