Investigating the Nonlinear Dynamics of Natural-Circulation, Boiling Two-Phase Flows

REFERENCES

• J. A. BOURE, A. E. BERGLES, and L. S. TONG, “Review of Two-Phase Flow Instability,” Nucl. Eng. Des., 25, 165 (1973).
   Web of Science ®Google Scholar
• G. YADIGAROGLU, “Two-Phase Flow Instabilities and Propagation Phenomena,” Thermohydraulics of Two-Phase Systems for Industrial Design and Nuclear Engineering, p. 353, J. M. DELHAYE, M. GIOT, and M. L. RIETHMULLER, Eds., Hemisphere Publishing Company, New York (1981).
   Google Scholar
• R. T. LAHEY, Jr., and F. J. MOODY, The Thermal-Hydraulics of a Boiling Water Nuclear Reactor, American Nuclear Society, La Grange Park, Illinois (1993).
   Google Scholar
• R. T. LAHEY, Jr., and M. Z. PODOWSKI, “On the Analyses of Instabilities in Two-Phase Flows,” Multiphase Science & Technology, Vol. 3, Hemisphere Publishing Company, New York (1987).
   Google Scholar
• J. L. ACHARD, D. A. DREW, and R. T. LAHEY, “The Analysis of Nonlinear Density-Wave Oscillations in Boiling Channels,” J. Fluid Mech., 155, 213 (1985).
   Web of Science ®Google Scholar
• RIZWAN-UDDIN and J. J. DORNING, “Nonlinear Stability Analysis of Density-Wave Oscillations in Nonuniformly Heated Channels,” Trans. Am. Nucl. Soc., 52, 404 (1987).
   Google Scholar
• RIZWAN-UDDIN and J. J. DORNING, “A Chaotic Attractor in a Periodically Forced Two-Phase Flow System,” Nucl. Eng. Des., 100, 393 (1988).
   Google Scholar
• RIZWAN-UDDIN and J. J. DORNING, “Chaotic Dynamics of a Triply-Forced Two-Phase Flow System,” Nucl. Eng. Des., 105, 123 (1990).
   Google Scholar
• A. CLAUSSE and R. T. LAHEY, Jr., “The Analysis of Periodic and Strange Attractors During Density-Wave Oscillations in Boiling Flows,” Chaos, Solitons & Fractals, 1, 167 (1991).
   Google Scholar
• C. J. CHANG and R. T. LAHEY, Jr., “Analysis of Chaotic Instabilities in Boiling Systems,” Nucl. Eng. Des., 167, 307 (1997).
   Web of Science ®Google Scholar
• P. SAHA, M. ISHII, and N. ZUBER, “An Experimental Investigation of the Thermally Induced Flow Oscillations in Two-Phase Systems,” J. Heat Transfer, 98, 616 (1976).
   Web of Science ®Google Scholar
• M. FURUTERA, “Validity of Homogeneous Flow Model for Instability Analysis,” Nucl. Eng. Des., 95, 65 (1986).
   Web of Science ®Google Scholar
• D. F. DELMASTRO, A. CLAUSSE, and J. CONVERTI, “The Influence of Gravity on the Stability of Boiling Flows,” Nucl. Eng. Des., 121, 129 (1991).
   Google Scholar
• I. S. KYUNG and S. Y. LEE, “Experimental Observation on Flow Characteristics in an Open Two-Phase Natural Circulation Loop,” Nucl. Eng. Des., 159, 163 (1994).
   Web of Science ®Google Scholar
• I. S. KYUNG and S. Y. LEE, “Periodic Flow Excursion in an Open Two-Phase Natural Circulation Loop,” Nucl. Eng. Des., 162, 233 (1996).
   Web of Science ®Google Scholar
• R. VAN DER GRAAF, T. H. J. J. VAN DER HAGEN, and R. F. MUDDE, “Scaling Laws and Design Aspects of a Natural-Circulation-Cooled Simulated Boiling Water Reactor Fuel Assembly,” Nucl. Technol., 105, 190 (1994).
   Google Scholar
• M. B. PRIESTLEY, Spectral Analysis and Time Series, Academic Press, London (1986).
   Google Scholar
• R. ZBORAY, A. MANERA, W. J. M. DE KRUIJF, T. H. J. J. VAN DER HAGEN, D. D. B. VAN BRAGT, and H. VAN DAM, “Experiments on Nonlinear Density-Wave Oscillations in the DESIRE Facility,” Proc. 9th Int. Mtg. Nuclear Reactor Thermal-Hydraulics (NURETH-9), San Francisco, California, October 3–8, 1999, American Nuclear Society (1999).
   Google Scholar
• R. ZBORAY, D. D. B. VAN BRAGT, RIZWAN-UDDIN, T. H. J. J. VAN DER HAGEN, and H. VAN DAM, “Influence of Asymmetrical Axial Power Distributions on Nonlinear BWR Dynamics,” Proc. 9th Int. Mtg. Nuclear Reactor Thermal-Hydraulics (NURETH-9), San Francisco, California, October 3–8, 1999, American Nuclear Society (1999).
   Google Scholar
• J. HALE and H. KOCAK, Dynamics and Bifurcations, Springer-Verlag, New York (1991).
   Google Scholar
• M. J. FEIGENBAUM, “The Transition to Aperiodic Behavior in Turbulent Systems,” Commun. Math. Phys., 77, 65 (1980).
   Web of Science ®Google Scholar
• P. S. LINSAY, “Period Doubling and Chaotic Behavior in a Driven Anharmonic Oscillator,” Phys. Rev. Lett., 47, 1349 (1981).
   Web of Science ®Google Scholar
• M. GIGLIO, S. MUSAZZI, and U. PERINI, “Transition to Chaotic Behavior Via a Reproducible Sequence of Period-Doubling Bifurcations,” Phys. Rev. Lett., 47, 243 (1981).
   Google Scholar
• H. M. GIBBS, F. A. HOPF, D. L. KAPLAN, and R. L. SHOEMAKER, “Observation of Chaos in Optical Bistability,” Phys. Rev. Lett., 46, 474 (1981).
   Web of Science ®Google Scholar
• C. W. SMITH, M. J. TEJWANI, and D. A. FARRIS, “Bifurcation Universality for First-Sound Subharmonic Generation in Superfluid Helium-4,” Phys. Rev. Lett., 48, 492 (1982).
   Google Scholar
• J. P. ECKMAN and D. RUELLE, “Ergodic Theory of Chaos and Strange Attractors,” Rev. Mod. Phys., 57, 617 (1985).
   Web of Science ®Google Scholar
• P. GRASSBERGER, T. SCHREIBER, and C. SCHAFFRATH “Nonlinear Time Sequence Analysis,” Int. J. Bif. and Chaos, 1, 521 (1991).
   Web of Science ®Google Scholar
• F. TAKENS, “Detecting Strange Attractors in Turbulence,” Lecture Notes in Mathematics, Springer-Verlag, Berlin (1981).
   Google Scholar
• J. C. SCHOUTEN, F. TAKENS, and C. M. VAN DEN BLEEK, “Maximum-Likelihood Estimation of the Entropy of an Attractor,” Phys. Rev. E, 49, 126 (1994).
   PubMed Web of Science ®Google Scholar
• J. C. SCHOUTEN, F. TAKENS, and C. M. VAN DEN BLEEK, “Estimation of the Dimension of a Noisy Attractor,” Phys. Rev. E, 50, 1851 (1994).
   PubMed Web of Science ®Google Scholar
• R. C. HILBORN, Chaos and Nonlinear Dynamics, Oxford University Press, Oxford (1994).
   Google Scholar
• P. GRASSBERGER and I. PROCACCIA, “Characterisation of Strange Attractors,” Phys. Rev. Lett., 50, 346 (1983).
   Web of Science ®Google Scholar
• A. WOLF, J. B. SWIFT, H. L. SWINNEY, and J. A. VASTANO, “Determining Lyapunov Exponents from Time Series,” Physica D, 16, 285 (1983).
   Google Scholar