Adjoint-based parametric sensitivity analysis for swirling M-flames

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Title: Adjoint-based parametric sensitivity analysis for swirling M-flames
Authors: Skene, CS
Schmid, PJ
Item Type: Journal Article
Abstract: A linear numerical study is conducted to quantify the effect of swirl on the response behaviour of premixed lean flames to general harmonic excitation in the inlet, upstream of combustion. This study considers axisymmetric M-flames and is based on the linearised compressible Navier–Stokes equations augmented by a simple one-step irreversible chemical reaction. Optimal frequency response gains for both axisymmetric and non-axisymmetric perturbations are computed via a direct–adjoint methodology and singular value decompositions. The high-dimensional parameter space, containing perturbation and base-flow parameters, is explored by taking advantage of generic sensitivity information gained from the adjoint solutions. This information is then tailored to specific parametric sensitivities by first-order perturbation expansions of the singular triplets about the respective parameters. Valuable flow information, at a negligible computational cost, is gained by simple weighted scalar products between direct and adjoint solutions. We find that for non-swirling flows, a mode with azimuthal wavenumber is the most efficiently driven structure. The structural mechanism underlying the optimal gains is shown to be the Orr mechanism for and a blend of Orr and other mechanisms, such as lift-up, for other azimuthal wavenumbers. Further to this, velocity and pressure perturbations are shown to make up the optimal input and output showing that the thermoacoustic mechanism is crucial in large energy amplifications. For these velocity perturbations are mainly longitudinal, but for higher wavenumbers azimuthal velocity fluctuations become prominent, especially in the non-swirling case. Sensitivity analyses are carried out with respect to the Mach number, Reynolds number and swirl number, and the accuracy of parametric gradients of the frequency response curve is assessed. The sensitivity analysis reveals that increases in Reynolds and Mach numbers yield higher gains, through a decrease in temperature diffusion. A rise in mean-flow swirl is shown to diminish the gain, with increased damping for higher azimuthal wavenumbers. This leads to a reordering of the most effectively amplified mode, with the axisymmetric ( ) mode becoming the dominant structure at moderate swirl numbers.
Issue Date: 21-Nov-2018
Date of Acceptance: 1-Nov-2018
ISSN: 0022-1120
Publisher: Cambridge University Press (CUP)
Start Page: 516
End Page: 542
Journal / Book Title: Journal of Fluid Mechanics
Volume: 859
Copyright Statement: © 2018 Cambridge University Press. This paper has been accepted for publication and will appear in a revised form, subsequent to peer-review and/or editorial input by Cambridge University Press.
Sponsor/Funder: Commission of the European Communities
Funder's Grant Number: 675585
Keywords: Science & Technology
Physical Sciences
Physics, Fluids & Plasmas
computational methods
reacting flows
01 Mathematical Sciences
09 Engineering
Fluids & Plasmas
Publication Status: Published
Online Publication Date: 2018-11-21
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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