Isentropic formulation of the linearized euler equations for perfectly premixed combustion systems

Pedro Romero Vega, Thomas Hofmeister, Gerrit Heilmann, Christoph Hirsch, Thomas Sattelmayer

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The linearized Euler equations (LEE) provide an accurate - yet computationally efficient - description of propagation and damping of acoustic waves in geometrically complex, non-uniform reactive mean flows like those found in gas turbine combustion chambers. However, direct application of the LEE to perfectly premixed combustors with highly turbulent flows overestimates entropy waves as the LEE solution inherently contains coupled acoustic, vortical and entropy modes. In the present work, the LEE are decomposed into isentropic and non-isentropic parts ultimately obtaining a simplified set of isentropic LEE, in which only acoustic and vortical modes propagate. In the isentropic LEE, only continuity and momentum equations need to be solved. The energy equation is replaced by the isentropic relation between acoustic pressure and density. From the decomposition, the unsteady heat release term, which acts as a source in the energy equation, naturally arises as a source in the continuity equation. This way, the thermoacoustic coupling is still preserved in the isentropic formulation. The derived isentropic set of equations is first tested with a one-dimensional benchmark configuration consisting of a mean flow temperature jump, non-uniform mean flow velocity and unsteady heat release sources. Solutions of the non-isentropic and isentropic set of LEE are compared and the avoidance of entropy waves proved. Finally, isentropic LEE are used for reproducing the frequency of the self-excited first transversal mode of a lab-scale swirl-stabilized premixed combustor. Furthermore, isentropic and non-isentropic LEE solutions are compared. The non-isentropic LEE yield too high levels of entropy at the combustor exit that may explain the increased damping rate of the non-isentropic LEE solution compared to the isentropic LEE solution. This shows the relevance of isentropic LEE for correctly predicting thermoacoustic stability limits at high frequencies in relevant industrial applications.

Original languageEnglish
Title of host publicationCombustion, Fuels, and Emissions
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Electronic)9780791884959
DOIs
StatePublished - 2021
EventASME Turbo Expo 2021: Turbomachinery Technical Conference and Exposition, GT 2021 - Virtual, Online
Duration: 7 Jun 202111 Jun 2021

Publication series

NameProceedings of the ASME Turbo Expo
Volume3B-2021

Conference

ConferenceASME Turbo Expo 2021: Turbomachinery Technical Conference and Exposition, GT 2021
CityVirtual, Online
Period7/06/2111/06/21

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