Efficient polynomials based method for a temporal stability investigation in a swirling flow stability problem

摘要

The main motivation for a temporal stability investigation of initially localized perturbations in a swirling flow stability problem consists in pointing out the critical frequencies at which instability can sets in, an important key in predicting and understanding the flow particularities. The linearized disturbance equations define a second order ordinary differential equation with non-constant coefficients which we solve in order to determine the critical frequency in different physical parameters spaces. A non-classical polynomials based spectral method is proposed for the numerical treatment of the resulting generalized eigenvalue problem governing the stability of the flow. Numerical investigation are performed in the inviscid case for a moderate level of swirl and dominant temporal instability modes are retrieved for each Fourier component pair. The obtained values of the growth rate associated with the most amplified wavenumber are compared with existing inviscid temporal instability evaluations and good agreements are found.