Abstract
The paper demonstrates the development of a numerical algorithm to solve a set of nonlinear hyperbolic equations in time domain in Eulerian frame of reference using a characteristics based finite difference implicit scheme to analyze density wave oscillations in boiling water nuclear reactor. The present algorithm removes the uncertainties existing in literature over the treatment of boundary conditions while simulating parallel channel instability of a reactor core by providing requisite mathematical support. The model is used to simulate parallel channel instability of a boiling water reactor core undergoing in-phase and out-of-phase modes of oscillations for both forced and natural circulation systems and numerical investigation confirms the existence of type-I and type-II instabilities in appropriate conditions. Next, the numerical simulations are conducted to evaluate the relative dominance of in-phase and out-of-phase modes of oscillations under various operational regime.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Boure, J.A., Bergles, A.E., Tong, L.S.: Review of Two-Phase Flow Instability. Nuclear Engineering and Design 25, 165–192 (1973)
Leuba, J.M., Rey, J.M.: Coupled Thermohydraulic-Neutronic Instabilities in Boiling Water Nuclear Reactors: A Review of the State of the Art. Nuclear Engineering and Design 145, 97–111 (1993)
Leuba, J.M., Blakeman, E.D.: A Mechanism for Out-of-phase Power Instabilities in Boiling Water Reactors. Nuclear Science and Engineering 107, 173–179 (1991)
Chatoorgoon, V.: Sports - A Simple Non-Linear Thermal Hydraulic Stability Code. Nuclear Engineering and Design 93, 51–67 (1986)
Bragt, D.D.B.V., Hagen, T.H.J.V.D.: Stability of Natural Circulation Boiling Water Reators: Part I – Description of Stability Model and Theoretical Analysis in terms of Dimensionless Groups. Nuclear Technology 121, 40–51 (1998)
Bragt, D.D.B.V., Hagen, T.H.J.V.D.: Stability of Natural Circulation Boiling Water Reators: Part II – Parametric Study of Coupled Neutronic-Thermohydraulic Stsbility. Nuclear Technology 121, 52–62 (1998)
Nayak, A.K., Vijayan, P.K., Saha, D., Raj, V.V., Aritomi, M.: Analytical Study of Nuclear Coupled Density Wave Oscillation in a Natural Circulation Pressure Tube Type Boiling Water Reactor. Nuclear Engineering and Design 195, 27–44 (2000)
Lin, Y.N., Pan, C.: Non-linear Analysis for a Natural Circulation Boiling Channel. Nuclear Engineering and Design 152, 349–360 (1994)
Aritomi, M., Aoki, S., Inoue, A.: Thermo-hydraulic Instabilities in Parallel Boiling Channel Systems Part 1. A Non-linear and a Linear Analytical Model. Nuclear Engineering and Design 95, 105–116 (1986)
Guido, G., Converti, J., Clausse, A.: Density Wave Oscillations in Parallel Channels - An Analytical Approach. Nuclear Engineering and Design 125, 121–136 (1991)
Hancox, W.T., Banerjee, S.: Numerical Standard for Flow Boiling Analysis. Nuclear Science and Engineering 64, 106–123 (1977)
Banerjee, S., Hancox, W.T.: On the Development of Methods for Analyzing Transient Flow-boiling. Int. J. Multiphase Flows 4, 437–460 (1978)
Dutta, G., Doshi, J.B.: Development of Characteristics Based Finite Difference Implicit Scheme to Analyze a Boiling Channel in Nuclear Reactors. In: 19th National and 8th ISHMT-ASME Heat and Mass Transfer Conference C193 (2008)
Dutta, G., Doshi, J.B.: A Characteristics-based Implicit Finite-difference Scheme for the Analysis of Instability in Water Cooled Reactors. Nuclear Engineering and Technology 40(6), 477–488 (2008)
Dutta, G.: Numerical Investigation of Nuclear Coupled Density Wave Oscillations in Reactors, Ph.D. Thesis, India Institute of Technology Bombay (2009)
Laney, C.B.: Computational Gasdynamics. Cambridge University Press, United Kingdom (1998)
Dutta, G., Doshi, J.B.: Development of a Nonlinear Thermal-hydraulic Model to Analyze Parallel Channel Instability of Boiling Water Reactor Core undergoing In-phase and Out-of-phase Modes of Oscillations. In: 20th National and 9th ISHMT-ASME Heat and Mass Transfer Conference 10HMTC276 (2010)
Munoz-Cobo, J.L., Rosello, R., Miro, R., Escriva, A., Ginestar, D., Verdu, G.: Coupling of Density Wave Oscillations in Parallel Channels with High Order Modal Kinetics; Application to BWR Out of Phase Oscillations. Annals of Nuclear Energy 27, 1345–1371 (2000)
Munoz-Cobo, J.L., Podowski, M.Z., Chiva, S.: Parallel Channel Instabilities in Boiling Water Reactor Systems: Boundary Conditions for Out of Phase Oscillations. Annals of Nuclear Energy 29, 1891–1917 (2002)
Munoz-Cobo, J.L., Chiva, S., Sekhri, A.: A Reduced Order Model of BWR Dynamics with Subcooled Boiling and Modal Kinetics: Application to Out of Phase Oscillations. Annals of Nuclear Energy 31, 1135–1162 (2004)
Ishii, M.: Thermally Induced Flow Instabilities in Two-phase Mixtures in Thermal Equilibrium, Ph.D. Thesis, Georgia Institute of Technology (1971)
Todreas, N.E., Kazimi, M.S.: Nuclear Systems I: Thermal Hydraulic Fundamentals. Hemisphere Publishing Corporation, New York (1989)
Dutta, G., Doshi, J.B.: Nonlinear Analysis of Nuclear Coupled Density Wave Instability in Time-domain for a Boiling Reactor Core undergoing Core-wide and Regional Modes of Oscillations. Progress in Nuclear Energy 51, 769–787 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dutta, G., Doshi, J.B. (2011). A Numerical Algorithm for the Solution of Simultaneous Nonlinear Equations to Simulate Instability in Nuclear Reactor and Its Analysis. In: Murgante, B., Gervasi, O., Iglesias, A., Taniar, D., Apduhan, B.O. (eds) Computational Science and Its Applications - ICCSA 2011. ICCSA 2011. Lecture Notes in Computer Science, vol 6783. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21887-3_52
Download citation
DOI: https://doi.org/10.1007/978-3-642-21887-3_52
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21886-6
Online ISBN: 978-3-642-21887-3
eBook Packages: Computer ScienceComputer Science (R0)