CUED Publications database

Continuous spectrum growth and modal instability in swirling duct flow

Heaton, CJ and Peake, N (2006) Continuous spectrum growth and modal instability in swirling duct flow. Collection of Technical Papers - 12th AIAA/CEAS Aeroacoustics Conference, 4. pp. 2310-2324.

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Abstract

We present results on the stability of compressible inviscid swirling flows in an annular duct. Such flows are present in aeroengines, for example in the by-pass duct, and there are also similar flows in many aeroacoustic or aeronautical applications. The linearised Euler equations have a ('critical layer') singularity associated with pure convection of the unsteady disturbance by the mean flow, and we focus our attention on this region of the spectrum. By considering the critical layer singularity, we identify the continuous spectrum of the problem and describe how it contributes to the unsteady field. We find a very generic family of instability modes near to the continuous spectrum, whose eigenvalue wavenumbers form an infinite set and accumulate to a point in the complex plane. We study this accumulation process asymptotically, and find conditions on the flow to support such instabilities. It is also found that the continuous spectrum can cause a new type of instability, leading to algebraic growth with an exponent determined by the mean flow, given in the analysis. The exponent of algebraic growth can be arbitrarily large. Numerical demonstrations of the continuous spectrum instability, and also the modal instabilities are presented.

Item Type: Article
Subjects: UNSPECIFIED
Divisions: Div A > Energy
Depositing User: Cron Job
Date Deposited: 07 Mar 2014 12:45
Last Modified: 26 Nov 2014 19:06
DOI: