Report for EU POLKA project

75 16 229 2 1050 document 229 adjoint Gf approach for flow duct .pdf application/pdf cc2c862d4920832686b1adff32d1c3b3 MD5 359500 2023-09-12 14:10:24 https://researchdata.keele.ac.uk/75/1/adjoint%20Gf%20approach%20for%20flow%20duct%20.pdf 75 1 1 application/pdf text en public cc_by_nd_4

adjoint Gf approach for flow duct .pdf

full_archive 323 2 1273 document 323 lightbox.jpg image/png 085b90836ba435c0b10ebe7a1748df85 MD5 35400 2023-12-17 10:40:36 https://researchdata.keele.ac.uk/75/3/lightbox.jpg 75 3 3 image/png other Thumbnails conversion from text to thumbnail_lightbox en public

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http://eprints.org/relation/isVersionOf https://researchdata.keele.ac.uk/id/document/229 http://eprints.org/relation/isVolatileVersionOf https://researchdata.keele.ac.uk/id/document/229 http://eprints.org/relation/isIndexCodesVersionOf https://researchdata.keele.ac.uk/id/document/229 archive 6 disk0/00/00/00/75 2023-09-13 10:32:30 2024-02-27 09:48:04 2023-09-13 10:54:18 data_collection show Heckl Maria m.a.heckl@keele.ac.uk 0000-0002-0192-7508 Report for EU POLKA project unpub QD sch_cps flow duct, unsteady heat source, acoustic analogy equation, adjoint Green's function, integral governing equation This document gives a detailed derivation of the integral governing equation for the velocity potential in the following setup: A finite duct with mean flow and frequency-dependent end conditions (described by reflection coefficients) houses a compact unsteady heat source; thermoacoustic instabilities arise in the duct because of the interaction between the sound field in the duct and the unsteady heat release rate from the heat source. The derivation of the governing integral equation is based on the acoustic analogy equation, i.e. the convected wave equation with a source term that represents the heat release rate. A series of mathematical steps are performed. These include an adjoint approach with a test function. This test function is shown to be the adjoint form of the tailored Green's function of the flow duct. It is calculated with a generalised function approach and turns out to be a superposition of duct modes. Expressions for the frequencies and amplitudes of these modes are found. they depend on the reflection coefficients, duct length and speed of the flow. The final result of this document is the integral governing equation for the velocity potential; this contains the adjoint Green's function, the heat release rate and initial conditions. It can be solved with a straightforward time-stepping approach. 2023 published EU POLKA https://www.polka-eu.org/index.htm 10.21252/bvre-5s91 Other research.openaccess@keele.ac.uk Horizon 2020 Heckl Maria m.a.heckl@keele.ac.uk POLKA EU project other http://polka-eu.org/ Open data requirement 2023-06-05 2023-06-05