首页|Asymptotic solutions for various thermoacoustic oscillations in Rijke tubes and one-dimensional combustors with different heating and closure conditions
Asymptotic solutions for various thermoacoustic oscillations in Rijke tubes and one-dimensional combustors with different heating and closure conditions
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NETL
NSTL
Elsevier
This work uses an asymptotic expansion technique to derive analytical solutions for the acoustic properties of one-dimensional combustors in general, and Rijke tubes in particular, assuming different endpoint conditions and thermal profiles. By leveraging Green's functions and integral formulations, the analysis provides closed-form expressions for acoustic frequencies and mode shapes, including those of the oscillatory pressure, velocity, temperature, heat release, density, entropy, energy density, intensity, boundary layer, and heat flux. In this process, attempts are made to clarify the dependency of various oscillatory properties on fundamental parameters such as the temperature gradient, thermal gain, heat source length and location, and stability regions. Special emphasis is placed on a logistic-exponential thermal profile, which offers a smooth and physically representative alternative to traditional piecewise models. At the outset, deeper insights are gained into the trends affecting frequency modulation and mode shape variations for diverse properties due to the attendant temperature distributions, thermal gradients, and endpoint boundary conditions. Moreover, a general interpretation of thermoacoustic phenomena in one-dimensional combustors with heat sources is confirmed, with tangible implications for the design and control of thermoacoustic instability in various combustors and solid rocket motors.
NETL
NSTL
Elsevier
