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Stability analysis for n -periodic arrays of fluid systems

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Schmid, PJ 
De Pando, MF 

Abstract

© 2017 American Physical Society. A computational framework is proposed for the linear modal and nonmodal analysis of fluid systems consisting of a periodic array of n identical units. A formulation in either time or frequency domain is sought and the resulting block-circulant global system matrix is analyzed using roots-of-unity techniques, which reduce the computational effort to only one unit while still accounting for the coupling to linked components. Modal characteristics as well as nonmodal features are treated within the same framework, as are initial-value problems and direct-adjoint looping. The simple and efficient formalism is demonstrated on selected applications, ranging from a Ginzburg-Landau equation with an n-periodic growth function to interacting wakes to incompressible flow through a linear cascade consisting of 54 blades. The techniques showcased here are readily applicable to large-scale flow configurations consisting of n-periodic arrays of identical and coupled fluid components, as can be found, for example, in turbomachinery, ring flame holders, or nozzle exit corrugations. Only minor corrections to existing solvers have to be implemented to allow this present type of analysis.

Description

Keywords

4012 Fluid Mechanics and Thermal Engineering, 40 Engineering

Journal Title

Physical Review Fluids

Conference Name

Journal ISSN

2469-990X
2469-990X

Volume Title

2

Publisher

American Physical Society (APS)