Uncertainty quantification of subcritical bifurcation in a Rijke Tube

Analyzing and quantifying parametric uncertainties numerically in thermoacoustic systems is a tedious task, even more so when the system exhibits triggering (pulsed instabilities). Here a novel interpolation based approach is presented and applied to a simplified model of a Rijke tube. It is seen that this integrated interpolation scheme is significantly faster than the traditional Monte Carlo simulations. The advantages of using this scheme and the reason for its success compared to other uncertainty quantification schemes are highlighted. The paper also discusses advantages of using an equi-probable node distribution which is seen to improve the accuracy of the scheme. The stochastic bifurcation diagrams and the probabilities of failure (POF) are obtained for various operating conditions and stability regions are plotted. © 2010 by Vineeth Nair, Sunetra Sarkar and R. I. Sujith.