Non-linear dynamics of a once-through steam generator

This dissertation presents a new analytical model for the Once-Through Steam Generator (OTSG), a component on the Pressurized Water Reactor (PWR) manufactured by Babcock & Wilcox Co. This model provides the explanation of the oscillatory phenomena observed in all PWRs that uses the OTSG. The oscillation is related with the friction pressure drop caused by the reduction in flow area due to the metal tube holders. The linear analysis performed have shown a pair of complex eigenvalues, with real negative parts indicating that the OTSG is stable for small. The global stability was investigated by the construction of the bifurcation diagram whereby the amplitude of the pressure oscillation was plotted against the friction corrector factor. The bifurcation diagram indicates that the limit cycle is stable within the range of physical values of the friction corrector factor. Power spectral density (PSD) of the plant data revealed a resonance at the frequency of oscillation of the limit cycle and a broadband region preceding the resonance peak. The present model does not reproduce the broadband region. A detailed simulation study of the modulation of the amplitude of a limit cycle both with band limited white noise and chaotic noise has shown that the broadband generated by band limited white noise exhibits a power-law, whereas the chaotic broadband decreases exponentially with frequency. The broadband obtained in the PSD of power plant data presented the later behavior leading to the conclusion that the OTSG limit cycle is modulated by a chaotic component. The calculation of the Lyapunov exponents using the plant data results in positive values reinforcing the above conclusion. Undersampling effects seriously hinder the chaotic signatures. The best criterion for determination of chaotic signature in experimental time series is the frequency dependence of the broadband structure in the signal PSD. The originalities of this work are: the model development and the implementation of the tests for chaotic signature identification. The recommendations for future work are the extension of the model to allow for motion of all nodal boundaries and the study of the interaction between the two steam generators in the plant.