Abstract:This paper is concerned with the theoretical study of thermo-acoustic instabilities in combustors and focuses upon recently discovered flame intrinsic modes. Here, a complete analytical description of the salient properties of intrinsic modes is provided for a linearized one-dimensional model of open-open combustors with temperature and crosssection jump across the flame taken into account. The standard n À model of heat release is adopted, where n is the interaction index and is the time lag. We build upon th… Show more
“…For the sake of simplicity, here we considered only a quarter wave resonator with ideal end conditions. Similar analysis was carried out for the ideal open-open system and the same four types of coupling were also found (Mukherjee, 2017(Mukherjee, , 2018. The coupling in combustors with non-ideal boundary conditions needs a dedicated investigation.…”
The work is concerned with the theoretical examination of a new type of thermo-acoustic instability in combustors not reported in the literature. The instability results from linear coupling between the conventional acoustic mode and the recently discovered 'flame intrinsic modes' (Hoeijmakers et al., 2014). Within the framework of a 1-D model of a quarter wave resonator with the standard n model of flame heat release, intrinsic-acoustic mode coupling occurs when the real parts of the frequencies of neighboring acoustic and flame intrinsic modes at small interaction index n are close. While at small n the eigen-functions of close acoustic and flame intrinsic modes clearly exhibit their distinctive identities, with increase of n the mode identities become blurred and the eigen-functions of acoustic modes resemble more and more those of flame intrinsic modes and at a certain n become indistinguishable. We refer them as coupled intrinsic-acoustic modes or coupled modes. When the 'Rayleigh index' for a coupled mode behaving as an acoustic mode at small n is negative, at a larger n such a mode can nevertheless become unstable at one of the nearby intrinsic mode frequencies. We find analytically the instability domain due to coupling in the parameter space. Near the instability boundary, we reduce the transcendental dispersion relation to a quadratic or, if higher accuracy is desired, to a quartic equation. These models capture well all four possible coupling scenarios.
“…For the sake of simplicity, here we considered only a quarter wave resonator with ideal end conditions. Similar analysis was carried out for the ideal open-open system and the same four types of coupling were also found (Mukherjee, 2017(Mukherjee, , 2018. The coupling in combustors with non-ideal boundary conditions needs a dedicated investigation.…”
The work is concerned with the theoretical examination of a new type of thermo-acoustic instability in combustors not reported in the literature. The instability results from linear coupling between the conventional acoustic mode and the recently discovered 'flame intrinsic modes' (Hoeijmakers et al., 2014). Within the framework of a 1-D model of a quarter wave resonator with the standard n model of flame heat release, intrinsic-acoustic mode coupling occurs when the real parts of the frequencies of neighboring acoustic and flame intrinsic modes at small interaction index n are close. While at small n the eigen-functions of close acoustic and flame intrinsic modes clearly exhibit their distinctive identities, with increase of n the mode identities become blurred and the eigen-functions of acoustic modes resemble more and more those of flame intrinsic modes and at a certain n become indistinguishable. We refer them as coupled intrinsic-acoustic modes or coupled modes. When the 'Rayleigh index' for a coupled mode behaving as an acoustic mode at small n is negative, at a larger n such a mode can nevertheless become unstable at one of the nearby intrinsic mode frequencies. We find analytically the instability domain due to coupling in the parameter space. Near the instability boundary, we reduce the transcendental dispersion relation to a quadratic or, if higher accuracy is desired, to a quartic equation. These models capture well all four possible coupling scenarios.
“…This model for an unflanged tube exit is widely employed in thermoacoustic studies (Moeck et al. 2009; Kraus, Selle & Poinsot 2018; Mukherjee 2018; Aguilar & Juniper 2020). Figure 3.Representation of the full thermoacoustic system as an ITA system coupled to an acoustic system.…”
“…All studies made for the quarter-wave resonator were repeated in Mukherjee 46 for the half-wave resonator. No significant differences were found.…”
Section: Intrinsic Thermoacoustic Modesmentioning
confidence: 99%
“…Non-ideal boundary conditions, described by |R|<1 were also considered in Mukherjee. 46 Such boundary conditions describe tube ends, where acoustic energy is lost from the tube. The ITA modes and TA modes could not be decoupled analytically for such a case.…”
This paper gives an overview of the research performed by the project TANGO-an Initial Training Network (ITN) with an international consortium of seven academic and five industrial partners. TANGO is the acronym for 'Thermoacoustic and Aeroacoustic Nonlinearities in Green combustors with Orifice structures'). The researchers in TANGO studied many of the intricate physical processes that are involved in thermoacoustic instabilities. The paper is structured in such a way that each section describes a topic investigated by one or more researchers. The topics include:
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