# BWR Stability Issues in Japan

Authors: Hideaki Ikeda; Takanori Fukahori; Yuichiro Kubo; Hideo Soneda; Shinya Mizokami
Journal: Science and Technology of Nuclear Installations
 (2008)

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## Abstract

The present paper reviews activates relevant to the boiling water reactor (BWR) stability phenomenon, which has a coupled neutronic and thermal-hydraulic nature, from the viewpoint of model and code developments and their applications to the BWR stability solution methodology in Japan.


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## Body

## 1. introduction

The core power oscillation phenomenon inherently
exists in BWR cores [1], as generally called by the
BWR stability or instability. The BWR instability is possible even at the normal
plant operation conditions, and significant core power oscillations may
threaten core fuel integrity due to the fuel cladding dryout occurrence and/or due
to the strong PCMI (pellet-cladding mechanical interaction). Therefore, an accurate
prediction for the onset of BWR instability is indispensable for the safety of BWR
core design and operation. Hence, numerous efforts have been paid to understand
the complicated BWR instability mechanism and to develop the advanced analysis
models.The stability problem has become an important
concern on safety of BWR operations, in particular, after the instability
incident at LaSalle-2. It should be emphasized that the applied analysis code
predicted a stable core condition while instability actually occurred.
Therefore, GE and US BWROG (BWR Owners’ Group) have improved the stability analysis models which can be
adequately applicable to the actual core design and operation, and have
developed the long-term stability solution methodologies with several
modifications in the plant installation.Also in Japan, similar activities have been
proceeded by the BWR plant/fuel vendors and utilities to exclude any
instability concern. Main goals in Japanese activities are as follows: (1) to
analytically investigate the complicated BWR instability mechanism, the power
oscillation onset/growth, and formation of the limit cycle oscillation, by
using the three-dimensional time-domain code; (2) to empirically define the
stability performance of the employed fuel design, and to assess the accuracy
of calculation results by stability analysis codes using the experimental data,
and (3) to establish the stability solution methodology, in which the selected control
rod insertion (SRI) system is installed to automatically exclude the operated core
from possibly unstable core condition.The present paper describes the BWR stability
issues in Japan. Researches related to the phenomena identification, models,
and codes applicable to the design analysis and stability solution
methodologies are described. Authors suppose that understanding the basis of
the BWR stability issues can be useful for future improvements in the BWR
stability solution methodology based on the advanced analysis models and codes.
In the last section of the present paper, an outline of the on-going research
on the advanced BWR stability solution methodology is to be introduced, which
employs the best-estimate analysis code and the statistical approach in the safety
evaluation methodology.


## 2. BWR Instabilities

The BWR instability can be subcategorized into
the three phenomena: (1) channel instability (density wave oscillation); (2) core
instability (global core power oscillation); and (3) regional instability
(powers in two halves of a core oscillate with an out-of-phase mode).


### 2.1. Channel Instability

The channel instability is equivalent to the
coolant density wave oscillation in a boiling channel, where the channel
pressure drop is kept constant by any constraint [2, 3].
As shown in Figure 1, the coolant void sweeps in the boiling region, which significantly
affects the 2-phase pressure drop, consequently leads to the coolant mass flow oscillation
at the channel inlet. Hence, the channel instability can be invoked in a
channel, where the 2-phase pressure drop is relatively larger than the
single-phase pressure drop, for such conditions as (1) higher channel power and
lower flow rate, (2) lower inlet coolant subcooling, (3) down-skewed axial power
shape, (4) numbers of fuel rods and of fuel spacers which tend to generate the larger
pressure drop in the 2-phase boiling region. In general, however, excitation of
the channel instability can be suppressed by many other stable channels via the neutronic
coupling effect among fuel bundles in an actual core.Figure 1
Schematic description for channel instability mechanism.


### 2.2. Core Instability

The coupled neutronic and thermal-hydraulic
power oscillation can be categorized into the global instability and into the
regional instability. In the first mode, the global core power oscillates
in-phase, while in the regional oscillating mode, the power in a half core
oscillates in an out-of-phase mode with respect to the other half. The core
power oscillation is mainly driven by the negative coolant void feedback with the
finite time del
ay
due to the fuel heat conduction [2]. This power oscillation can be actually excited
by synchronizing with the mentioned density wave oscillation, as schematically
described in Figure 2.
a range from 0.3 to 0.6 Hz [4, 5], which are correlated with the wave
propagation velocity through the core fuel channel.Figure 2
Schematic description for core instability mechanism.The core power oscillation becomes unstable
under the lower flow and higher power core operation condition, corresponding
to the density wave oscillation behavior. Large negative void feedback and faster
fuel heat conduction make the core state unstable. In addition, the past
investigation using frequency-domain stability analysis codes revealed interesting
sensitivity with respect to the core power distribution, as shown in Figure3 [6]. As for the radial power shape, fuel bundles with
high power peaking factors tend to reduce
the channel stability in the entire core, resulting in the core instability. The
sensitivity regarding the axial power shape has more complicated nature as described
below. The down-skewed shape leads to the longer boiling length, which makes
the frequency of the density wave oscillation greater than the time constant in
the fuel heat conduction. This mismatch tends to result in the stable core
power oscillation. On the other hand, the flat and/or the middle-skewed shapes
make the greater influence of neutronics in the high void region of the core,
inducing the core instability due to increase in the negative void feedback.Sensitivity of core power shape to core stability decay ratio.
(a)
Sensitivity of radial core power shape(b)
Sensitivity of axial core power shape


### 2.3. Regional Instability

The basic phenomenon dominating the regional
instability is similar to that for the core instability, and the coupled
neutronic and thermal-hydraulic oscillation can be individually excited in two halves of a core with an out-of-phase
mode. Previous researchers proposed that the regional instability is equivalent
to the oscillation of the higher harmonics (1st azimuthal mode) of
the neutron flux distribution, while the core instability is to the oscillation
of the fundamental mode (see Figure4) [7]. Hashimoto derived the so-called ‘modal point
neutron kinetics equations in order to analytically represent the phenomenon,
in stead of the ordinary point kinetics equations [8]:
(1)dNm(t)dt=ρms−βΛmNm(t)+ρm0(t)ΛmN0+∑n=0∞ρmn(t)ΛmNn(t)+λcm(t),(2)dcm(t)dt=βΛmNm(t)−λcm(t),
where
(3)ρms=1−1/km,(4)ρmn=〈ϕm*,(δM−δL)ϕn〉/〈ϕm*,M0ϕm〉.m is the order of the higher harmonic mode (m=1,2,…); N, c,
and β are the core-averaged neutron flux, del
ayed neutron precursor,
and delayed neutron fraction, respectively. The other variables and notations
are defined in the original paper [8]. Physically, ρms represents the subcriticality of the mth harmonic mode, which is mathematically
corresponding to the eigenvalue separation, and is a negative value in the
above definition. Hashimoto [8] and Takeuchi et al. [9] pointed out that a smaller
absolute value of the subcriticality makes the feedback gain of the regional
oscillation larger, which is correlated to the first term of the right-hand
side of (1), inducing the regional
instability.Sample of spatial neutron harmonics modes.
(a)
Fundamental mode(b)
Higher harmonics (1st Azimuthal) modeAs mentioned above, powers in two halves of a core
oscillate with an out-of-phase mode, therefore, significant oscillations cannot
be observed in the core-averaged power and inlet coolant flow responses. This
results in that the hydraulic flow response via the recirculation loop is less
sensitive to the regional stability.


## 2.1. Channel Instability

The channel instability is equivalent to the
coolant density wave oscillation in a boiling channel, where the channel
pressure drop is kept constant by any constraint [2, 3].
As shown in Figure 1, the coolant void sweeps in the boiling region, which significantly
affects the 2-phase pressure drop, consequently leads to the coolant mass flow oscillation
at the channel inlet. Hence, the channel instability can be invoked in a
channel, where the 2-phase pressure drop is relatively larger than the
single-phase pressure drop, for such conditions as (1) higher channel power and
lower flow rate, (2) lower inlet coolant subcooling, (3) down-skewed axial power
shape, (4) numbers of fuel rods and of fuel spacers which tend to generate the larger
pressure drop in the 2-phase boiling region. In general, however, excitation of
the channel instability can be suppressed by many other stable channels via the neutronic
coupling effect among fuel bundles in an actual core.Figure 1
Schematic description for channel instability mechanism.


## 2.2. Core Instability

The coupled neutronic and thermal-hydraulic
power oscillation can be categorized into the global instability and into the
regional instability. In the first mode, the global core power oscillates
in-phase, while in the regional oscillating mode, the power in a half core
oscillates in an out-of-phase mode with respect to the other half. The core
power oscillation is mainly driven by the negative coolant void feedback with the
finite time del
ay
due to the fuel heat conduction [2]. This power oscillation can be actually excited
by synchronizing with the mentioned density wave oscillation, as schematically
described in Figure 2.
a range from 0.3 to 0.6 Hz [4, 5], which are correlated with the wave
propagation velocity through the core fuel channel.Figure 2
Schematic description for core instability mechanism.The core power oscillation becomes unstable
under the lower flow and higher power core operation condition, corresponding
to the density wave oscillation behavior. Large negative void feedback and faster
fuel heat conduction make the core state unstable. In addition, the past
investigation using frequency-domain stability analysis codes revealed interesting
sensitivity with respect to the core power distribution, as shown in Figure3 [6]. As for the radial power shape, fuel bundles with
high power peaking factors tend to reduce
the channel stability in the entire core, resulting in the core instability. The
sensitivity regarding the axial power shape has more complicated nature as described
below. The down-skewed shape leads to the longer boiling length, which makes
the frequency of the density wave oscillation greater than the time constant in
the fuel heat conduction. This mismatch tends to result in the stable core
power oscillation. On the other hand, the flat and/or the middle-skewed shapes
make the greater influence of neutronics in the high void region of the core,
inducing the core instability due to increase in the negative void feedback.Sensitivity of core power shape to core stability decay ratio.
(a)
Sensitivity of radial core power shape(b)
Sensitivity of axial core power shape


## 2.3. Regional Instability

The basic phenomenon dominating the regional
instability is similar to that for the core instability, and the coupled
neutronic and thermal-hydraulic oscillation can be individually excited in two halves of a core with an out-of-phase
mode. Previous researchers proposed that the regional instability is equivalent
to the oscillation of the higher harmonics (1st azimuthal mode) of
the neutron flux distribution, while the core instability is to the oscillation
of the fundamental mode (see Figure4) [7]. Hashimoto derived the so-called ‘modal point
neutron kinetics equations in order to analytically represent the phenomenon,
in stead of the ordinary point kinetics equations [8]:
(1)dNm(t)dt=ρms−βΛmNm(t)+ρm0(t)ΛmN0+∑n=0∞ρmn(t)ΛmNn(t)+λcm(t),(2)dcm(t)dt=βΛmNm(t)−λcm(t),
where
(3)ρms=1−1/km,(4)ρmn=〈ϕm*,(δM−δL)ϕn〉/〈ϕm*,M0ϕm〉.m is the order of the higher harmonic mode (m=1,2,…); N, c,
and β are the core-averaged neutron flux, del
ayed neutron precursor,
and delayed neutron fraction, respectively. The other variables and notations
are defined in the original paper [8]. Physically, ρms represents the subcriticality of the mth harmonic mode, which is mathematically
corresponding to the eigenvalue separation, and is a negative value in the
above definition. Hashimoto [8] and Takeuchi et al. [9] pointed out that a smaller
absolute value of the subcriticality makes the feedback gain of the regional
oscillation larger, which is correlated to the first term of the right-hand
side of (1), inducing the regional
instability.Sample of spatial neutron harmonics modes.
(a)
Fundamental mode(b)
Higher harmonics (1st Azimuthal) modeAs mentioned above, powers in two halves of a core
oscillate with an out-of-phase mode, therefore, significant oscillations cannot
be observed in the core-averaged power and inlet coolant flow responses. This
results in that the hydraulic flow response via the recirculation loop is less
sensitive to the regional stability.


## 3.BWR Stability Analysis Codes, Verifications, and Applications

Several stability analysis codes have been developed so as
to investigate the BWR instability phenomena in detail, and to apply on the BWR core design
in Japan. The analysis codes can be mainly classified into the two categories, the
frequency-domain code and the time-domain code. Features of the
frequency-domain stability analysis code and of the time-domain code are
summarized in Table1, respectively.Table 1
Features in frequency-domain and time-domain stability analysis codes.
Frequency-domain code (reduced-order model)Time-domain code (3D kinetics model)Computation speedFastSlower than Freq. modelNumerical diffusionNoDependent on numerical schemeDecay ratioDeterminable by the unique way from the Nyquist curve for the system transfer functionSensitive to time-step size, disturbance condition to activate transient state,
in numerical simulationModel limitation1st-order linear perturbation to the nonlinear physical systemsBasically NoSpatial behaviorNoYesNonlinear behaviorNoYes


### 3.1. Reduced-Order Frequency-Domain Codes

In general, the frequency-domain code employs
the reduced-order model like the point neutron kinetics, to mathematically
simplify the phenomenological representation, and to attain the faster
computation time. In addition, the decay ratio, representing the stability
degree of an oscillation, is determinable by the unique methodology based on
the system transfer functions. These features are favorable in the design
analysis. All the equations representing the physical phenomena are linearized
for small perturbations to yield the system transfer functions via the Laplace transformation, which characterize the channel,
core, and regional stabilities. The primary physical equations employed in a
representative frequency-domain code are the followings:(1)
mass, energy, and momentum equations for 2-phase mixture boiling coolant flow;(2)
radial one-dimensional fuel heat conduction equations; and(3)
point neutron kinetics equations.
The thermal-hydraulic behavior in a core is
modeled with the parallel channel geometry, and the fuel heat conduction is
accounted in each hydraulic calculation node. As for the regional stability
analysis, the point neutron kinetics equation is replaced by the modal point
kinetics equation as mentioned in the previous section.Figure5 shows a sample of verification result for the
frequency-domain code, which is currently applied on the BWR core design
analysis. The code is able to derive good correlations over the wide stability
range for the core stability analysis as well as for the regional stability
analysis, while the code models are conservative a priori.Sample of verification for the frequency-domain code using stability test data.
(a)(b)


### 3.2. Three-Dimensional Time-Domain Codes

As described above, the frequency-domain codes
generally employ the simpler fundamental equation set in order to avoid mathematical
difficulties in derivation of the system transfer functions representing the coupled
neutronic and thermal-hydraulic phenomena in a BWR. The time-domain code, on
the other hand, adopts the more sophisticated physical models, like the spatial
neutron kinetics model. In fact, their implementation on a code is simple and
straightforward, while it consumes larger computational time than the mentioned
reduced-order model. Since 1990s, however, the significant advance in
computation technologies has facilitated development of time-domain codes that
employ the complicated three-dimensional and multigroup neutron diffusion
kinetics model [1, 10–14]. Several
time-domain codes developed by
Japanese organizations are listed in Table 2.
The most significant advantage in these codes is
that the detailed spatial kinetics behavior in a core can be explicitly
simulated, namely, both the core stability and the regional stability can be
evaluated using a single three-dimensional time-domain code without any
modification. However, users have to pay attention to the applied numerical
time step size, which is sensitive to the simulated oscillation and decay ratio
[15, 16].Table 2
Three-dimensional stability analysis code in Japan.
CodeDevelopmentCode qualificationsTOSDYNToshibaPeach Bottom-2, Vermont Yankee,
LaSalle-2, Caorso, Leibstadt, KRB-B/C,
BWRS Startup Data, parallel loop channel stability testSTANDYHitachi Toshiba BWR utilities in JapanPeach Bottom-2, Vermont Yankee, LaSalle-2, Caorso,
KRB-B/C, etc.TRACGGeneral electric GNF-A/GNF-J Toshiba HitachiLaSalle-2, Cofrentes, Leibstadt, Forsmark-1, etc.DYNAS-2Nuclear fuel industriesPB-2, WNP-2, KRB-B/C, KKK, Ringhals-1, parallel loop channel stability test, etc.TRAC-BF1/ENTRÉETEPCO systemsRinghals-1Furthermore, a simulator has been implemented on the recent time-domain codes in order to
accomplish the more realistic dynamic simulation reflecting the actual core
state including the fuel history data thus being seamlessly consistent to the
static core design [17, 18].
Figure 6 shows a sample of verification for the
three-dimensional time-domain stability analysis code, SIMULATE-Kinetics,
using the Ringhals-1 stability test data [19, 20]. It can be confirmed that
the code is basically targeting on the best-estimate stability analysis on the contrary to
conservative approach applied in the frequency-domain code. The Ringhals-1 cycle-14 PT9
stability test, where a regional
instability was observed, was accurately simulated as shown in Figure 7
[19]. In addition, the results of numerical
simulation demonstrated that the observed regional instability is equivalent to
an oscillation of the higher harmonics mode (1st azimuthal, N1 defined by (3),
and that modal reactivities (ρ10 and ρ01 defined by (4)
are dominant in the regional event as shown in Figure 8.Sample of verification for the time-domain code using Ringhals-1 stability test data.
(a)(b)Figure 7
Simulated regional instability at Ringhals-1 C14/PT9 stability test.Modal parameter responses under simulated Ringhals-1 C14/PT9 regional instability.
(a)
Simulated modal responses(b)
Simulated modal reactivity responsesA feature of the three-dimensional time-domain
code is that it is applicable to the analytical investigation of the limit
cycle oscillation which is driven by the complicated nonlinear effects [21–23]. Figure 9 schematically describes the del
iberated mechanism in the formation of
limit cycle oscillation. The nonlinear behavior in the 2-phase boiling flow
tend to increase the core-averaged void fraction and the negative void
feedback, which suppresses the growing neutron flux oscillation due to nonlinearity
in the neutron kinetics, resulting in the limit cycles. Any power shift observed
in the measured core power responses and/or in the numerically simulated power
responses (see Figure 10) is due to the above nonlinearities.Figure 9
Mechanism in formation of limit cycle oscillations.Figure 10
Average power shift in simulated Ringhals-1 C14/PT9 regional instability.As for another scientific interest on the regional
limit cycle oscillation, the bifurcation behavior observed via the spectrum
analysis of the measured core power responses [24], Farawila theoretically proposed
that the nonlinear interaction in the modal reactivities defined by (4)
plays an important role in this phenomenon [25]. In addition, Ikeda et al. have
numerically demonstrated that the nonlinearity excites the different higher
harmonics of the core-averaged and regional power responses, respectively, as
shown in Figure 11 [23], which was obtained by applying a spectrum
analysis to the simulated fundamental and higher modal responses (refer to Figure 8).Harmonics excitations under regional limit cycle oscillations.
(a)
Harmonics excitation in measured modal responses [24](b)
Harmonics excitations in simulated modal responses


## 3.1. Reduced-Order Frequency-Domain Codes

In general, the frequency-domain code employs
the reduced-order model like the point neutron kinetics, to mathematically
simplify the phenomenological representation, and to attain the faster
computation time. In addition, the decay ratio, representing the stability
degree of an oscillation, is determinable by the unique methodology based on
the system transfer functions. These features are favorable in the design
analysis. All the equations representing the physical phenomena are linearized
for small perturbations to yield the system transfer functions via the Laplace transformation, which characterize the channel,
core, and regional stabilities. The primary physical equations employed in a
representative frequency-domain code are the followings:(1)
mass, energy, and momentum equations for 2-phase mixture boiling coolant flow;(2)
radial one-dimensional fuel heat conduction equations; and(3)
point neutron kinetics equations.
The thermal-hydraulic behavior in a core is
modeled with the parallel channel geometry, and the fuel heat conduction is
accounted in each hydraulic calculation node. As for the regional stability
analysis, the point neutron kinetics equation is replaced by the modal point
kinetics equation as mentioned in the previous section.Figure5 shows a sample of verification result for the
frequency-domain code, which is currently applied on the BWR core design
analysis. The code is able to derive good correlations over the wide stability
range for the core stability analysis as well as for the regional stability
analysis, while the code models are conservative a priori.Sample of verification for the frequency-domain code using stability test data.
(a)(b)


## 3.2. Three-Dimensional Time-Domain Codes

As described above, the frequency-domain codes
generally employ the simpler fundamental equation set in order to avoid mathematical
difficulties in derivation of the system transfer functions representing the coupled
neutronic and thermal-hydraulic phenomena in a BWR. The time-domain code, on
the other hand, adopts the more sophisticated physical models, like the spatial
neutron kinetics model. In fact, their implementation on a code is simple and
straightforward, while it consumes larger computational time than the mentioned
reduced-order model. Since 1990s, however, the significant advance in
computation technologies has facilitated development of time-domain codes that
employ the complicated three-dimensional and multigroup neutron diffusion
kinetics model [1, 10–14]. Several
time-domain codes developed by
Japanese organizations are listed in Table 2.
The most significant advantage in these codes is
that the detailed spatial kinetics behavior in a core can be explicitly
simulated, namely, both the core stability and the regional stability can be
evaluated using a single three-dimensional time-domain code without any
modification. However, users have to pay attention to the applied numerical
time step size, which is sensitive to the simulated oscillation and decay ratio
[15, 16].Table 2
Three-dimensional stability analysis code in Japan.
CodeDevelopmentCode qualificationsTOSDYNToshibaPeach Bottom-2, Vermont Yankee,
LaSalle-2, Caorso, Leibstadt, KRB-B/C,
BWRS Startup Data, parallel loop channel stability testSTANDYHitachi Toshiba BWR utilities in JapanPeach Bottom-2, Vermont Yankee, LaSalle-2, Caorso,
KRB-B/C, etc.TRACGGeneral electric GNF-A/GNF-J Toshiba HitachiLaSalle-2, Cofrentes, Leibstadt, Forsmark-1, etc.DYNAS-2Nuclear fuel industriesPB-2, WNP-2, KRB-B/C, KKK, Ringhals-1, parallel loop channel stability test, etc.TRAC-BF1/ENTRÉETEPCO systemsRinghals-1Furthermore, a simulator has been implemented on the recent time-domain codes in order to
accomplish the more realistic dynamic simulation reflecting the actual core
state including the fuel history data thus being seamlessly consistent to the
static core design [17, 18].
Figure 6 shows a sample of verification for the
three-dimensional time-domain stability analysis code, SIMULATE-Kinetics,
using the Ringhals-1 stability test data [19, 20]. It can be confirmed that
the code is basically targeting on the best-estimate stability analysis on the contrary to
conservative approach applied in the frequency-domain code. The Ringhals-1 cycle-14 PT9
stability test, where a regional
instability was observed, was accurately simulated as shown in Figure 7
[19]. In addition, the results of numerical
simulation demonstrated that the observed regional instability is equivalent to
an oscillation of the higher harmonics mode (1st azimuthal, N1 defined by (3),
and that modal reactivities (ρ10 and ρ01 defined by (4)
are dominant in the regional event as shown in Figure 8.Sample of verification for the time-domain code using Ringhals-1 stability test data.
(a)(b)Figure 7
Simulated regional instability at Ringhals-1 C14/PT9 stability test.Modal parameter responses under simulated Ringhals-1 C14/PT9 regional instability.
(a)
Simulated modal responses(b)
Simulated modal reactivity responsesA feature of the three-dimensional time-domain
code is that it is applicable to the analytical investigation of the limit
cycle oscillation which is driven by the complicated nonlinear effects [21–23]. Figure 9 schematically describes the del
iberated mechanism in the formation of
limit cycle oscillation. The nonlinear behavior in the 2-phase boiling flow
tend to increase the core-averaged void fraction and the negative void
feedback, which suppresses the growing neutron flux oscillation due to nonlinearity
in the neutron kinetics, resulting in the limit cycles. Any power shift observed
in the measured core power responses and/or in the numerically simulated power
responses (see Figure 10) is due to the above nonlinearities.Figure 9
Mechanism in formation of limit cycle oscillations.Figure 10
Average power shift in simulated Ringhals-1 C14/PT9 regional instability.As for another scientific interest on the regional
limit cycle oscillation, the bifurcation behavior observed via the spectrum
analysis of the measured core power responses [24], Farawila theoretically proposed
that the nonlinear interaction in the modal reactivities defined by (4)
plays an important role in this phenomenon [25]. In addition, Ikeda et al. have
numerically demonstrated that the nonlinearity excites the different higher
harmonics of the core-averaged and regional power responses, respectively, as
shown in Figure 11 [23], which was obtained by applying a spectrum
analysis to the simulated fundamental and higher modal responses (refer to Figure 8).Harmonics excitations under regional limit cycle oscillations.
(a)
Harmonics excitation in measured modal responses [24](b)
Harmonics excitations in simulated modal responses


## 4. Current BWR Stability Solution  Methodology

Since the instability incident at LaSalle-2 [26],
GE, and US-BWROG has developed several long-term stability solution
methodologies [27, 28]. Also in Japan,
a similar stability solution methodology was established, where the adequate
stability margin must be ensured in the core design process, and the selected
control rod insertion (SRI) system is equipped to exclude the BWR core from the
unstable operation region (stability exclusion region) as shown in Figure 12 [29].The SRI system is activated to suppress the
core power when the core coolant recirculation pumps are tripped and the core
goes into the preliminary determined stability exclusion region. The stability
exclusion is to be determined by using stability design codes certified via the
regulatory assessments, with the conservative stability criteria (decay ratio
is less than 0.8). Consequently, this methodology is targeting on that the BWR
instabilities are not possible in the operated core in Japan.Figure 12
Outline of approved stability solution methodology in Japan.


## 5. Research on Advanced BWR Stability  Solution Methodology

The current stability solution methodology is
effectively contributing to safety of BWR plant operations in Japan. However, considering the
recent occurrences of BWR instabilities [30, 31], authors suppose that
any improvement may be indispensable for the future stability solution
methodology, which is able to correspond to the recent modifications in the
existent BWR plants as the extended core thermal power-uprate [32] with the advanced fuel designs
[33–35]. An approach to resolve this concern is that sufficient stability
margin is to be introduced, namely, the plant operable region is limited by the
wider stability exclusion region, which can be determined by using the current
conservative stability analysis code, as shown in Figure 13. This approach, however, possibly leads to the
economical loss by consuming longer time for the plant startup operation.
Reactors with the larger stability exclusion region are generally allowed to
adopt few continuous withdrawals of control rods under the lower power
condition. This is because the continuous-withdrawal operation induces
significant increase in core power at the fixed core flow condition, possibly removing
the core into the prohibited stability exclusion region. Therefore, a lot of
control rod operations, which must be conducted slowly and intermittently to
maintain the fuel mechanical integrity, are required under the higher power
condition to attain the target control rod pattern at the rated power
operation. Consequently, the overall plant startup time tends to become longer
in the BWR plant with the larger stability exclusion region.Figure 13
Plant operable region for the power-uprated core.In order to reasonably enhance the operable
region even under the power-uprated core, a joint research group organized by several
Japanese industrial and academic organizations has started a development of an
advanced stability solution methodology based on the best-estimate code system
[36]. Basis of the present research is to apply the original regulatory criterion
with respect to the BWR instability [37], that is, “exceeding specified acceptable fuel design limits (SAFDLs) are not possible”,
not prevention from the instability occurrence. From the viewpoint of the applicable SAFDLs on
the BWR instability, the PCMI and the material fatigue via the power oscillation
possibly make no significant affect on the fuel integrity, because temperature
responses of the fuel pellet and cladding are negligibly small as shown in Figure 14. Therefore, occurrence of the core coolant
boiling transition (BT) can be a primary cause for the fuel failure under the
BWR instabilities. So as to accurately and mechanistically predict the BT onset
even under the BWR instabilities, the research group is applying an advanced
code system based on the best-estimate plant simulator, TRAC-BF1/ENTRÉE [13], and the 2-fluid/3-field subchannel code, NASCA
[38]. As schematically described in Figure 15, TRAC-BF1/ENTRÉE provides the pin-by-pin-based
power responses in each fuel bundle; the subchannel thermal-hydraulic behavior
and BT onset on the local rods are evaluated by NASCA with the boundary
conditions supplied by the TRAC-BF1/ENTRÉE.Figure 14
Fuel temperature responses under the representative BWR instability.Figure 15
Outline of TRAC-BF1/ENTRÉE and NASCA code system.The research group is also investigating the
possibilities to introduce the statistical safety evaluation methodology [39] so
as to establish the reasonable conservatism in the stability exclusion region
determined by using the above best-estimate code system. The research, in
particular, currently pays a lot of efforts to establish the phenomena
identification ranking table (PIRT) applicable to BWR instabilities including
the subchannel thermal hydraulics, based on the existent stability PIRTs [40–42].
This is the basis of the uncertainty evaluation for the best-estimate BWR
stability analysis.


## 6. Conclusions

Many efforts have been paid to research on BWR stability
issues in Japan, as introduced in the present paper. The industrial organizations have developed
and improved the BWR stability analysis using computational tools specific for
the reduced-order frequency-domain and three-dimensional time-domain codes. The
first category is currently applied to the BWR stability design analysis, while
the latter one has been exploited to understand the complicated phenomena
related to BWR stability. The current stability solution methodology based on
the SRI system with the stability exclusion region is successfully preventing
the occurrence of BWR instabilities in Japan. However, authors suppose
that the future application of the extended core power uprate requires further
improvements to the current solution methodology in order to reasonably
minimize the stability exclusion region. A Japanese research group is currently
proposing to apply the best-estimate analysis code with the statistical safety
evaluation methodology. This will allow better evaluation of the stability
exclusion region, and will be consequently applied to the BWR plants with the
extended core power uprate.



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*Source: 358616-2007-12-13.xml*