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State prediction of an entropy wave advecting through a turbulent channel flow

Published online by Cambridge University Press:  06 November 2019

Loizos Christodoulou Open the ORCID record for Loizos Christodoulou [Opens in a new window] ,
Nader Karimi Open the ORCID record for Nader Karimi [Opens in a new window] ,
Andrea Cammarano Open the ORCID record for Andrea Cammarano [Opens in a new window] ,
Manosh Paul Open the ORCID record for Manosh Paul [Opens in a new window]  and
Salvador Navarro-Martinez Open the ORCID record for Salvador Navarro-Martinez [Opens in a new window]
Loizos Christodoulou
Affiliation:
James Watt School of Engineering, University of Glasgow, Glasgow G12 8QQ, UK
Nader Karimi*
Affiliation:
James Watt School of Engineering, University of Glasgow, Glasgow G12 8QQ, UK
Andrea Cammarano
Affiliation:
James Watt School of Engineering, University of Glasgow, Glasgow G12 8QQ, UK
Manosh Paul
Affiliation:
James Watt School of Engineering, University of Glasgow, Glasgow G12 8QQ, UK
Salvador Navarro-Martinez
Affiliation:
Department of Mechanical Engineering, Imperial College London, London SW7 1AL, UK
*
†Email address for correspondence: Nader.Karimi@glasgow.ac.uk
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Abstract

Survival of entropy waves during their advection throughout a combustor is central to the generation of entropic sound and the subsequent effects upon thermoacoustic stability of the system. However, the decay and spatial non-uniformity of entropy waves are largely ignored by the existing models used for the calculation of entropy noise generation. Recent investigations have demonstrated the complex spatio-temporal dynamics of entropy waves and cast doubts on the sufficiency of the one-dimensional approach, conventionally used for the analysis of these waves. Hence, this paper proposes a novel approach to the low-order modelling of entropy wave evolution wherein the wave is described by the two states of position and amplitude in the streamwise direction. A high-order model is first developed through direct numerical simulation of the advection of entropy waves in a fully developed, heat transferring, compressible, turbulent channel flow. The data are then utilised to build and validate a series of nonlinear, low-order models that provide an unsteady two-dimensional representation of the decaying and partially annihilating entropy waves. It is shown that these models need, at most, approximately $12.5\,\%$ of the total trace of entropy wave advection to predict the wave dynamics accurately. The results further reveal that the existing linear low-order models are truly predictive only for the entropy waves with less than $2\,\%$ increase in the gas temperature compared to that of the surrounding flow. Yet, in agreement with the assumption of existing models, it is shown that entropy waves travel with the mean flow speed.

JFM classification

Nonlinear Dynamical Systems: Low-dimensional models Reacting Flows: Combustion
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 882 , 10 January 2020 , A8
Copyright
© 2019 Cambridge University Press 

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