A bifurcation analysis of the dynamical behavior of a horizontal Rijke tube model is performed in this paper. The method of numerical continuation is used to obtain the bifurcation plots, including the amplitude of the unstable limit cycles. Bifurcation plots for the variation of nondimensional heater power, damping coefficient and the heater location are obtained for different values of time lag in the system. Subcritical bifurcation was observed for variation of parameters and regions of global stability, global instability and bistability are characterized. Linear and nonlinear stability boundaries are obtained for the simultaneous variation of two parameters of the system. The validity of the small time lag assumption in the calculation of linear stability boundary has been shown to fail at typical values of time lag of system. Accurate calculation of the linear stability boundary in systems with explicit time delay models, must therefore, not assume a small time lag assumption. Interesting dynamical behavior such as co-existing multiple attractors, quasiperiodic behavior and period doubling route to chaos have been observed in the analysis of the model. Comparison of the linear stability boundaries and bifurcation behavior from this reduced order model are shown to display trends similar to experimental data.
Publication details: International Journal of Spray and Combustion Dynamics, vol. 2(4), pg. 325–356, 2010.