MULTIMODAL PROPAGATION IN A DUCT WITH VAR YING CROSS-SECTION

Some authors have tried to calculate propagation in a varying cross se ction duct by slicing it into cylindrical elements with length small c ompared to wavelength. This enables to solve the wave equation with th e multimodal decomposition formulation. The results compared favorably with experimental data. However, this approach have certain limitatio ns and we, therefore, wanted to study this problem by writing continuo us equations. First of all, we develop a matricial horns equation exte nding the classical Horn equation. Then, we find a matricial Riccati e quation for the impedance matrix which is symmetric and only depends o n the axial coordinate. This equation for the impedance avoid spurious divergence due to vanishing modes. Finally we are able to get the pre ssure or the velocity field by a calculation of a kind of argument mat rix (similar to the usual jkx for plane wave) with another continuous equation slave to the matrix impedance variation. The computations are performed with a Runge-Kutta method of order 3 and are apllied to a p articular geometry in the case of monopole source the solution of whic h is known for a straight duct.