A parallel integration scheme of eigen solutions for duct acoustic modes

摘要

Acoustic liners are widely applied in the aircraft engines to reduce the emission of noise. It is important to acquire the accurate acoustic modes in the duct. A parallel integration scheme based on the classical Runge-Kutta method is proposed to calculate the eigenvalues of duct acoustic modes with a uniform mean flow and an impedance boundary condition. The scheme solves the left-propagating modes and the right-propagating modes separately by a numerical integration method. The transverse wavenumbers and the axial wavenumbers of different acoustic modes are integrated simultaneously. The scheme can deal with Ingard-Myers boundary condition and other modified boundary conditions without any transcendental hypothesis in duct acoustics. The convected instability of at most two duct modes is detected via the parallel integration scheme, which is also verified by the Briggs-Bers stability criterion. The parallel integration scheme would give full numerical solutions of duct acoustic modes. Comparing with previous results, it provides a better way to determine the stability of duct modes directly.