Date of Award


Degree Type


Degree Name

Doctor of Philosophy


Nuclear Engineering

Major Professor

R. B. Perez

Committee Members

Belle R. Upadhyaya, J. Reece Roth, Paul M. Stevens


This dissertation presents a new analytical model for the Once-Through Steam Generator (OTSG) which is a component responsible for the primary coolant heat removal and the generation and supply of superheated steam to the turbine of the Pressurized Water Reactor (PWR) manufactured by Babcock & Wilcox (B&W) Co. This new analytical model provides the explanation of the oscillatory phenomenon observed in all PWRs manufactured by B&W that uses the OTSG as part of the steam supply system. It was found that the oscillatory behavior is related to the friction pressure drop caused by the reduction in flow area due to the presence of the metal tube holders. The linear analysis performed has shown a pair of complex conjugate eigenvalues with real negative parts, indicating that the OTSG is stable for small perturbations. 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 of the plant data revealed two marked features: a resonance at the frequency of oscillation of the limit cycle and a broadband region preceding the location of 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 dependence on the frequency whereas the chaotic broadband decreases exponentially with frequency. The broadband obtained in the power spectral density of power plant data presented the latter behavior leading to the conclusion that the OTSG limit cycle is modulated by a chaotic component. Furthermore, the calculation of the Lyapunov exponents using the plant data results in positive values reinforcing the above conclusion. It is also demonstrated in this work that undersampling effects seriously hinder the chaotic signatures. This study has shown that the best criterion to determine the chaotic signature in experimental time series is the frequency dependence of the broadband structure in the signal power spectral density. The originality of this work is two fold. First is the model development that leads to the identification of the causative mechanism for the observed OTSG limit cycle. Second is the novel use of otherwise well established tests in the simulation studies of degraded signals for the identification of chaotic components. The recommendations for future work are the extension of the model to allow for motion of all nodal boundaries rather than just the uppermost nodal limits, study of the interaction between the two steam generators in the plant, study of the dependency of the OTSG model eigenvalues with reactor power, and availability of better quality plant data is stressed.

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