Nonlinear Thermal Hydraulic Model to Analyze Parallel Channel Density Wave Instabilities in Natural Circulation Boiling Water Reactor with Asymmetric Power Distribution
The paper investigates parallel channel instabilities of
natural circulation boiling water reactor. A thermal-hydraulic model
is developed to simulate two-phase flow behavior in the natural circulation boiling water reactor (NCBWR) with the incorporation of
ex-core components and recirculation loop such as steam separator, down-comer, lower-horizontal section and upper-horizontal section
and then, numerical analysis is carried out for parallel channel
instabilities of the reactor undergoing both in-phase and out-of-phase
modes of oscillations. To analyze the relative effect on stability of the reactor due to inclusion of various ex-core components and
recirculation loop, marginal stable point is obtained at a particular inlet enthalpy of the reactor core without the inclusion of ex-core
components and recirculation loop and then with the inclusion of the
same. Numerical simulations are also conducted to determine the
relative dominance between two modes of oscillations i.e. in-phase and out-of-phase. Simulations are also carried out when the channels
are subjected to asymmetric power distribution keeping the inlet enthalpy same.
[1] O. J. A. Boure, A. .E. Bergles and L. S. Tong, Review of Two-Phase
Flow Instability, Nuclear Engineering and Design 25 (1973) 165-192..
[2] J. M. Leuba and J. M. Rey, Coupled Thermohydraulic-Neutronic Instabilities
in Boiling Water Nuclear Reactors: A Review of the State of the
Art, Nuclear Engineering and Design 145 (1993) 97-111..
[3] F. D'Auria (Project Coordinator), Neutronics/Thermal-hydraulics Coupling
in LWR Technology, Tech. rep., Vol. 2, CRISSUE-S WP2: Stateof-the-Art Report, OECD/NEAN. 5436 (2004).
[4] G. V. D. Prasad, M. Pandey and M. S. Kalra, Review of Research on
Flow Instabilities in Natural Circulation Boiling Systems, Progress in
Nuclear Energy 49 (2007) 429-451.
[5] A. K. Nayak and P. K. Vijayan, Flow Instabilities in Boiling Two-phase
Natural Circulation Systems: A Review, Science and Technology of Nuclear Installations (Article ID 573192, 15 pages,
doi:10.1155/2008/573192).
[6] W. Ambrosini, P. D. Marco and J. C. Ferreri, Linear and Nonlinear Analysis of Density Wave Instability Phenomena, Publicado en International
Journal of Heat and Technology 18 (1) (2000) 27-36.
[7] Rizwan-uddin, On Density-Wave Oscillations in Two-Phase Flows, Int.
J. Multiphase Flow 20 (4) (1994) 721-737. Rizwan-uddin and J. J.
Dorning, A Chaotic Attractor in a Periodically Forced Two-Phase Flow
System, Nuclear Science and Engineering 100 (1988) 393-404.
[8] Rizwan-uddin and J. J. Dorning, Chatic Dynamics of a Triply-Forced
Two-Phase Flow System, Nuclear Science and Engineering 105 (1990)
123-135.
[9] A. Clausse and Jr. R. T. Lahey, The Analysis of Periodic and Strange
Attractors during Density-Wave Oscillations in Boiling Flows, Chaos,
Solitons and Fructals 1(2) (1991) 167-178.
[10] R. O. S. Prasad, J. B. Doshi and K. Iyer, A Numerical Investigation of
Nuclear Coupled Density Wave Oscillations, Nuclear Engineering and
Design 154 (1995) 381-396.
[11] S. Narayanan, B. Srinivas, S. Pushpavanan and S. M. Bhallamudi, Nonlinear
Dynamics of a Two Phase Flow System in an Evaporator: The
Effects of (i) a Time Varying Pressure Drop, (ii) an Axially Varying
Heat Flux, Nuclear Engineering and Design 178 (1997) 279-294.
[12] G. Dutta, J. B. Doshi, A Characteristics-Based Implicit Finite-Difference Scheme for the Analysis of Instability in Water Cooled Reactors,
Nuclear Engineering and Technology 40 (6) (2008) 477-488.
[13] D. Hennig, A Study of Boiling Water Reactor Stability Behavior, Nuclear
Technology 126 (1999) 10-31.
[14] H. Ikeda, T. Ama, K. Hashimoto and T. Takeda, Nonlinear Behavior
under Regional Neutron Flux Oscillations in BWR Cores, Journal of Nuclear Science and Technology 38 (5) (2001) 312-323.
[15] H. I. F. F. Y. K. H. Soneda, S. Mizokami, BWR Stability Issues in
Japan, Science and Technology of Nuclear Installations (Article ID
358616, 11 pages, doi: 10.1155/2008/358616).
[16] G. Dutta and J. B. Doshi, Nonlinear Analysis of Nuclear Coupled Density
Wave Instability in Time Domain for Boiling Water Reactor Core
undergoing Core-wide and Regional Modes of Oscillations, Progress in
Nuclear Energy 51 (2009) 769-787.
[17] Y. N. Lin, J. D. Lee and C. Pan, Nonlinear Dymanics of Nuclear-Coupled Boiling Channel with Forced Flows, Nuclear Engineering and
Design 179 (1998) 31-49.
[18] J. M. Leuba and E. D. Blakeman, A Mechanism for Out-of-phase Power
Instabilities in Boiling Water Reactors, Nuclear Science and Engineering 107 (1991) 173-179.
[19] M. Aritomi, S. Aoki and A. Inoue, Thermo-hydraulic Instabilities in Parallel Boiling Channel Systems Part 1. A Non-linear and a Linear
Analytical Model, Nuclear Engineering and Design 95 (1986) 105-116.
[20] J. L. Munoz-Cobo, R. B. Perez, D. Ginestar, A. Escriva and G. Verdu,
Non Linear Analysis of Out of Phase Oscillations in Boiling Water Reactors,
Annals of Nuclear Energy 23, No. 16 (1996) 1301-1335.
[21] J. L. Munoz-Cobo, M. Z. Podowski and S. Chiva, Parallel Channel
Instabilities in Boiling Water Reactor Systems: Boundary Conditions for
Out of Phase Oscillations, Annals of Nuclear Energy 29 (2002) 1891-
1917.
[22] J. D. Lee and C. Pan, Dymanics of Multiple Parallel Boiling Channel
Systems with Forced Flows, Nuclear Engineering and Design 192 (1999) 31-44.
[23] W. T. Hancox and S. Banerjee, Numerical Standards for Flow-Boiling
Analysis, Nuclear Science and Engineering 64 (1977) 106-123.
[24] S. Banerjee and W. T. Hancox, On the Development of Methods for
Analysing Transient Flow-Boiling, Int. J. Multiphase Flow 4 (1978) 37-460.
[25] G. Dutta and J. B. Doshi, A Numerical Algorithm for the Solution of Simultaneous Nonlinear Equations to Simulate Instability in Nuclear
Reactor and its Analysis, in: 11th International Conference on Computational
Science and its Applications, Vol. 6783 of Lecture Notes in
Computer Science, Springer, University of Cantabria, Santander, Spain,
2011, pp. 695-710.
[26] J. L. Munoz-Cobo, O. Rosello, R. Miro, A. Escriva, D. Ginestar and G.
Verdu, 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 (2000) 1345-1371
[1] O. J. A. Boure, A. .E. Bergles and L. S. Tong, Review of Two-Phase
Flow Instability, Nuclear Engineering and Design 25 (1973) 165-192..
[2] J. M. Leuba and J. M. Rey, Coupled Thermohydraulic-Neutronic Instabilities
in Boiling Water Nuclear Reactors: A Review of the State of the
Art, Nuclear Engineering and Design 145 (1993) 97-111..
[3] F. D'Auria (Project Coordinator), Neutronics/Thermal-hydraulics Coupling
in LWR Technology, Tech. rep., Vol. 2, CRISSUE-S WP2: Stateof-the-Art Report, OECD/NEAN. 5436 (2004).
[4] G. V. D. Prasad, M. Pandey and M. S. Kalra, Review of Research on
Flow Instabilities in Natural Circulation Boiling Systems, Progress in
Nuclear Energy 49 (2007) 429-451.
[5] A. K. Nayak and P. K. Vijayan, Flow Instabilities in Boiling Two-phase
Natural Circulation Systems: A Review, Science and Technology of Nuclear Installations (Article ID 573192, 15 pages,
doi:10.1155/2008/573192).
[6] W. Ambrosini, P. D. Marco and J. C. Ferreri, Linear and Nonlinear Analysis of Density Wave Instability Phenomena, Publicado en International
Journal of Heat and Technology 18 (1) (2000) 27-36.
[7] Rizwan-uddin, On Density-Wave Oscillations in Two-Phase Flows, Int.
J. Multiphase Flow 20 (4) (1994) 721-737. Rizwan-uddin and J. J.
Dorning, A Chaotic Attractor in a Periodically Forced Two-Phase Flow
System, Nuclear Science and Engineering 100 (1988) 393-404.
[8] Rizwan-uddin and J. J. Dorning, Chatic Dynamics of a Triply-Forced
Two-Phase Flow System, Nuclear Science and Engineering 105 (1990)
123-135.
[9] A. Clausse and Jr. R. T. Lahey, The Analysis of Periodic and Strange
Attractors during Density-Wave Oscillations in Boiling Flows, Chaos,
Solitons and Fructals 1(2) (1991) 167-178.
[10] R. O. S. Prasad, J. B. Doshi and K. Iyer, A Numerical Investigation of
Nuclear Coupled Density Wave Oscillations, Nuclear Engineering and
Design 154 (1995) 381-396.
[11] S. Narayanan, B. Srinivas, S. Pushpavanan and S. M. Bhallamudi, Nonlinear
Dynamics of a Two Phase Flow System in an Evaporator: The
Effects of (i) a Time Varying Pressure Drop, (ii) an Axially Varying
Heat Flux, Nuclear Engineering and Design 178 (1997) 279-294.
[12] G. Dutta, J. B. Doshi, A Characteristics-Based Implicit Finite-Difference Scheme for the Analysis of Instability in Water Cooled Reactors,
Nuclear Engineering and Technology 40 (6) (2008) 477-488.
[13] D. Hennig, A Study of Boiling Water Reactor Stability Behavior, Nuclear
Technology 126 (1999) 10-31.
[14] H. Ikeda, T. Ama, K. Hashimoto and T. Takeda, Nonlinear Behavior
under Regional Neutron Flux Oscillations in BWR Cores, Journal of Nuclear Science and Technology 38 (5) (2001) 312-323.
[15] H. I. F. F. Y. K. H. Soneda, S. Mizokami, BWR Stability Issues in
Japan, Science and Technology of Nuclear Installations (Article ID
358616, 11 pages, doi: 10.1155/2008/358616).
[16] G. Dutta and J. B. Doshi, Nonlinear Analysis of Nuclear Coupled Density
Wave Instability in Time Domain for Boiling Water Reactor Core
undergoing Core-wide and Regional Modes of Oscillations, Progress in
Nuclear Energy 51 (2009) 769-787.
[17] Y. N. Lin, J. D. Lee and C. Pan, Nonlinear Dymanics of Nuclear-Coupled Boiling Channel with Forced Flows, Nuclear Engineering and
Design 179 (1998) 31-49.
[18] J. M. Leuba and E. D. Blakeman, A Mechanism for Out-of-phase Power
Instabilities in Boiling Water Reactors, Nuclear Science and Engineering 107 (1991) 173-179.
[19] M. Aritomi, S. Aoki and A. Inoue, Thermo-hydraulic Instabilities in Parallel Boiling Channel Systems Part 1. A Non-linear and a Linear
Analytical Model, Nuclear Engineering and Design 95 (1986) 105-116.
[20] J. L. Munoz-Cobo, R. B. Perez, D. Ginestar, A. Escriva and G. Verdu,
Non Linear Analysis of Out of Phase Oscillations in Boiling Water Reactors,
Annals of Nuclear Energy 23, No. 16 (1996) 1301-1335.
[21] J. L. Munoz-Cobo, M. Z. Podowski and S. Chiva, Parallel Channel
Instabilities in Boiling Water Reactor Systems: Boundary Conditions for
Out of Phase Oscillations, Annals of Nuclear Energy 29 (2002) 1891-
1917.
[22] J. D. Lee and C. Pan, Dymanics of Multiple Parallel Boiling Channel
Systems with Forced Flows, Nuclear Engineering and Design 192 (1999) 31-44.
[23] W. T. Hancox and S. Banerjee, Numerical Standards for Flow-Boiling
Analysis, Nuclear Science and Engineering 64 (1977) 106-123.
[24] S. Banerjee and W. T. Hancox, On the Development of Methods for
Analysing Transient Flow-Boiling, Int. J. Multiphase Flow 4 (1978) 37-460.
[25] G. Dutta and J. B. Doshi, A Numerical Algorithm for the Solution of Simultaneous Nonlinear Equations to Simulate Instability in Nuclear
Reactor and its Analysis, in: 11th International Conference on Computational
Science and its Applications, Vol. 6783 of Lecture Notes in
Computer Science, Springer, University of Cantabria, Santander, Spain,
2011, pp. 695-710.
[26] J. L. Munoz-Cobo, O. Rosello, R. Miro, A. Escriva, D. Ginestar and G.
Verdu, 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 (2000) 1345-1371
@article{"International Journal of Electrical, Electronic and Communication Sciences:61600", author = "Sachin Kumar and Vivek Tiwari and Goutam Dutta", title = "Nonlinear Thermal Hydraulic Model to Analyze Parallel Channel Density Wave Instabilities in Natural Circulation Boiling Water Reactor with Asymmetric Power Distribution", abstract = "The paper investigates parallel channel instabilities of
natural circulation boiling water reactor. A thermal-hydraulic model
is developed to simulate two-phase flow behavior in the natural circulation boiling water reactor (NCBWR) with the incorporation of
ex-core components and recirculation loop such as steam separator, down-comer, lower-horizontal section and upper-horizontal section
and then, numerical analysis is carried out for parallel channel
instabilities of the reactor undergoing both in-phase and out-of-phase
modes of oscillations. To analyze the relative effect on stability of the reactor due to inclusion of various ex-core components and
recirculation loop, marginal stable point is obtained at a particular inlet enthalpy of the reactor core without the inclusion of ex-core
components and recirculation loop and then with the inclusion of the
same. Numerical simulations are also conducted to determine the
relative dominance between two modes of oscillations i.e. in-phase and out-of-phase. Simulations are also carried out when the channels
are subjected to asymmetric power distribution keeping the inlet enthalpy same.", keywords = "Asymmetric power distribution, Density wave oscillations, In-phase and out-of-phase modes of instabilities, Natural circulation boiling water reactor", volume = "6", number = "1", pages = "120-8", }
