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ThinkMind // International Journal On Advances in Systems and Measurements, volume 11, numbers 3 and 4, 2018 // View article sysmea_v11_n34_2018_12


Dynamics Analysis of the Rijke Tube Thermoacoustics: Mathematical Modeling using Luikov and Wave Equations with its Experimental Validation

Authors:
Israel Mejia Alonso
Eloy Edmundo Rodríguez Vázquez
Carlos Alexander Núñez Martín
Luis Alvaro Montoya Santiyanes
Helen Janeth Zuñiga Osorio

Keywords: Rijke tube experiment; Luikov equations and wave equation.

Abstract:
This paper deals with the mathematical modeling for the thermoacoustic phenomena in a simple geometry combustion chamber represented as the Rijke tube. The methodology developed to get an analytical model from the Luikov equations for the dynamical behavior of both variables of interest the temperature and pressure distributions into the cited chamber is described briefly. Through this model, the time and space Eigenvalues are calculated to interpret them in terms of the combustion chamber geometry; also the spatial distribution (modal shapes or Eigenvectors) of both variables into the confined volume in the chamber are analyzed by the boundary conditions. The obtained analytical model from the Luikov modified equations is complemented with an experimental modeling for the dynamics of the same variables of interest, but based on the wave equation and considering the same boundary conditions. To validate both models for the thermoacoustics dynamics, a Rijke tube experiment was developed, by getting the experimental data to support the analytical hypothesis from the synthetized models. The main purpose of this paper is to compare the two mathematical modeling methodologies to know the set of assumptions needed to have a real idea of the fundamental modal shapes for the temperature and pressure in this combustion chamber geometry when the thermoacoustic phenomena is presented.

Pages: 363 to 372

Copyright: Copyright (c) to authors, 2018. Used with permission.

Publication date: December 30, 2018

Published in: journal

ISSN: 1942-261x

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