SIAMUF seminar Aspenäs herrgård, Lerum, October 20-21, 2005 Instabilities in Boiling Water Reactors and analysis of flashing-induced instabilities at the CIRCUS test facility C. Demazière Department of Nuclear Engineering Chalmers University of Technology SE-412 96 Göteborg Sweden E-mail: demaz@nephy.chalmers.se C. Demazière SIAMUF seminar, October 20-21, 2005 page -1-
1. Introduction 2 predominant types of existing commercial nuclear power plants: Pressurized Water Reactors (PWRs) and Boiling Water Reactors (BWRs). In BWRs, coolant in the primary system allowed to boil. possibility of density wave instabilities. Overview of the presentation: instabilities in forced-circulation BWRs; instabilities in natural-circulation BWRs. C. Demazière SIAMUF seminar, October 20-21, 2005 page -2-
2. Instabilities in forced-circulation BWRs Existing commercial BWRs of the so-called Gen-II type: C. Demazière SIAMUF seminar, October 20-21, 2005 page -3-
Strong coupling between the neutronics and the thermalhydraulics: Fig. 1. Stability mechanism of a BWR. C. Demazière SIAMUF seminar, October 20-21, 2005 page -4-
Possible self-sustained oscillations due to the time delay between the initial perturbation and the corresponding feedback mechanism, which might reinforce the initial perturbation (instead of damping it): 2 1.5 Reactivity Neutron flux Void Feedback 1 Fluctuations (AU) 0.5 0 0.5 + + + + + 1 1.5 2 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (s) C. Demazière SIAMUF seminar, October 20-21, 2005 page -5-
3 types of instability, all of them involving density waves in the core. 2 (out of 3) modes of instabilities due to the interplay between the neutronics and the thermalhydraulics (the last being a pure thermalhydraulic instability). Decomposition of the neutron flux on a set of orthogonal eigenfunctions ϕ n ( r) in order to understand the radial space-dependence of the coupled instabilities: φ( r, t) = a n ()ϕ t n ( r) n = 0 (1) C. Demazière SIAMUF seminar, October 20-21, 2005 page -6-
where for instance in 1-group age+diffusion theory and for a homogeneous reactor one has: a k () t A n0 ( k n 1) t t 0 = exp ----------- k k exp( B 2 n τ T ) n = ------------------------------------- 1 B 2 2 + n L T t n (2) (3) t n = t d ---------------------- 1 B 2 2 + n L T (4) and B 1 < B 2 < B 3 k 1 > k 2 > k 3 (5) (6) (ordinarily only k 1 which can be larger than 1) C. Demazière SIAMUF seminar, October 20-21, 2005 page -7-
3 types of instability, all of them involving density waves in the core: Fundamental mode or global (in-phase) oscillation fundamental mode oscillating over the whole core; interplay between the neutronics (destabilizing effect since supercritical mode) and the thermalhydraulics (stabilizing effect due to the damping of the pressure/flow oscillations by the recirculation loop). ± ± P Oscillates P39.cvs C. Demazière SIAMUF seminar, October 20-21, 2005 page -8-
Fundamental mode or global (in-phase) oscillation (cont.) fundamental mode oscillating over the whole core; interplay between the neutronics (destabilizing effect since supercritical mode) and the thermalhydraulics (stabilizing effect due to the damping of the pressure/flow oscillations by the recirculation loop). simulation C. Demazière SIAMUF seminar, October 20-21, 2005 page -9-
Reactor Pressure 6.92 MPa 6.9 6.88 0 100 200 300 400 500 600 APRM (A) 100 Unit (%) 80 60 40 0 100 200 300 400 500 600 Coolant Flow 5000 Kg/s 4500 4000 0 100 200 300 400 500 600 Coolant Temperature 268 267 Celcius 266 265 264 0 100 200 300 400 500 600 Time (s) Fig. 2. Example of an in-phase instability event (Oskarshamn-3, February 1998). C. Demazière SIAMUF seminar, October 20-21, 2005 page -10-
Azimuthal mode or regional (out-of-phase) oscillation two first azimuthal (+ axial) modes oscillating over the whole core; interplay between the neutronics (stabilizing effect) and the thermal-hydraulics (destabilizing effect since flow redistribution through the core that always fulfils the boundary conditions imposed by the recirculation loop); eigenvalue separation might be overcome by enough thermal-hydraulic feedback. Core A ± Core B ± P Constant P40.cvs C. Demazière SIAMUF seminar, October 20-21, 2005 page -11-
Azimuthal mode or regional (out-of-phase) oscillation (cont.) two first azimuthal (+ axial) modes oscillating over the whole core; interplay between the neutronics (stabilizing effect) and the thermal-hydraulics (destabilizing effect since flow redistribution through the core that always fulfils the boundary conditions imposed by the recirculation loop); eigenvalue separation might be overcome by enough thermal-hydraulic feedback. simulation C. Demazière SIAMUF seminar, October 20-21, 2005 page -12-
Azimuthal mode or regional (out-of-phase) oscillation (cont.) possible rotating symmetry or neutral line due to the superposition of the two first azimuthal modes, with a phase shift ϕ() t that can vary with time (or equivalently superposition of the two first azimuthal modes with slightly different oscillation frequencies). + ϕ() t ϕ() t C. Demazière SIAMUF seminar, October 20-21, 2005 page -13-
Fig. 3. Example of a stability test with the presence of combined in-phase and out-of-phase oscillations (Ringhals-1, September 2002). C. Demazière SIAMUF seminar, October 20-21, 2005 page -14-
Channel instability or Density Wave Oscillation (DWO) or local oscillation due to a purely thermal-hydraulic feedback effect: fluctuations of pressure drop propagating up and down in the channel (fixed pressure drop over the core). C. Demazière SIAMUF seminar, October 20-21, 2005 page -15-
Channel instability or Density Wave Oscillation (DWO) or local oscillation (cont.) local noise source in a certain channel; can be induced by an unseated fuel assembly, where some of the coolant bypasses the fuel channel. simulation C. Demazière SIAMUF seminar, October 20-21, 2005 page -16-
Fig. 4. Example of a stability test with presence of local oscillations (Forsmark-1, January 1997). C. Demazière SIAMUF seminar, October 20-21, 2005 page -17-
3. Analysis of flashing-induced instabilities in natural-circulation BWRs ESBWR (Economic Simplified Boiling Water Reactor) from General Electric: new nuclear reactor type based on natural circulation. Natural circulation enhanced by a long riser possibility of flashing during startup conditions (in addition to the other types of instabilities in forced-circulation BWRs). C. Demazière SIAMUF seminar, October 20-21, 2005 page -18-
CIRCUS facility at TU Delft for studying flashing-induced instabilities: Different types of oscillations depending on the inlet temperature. C. Demazière SIAMUF seminar, October 20-21, 2005 page -19-
In-phase oscillations: wavelet analysis C. Demazière SIAMUF seminar, October 20-21, 2005 page -20-
Chaotic region: wavelet analysis C. Demazière SIAMUF seminar, October 20-21, 2005 page -21-
Out-of-phase oscillations: wavelet analysis C. Demazière SIAMUF seminar, October 20-21, 2005 page -22-
Continuous flashing in one channel, reverse-flow in the other channel: wavelet analysis C. Demazière SIAMUF seminar, October 20-21, 2005 page -23-
Self-similarity between different scales for the chaotic region fractal Estimation of the fractal dimension based on wavelet methods: partition function (based on the structure of the wavelet-transform modulus maxima): Z( q, a) = ( sup ( xa, ) l W ψ [ s] ( xa, ) ) q l L( a) a τ( q) (7) C. Demazière SIAMUF seminar, October 20-21, 2005 page -24-
Pseudo frequencies (Hz) 0.0130 0.0135 0.0141 0.0148 0.0155 0.0162 0.0171 0.0180 0.0191 0.0203 0.0216 0.0232 0.0250 0.0270 0.0295 0.0324 0.0360 0.0405 0.0463 0.0539 0.0647 0.0807 0.1074 0.1605 0.3171 13.0000 30 30.5 31 31.5 32 32.5 33 33.5 34 34.5 Time (min) Fig. 5. Skeleton of the wavelet-transform modulus maxima (i.e. the maxima lines). C. Demazière SIAMUF seminar, October 20-21, 2005 page -25-
Boltzmann weights: Ŵψ s [ ]( qla,, ) = ( sup ( xa, ) l W ψ [ s] ( xa, ) ) q ----------------------------------------------------------------------------------- ( W ψ [ s] ( xa, ) ) q l L( a) sup ( xa, ) l (8) expectation values: h( qa, ) = Ŵ ψ [ s] ( qla,, ) ln( sup ( xa, ) l W ψ [ s] ( xa, ) ) l L( a) D( qa, ) = Ŵψ[ s] ( qla,, ) lnŵψ[ s] ( qla,, ) l L( a) (9) (10) extraction of: hq ( ) = hqa (, ) lna Dq ( ) = Dqa (, ) lna (11) (12) singularity spectrum Dhq ( ( )). C. Demazière SIAMUF seminar, October 20-21, 2005 page -26-
2 1.5 1 d(h(q)) 0.5 0 0.5 1 0.5 0 0.5 1 1.5 h(q) Fig. 6. Singularity spectrum (preliminary results). C. Demazière SIAMUF seminar, October 20-21, 2005 page -27-
4. Conclusions Presentation of the different types of instabilities in both forced- and natural-circulation BWRs. BWR instabilities still an open issue operating maps inside which the reactor is stable. Wavelet-based methods very good for studying the non-stationary and multifractal character of the BWR instabilities. C. Demazière SIAMUF seminar, October 20-21, 2005 page -28-