Stability analysis for n-periodic arrays of fluid systems

Peter J. Schmid, Miguel Fosas de Pando, and N. Peake
Phys. Rev. Fluids 2, 113902 – Published 13 November 2017

Abstract

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.

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  • Received 17 February 2017

DOI:https://doi.org/10.1103/PhysRevFluids.2.113902

©2017 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Peter J. Schmid*

  • Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom

Miguel Fosas de Pando

  • Department of Mechanical Engineering and Industrial Design, University of Cádiz, 11519 Puerto Real, Spain

N. Peake

  • Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom

  • *pjschmid@imperial.ac.uk
  • miguel.fosas@uca.es
  • n.peake@damtp.cam.ac.uk

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Issue

Vol. 2, Iss. 11 — November 2017

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