In-duct flow computation and acoustic propagation using the admittance multimodal formulation

A multimodal method for computing the potential base flow and propagating acoustic perturbations inside axisymmetric ducts is presented. Instead of using the standard modal basis, a polynomial basis is used in the radial direction to reduce the computational cost of the method, but this introduces non-physical high-order modes. The impact of these modes on the stability of the calculation is examined, and for the acoustic computation, a modification of the axial integration is proposed to improve the conditioning of the matrices involved. The flow computation is achieved by applying the method (initially devoted to acoustics) at a zero frequency without convective effects, by modifying the definition of the admittance at the exit of the duct, and by performing an induction process on the density. The method is validated against a finite element method for ducts with hard walls or lined walls. The results show that the proposed multimodal method is very efficient in computing the mean flow and propagating the sound disturbances inside axisymmetric ducts.