# Reliability Assessment of 2400 MWth Gas-Cooled  Fast Reactor Natural Circulation Decay Heat Removal in  Pressurized Situations

Authors: C. Bassi; M. Marques
Journal: Science and Technology of Nuclear Installations
 (2008-01-13)

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## Abstract

As the 2400 MWth gas-cooled fast reactor concept makes use of passive safety features in combination with active safety systems, the question of natural circulation decay heat removal (NCDHR) reliability and performance assessment into the ongoing probabilistic safety assessment in support to the reactor design, named “probabilistic engineering assessment” (PEA), constitutes a challenge. Within the 5th Framework Program for Research and Development (FPRD) of the European Community, a methodology has been developed to evaluate the reliability of passive systems characterized by a moving fluid and whose operation is based on physical principles, such as the natural circulation. This reliability method for passive systems (RMPSs) is based on uncertainties propagation into thermal-hydraulic (T-H) calculations. The aim of this exercise is finally to determine the performance reliability of the DHR system operating in a “passive” mode, taking into account the uncertainties of parameters retained for thermal-hydraulical calculations performed with the CATHARE 2 code. According to the PEA preliminary results, exhibiting the weight of pressurized scenarios (i.e., with intact primary circuit boundary) for the core damage frequency (CDF), the RMPS exercise is first focusing on the NCDHR performance at these T-H conditions.


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## Body

## 1. Introduction

The trend for safety demonstration of new
reactor concepts is, nowadays,  based on the combined application of
deterministic and probabilistic tools (i.e., “risk-informed design guidance”
[1]). In general, the main benefits of the use of probabilistic safety assessment
(PSA) are to provide a risk measurement, which is useful to improve the
concept. It is performed through the identification of plant vulnerabilities,
of intersystem dependencies, and of potential common cause failures (CCFs).
During conceptual design studies, the probabilistic engineering assessment
(PEA), a simplified PSA in support of the design, provides useful insights about
the examination of risk benefits from different design options and helps
designers to improve the concept from safety and economical points of view.
Finally, it anticipates design justifications during the licensing process and
the deterministic safety demonstration.The gas-cooled fast reactor is considered as a
promising concept and has a high priority in CEA R&D work program on future
nuclear energy systems [2, 3]. The main specifications of
the 2400 MWth
GFR concept are driven by the internationally agreed
Generation IV objectives,
which have been “translated” into the main features of the
concept:(i)
a fast neutron
core with a zero breeding gain (without fertile blankets) and characterized by
an initial plutonium inventory allowing for the deployment of a GFR fleet near
2040 (sustainability and proliferation resistance concerns);(ii)
a helium-cooled
primary circuit (7 MPa, 850°C at core
outlet) connected to a Brayton secondary circuit allowing for a high-thermodynamic efficiency (economics concern);(iii)
a decay heat removal
(DHR) system based on dedicated loops allowing for forced or natural
circulation (safety concern).
According to the strategy proposed by the GFR
design team [4], the natural circulation (NC) of gas, through the (DHR) system
(dedicated loops for forced or natural circulation of gas, with passive
water-filled secondary circuit) is foreseen:(i)
for pressurized situations (i.e., with
intact helium pressure boundary);(ii)
for the transient termination (here called
“late phase,” starting around one day after the initiating event) of
depressurized situations.
For the later, owing to the poor NC capability
of gaseous coolant, a pressure level, evaluated at around 1.0 MPa and provided
by a closed-guard containment, should be maintained to guarantee that the
temperatures in the core vessel are kept at acceptable values.As the GFR reactor concept makes use of passive
safety features in combination with active safety systems, the question of natural
circulation decay heat removal (NCDHR) reliability and performance assessment
into the ongoing PEA constitutes a challenge. Within the 5th Framework Program
for Research and Development (FPRD), a methodology has been developed to
evaluate the reliability of passive systems characterized by a moving fluid and
whose operation is based on physical principles, such as the natural
circulation. This reliability method for passive systems (RMPSs) [5] is based,
in particular, on uncertainties propagation into thermal-hydraulic (T-H)
calculations. The aim of this RMPS exercise is finally to determine the
performance reliability of the DHR system operating in a “passive” mode, taking
into account the uncertainties of parameters retained for T-H calculations
(distributions attached to critical parameters and uncertainties propagation). According to the PEA preliminary results,
exhibiting the importance of pressurized scenarios (i.e., with intact primary
circuit boundary) for the core damage frequency (see Section 2.), the RMPS exercise is first focusing on the
NCDHR perfomance at high-primary pressure and decay heat. At this point, some publications which discuss this
topic, for depressurized scenarios, are referred in [6, 7].


## 2. The GFR Decay Heat Removal Strategy

The DHR system has a strong impact on the overall reactor
architecture. On the contrary with other gas-cooled reactor concepts (like high-temperature
reactors), solutions based on core thermal inertia plus conduction and
radiation to remove heat were not applicable to the GFR due to the high core
power density (100 MW/m3 compared to 5–10 MW/m3 in
HTRs). Therefore, the decision was taken to study with more details systems
relying on helium circulation, based on natural circulation as far as possible.
This explains some design criteria and options:(i)
an upward core cooling flow and a location of the
exchangers (DHR and IHX) above the core level;(ii)
a core design criterion based on a low-pressure drop
(which eases the He circulation);(iii)
the use of a guard containment in order to limit
the loss of pressure (sufficient backup pressure) after a primary circuit
depressurization;(iv)
the use of dedicated DHR  loops, allowing to increase
the difference of elevation between the DHR heat exchanger and the core, as
shown in Figure1. If needed, the primary DHR circuit can operate with a
blower, generating a forced circulation in addition to the natural circulation;(v)
the use of three loops (3× 100% redundancy) assuming
that one could be lost due to the accident initiating event (e.g., break)  and that another one must be supposed unavailable (single-failure criterion).
The strategy for the depressurization/backup pressure of
the GFR 2400 MWth has been decided already. The most attractive option is the
“medium” backup pressure strategy: the pressure is kept “high enough” in order
to obtain sufficient margin and to significantly ease the safety demonstration.
In fact, for laminar flow conditions and for a given mass flow, the pumping
power is almost inversely proportional to the square of the gas pressure, this
means that the pumping power decreases very significantly when the pressure
increases. At 1.0 MPa, about 15 to 20 kW are
required few minutes after the reactor SCRAM instead of more than 1 MW at
0.1 MPa. In addition, for scenarios characterized by a loss of primary circuit
integrity (e.g., LOCA), keeping some “backup” pressure at 1.0 MPa allows the
possibility to use natural circulation after some time delay (typically 24 hours)
due to the decay heat decrease. Finally, such medium backup pressure could be
coherent with the use of a metallic containment, also simpler and smaller
systems could be used thus limiting investment, operation, and maintenance
costs.Figure 1
Schematic
of the DHR system.Therefore, the DHR system consists of the following:(i)
a
metallic guard containment enclosing the primary system, not pressurized in
normal operation, and having a free volume such as the fast primary helium
expansion is leading to an
equilibrium pressure of 1.0 MPa;(ii)
three dedicated DHR loops (redundancy) with secondary loops connected to an external water pool
(the ultimate heat sink).This
strategy and the means (systems, phenomena) to achieve their intended mission
are depicted in Figure 2.Figure 2
Schematic of the DHR
strategy based on mixed natural and forced mechanisms [4].


## 3. Sources of Uncertainties in the GFR Probabilistic Engineering Assessment [8]

Until now, a focus is held in the PEA on the two first
families (loss of coolant accidents and loss of offsite power) in order to
check the consistency of the DHR systems layout (two DHR loops operating in a
“dual” circulation scheme: forced circulations (FCs) and natural circulations,
and two DHR loops for forced circulation only and designed according to the
systems diversification principle). The choice of these two families is driven
by the aforementioned DHR strategy (see Section2) depending on the primary
circuit integrity status (LOCAs are representative of depressurized situations
and LOOP of pressurized ones). In Figure 3 is
reported the event tree for the LOOP initiating event.Figure 3
Event tree for LOOP
IE (representative of the pressurized situation) in GFR PEA.It seems important to notice that the two time periods
are distinguished according to the systems or mechanisms potentially involved
for DHR (“early phase” during the first 24 hours, and “late phase” from 24 to 168 hours). Many reasons have led to this choice: the first is design dependant
(batteries or DHR ternary pools autonomy, systems or mechanisms involved during
the two time periods), and the second is relative to some deterministic
practices leading to combine some “frequent IEs” with short-duration LOOP or blackout. Therefore, this PEA will furnish some
relevant results for the design basis events classification. An iterative
process through sensitivity studies (importance measures assessment, sensitivity indices) and
cost-benefit evaluation (systems redundancy level) would finally help to
optimize the concept without safety weakening.Usually, uncertainties are categorized as “aleatory”
(i.e., inability to predict random observable events) or as epistemic [9]
(i.e., our confidence in the knowledge of a model or in some data). These
epistemic uncertainties are roughly related to the input parameters, the
structure of the model, and finally to its completeness.For input parameters, lognormal probability distribution
functions are systematically attached to components-failure rates, with error
factor (i.e., the square root of the 95 to 5 percentile ratio) set to the
following:(i)
three for components with
operational feedback (e.g., water circuits);(ii)
ten for components in a gaseous
environment (e.g,. blowers, valves, etc.).The uncertainty propagation is performed thanks to the Risk
Spectrum [10] software.Model uncertainties are studied through parametric
studies to analyze the effects of simplifying assumptions on the model output
(core bypass assumption weight, e.g., in GFR PEA).Regarding the uncertainties associated with the model
completeness, until now, the PEA model is focusing on representative
situations according to the various means and systems retained in the DHR
strategy; the model is then partial and the PEA results should be affected by a
large amount of uncertainties. The next PEA model, for which initiating events
and scenarios coverage will be enlarged, may lead to a reduction of model
uncertainties.In addition to these common sources of uncertainties for
probabilistic models, the GFR PEA model introduces technological risk
uncertainties (i.e., ability to develop an innovative component or system, and
uncertainties related to the ability of an innovative system to perform the
mission it was designed for). Another significant feature of this probabilistic
assessment representation of the 2400 MWth GFR will be the combination of
systems and T-H reliability models.


## 4. Identification and Quantification of the Sources of Uncertainties for the Natural Circulation Performance Assessment

### 4.1. Influence of the Time Limit Before the Loss of the Forced Circulation Decay Heat
Removal (FCDHR) Process

In order to
define the most relevant case for the RMPS exercise, sensitivity studies were
performed with the CATHARE 2 code. Due to its relatively
high-occurrence
frequency in the GFR PEA (i.e., 10−2/reactor.year), the short
duration loss of offsite power transient (LOOP < 2 hours) is considered as reference scenario for the pressurized situation
depiction. As stated here above, the forced circulation of primary helium is
foreseen in the first
stage to remove the core decay heat. In the LOOP situation, the electrical supply will be provided by emergency diesel generators
(EDGs) or batteries (1 unit per electrical train) to the dedicated circulators.
The combination of components losses leading to the complete loss of FCDHR at
initiating event (e.g., EDGs fail to start or DHR circulators failures)
provides the most stringent case in terms of decay power.For the
2400 MWth GFR, neutronic calculations were performed with the
Darwin code [11] to
estimate the decay heat curve for several minor actinides contents. As reported
in Figure 4, the core power decreases to around 15% of nominal value just after
the control rods full insertion, and decreases rapidly to 3% of nominal power five minutes after
scram.Figure 4
GFR 2400 MWth core decay heat evolution with
time.Despite the
weak occurrence probability of such failures combination, it seems clear that
this situation would provide the most stringent case for NCDHR performance and
reliability assessment (maximum core power). On the other hand, just after the
reactor scram, the pressure level in the primary circuit and the density
difference between hot and cold parts of the DHR loop are maximum, providing
potential high-engaged forces for natural circulation. Sensitivity studies
were performed with the CATHARE 2 code to assess the influence (core decay heat included) at NCDHR actuation, for example, after
the FCDHR phase. Several times before NC, actuation was investigated in comparison with
the a priori most severe case (NCDHR actuation at initiating event,
representative of a blackout transient).In Figure5
are reported the primary pressure evolutions with time for time limits before
FC loss ranging from 1 to 24 hours. As a result, one should notice that the
primary circuit pressure evolutions are similar, monotonic, and ranging from
7.0 to 5.4 MPa during the first 24 hours.Figure 5
Influence of the time limit before NC
actuation on the primary pressure evolutions
(1 DHR loop available).Correlatively with the primary pressure evolutions, the mass flow at core inlet ranges from
23 to 30 kg/s in an FC operating mode (due to a DHR blower rotational speed control scheme, so that DHR circuit pressure drop and blower pressure
rise would be matched for an unchanged mass flow rate when pressure decreases) and from 32 to 25 kg/s in natural
circulation (see Figure6). Indeed, according to the circulator performance map
depiction in the CATHARE 2 model, the mass flow at DHR loop outlet is inversely
proportional to the primary pressure level when the circulator(s) is in
operation. When they fail, the natural circulation is established at a mass
directly depending on the pressure level in the circuit.Figure 6
Influence of the time
limit before NC actuation on the core inlet mass flow evolutions (1 DHR loop
available).In
Figure7 are reported the maximum temperature evolutions in the core with time.
In line with the mass flow at core inlet (between 32 and 20 kg/s), and the
decay heat to extract (between 3 and 0,6%, resp., 5 minutes and 24 hours
after scram), the maximum temperature in the core is monotonically decreasing.
As a result, one should notice that results do not depend on the time limit
before FCDHR loss, indicating that the heat extraction potential by the
secondary and ternary DHR circuits is largely enough to cope with these
situations.Figure 7
Influence of the time
delay before NC actuation on the core temperatures evolutions
(1 DHR loop available).Figure 8
Deductive
approach for RMPS critical parameters determination.In summary,
the core decay heat and primary pressure levels at NCDHR actuation do not
appear as critical parameters for the reliability and performance assessment of
this passive system. Moreover, as the time delay before FC failure is not
influencing the NCDHR performance, it validates the event representation in a
Boolean model for the GFR PEA, as all active system failures during the first
24 hours are aggregated as they occur at initiating event (“static”
probabilistic model).


### 4.2. Other Elements Related to the NCDHR Question

Owing to the
DHR system features design, it is worth noticing that primary gaseous coolant
NC performance is directly related to the natural circulation capability in the
secondary side pressurized water circuit (around 1.0 MPa) through the heat
exchange coefficient in the DHX. Then, the frame of RMPS exercise for the GFR
DHR system is involving a “two-in-one” exercise: one for gaseous coolant, the
second for pressurized water natural circulation.Regarding the NC loop in the primary circuit (from the
core to the dedicated heat exchanger for DHR), the natural circulation of a
gaseous coolant may be subject to several and diverse “disruptions” potentially
challenging its capability to achieve the function it was designed for. One
important feature of gas is owing to the fact that viscosity is increasing with
temperature. Then, since the viscosity increases as the temperature of the gas increase, the Reynolds
number decreases. For the DHR operating conditions, the flow regime is laminar
and friction losses are proportional to the inverse the Reynolds number
(eventually with an exponent, namedm,
i.e., f∝Re−m). Thus as the temperature
increases along the channel, friction losses rise leading potentially to the
flow blockage. For a single gaseous heated channel (i.e., one single core
channel), the laminar flow instability may lead to flow blockage that could be
expressed in terms of temperature difference between the inlet and the outlet
of this channel. These results may be obtained with a simplified development of
the momentum equation in a steady-state approach.For the GFR core, assuming two enrichments core zones
and a radial power profile of about 1.2 (i.e., “parallel” heated channel
characterized by different generated power levels), flow redistribution due to
viscosity effects in the hottest core channels (increased pressure drop
compared to other parallel channels) could occur. Within this frame, simplified
methods could not be employed and the use of the CATHARE 2 code is required.Regarding the
DHR secondary circuit, the natural circulation phenomena are driven by the
density (i.e., typically temperature for pressurized water) change between hot
(i.e., secondary side of the primary to secondary HX) and cold (i.e., primary
side of the secondary to pool HX) parts of the loop, then by at
the exchange at the interfaces between circuits.


### 4.3. Identification of Critical Parameters

#### 4.3.1. Mission of the System

As reported
in Section2,
the major mission of the DHR system is to remove the core decay heat during the
mission time defined for the two representative scenarios:(i)
from nearly 0 to 24 hours for pressurized situations (with intact helium
pressure boundary);(ii)
from 24 to 168 hours for depressurized ones (this mission time is related to
the choice made for the simplified PSA application for GFR); in a first
approach, the mission success will be checked at 48, 72, and 168 hours after
the initiating event, assuming the electrical supplies recovery at these successive time delays.
For both
situations, it is implicitly assumed that additional measures will be taken in order to
guarantee a safe termination of the transient (mobile active systems linked to
the guard containment, for example, recovery of electrical supplies allowing
for a forced circulation transient termination).


#### 4.3.2. Failure Criteria

The DHR
system failure criteria are defined as the failure to maintain a decay heat
removal rate that is required to limit vital component temperatures (vessel
boundary, core plates) to the values of the “IVth category” design safety
limits defined, to date, for GFR safety studies:(i)
1600°C for fissile core (cladding temperature),(ii)
1250°C for He temperature in upper plenum (vessel structures).
By now, these
failure criteria are based on preliminary values used for GFR design and safety
studies. In parallel, some R&D effort is provided by CEA in order to
increase our confidence for future studies.At this
point, it is worth to notice the close interaction between deterministic and
probabilistic studies in support to the safety demonstration. Uncertainties
taken into account through the RMPS exercise will furnish and quantify safety
margins reservations for the deterministic analysis.


#### 4.3.3. Failure Modes and Critical Parameters Identification

It seems not
always obvious to associate a failure mode to the mission of the system due to
the complexity of T-H phenomena and interaction between the passive system and
components present in the fluid potential pathway. As proposed in [5], a qualitative
analysis as the failure mode and effect analysis (FMEA) could be performed
(with a “virtual component” for NC process simulation) to help defining
critical parameters.The proposal
is to determine the critical parameters according to “engineering judgment”
based upon a simplified “deductive analysis” (or cause consequence analysis).
This approach is chosen due to the complexity of the involved phenomena
reported here above, an
FMEA starting from components failure mode and ending at consequences, as the
“deductive analysis” is more attached to physical phenomena. Furthermore, the
method employed for the critical parameters determination is linked to the
level of detail of the systems. As yet, the GFR concept is still under
development and, therefore, the design is not strictly fixed.The
cause-consequence diagrams for this deductive analysis are developed upon
simplified principles:(i)
T-H parameters like pressure, temperature, and gas densities and velocities are
calculated by the CATHARE 2 code; therefore, they are not appearing in block
diagrams introduced in the development of trees;(ii)
according to the former point, the analysis is then based on the development of
diagrams in a “quasi” steady-state approach (a time- and space-dependent
analysis being to complicate without the use of a detailed T-H code); at each
stage, the cause potentially leading to the consequence placed above is
developed until “critical parameters” like code user parameters (e.g., valves
opening fraction, i.e., related singular pressure drop) or specific T-H
features characterized by a lack of knowledge (e.g.,N2 fraction reentering
in the primary circuit through the break) are reached;(iii)
in most cases, the analysis is developed in consistency with the foreseen flow
circulation, for example, starting from the core region going into a dedicated
DHR loop, passing through the DHX, the stopped blower (or the ejector in an
alternative design) and the isolation valve (potentially not fully closed) exiting above the
downcomer and reentering in the core.
The first step for the determination of critical parameters based on this deductive analysis is represented in Figure 8. Starting from the defined mission of the system (decay heat removal during the mission time), referenced as  Stage 0,
the success/failure criteria (see Section 4.3.2) are developed just under this “top
goal” (Stage 1). For the first success/failure criteria (keeping the maximum
fuel temperature under 1600°C in every core channels), two potential failure
modes during the transient phase are defined. Concerning the second success/failure criteria (keeping the maximum coolant temperature at core outlet below
1250°C), we implicitly assume that the gas flow (and temperature) harmonization
at core channels outlet is sufficient to consider the reduction of mass flow at core inlet as the only mean for leading to unacceptable temperature for upper head internal structures (assumption schematized by a red arrow in Figure 8).
In complement to the former point, it is worth to notice the following:(i)
first, the gas temperature at each representative channel output could be a
meaningful indicator for this success/failure criteria, if needed;(ii)
secondly, the precise calculation of heat exchange between the coolant and the
upper head structures necessitate a multidimensional code due to the probable
internal circulation of gas in the upper plenum.
The next step
is then to develop the success/failure criteria into the potential failure
modes (Stage 2). Two ways were determined leading to the increase of the
maximum fuel temperature in a core channel, which are as follows:(i)
the apparition of a “sharp distortion of mass flow between core channels;”(ii)
an “insufficient mass flow at core inlet.”
At this
point, it seems important to remark that the first failure mode addresses
exclusively to the core region, as the second is more related to the gas flow
path from the core boundaries (through the DHR system and eventually through
the main loops if they are not fully closed).The
distortion of mass flow between different core channels could be associated with
the following:(i)
a “spurious closure of an inlet flow gag or flow blockage by foreign object:”
it is assumed that inlet flow restrictions located at assemblies entrance are
designed for a gas outlet temperature equalization at nominal full power
(avoiding hot spots for upper head internal structures and providing an
optimized fuel consumption during the batch cycle); the “inadvertent” closure
would then be assimilated as an “additional event” following the initiating event. This point is also applicable to the potential flow blockage by a foreign
object (or eventually by accumulation of foreign materials) at core inlet;(ii)
the “temperature viscosity-induced laminar instabilities” phenomena for single
heated and, by consequence, for parallel core channels.
Concerning
the insufficient mass flow at core inlet, this consequence is associated with
the following:(i)
a DHR system-related cause (linked to the “NCDHR” capability);(ii)
a main circuit-related cause (“core bypass through the IHX vessel”).
The
development of the cause-consequence diagram for the first point is depicted in
Figure 9 (Stage 3). The steady-state approach is employed in order to assess
the critical parameters for the NC phenomenon with the dedicated decay heat
exchanger. The mass flow decrease at core inlet is linked either to a “decrease
of the NC driving term” or to an “increase of the whole loop friction terms”
(starting from the core inlet, passing through the DHR specific components,
flowing in core vessel, and down to the core), referenced as Stage 4.Figure 9
Development
of the deductive approach for critical parameters determination
(NCDHR pressure drops “1”).The “driving
term” is decomposed into the gas densities difference and the driving height
for NCDHR. It is assumed that thermal dilation of materials (i.e., variation of
the driving height) is negligible compared to the potential variation of gas
densities difference. Therefore, the “driving term decrease” is only related to
the gas densities difference variation, which decomposes in a “decrease of the
mean gas density at DHX” and/or an “increase of the gas density in the core
region” (Stage 5). This increase is related to the critical parameter ECPLAQ, which corresponds to a multiplicative factor for core materials to fluid heat
transfer coefficient.At DHX
primary side, the perfect gas law is employed for defining the causes of a mean
gas density decrease, for example, a “decrease of the mean gas pressure at DHX”
and/or an “increase of the mean gas temperature at DHX.” Concerning the
pressure decrease, we talk about a pressure decrease not due to a pressure drop
increase until the DHX is reached (this effect being reviewed during the
development of the “increase of the whole loop friction terms” block), but
consecutive to a whole circuit pressure decrease. This pressure dropoff in the
primary circuit is assumed to be driven by the “primary circuit natural
leakage” (critical parameter, named FUITE). For the gas mean temperature at DHX
primary side, its increase is attributed to the “decrease of the gas convective
heat transfer in DHX” and/or to the “decrease of the water convective heat
transfer in DHX” (parameter, named ECDHX1 hereafter).Concerning
the gaseous side, the convective heat transfer is proportional to the gas mean
heat conductivity, to the hydraulic diameter in the DHX primary side, and to
the inverse of the Nusselt number of the flow. As for the driving height
variation with temperature (thermal dilatation), the hydraulic diameter
decrease is not taken into account for the determination of critical parameters.
This means that the material accumulation (i.e., fouling) of the DHX at primary
side is not judged as critical as variations of the gas T-H properties (driving
term concern), or as singular pressure drop along the flow path (stopped
blower, isolating valve).The
development of the block entitled “decrease of the water convective heat
transfer in the DHX” emphasizes the so-called “two-in-one” RMPS exercise.
Indeed, as the DHR system secondary side is made of pressurized water (1.0 MPa)
set in motion by natural circulation with an above-positioned immerged heat
exchanger (with a dedicated pool), one should extend the RMPS exercise frame to
the DHR secondary side. According to previous work performed for potential
passive systems designed for pressurized water reactors, the critical
parameters for this part of the RMPS application are directly issued from [5].
Then, in the DHR secondary side, the characteristic parameters will be as
follows:(i)
the initial temperature of water in the pool (named T2DHR);(ii)
the mean temperature of pressurized water in DHR system (i.e., the pool
temperature T2DHR due to secondary-to-ternary thermal equilibrium);(iii)
the pressure in DHR system secondary side (named P2DHR);(iv)
the rate of incondensable gases at the inlet of the pool HX (simulating a
potential leakage through the DHX);(v)
the fouling of the pool HX;(vi)
the number of broken tubes in the pool HX.
The last
three critical parameters are jointly described by a corrective factor of the
exchange coefficient between secondary and ternary “circuits”, that is, ECDHX2.The decrease
of NC driving term (Stage 4) could also be a result of a spurious “increase of
the mean gas density in the core region.” Assuming the gas gaseous coolant as a
perfect gas, this density increase is attributed to a pressure increase and/or
to a mean temperature decrease. Assuming that the pressure increase will solely
be caused by a lack of heat extraction (i.e., a DHR loop inadvertent closure,
or a lack of extraction by secondary circuit, which is the main issue of the
RMPS exercise), the gas mixture increase in the core region is only attributed
to the mean gas temperature decrease. The mean temperature decrease is,
therefore, consecutive to a gas temperature decrease at core inlet and then to
increased exchange terms in the core vessel (not considered for this first
analysis) or at DHX (critical parameter ECDHX1).As for the
determination of the critical parameters related to the “driving term” concern,
the same approach is followed for the “increase of the whole loop friction
terms.” The analysis focuses on the regular and singular pressure drop on the
flow path of the
gaseous mixture (in the representative “loop” starting from the core inlet). In
Figure10 is depicted the development of the block diagram for the potential
increase of “whole loop” pressure drops. In dashed lines are represented two
groups characterized by “structural” (singular pressure drops) and “T-H”
(regular pressure drops) concerns.Figure 10
Development
of the deductive approach for critical parameters determination
(NCDHR pressure drops “2”).It is worth
to notice that only four “major components” are taken into account at the flow
path for pressure drop analysis: the core assemblies (including for each
representative one the inlet flow gag, the lower and upper neutron shielding
zone, and the fissile part), the DHX, the DHR blower (singular pressure drop
when stopped), and the isolation valve. This choice is performed according to
the meaning that they will be the most important contributors for the whole
“loop” pressure drops. Moreover, this choice is linked to the present
complexity of the CATHARE 2 model for the GFR concept whose design is still in
progress.According to
this development, and to the sources of known uncertainties in the CATHARE 2
model, critical parameters potentially challenging the engaged forces are
related to the plate-type core regular pressure drop in laminar conditions (FRPLAQ),
the turbulent-to-laminar transition Reynolds number (REPLAQ) for exchange (cf. ECPLAQ
above) and regular pressure drop assessment in the core region, and the
singular pressure drop provided by the stopped DHR blower (DPSOUF). In a first
step, the singular and regular pressure drop at DHR heat exchanger are not
taken into account, owing to the fact that correlations for circular tubes are
less subject to large uncertainties. In anyway, a sensitivity study is reported
at the end of this document and related to the impact of pressure drop
reservations on margins to failure/success criteria. This work is performed
through the DHR loop isolating valves partial opening and is finally translated
into additional pressure drops in the loops. Therefore, they should
also be investigated as a
combination of other singular pressure drops in the loop
(for DHR HX, e.g.).


## 4.1. Influence of the Time Limit Before the Loss of the Forced Circulation Decay Heat
Removal (FCDHR) Process

In order to
define the most relevant case for the RMPS exercise, sensitivity studies were
performed with the CATHARE 2 code. Due to its relatively
high-occurrence
frequency in the GFR PEA (i.e., 10−2/reactor.year), the short
duration loss of offsite power transient (LOOP < 2 hours) is considered as reference scenario for the pressurized situation
depiction. As stated here above, the forced circulation of primary helium is
foreseen in the first
stage to remove the core decay heat. In the LOOP situation, the electrical supply will be provided by emergency diesel generators
(EDGs) or batteries (1 unit per electrical train) to the dedicated circulators.
The combination of components losses leading to the complete loss of FCDHR at
initiating event (e.g., EDGs fail to start or DHR circulators failures)
provides the most stringent case in terms of decay power.For the
2400 MWth GFR, neutronic calculations were performed with the
Darwin code [11] to
estimate the decay heat curve for several minor actinides contents. As reported
in Figure 4, the core power decreases to around 15% of nominal value just after
the control rods full insertion, and decreases rapidly to 3% of nominal power five minutes after
scram.Figure 4
GFR 2400 MWth core decay heat evolution with
time.Despite the
weak occurrence probability of such failures combination, it seems clear that
this situation would provide the most stringent case for NCDHR performance and
reliability assessment (maximum core power). On the other hand, just after the
reactor scram, the pressure level in the primary circuit and the density
difference between hot and cold parts of the DHR loop are maximum, providing
potential high-engaged forces for natural circulation. Sensitivity studies
were performed with the CATHARE 2 code to assess the influence (core decay heat included) at NCDHR actuation, for example, after
the FCDHR phase. Several times before NC, actuation was investigated in comparison with
the a priori most severe case (NCDHR actuation at initiating event,
representative of a blackout transient).In Figure5
are reported the primary pressure evolutions with time for time limits before
FC loss ranging from 1 to 24 hours. As a result, one should notice that the
primary circuit pressure evolutions are similar, monotonic, and ranging from
7.0 to 5.4 MPa during the first 24 hours.Figure 5
Influence of the time limit before NC
actuation on the primary pressure evolutions
(1 DHR loop available).Correlatively with the primary pressure evolutions, the mass flow at core inlet ranges from
23 to 30 kg/s in an FC operating mode (due to a DHR blower rotational speed control scheme, so that DHR circuit pressure drop and blower pressure
rise would be matched for an unchanged mass flow rate when pressure decreases) and from 32 to 25 kg/s in natural
circulation (see Figure6). Indeed, according to the circulator performance map
depiction in the CATHARE 2 model, the mass flow at DHR loop outlet is inversely
proportional to the primary pressure level when the circulator(s) is in
operation. When they fail, the natural circulation is established at a mass
directly depending on the pressure level in the circuit.Figure 6
Influence of the time
limit before NC actuation on the core inlet mass flow evolutions (1 DHR loop
available).In
Figure7 are reported the maximum temperature evolutions in the core with time.
In line with the mass flow at core inlet (between 32 and 20 kg/s), and the
decay heat to extract (between 3 and 0,6%, resp., 5 minutes and 24 hours
after scram), the maximum temperature in the core is monotonically decreasing.
As a result, one should notice that results do not depend on the time limit
before FCDHR loss, indicating that the heat extraction potential by the
secondary and ternary DHR circuits is largely enough to cope with these
situations.Figure 7
Influence of the time
delay before NC actuation on the core temperatures evolutions
(1 DHR loop available).Figure 8
Deductive
approach for RMPS critical parameters determination.In summary,
the core decay heat and primary pressure levels at NCDHR actuation do not
appear as critical parameters for the reliability and performance assessment of
this passive system. Moreover, as the time delay before FC failure is not
influencing the NCDHR performance, it validates the event representation in a
Boolean model for the GFR PEA, as all active system failures during the first
24 hours are aggregated as they occur at initiating event (“static”
probabilistic model).


## 4.2. Other Elements Related to the NCDHR Question

Owing to the
DHR system features design, it is worth noticing that primary gaseous coolant
NC performance is directly related to the natural circulation capability in the
secondary side pressurized water circuit (around 1.0 MPa) through the heat
exchange coefficient in the DHX. Then, the frame of RMPS exercise for the GFR
DHR system is involving a “two-in-one” exercise: one for gaseous coolant, the
second for pressurized water natural circulation.Regarding the NC loop in the primary circuit (from the
core to the dedicated heat exchanger for DHR), the natural circulation of a
gaseous coolant may be subject to several and diverse “disruptions” potentially
challenging its capability to achieve the function it was designed for. One
important feature of gas is owing to the fact that viscosity is increasing with
temperature. Then, since the viscosity increases as the temperature of the gas increase, the Reynolds
number decreases. For the DHR operating conditions, the flow regime is laminar
and friction losses are proportional to the inverse the Reynolds number
(eventually with an exponent, namedm,
i.e., f∝Re−m). Thus as the temperature
increases along the channel, friction losses rise leading potentially to the
flow blockage. For a single gaseous heated channel (i.e., one single core
channel), the laminar flow instability may lead to flow blockage that could be
expressed in terms of temperature difference between the inlet and the outlet
of this channel. These results may be obtained with a simplified development of
the momentum equation in a steady-state approach.For the GFR core, assuming two enrichments core zones
and a radial power profile of about 1.2 (i.e., “parallel” heated channel
characterized by different generated power levels), flow redistribution due to
viscosity effects in the hottest core channels (increased pressure drop
compared to other parallel channels) could occur. Within this frame, simplified
methods could not be employed and the use of the CATHARE 2 code is required.Regarding the
DHR secondary circuit, the natural circulation phenomena are driven by the
density (i.e., typically temperature for pressurized water) change between hot
(i.e., secondary side of the primary to secondary HX) and cold (i.e., primary
side of the secondary to pool HX) parts of the loop, then by at
the exchange at the interfaces between circuits.


## 4.3. Identification of Critical Parameters

### 4.3.1. Mission of the System

As reported
in Section2,
the major mission of the DHR system is to remove the core decay heat during the
mission time defined for the two representative scenarios:(i)
from nearly 0 to 24 hours for pressurized situations (with intact helium
pressure boundary);(ii)
from 24 to 168 hours for depressurized ones (this mission time is related to
the choice made for the simplified PSA application for GFR); in a first
approach, the mission success will be checked at 48, 72, and 168 hours after
the initiating event, assuming the electrical supplies recovery at these successive time delays.
For both
situations, it is implicitly assumed that additional measures will be taken in order to
guarantee a safe termination of the transient (mobile active systems linked to
the guard containment, for example, recovery of electrical supplies allowing
for a forced circulation transient termination).


### 4.3.2. Failure Criteria

The DHR
system failure criteria are defined as the failure to maintain a decay heat
removal rate that is required to limit vital component temperatures (vessel
boundary, core plates) to the values of the “IVth category” design safety
limits defined, to date, for GFR safety studies:(i)
1600°C for fissile core (cladding temperature),(ii)
1250°C for He temperature in upper plenum (vessel structures).
By now, these
failure criteria are based on preliminary values used for GFR design and safety
studies. In parallel, some R&D effort is provided by CEA in order to
increase our confidence for future studies.At this
point, it is worth to notice the close interaction between deterministic and
probabilistic studies in support to the safety demonstration. Uncertainties
taken into account through the RMPS exercise will furnish and quantify safety
margins reservations for the deterministic analysis.


### 4.3.3. Failure Modes and Critical Parameters Identification

It seems not
always obvious to associate a failure mode to the mission of the system due to
the complexity of T-H phenomena and interaction between the passive system and
components present in the fluid potential pathway. As proposed in [5], a qualitative
analysis as the failure mode and effect analysis (FMEA) could be performed
(with a “virtual component” for NC process simulation) to help defining
critical parameters.The proposal
is to determine the critical parameters according to “engineering judgment”
based upon a simplified “deductive analysis” (or cause consequence analysis).
This approach is chosen due to the complexity of the involved phenomena
reported here above, an
FMEA starting from components failure mode and ending at consequences, as the
“deductive analysis” is more attached to physical phenomena. Furthermore, the
method employed for the critical parameters determination is linked to the
level of detail of the systems. As yet, the GFR concept is still under
development and, therefore, the design is not strictly fixed.The
cause-consequence diagrams for this deductive analysis are developed upon
simplified principles:(i)
T-H parameters like pressure, temperature, and gas densities and velocities are
calculated by the CATHARE 2 code; therefore, they are not appearing in block
diagrams introduced in the development of trees;(ii)
according to the former point, the analysis is then based on the development of
diagrams in a “quasi” steady-state approach (a time- and space-dependent
analysis being to complicate without the use of a detailed T-H code); at each
stage, the cause potentially leading to the consequence placed above is
developed until “critical parameters” like code user parameters (e.g., valves
opening fraction, i.e., related singular pressure drop) or specific T-H
features characterized by a lack of knowledge (e.g.,N2 fraction reentering
in the primary circuit through the break) are reached;(iii)
in most cases, the analysis is developed in consistency with the foreseen flow
circulation, for example, starting from the core region going into a dedicated
DHR loop, passing through the DHX, the stopped blower (or the ejector in an
alternative design) and the isolation valve (potentially not fully closed) exiting above the
downcomer and reentering in the core.
The first step for the determination of critical parameters based on this deductive analysis is represented in Figure 8. Starting from the defined mission of the system (decay heat removal during the mission time), referenced as  Stage 0,
the success/failure criteria (see Section 4.3.2) are developed just under this “top
goal” (Stage 1). For the first success/failure criteria (keeping the maximum
fuel temperature under 1600°C in every core channels), two potential failure
modes during the transient phase are defined. Concerning the second success/failure criteria (keeping the maximum coolant temperature at core outlet below
1250°C), we implicitly assume that the gas flow (and temperature) harmonization
at core channels outlet is sufficient to consider the reduction of mass flow at core inlet as the only mean for leading to unacceptable temperature for upper head internal structures (assumption schematized by a red arrow in Figure 8).
In complement to the former point, it is worth to notice the following:(i)
first, the gas temperature at each representative channel output could be a
meaningful indicator for this success/failure criteria, if needed;(ii)
secondly, the precise calculation of heat exchange between the coolant and the
upper head structures necessitate a multidimensional code due to the probable
internal circulation of gas in the upper plenum.
The next step
is then to develop the success/failure criteria into the potential failure
modes (Stage 2). Two ways were determined leading to the increase of the
maximum fuel temperature in a core channel, which are as follows:(i)
the apparition of a “sharp distortion of mass flow between core channels;”(ii)
an “insufficient mass flow at core inlet.”
At this
point, it seems important to remark that the first failure mode addresses
exclusively to the core region, as the second is more related to the gas flow
path from the core boundaries (through the DHR system and eventually through
the main loops if they are not fully closed).The
distortion of mass flow between different core channels could be associated with
the following:(i)
a “spurious closure of an inlet flow gag or flow blockage by foreign object:”
it is assumed that inlet flow restrictions located at assemblies entrance are
designed for a gas outlet temperature equalization at nominal full power
(avoiding hot spots for upper head internal structures and providing an
optimized fuel consumption during the batch cycle); the “inadvertent” closure
would then be assimilated as an “additional event” following the initiating event. This point is also applicable to the potential flow blockage by a foreign
object (or eventually by accumulation of foreign materials) at core inlet;(ii)
the “temperature viscosity-induced laminar instabilities” phenomena for single
heated and, by consequence, for parallel core channels.
Concerning
the insufficient mass flow at core inlet, this consequence is associated with
the following:(i)
a DHR system-related cause (linked to the “NCDHR” capability);(ii)
a main circuit-related cause (“core bypass through the IHX vessel”).
The
development of the cause-consequence diagram for the first point is depicted in
Figure 9 (Stage 3). The steady-state approach is employed in order to assess
the critical parameters for the NC phenomenon with the dedicated decay heat
exchanger. The mass flow decrease at core inlet is linked either to a “decrease
of the NC driving term” or to an “increase of the whole loop friction terms”
(starting from the core inlet, passing through the DHR specific components,
flowing in core vessel, and down to the core), referenced as Stage 4.Figure 9
Development
of the deductive approach for critical parameters determination
(NCDHR pressure drops “1”).The “driving
term” is decomposed into the gas densities difference and the driving height
for NCDHR. It is assumed that thermal dilation of materials (i.e., variation of
the driving height) is negligible compared to the potential variation of gas
densities difference. Therefore, the “driving term decrease” is only related to
the gas densities difference variation, which decomposes in a “decrease of the
mean gas density at DHX” and/or an “increase of the gas density in the core
region” (Stage 5). This increase is related to the critical parameter ECPLAQ, which corresponds to a multiplicative factor for core materials to fluid heat
transfer coefficient.At DHX
primary side, the perfect gas law is employed for defining the causes of a mean
gas density decrease, for example, a “decrease of the mean gas pressure at DHX”
and/or an “increase of the mean gas temperature at DHX.” Concerning the
pressure decrease, we talk about a pressure decrease not due to a pressure drop
increase until the DHX is reached (this effect being reviewed during the
development of the “increase of the whole loop friction terms” block), but
consecutive to a whole circuit pressure decrease. This pressure dropoff in the
primary circuit is assumed to be driven by the “primary circuit natural
leakage” (critical parameter, named FUITE). For the gas mean temperature at DHX
primary side, its increase is attributed to the “decrease of the gas convective
heat transfer in DHX” and/or to the “decrease of the water convective heat
transfer in DHX” (parameter, named ECDHX1 hereafter).Concerning
the gaseous side, the convective heat transfer is proportional to the gas mean
heat conductivity, to the hydraulic diameter in the DHX primary side, and to
the inverse of the Nusselt number of the flow. As for the driving height
variation with temperature (thermal dilatation), the hydraulic diameter
decrease is not taken into account for the determination of critical parameters.
This means that the material accumulation (i.e., fouling) of the DHX at primary
side is not judged as critical as variations of the gas T-H properties (driving
term concern), or as singular pressure drop along the flow path (stopped
blower, isolating valve).The
development of the block entitled “decrease of the water convective heat
transfer in the DHX” emphasizes the so-called “two-in-one” RMPS exercise.
Indeed, as the DHR system secondary side is made of pressurized water (1.0 MPa)
set in motion by natural circulation with an above-positioned immerged heat
exchanger (with a dedicated pool), one should extend the RMPS exercise frame to
the DHR secondary side. According to previous work performed for potential
passive systems designed for pressurized water reactors, the critical
parameters for this part of the RMPS application are directly issued from [5].
Then, in the DHR secondary side, the characteristic parameters will be as
follows:(i)
the initial temperature of water in the pool (named T2DHR);(ii)
the mean temperature of pressurized water in DHR system (i.e., the pool
temperature T2DHR due to secondary-to-ternary thermal equilibrium);(iii)
the pressure in DHR system secondary side (named P2DHR);(iv)
the rate of incondensable gases at the inlet of the pool HX (simulating a
potential leakage through the DHX);(v)
the fouling of the pool HX;(vi)
the number of broken tubes in the pool HX.
The last
three critical parameters are jointly described by a corrective factor of the
exchange coefficient between secondary and ternary “circuits”, that is, ECDHX2.The decrease
of NC driving term (Stage 4) could also be a result of a spurious “increase of
the mean gas density in the core region.” Assuming the gas gaseous coolant as a
perfect gas, this density increase is attributed to a pressure increase and/or
to a mean temperature decrease. Assuming that the pressure increase will solely
be caused by a lack of heat extraction (i.e., a DHR loop inadvertent closure,
or a lack of extraction by secondary circuit, which is the main issue of the
RMPS exercise), the gas mixture increase in the core region is only attributed
to the mean gas temperature decrease. The mean temperature decrease is,
therefore, consecutive to a gas temperature decrease at core inlet and then to
increased exchange terms in the core vessel (not considered for this first
analysis) or at DHX (critical parameter ECDHX1).As for the
determination of the critical parameters related to the “driving term” concern,
the same approach is followed for the “increase of the whole loop friction
terms.” The analysis focuses on the regular and singular pressure drop on the
flow path of the
gaseous mixture (in the representative “loop” starting from the core inlet). In
Figure10 is depicted the development of the block diagram for the potential
increase of “whole loop” pressure drops. In dashed lines are represented two
groups characterized by “structural” (singular pressure drops) and “T-H”
(regular pressure drops) concerns.Figure 10
Development
of the deductive approach for critical parameters determination
(NCDHR pressure drops “2”).It is worth
to notice that only four “major components” are taken into account at the flow
path for pressure drop analysis: the core assemblies (including for each
representative one the inlet flow gag, the lower and upper neutron shielding
zone, and the fissile part), the DHX, the DHR blower (singular pressure drop
when stopped), and the isolation valve. This choice is performed according to
the meaning that they will be the most important contributors for the whole
“loop” pressure drops. Moreover, this choice is linked to the present
complexity of the CATHARE 2 model for the GFR concept whose design is still in
progress.According to
this development, and to the sources of known uncertainties in the CATHARE 2
model, critical parameters potentially challenging the engaged forces are
related to the plate-type core regular pressure drop in laminar conditions (FRPLAQ),
the turbulent-to-laminar transition Reynolds number (REPLAQ) for exchange (cf. ECPLAQ
above) and regular pressure drop assessment in the core region, and the
singular pressure drop provided by the stopped DHR blower (DPSOUF). In a first
step, the singular and regular pressure drop at DHR heat exchanger are not
taken into account, owing to the fact that correlations for circular tubes are
less subject to large uncertainties. In anyway, a sensitivity study is reported
at the end of this document and related to the impact of pressure drop
reservations on margins to failure/success criteria. This work is performed
through the DHR loop isolating valves partial opening and is finally translated
into additional pressure drops in the loops. Therefore, they should
also be investigated as a
combination of other singular pressure drops in the loop
(for DHR HX, e.g.).


## 4.3.1. Mission of the System

As reported
in Section2,
the major mission of the DHR system is to remove the core decay heat during the
mission time defined for the two representative scenarios:(i)
from nearly 0 to 24 hours for pressurized situations (with intact helium
pressure boundary);(ii)
from 24 to 168 hours for depressurized ones (this mission time is related to
the choice made for the simplified PSA application for GFR); in a first
approach, the mission success will be checked at 48, 72, and 168 hours after
the initiating event, assuming the electrical supplies recovery at these successive time delays.
For both
situations, it is implicitly assumed that additional measures will be taken in order to
guarantee a safe termination of the transient (mobile active systems linked to
the guard containment, for example, recovery of electrical supplies allowing
for a forced circulation transient termination).


## 4.3.2. Failure Criteria

The DHR
system failure criteria are defined as the failure to maintain a decay heat
removal rate that is required to limit vital component temperatures (vessel
boundary, core plates) to the values of the “IVth category” design safety
limits defined, to date, for GFR safety studies:(i)
1600°C for fissile core (cladding temperature),(ii)
1250°C for He temperature in upper plenum (vessel structures).
By now, these
failure criteria are based on preliminary values used for GFR design and safety
studies. In parallel, some R&D effort is provided by CEA in order to
increase our confidence for future studies.At this
point, it is worth to notice the close interaction between deterministic and
probabilistic studies in support to the safety demonstration. Uncertainties
taken into account through the RMPS exercise will furnish and quantify safety
margins reservations for the deterministic analysis.


## 4.3.3. Failure Modes and Critical Parameters Identification

It seems not
always obvious to associate a failure mode to the mission of the system due to
the complexity of T-H phenomena and interaction between the passive system and
components present in the fluid potential pathway. As proposed in [5], a qualitative
analysis as the failure mode and effect analysis (FMEA) could be performed
(with a “virtual component” for NC process simulation) to help defining
critical parameters.The proposal
is to determine the critical parameters according to “engineering judgment”
based upon a simplified “deductive analysis” (or cause consequence analysis).
This approach is chosen due to the complexity of the involved phenomena
reported here above, an
FMEA starting from components failure mode and ending at consequences, as the
“deductive analysis” is more attached to physical phenomena. Furthermore, the
method employed for the critical parameters determination is linked to the
level of detail of the systems. As yet, the GFR concept is still under
development and, therefore, the design is not strictly fixed.The
cause-consequence diagrams for this deductive analysis are developed upon
simplified principles:(i)
T-H parameters like pressure, temperature, and gas densities and velocities are
calculated by the CATHARE 2 code; therefore, they are not appearing in block
diagrams introduced in the development of trees;(ii)
according to the former point, the analysis is then based on the development of
diagrams in a “quasi” steady-state approach (a time- and space-dependent
analysis being to complicate without the use of a detailed T-H code); at each
stage, the cause potentially leading to the consequence placed above is
developed until “critical parameters” like code user parameters (e.g., valves
opening fraction, i.e., related singular pressure drop) or specific T-H
features characterized by a lack of knowledge (e.g.,N2 fraction reentering
in the primary circuit through the break) are reached;(iii)
in most cases, the analysis is developed in consistency with the foreseen flow
circulation, for example, starting from the core region going into a dedicated
DHR loop, passing through the DHX, the stopped blower (or the ejector in an
alternative design) and the isolation valve (potentially not fully closed) exiting above the
downcomer and reentering in the core.
The first step for the determination of critical parameters based on this deductive analysis is represented in Figure 8. Starting from the defined mission of the system (decay heat removal during the mission time), referenced as  Stage 0,
the success/failure criteria (see Section 4.3.2) are developed just under this “top
goal” (Stage 1). For the first success/failure criteria (keeping the maximum
fuel temperature under 1600°C in every core channels), two potential failure
modes during the transient phase are defined. Concerning the second success/failure criteria (keeping the maximum coolant temperature at core outlet below
1250°C), we implicitly assume that the gas flow (and temperature) harmonization
at core channels outlet is sufficient to consider the reduction of mass flow at core inlet as the only mean for leading to unacceptable temperature for upper head internal structures (assumption schematized by a red arrow in Figure 8).
In complement to the former point, it is worth to notice the following:(i)
first, the gas temperature at each representative channel output could be a
meaningful indicator for this success/failure criteria, if needed;(ii)
secondly, the precise calculation of heat exchange between the coolant and the
upper head structures necessitate a multidimensional code due to the probable
internal circulation of gas in the upper plenum.
The next step
is then to develop the success/failure criteria into the potential failure
modes (Stage 2). Two ways were determined leading to the increase of the
maximum fuel temperature in a core channel, which are as follows:(i)
the apparition of a “sharp distortion of mass flow between core channels;”(ii)
an “insufficient mass flow at core inlet.”
At this
point, it seems important to remark that the first failure mode addresses
exclusively to the core region, as the second is more related to the gas flow
path from the core boundaries (through the DHR system and eventually through
the main loops if they are not fully closed).The
distortion of mass flow between different core channels could be associated with
the following:(i)
a “spurious closure of an inlet flow gag or flow blockage by foreign object:”
it is assumed that inlet flow restrictions located at assemblies entrance are
designed for a gas outlet temperature equalization at nominal full power
(avoiding hot spots for upper head internal structures and providing an
optimized fuel consumption during the batch cycle); the “inadvertent” closure
would then be assimilated as an “additional event” following the initiating event. This point is also applicable to the potential flow blockage by a foreign
object (or eventually by accumulation of foreign materials) at core inlet;(ii)
the “temperature viscosity-induced laminar instabilities” phenomena for single
heated and, by consequence, for parallel core channels.
Concerning
the insufficient mass flow at core inlet, this consequence is associated with
the following:(i)
a DHR system-related cause (linked to the “NCDHR” capability);(ii)
a main circuit-related cause (“core bypass through the IHX vessel”).
The
development of the cause-consequence diagram for the first point is depicted in
Figure 9 (Stage 3). The steady-state approach is employed in order to assess
the critical parameters for the NC phenomenon with the dedicated decay heat
exchanger. The mass flow decrease at core inlet is linked either to a “decrease
of the NC driving term” or to an “increase of the whole loop friction terms”
(starting from the core inlet, passing through the DHR specific components,
flowing in core vessel, and down to the core), referenced as Stage 4.Figure 9
Development
of the deductive approach for critical parameters determination
(NCDHR pressure drops “1”).The “driving
term” is decomposed into the gas densities difference and the driving height
for NCDHR. It is assumed that thermal dilation of materials (i.e., variation of
the driving height) is negligible compared to the potential variation of gas
densities difference. Therefore, the “driving term decrease” is only related to
the gas densities difference variation, which decomposes in a “decrease of the
mean gas density at DHX” and/or an “increase of the gas density in the core
region” (Stage 5). This increase is related to the critical parameter ECPLAQ, which corresponds to a multiplicative factor for core materials to fluid heat
transfer coefficient.At DHX
primary side, the perfect gas law is employed for defining the causes of a mean
gas density decrease, for example, a “decrease of the mean gas pressure at DHX”
and/or an “increase of the mean gas temperature at DHX.” Concerning the
pressure decrease, we talk about a pressure decrease not due to a pressure drop
increase until the DHX is reached (this effect being reviewed during the
development of the “increase of the whole loop friction terms” block), but
consecutive to a whole circuit pressure decrease. This pressure dropoff in the
primary circuit is assumed to be driven by the “primary circuit natural
leakage” (critical parameter, named FUITE). For the gas mean temperature at DHX
primary side, its increase is attributed to the “decrease of the gas convective
heat transfer in DHX” and/or to the “decrease of the water convective heat
transfer in DHX” (parameter, named ECDHX1 hereafter).Concerning
the gaseous side, the convective heat transfer is proportional to the gas mean
heat conductivity, to the hydraulic diameter in the DHX primary side, and to
the inverse of the Nusselt number of the flow. As for the driving height
variation with temperature (thermal dilatation), the hydraulic diameter
decrease is not taken into account for the determination of critical parameters.
This means that the material accumulation (i.e., fouling) of the DHX at primary
side is not judged as critical as variations of the gas T-H properties (driving
term concern), or as singular pressure drop along the flow path (stopped
blower, isolating valve).The
development of the block entitled “decrease of the water convective heat
transfer in the DHX” emphasizes the so-called “two-in-one” RMPS exercise.
Indeed, as the DHR system secondary side is made of pressurized water (1.0 MPa)
set in motion by natural circulation with an above-positioned immerged heat
exchanger (with a dedicated pool), one should extend the RMPS exercise frame to
the DHR secondary side. According to previous work performed for potential
passive systems designed for pressurized water reactors, the critical
parameters for this part of the RMPS application are directly issued from [5].
Then, in the DHR secondary side, the characteristic parameters will be as
follows:(i)
the initial temperature of water in the pool (named T2DHR);(ii)
the mean temperature of pressurized water in DHR system (i.e., the pool
temperature T2DHR due to secondary-to-ternary thermal equilibrium);(iii)
the pressure in DHR system secondary side (named P2DHR);(iv)
the rate of incondensable gases at the inlet of the pool HX (simulating a
potential leakage through the DHX);(v)
the fouling of the pool HX;(vi)
the number of broken tubes in the pool HX.
The last
three critical parameters are jointly described by a corrective factor of the
exchange coefficient between secondary and ternary “circuits”, that is, ECDHX2.The decrease
of NC driving term (Stage 4) could also be a result of a spurious “increase of
the mean gas density in the core region.” Assuming the gas gaseous coolant as a
perfect gas, this density increase is attributed to a pressure increase and/or
to a mean temperature decrease. Assuming that the pressure increase will solely
be caused by a lack of heat extraction (i.e., a DHR loop inadvertent closure,
or a lack of extraction by secondary circuit, which is the main issue of the
RMPS exercise), the gas mixture increase in the core region is only attributed
to the mean gas temperature decrease. The mean temperature decrease is,
therefore, consecutive to a gas temperature decrease at core inlet and then to
increased exchange terms in the core vessel (not considered for this first
analysis) or at DHX (critical parameter ECDHX1).As for the
determination of the critical parameters related to the “driving term” concern,
the same approach is followed for the “increase of the whole loop friction
terms.” The analysis focuses on the regular and singular pressure drop on the
flow path of the
gaseous mixture (in the representative “loop” starting from the core inlet). In
Figure10 is depicted the development of the block diagram for the potential
increase of “whole loop” pressure drops. In dashed lines are represented two
groups characterized by “structural” (singular pressure drops) and “T-H”
(regular pressure drops) concerns.Figure 10
Development
of the deductive approach for critical parameters determination
(NCDHR pressure drops “2”).It is worth
to notice that only four “major components” are taken into account at the flow
path for pressure drop analysis: the core assemblies (including for each
representative one the inlet flow gag, the lower and upper neutron shielding
zone, and the fissile part), the DHX, the DHR blower (singular pressure drop
when stopped), and the isolation valve. This choice is performed according to
the meaning that they will be the most important contributors for the whole
“loop” pressure drops. Moreover, this choice is linked to the present
complexity of the CATHARE 2 model for the GFR concept whose design is still in
progress.According to
this development, and to the sources of known uncertainties in the CATHARE 2
model, critical parameters potentially challenging the engaged forces are
related to the plate-type core regular pressure drop in laminar conditions (FRPLAQ),
the turbulent-to-laminar transition Reynolds number (REPLAQ) for exchange (cf. ECPLAQ
above) and regular pressure drop assessment in the core region, and the
singular pressure drop provided by the stopped DHR blower (DPSOUF). In a first
step, the singular and regular pressure drop at DHR heat exchanger are not
taken into account, owing to the fact that correlations for circular tubes are
less subject to large uncertainties. In anyway, a sensitivity study is reported
at the end of this document and related to the impact of pressure drop
reservations on margins to failure/success criteria. This work is performed
through the DHR loop isolating valves partial opening and is finally translated
into additional pressure drops in the loops. Therefore, they should
also be investigated as a
combination of other singular pressure drops in the loop
(for DHR HX, e.g.).


## 5. Reliability Evaluation of Passive Systems with the Cathare 2 Code

### 5.1. The CATHARE 2 Model for GFR

The complete
CATHARE 2 [12, 13] model for 2400 MWth GFR is composed of the following:(i)
the primary circuit with helium as coolant, includingthe main reactor
vessel comprising the core, three principal-independent loops each containing a
finned plate intermediate heat exchanger (IHX) and a blower, three tanks for
helium supply (for guard containment pressure), and three dedicated DHR
loops, each with its own water-filled secondary and pool-type ternary
circuits;(ii)
each principal loop has its own secondary circuit for power conversion,
includingthe second part of IHX, a single shaft-mounted turbomachinery,
and a steam generator; the working fluid in the secondary circuit is a mixture
of helium and nitrogen with mass fractions, respectively, equal to 20% and
80%;(iii)
a ternary steam-water circuit (second part of the once-through counter-current
plate-shape steam generator).Each
dedicated DHR loop is composed of the following:(i)
a primary loop (crossduct connected to the core vessel), with a driving height
of 10 m between core and DHX midplan;(ii)
a secondary circuit filled with pressurized water at 1.0 MPa (driving height
for NCDHR of 5 m);(iii)
a ternary pool, initially at 50°C, whose volume is determined to handle one-day
heat extraction (after this time delay, additional measures are foreseen
to fill up the pool).
In addition,
a large free volume filled with nitrogen is described for guard containment
simulation in case of a depressurization accident. This free volume is
hydraulically and energetically linked to the primary circuit by specific
functionalities implemented in the CATHARE 2.5 version.A special
care was put on the core model, taking into account the heterogeneous plate
structure, the core radial dimension and power profiles (6 hydraulics channels
with singular pressure drop in order to equalize the outlet temperature in
nominal conditions, etc.).In Figure11
are reported the main features of one dedicated DHR loop modeled in the CATHARE
2 input data deck for 2400 MWth GFR [14].Figure 11
DHR loop features and nodalization in the
CATHARE 2 code.


### 5.2. Critical Parameters Distributions and Sampling

The first
class of parameters addresses the specific uncertainties associated with
factors on which the magnitude of the engaged forces and counter forces depends
(values of heat transfer coefficients and pressure losses) on the following:(i)
in the core region: correlations
used to calculate the Nusselt number and the friction factor have different
functional forms depending on the geometry, fluid characteristics, and flow
regime (forced, natural, or mixed); as natural and mixed convection
correlations are not supported by extensive experimental results, the resulting
correlations in natural convection laminar regime are subject to large
uncertainties; for the GFR core (plate-type core),
an R&D program is underway in CEA to
establish specific correlations for these geometry and T-H conditions [15]; however,
multiplicative factors are retained in the present CATHARE 2 input data deck
for exchanging coefficients and regular friction factors in laminar regime (the
transition regime Reynolds number being also a critical parameter);(ii)
in the DHR loop: exchange
coefficients multiplicative factors for primary to secondary, and
from secondary to ternary pool heat exchangers.
The second
class of parameters addresses the uncertainties associated with the potential
discrepancy of T-H parameters at transient initiation:(i)
a first subclass is related to the ternary and secondary DHR circuits initial
temperature and pressure; by this way, we implicitly assume that small
deviations are possible within the allowable range defined by the protection
system; therefore, these parameters are characterized by lower and upper bounds
between−   15% and  +  15%
around their nominal values;(ii)
the second subclass concerns the primary circuit natural leakage (named FUITE),
and is very concept dependant (number of loops, nozzles, sealing systems for
rotating machines, etc.).
The critical
parameters and their distribution features are given in Table 1, which have
been established by engineering judgment.Owing to the precision required for this first NCDHR
performance and reliability assessment, and compared to the magnitude of other
sources of uncertainties in the PEA model, the number of calculations is first
limited at 100. An optimized Latin hypercube sampling (LHS) is then performed
according to the distributions and bounds selected reported in Table1 and
furnishes a set of values as input parameters for the CATHARE 2 calculations.
In Table 2 are given the mean, standard deviation, and minimum and maximum
values for each critical parameter after LHS.Table 1
Critical parameters distributions.
MeanDistributionMin. valueMax. valueT2DHR50°CNormal42.5°C57.5°CP2DHR1.0 MPanormal0.85 MPa1.15 MPaFRPLAQ15%Normal030%ECPLAQ5%Normal010%REPLAQ5000Normal40006000ECDHX15%Normal010%ECDHX25%normal010%DPSOUF15%Normal030%Max.DistributionLower boundUpper boundFUITE2e− 04Triangular2e− 52e− 3Table 2
Mean, standard
deviation (SD), and upper and lower bounds for critical parameters after LHS
(100 values).
MeanSDMin. valueMax. valueT2DHR50.0093.308e+ 004.293e+ 015.720e+ 01P2DHR9.998e+  056.625e+ 048.583e+ 051.144e+ 06FUITE7.40e− 044.487e− 046.287e− 051.812e− 03FRPLAQ1.50e− 016.639e− 025.444e− 032.972e− 01ECPLAQ4.99e− 022.212e− 024.632e− 059.773e− 02REPLAQ4.99e+ 034.411e+ 024.063e+ 035.930e+ 03ECDHX14.99e− 022.211e− 021.423e− 039.634e− 02ECDHX24.99e− 022.213e− 022.564e− 039.888e− 02DPSOUF1.50e− 016.614e− 026.816e− 032.895e− 01In
Figures12, 13 are, respectively, plotted the 100 values and the final distribution
for the first critical parameter, for example, T2DHR, in order to check the
consistency of the sampling.Figure 12
Optimized
LHS (100 values for T2DHR).Figure 13
Verification of the T2DHR distribution after
sampling.


### 5.3. RMPS Exercise Results

The process
followed for this RMPS exercise implies to combine the steady state (due to the
secondary circuit pressure and ternary pool temperature initialization) and the
transient calculations with CATHARE 2.  Each calculation takes around 5000 seconds
CPU on a personal computer under LINUX operating system.The results
obtained with  the CATHARE 2 code are plotted in Figure14 showing the core
maximum temperature evolution with time.Figure 14
RMPS reference case—maximum temperature in the core region
evolutions.As shown by Figure14, a sharp decrease of the core temperature occurs during the first minute of
the transient due to the reactor scram and the main blower rundown on their inertia. Until the NCDHR is established, the
temperatures are increasing up to around 1030°C and then decrease owing to the
large amount of energy exchanged with the secondary (and ternary) DHR circuit.
As a result, one should notice the weak discrepancy of the temperature
evolutions with time and of the maximum level reached. In Figure 15 is reported
the maximum temperature distribution for these 100 calculations. At this stage,
it is worth mentioning the robustness of the CATHARE 2 code as around 94%
calculations performed provide
results (6 calculations exiting without results).Figure 15
RMPS reference case—maximum temperature in the core region
distribution.This temperature distribution is characterized by a
mean value of 1029°C and a standard deviation of 4.3°C (see Table 3).Table 3
Results for the RMPS
reference case.
MeanSDLowerUpperTMAX (°C)10294.3210191037TUPPER (°C)9072.35903913Compared to the failure/success criteria fixed at
1600°C as mentioned earlier in this document, the results obtained with the
CATHARE 2 code are exhibiting the safety margin conferred by the DHR loop
structural and thermodynamical design. For the ongoing PEA, it seems that the
reliability of the natural circulation in pressurized situation is close to
unity. In order to determine a more precise value of the NCDHR unreliability
(if necessary, according to the magnitude of the other sources of uncertainties
in the PEA model), the percentile corresponding to 1600°C can be calculated.
Another way to evaluate the NCDHR unreliability consists in the research of
linear correlation between the response result and the input parameters, in
order to increase the number of calculations with a low CPU cost.


#### 5.3.1. Correlations between Input Parameters and Temperature Results

A linear correlation between TMAX (maximum temperature
in the core region) and input parameters has been determined:(1)TMAX=1016.5+(T2DHR*0.30211)−(FUITE*449.71)+(FRPLAQ*63.027)−(ECPLAQ*18.222)−(REPLAQ*2.4157*10−3)+(ECDHX1*5.5575).
It should be mentioned that this linear correlation is
based only on 6 input parameters (the last three ones having a negligible
influence for the response). The  R2 coefficient of determination for
this linear model is equal to 97%. Figure 16 compares TMAX calculated by the
CATHARE 2 code and simulated by the linear model.Figure 16
Real versus
simulated maximum temperature in the core region.According to this result, the utilization of linear standard
regression coefficients is justified in order to rank the most influent
parameters (see Table4).Table 4
Linear correlation
standard regression coefficient.
TMAXTUPPERSRCRankSRCRankT2DHR0.2330.302P2DHR0.027−0.087FUITE−0.0550.085FRPLAQ0.9610.019ECPLAQ−0.094−0.083REPLAQ−0.2420.801ECDHX10.036−0.018ECDHX20.018−0.084DPSOUF−0.0190.086The ranking is based on absolute values, as the sign
is indicating the effect of variation of the input parameter for the response.
For TMAX, the most influent parameters are, according to importance, FRPLAQ (multiplicative factor for
laminar NC pressure drop in the core region), REPLAQ (Reynolds number for
turbulent to laminar transition in the core region), and T2DHR (ternary pool
and secondary circuit temperature level at DHR initiation).According to the above-mentioned linear regression,
106 simulations are performed to increase the number of calculations (compared to
the 100 ones performed with CATHARE 2) and then to improve the probability
value of the NC reliability assessment in the PEA model.The results are leading to a value of NCDHR
unreliability performance less than5.10−6 with a confidence
level above 99%. It is worth to notice that this unreliability value is surely
overestimated as the upper value of TMAX (1041°C) estimated by 106 simulations is far from the 1600°C limit. This result will be incorporated in
the next PEA model.


#### 5.3.2. Sensitivity Study upon the DHR Isolating Valve Opening Fraction

Concerning
the isolation valves opening fraction, the CATHARE 2 code requires an evolution
law of the valve flow coefficient (Cv) with the valve’s stem position (Pu). The
assumption made in the input data deck is considering a linear evolution of Cv
with Pu ranging from105 (for  Pu = 0) and 0 (for  pu = 1). The law valve
expression in CATHARE 2 code is (2)Cv=3600⋅q27,3⋅Y⋅x⋅Pa⋅ρa⋅10−5,
where Y=1−x/(3⋅Fγ⋅xt),  x=ΔP/Pa,  Fγ=γ/1.4≈1,67/1.4,
xt=0.6804,q    is the mass flow in sonic condition
(in kg/s),  Pa is the upstream pressure (in Pa),    ΔP
is the pressure drop (in Pa),  ρa is the upstream gas density (in kg/m3).According
to this expression and the bounding values of Cv, it seems more efficient to
translate the stem position in terms of additional singular pressure drop in
the NC loop (and here provided by the DHR isolating valve). As reported in Figure17, the pressure drop stays under 1000 Pa for a valve opening fraction above
25%, and increases rapidly for a stem position less than 10% (around 10000 Pa
for a stem position close to 7%).Figure 17
Flow coefficient and
related pressure drop versus stem position for DHR isolating valves.Sensitivity calculations were performed with the CATHARE
2 code in order to feel the impact of this additional pressure loss related to
the valve depiction in the code (see Figure18).Figure 18
Maximum fuel
temperature evolutions for different values of DHR valve stem position (1 DHR
loop available).If we consider a maximum opened fraction for the DHR isolating
valve of 10%, the maximum temperature in the core is around 1400°C. However,
for this opened fraction (or additional pressure drop in the primary NC loop,
evaluated at 5200 Pa according to the  Cv  versus  Pu  valve law), the gas
temperature at core outlet reaches 1286°C, that is, just above the 1250°C
criteria defined in Section 4.3.2. For a valve opening fraction close to 7%, which is
giving an additional pressure drop in the NC loop of about
10000 Pa, the 1600°C
criterion is  approximately reached. In Figure 19 are reported the maximum temperatures in the core
region and of the gas at core outlet versus  the additional singular pressure
drop in the  NC loop.Figure 19
Fuel and gas
temperature evolutions versus additional pressure drop in the DHR loop.According to
the results obtained in this sensitivity study, it was decided to perform
another set of calculations for an additional singular pressure drop in the NC
loop of about 10000 Pa  (i.e., valve opening fraction close to 7%). The RMPS
methodology was applied with the same set of values for critical parameters as
generated by LHS in the RMPS reference case. The temperature evolutions with
time are reported in Figure20.Figure 20
RMPS alternative
case (1 DHR loop, valve opening fraction=  7%).In Table5 are given the statistical results of the
responses provided by the CATHARE 2 calculations.Table 5
Results for the RMPS alternative case.
MeanSDLowerUpperTMAX
(°C)157510.0915471595TUPPER
(°C)14516.8114341465As in the reference case, a linear correlation has
been determined in order  to increase the number of calculations (up to106)
and correlatively, the statistics precision for the NC reliability evaluation.
Considering a pressure loss penalty of about 0.1 MPa, the unreliability of the
NC process is evaluated at about  2,3,10−3 considering
only the TMAX criterion. The most influent parameters for the NC performance
and reliability are the same as in the reference case (i.e., T2DHR, FRPLAQ, and
REPLAQ).


## 5.1. The CATHARE 2 Model for GFR

The complete
CATHARE 2 [12, 13] model for 2400 MWth GFR is composed of the following:(i)
the primary circuit with helium as coolant, includingthe main reactor
vessel comprising the core, three principal-independent loops each containing a
finned plate intermediate heat exchanger (IHX) and a blower, three tanks for
helium supply (for guard containment pressure), and three dedicated DHR
loops, each with its own water-filled secondary and pool-type ternary
circuits;(ii)
each principal loop has its own secondary circuit for power conversion,
includingthe second part of IHX, a single shaft-mounted turbomachinery,
and a steam generator; the working fluid in the secondary circuit is a mixture
of helium and nitrogen with mass fractions, respectively, equal to 20% and
80%;(iii)
a ternary steam-water circuit (second part of the once-through counter-current
plate-shape steam generator).Each
dedicated DHR loop is composed of the following:(i)
a primary loop (crossduct connected to the core vessel), with a driving height
of 10 m between core and DHX midplan;(ii)
a secondary circuit filled with pressurized water at 1.0 MPa (driving height
for NCDHR of 5 m);(iii)
a ternary pool, initially at 50°C, whose volume is determined to handle one-day
heat extraction (after this time delay, additional measures are foreseen
to fill up the pool).
In addition,
a large free volume filled with nitrogen is described for guard containment
simulation in case of a depressurization accident. This free volume is
hydraulically and energetically linked to the primary circuit by specific
functionalities implemented in the CATHARE 2.5 version.A special
care was put on the core model, taking into account the heterogeneous plate
structure, the core radial dimension and power profiles (6 hydraulics channels
with singular pressure drop in order to equalize the outlet temperature in
nominal conditions, etc.).In Figure11
are reported the main features of one dedicated DHR loop modeled in the CATHARE
2 input data deck for 2400 MWth GFR [14].Figure 11
DHR loop features and nodalization in the
CATHARE 2 code.


## 5.2. Critical Parameters Distributions and Sampling

The first
class of parameters addresses the specific uncertainties associated with
factors on which the magnitude of the engaged forces and counter forces depends
(values of heat transfer coefficients and pressure losses) on the following:(i)
in the core region: correlations
used to calculate the Nusselt number and the friction factor have different
functional forms depending on the geometry, fluid characteristics, and flow
regime (forced, natural, or mixed); as natural and mixed convection
correlations are not supported by extensive experimental results, the resulting
correlations in natural convection laminar regime are subject to large
uncertainties; for the GFR core (plate-type core),
an R&D program is underway in CEA to
establish specific correlations for these geometry and T-H conditions [15]; however,
multiplicative factors are retained in the present CATHARE 2 input data deck
for exchanging coefficients and regular friction factors in laminar regime (the
transition regime Reynolds number being also a critical parameter);(ii)
in the DHR loop: exchange
coefficients multiplicative factors for primary to secondary, and
from secondary to ternary pool heat exchangers.
The second
class of parameters addresses the uncertainties associated with the potential
discrepancy of T-H parameters at transient initiation:(i)
a first subclass is related to the ternary and secondary DHR circuits initial
temperature and pressure; by this way, we implicitly assume that small
deviations are possible within the allowable range defined by the protection
system; therefore, these parameters are characterized by lower and upper bounds
between−   15% and  +  15%
around their nominal values;(ii)
the second subclass concerns the primary circuit natural leakage (named FUITE),
and is very concept dependant (number of loops, nozzles, sealing systems for
rotating machines, etc.).
The critical
parameters and their distribution features are given in Table 1, which have
been established by engineering judgment.Owing to the precision required for this first NCDHR
performance and reliability assessment, and compared to the magnitude of other
sources of uncertainties in the PEA model, the number of calculations is first
limited at 100. An optimized Latin hypercube sampling (LHS) is then performed
according to the distributions and bounds selected reported in Table1 and
furnishes a set of values as input parameters for the CATHARE 2 calculations.
In Table 2 are given the mean, standard deviation, and minimum and maximum
values for each critical parameter after LHS.Table 1
Critical parameters distributions.
MeanDistributionMin. valueMax. valueT2DHR50°CNormal42.5°C57.5°CP2DHR1.0 MPanormal0.85 MPa1.15 MPaFRPLAQ15%Normal030%ECPLAQ5%Normal010%REPLAQ5000Normal40006000ECDHX15%Normal010%ECDHX25%normal010%DPSOUF15%Normal030%Max.DistributionLower boundUpper boundFUITE2e− 04Triangular2e− 52e− 3Table 2
Mean, standard
deviation (SD), and upper and lower bounds for critical parameters after LHS
(100 values).
MeanSDMin. valueMax. valueT2DHR50.0093.308e+ 004.293e+ 015.720e+ 01P2DHR9.998e+  056.625e+ 048.583e+ 051.144e+ 06FUITE7.40e− 044.487e− 046.287e− 051.812e− 03FRPLAQ1.50e− 016.639e− 025.444e− 032.972e− 01ECPLAQ4.99e− 022.212e− 024.632e− 059.773e− 02REPLAQ4.99e+ 034.411e+ 024.063e+ 035.930e+ 03ECDHX14.99e− 022.211e− 021.423e− 039.634e− 02ECDHX24.99e− 022.213e− 022.564e− 039.888e− 02DPSOUF1.50e− 016.614e− 026.816e− 032.895e− 01In
Figures12, 13 are, respectively, plotted the 100 values and the final distribution
for the first critical parameter, for example, T2DHR, in order to check the
consistency of the sampling.Figure 12
Optimized
LHS (100 values for T2DHR).Figure 13
Verification of the T2DHR distribution after
sampling.


## 5.3. RMPS Exercise Results

The process
followed for this RMPS exercise implies to combine the steady state (due to the
secondary circuit pressure and ternary pool temperature initialization) and the
transient calculations with CATHARE 2.  Each calculation takes around 5000 seconds
CPU on a personal computer under LINUX operating system.The results
obtained with  the CATHARE 2 code are plotted in Figure14 showing the core
maximum temperature evolution with time.Figure 14
RMPS reference case—maximum temperature in the core region
evolutions.As shown by Figure14, a sharp decrease of the core temperature occurs during the first minute of
the transient due to the reactor scram and the main blower rundown on their inertia. Until the NCDHR is established, the
temperatures are increasing up to around 1030°C and then decrease owing to the
large amount of energy exchanged with the secondary (and ternary) DHR circuit.
As a result, one should notice the weak discrepancy of the temperature
evolutions with time and of the maximum level reached. In Figure 15 is reported
the maximum temperature distribution for these 100 calculations. At this stage,
it is worth mentioning the robustness of the CATHARE 2 code as around 94%
calculations performed provide
results (6 calculations exiting without results).Figure 15
RMPS reference case—maximum temperature in the core region
distribution.This temperature distribution is characterized by a
mean value of 1029°C and a standard deviation of 4.3°C (see Table 3).Table 3
Results for the RMPS
reference case.
MeanSDLowerUpperTMAX (°C)10294.3210191037TUPPER (°C)9072.35903913Compared to the failure/success criteria fixed at
1600°C as mentioned earlier in this document, the results obtained with the
CATHARE 2 code are exhibiting the safety margin conferred by the DHR loop
structural and thermodynamical design. For the ongoing PEA, it seems that the
reliability of the natural circulation in pressurized situation is close to
unity. In order to determine a more precise value of the NCDHR unreliability
(if necessary, according to the magnitude of the other sources of uncertainties
in the PEA model), the percentile corresponding to 1600°C can be calculated.
Another way to evaluate the NCDHR unreliability consists in the research of
linear correlation between the response result and the input parameters, in
order to increase the number of calculations with a low CPU cost.


### 5.3.1. Correlations between Input Parameters and Temperature Results

A linear correlation between TMAX (maximum temperature
in the core region) and input parameters has been determined:(1)TMAX=1016.5+(T2DHR*0.30211)−(FUITE*449.71)+(FRPLAQ*63.027)−(ECPLAQ*18.222)−(REPLAQ*2.4157*10−3)+(ECDHX1*5.5575).
It should be mentioned that this linear correlation is
based only on 6 input parameters (the last three ones having a negligible
influence for the response). The  R2 coefficient of determination for
this linear model is equal to 97%. Figure 16 compares TMAX calculated by the
CATHARE 2 code and simulated by the linear model.Figure 16
Real versus
simulated maximum temperature in the core region.According to this result, the utilization of linear standard
regression coefficients is justified in order to rank the most influent
parameters (see Table4).Table 4
Linear correlation
standard regression coefficient.
TMAXTUPPERSRCRankSRCRankT2DHR0.2330.302P2DHR0.027−0.087FUITE−0.0550.085FRPLAQ0.9610.019ECPLAQ−0.094−0.083REPLAQ−0.2420.801ECDHX10.036−0.018ECDHX20.018−0.084DPSOUF−0.0190.086The ranking is based on absolute values, as the sign
is indicating the effect of variation of the input parameter for the response.
For TMAX, the most influent parameters are, according to importance, FRPLAQ (multiplicative factor for
laminar NC pressure drop in the core region), REPLAQ (Reynolds number for
turbulent to laminar transition in the core region), and T2DHR (ternary pool
and secondary circuit temperature level at DHR initiation).According to the above-mentioned linear regression,
106 simulations are performed to increase the number of calculations (compared to
the 100 ones performed with CATHARE 2) and then to improve the probability
value of the NC reliability assessment in the PEA model.The results are leading to a value of NCDHR
unreliability performance less than5.10−6 with a confidence
level above 99%. It is worth to notice that this unreliability value is surely
overestimated as the upper value of TMAX (1041°C) estimated by 106 simulations is far from the 1600°C limit. This result will be incorporated in
the next PEA model.


### 5.3.2. Sensitivity Study upon the DHR Isolating Valve Opening Fraction

Concerning
the isolation valves opening fraction, the CATHARE 2 code requires an evolution
law of the valve flow coefficient (Cv) with the valve’s stem position (Pu). The
assumption made in the input data deck is considering a linear evolution of Cv
with Pu ranging from105 (for  Pu = 0) and 0 (for  pu = 1). The law valve
expression in CATHARE 2 code is (2)Cv=3600⋅q27,3⋅Y⋅x⋅Pa⋅ρa⋅10−5,
where Y=1−x/(3⋅Fγ⋅xt),  x=ΔP/Pa,  Fγ=γ/1.4≈1,67/1.4,
xt=0.6804,q    is the mass flow in sonic condition
(in kg/s),  Pa is the upstream pressure (in Pa),    ΔP
is the pressure drop (in Pa),  ρa is the upstream gas density (in kg/m3).According
to this expression and the bounding values of Cv, it seems more efficient to
translate the stem position in terms of additional singular pressure drop in
the NC loop (and here provided by the DHR isolating valve). As reported in Figure17, the pressure drop stays under 1000 Pa for a valve opening fraction above
25%, and increases rapidly for a stem position less than 10% (around 10000 Pa
for a stem position close to 7%).Figure 17
Flow coefficient and
related pressure drop versus stem position for DHR isolating valves.Sensitivity calculations were performed with the CATHARE
2 code in order to feel the impact of this additional pressure loss related to
the valve depiction in the code (see Figure18).Figure 18
Maximum fuel
temperature evolutions for different values of DHR valve stem position (1 DHR
loop available).If we consider a maximum opened fraction for the DHR isolating
valve of 10%, the maximum temperature in the core is around 1400°C. However,
for this opened fraction (or additional pressure drop in the primary NC loop,
evaluated at 5200 Pa according to the  Cv  versus  Pu  valve law), the gas
temperature at core outlet reaches 1286°C, that is, just above the 1250°C
criteria defined in Section 4.3.2. For a valve opening fraction close to 7%, which is
giving an additional pressure drop in the NC loop of about
10000 Pa, the 1600°C
criterion is  approximately reached. In Figure 19 are reported the maximum temperatures in the core
region and of the gas at core outlet versus  the additional singular pressure
drop in the  NC loop.Figure 19
Fuel and gas
temperature evolutions versus additional pressure drop in the DHR loop.According to
the results obtained in this sensitivity study, it was decided to perform
another set of calculations for an additional singular pressure drop in the NC
loop of about 10000 Pa  (i.e., valve opening fraction close to 7%). The RMPS
methodology was applied with the same set of values for critical parameters as
generated by LHS in the RMPS reference case. The temperature evolutions with
time are reported in Figure20.Figure 20
RMPS alternative
case (1 DHR loop, valve opening fraction=  7%).In Table5 are given the statistical results of the
responses provided by the CATHARE 2 calculations.Table 5
Results for the RMPS alternative case.
MeanSDLowerUpperTMAX
(°C)157510.0915471595TUPPER
(°C)14516.8114341465As in the reference case, a linear correlation has
been determined in order  to increase the number of calculations (up to106)
and correlatively, the statistics precision for the NC reliability evaluation.
Considering a pressure loss penalty of about 0.1 MPa, the unreliability of the
NC process is evaluated at about  2,3,10−3 considering
only the TMAX criterion. The most influent parameters for the NC performance
and reliability are the same as in the reference case (i.e., T2DHR, FRPLAQ, and
REPLAQ).


## 5.3.1. Correlations between Input Parameters and Temperature Results

A linear correlation between TMAX (maximum temperature
in the core region) and input parameters has been determined:(1)TMAX=1016.5+(T2DHR*0.30211)−(FUITE*449.71)+(FRPLAQ*63.027)−(ECPLAQ*18.222)−(REPLAQ*2.4157*10−3)+(ECDHX1*5.5575).
It should be mentioned that this linear correlation is
based only on 6 input parameters (the last three ones having a negligible
influence for the response). The  R2 coefficient of determination for
this linear model is equal to 97%. Figure 16 compares TMAX calculated by the
CATHARE 2 code and simulated by the linear model.Figure 16
Real versus
simulated maximum temperature in the core region.According to this result, the utilization of linear standard
regression coefficients is justified in order to rank the most influent
parameters (see Table4).Table 4
Linear correlation
standard regression coefficient.
TMAXTUPPERSRCRankSRCRankT2DHR0.2330.302P2DHR0.027−0.087FUITE−0.0550.085FRPLAQ0.9610.019ECPLAQ−0.094−0.083REPLAQ−0.2420.801ECDHX10.036−0.018ECDHX20.018−0.084DPSOUF−0.0190.086The ranking is based on absolute values, as the sign
is indicating the effect of variation of the input parameter for the response.
For TMAX, the most influent parameters are, according to importance, FRPLAQ (multiplicative factor for
laminar NC pressure drop in the core region), REPLAQ (Reynolds number for
turbulent to laminar transition in the core region), and T2DHR (ternary pool
and secondary circuit temperature level at DHR initiation).According to the above-mentioned linear regression,
106 simulations are performed to increase the number of calculations (compared to
the 100 ones performed with CATHARE 2) and then to improve the probability
value of the NC reliability assessment in the PEA model.The results are leading to a value of NCDHR
unreliability performance less than5.10−6 with a confidence
level above 99%. It is worth to notice that this unreliability value is surely
overestimated as the upper value of TMAX (1041°C) estimated by 106 simulations is far from the 1600°C limit. This result will be incorporated in
the next PEA model.


## 5.3.2. Sensitivity Study upon the DHR Isolating Valve Opening Fraction

Concerning
the isolation valves opening fraction, the CATHARE 2 code requires an evolution
law of the valve flow coefficient (Cv) with the valve’s stem position (Pu). The
assumption made in the input data deck is considering a linear evolution of Cv
with Pu ranging from105 (for  Pu = 0) and 0 (for  pu = 1). The law valve
expression in CATHARE 2 code is (2)Cv=3600⋅q27,3⋅Y⋅x⋅Pa⋅ρa⋅10−5,
where Y=1−x/(3⋅Fγ⋅xt),  x=ΔP/Pa,  Fγ=γ/1.4≈1,67/1.4,
xt=0.6804,q    is the mass flow in sonic condition
(in kg/s),  Pa is the upstream pressure (in Pa),    ΔP
is the pressure drop (in Pa),  ρa is the upstream gas density (in kg/m3).According
to this expression and the bounding values of Cv, it seems more efficient to
translate the stem position in terms of additional singular pressure drop in
the NC loop (and here provided by the DHR isolating valve). As reported in Figure17, the pressure drop stays under 1000 Pa for a valve opening fraction above
25%, and increases rapidly for a stem position less than 10% (around 10000 Pa
for a stem position close to 7%).Figure 17
Flow coefficient and
related pressure drop versus stem position for DHR isolating valves.Sensitivity calculations were performed with the CATHARE
2 code in order to feel the impact of this additional pressure loss related to
the valve depiction in the code (see Figure18).Figure 18
Maximum fuel
temperature evolutions for different values of DHR valve stem position (1 DHR
loop available).If we consider a maximum opened fraction for the DHR isolating
valve of 10%, the maximum temperature in the core is around 1400°C. However,
for this opened fraction (or additional pressure drop in the primary NC loop,
evaluated at 5200 Pa according to the  Cv  versus  Pu  valve law), the gas
temperature at core outlet reaches 1286°C, that is, just above the 1250°C
criteria defined in Section 4.3.2. For a valve opening fraction close to 7%, which is
giving an additional pressure drop in the NC loop of about
10000 Pa, the 1600°C
criterion is  approximately reached. In Figure 19 are reported the maximum temperatures in the core
region and of the gas at core outlet versus  the additional singular pressure
drop in the  NC loop.Figure 19
Fuel and gas
temperature evolutions versus additional pressure drop in the DHR loop.According to
the results obtained in this sensitivity study, it was decided to perform
another set of calculations for an additional singular pressure drop in the NC
loop of about 10000 Pa  (i.e., valve opening fraction close to 7%). The RMPS
methodology was applied with the same set of values for critical parameters as
generated by LHS in the RMPS reference case. The temperature evolutions with
time are reported in Figure20.Figure 20
RMPS alternative
case (1 DHR loop, valve opening fraction=  7%).In Table5 are given the statistical results of the
responses provided by the CATHARE 2 calculations.Table 5
Results for the RMPS alternative case.
MeanSDLowerUpperTMAX
(°C)157510.0915471595TUPPER
(°C)14516.8114341465As in the reference case, a linear correlation has
been determined in order  to increase the number of calculations (up to106)
and correlatively, the statistics precision for the NC reliability evaluation.
Considering a pressure loss penalty of about 0.1 MPa, the unreliability of the
NC process is evaluated at about  2,3,10−3 considering
only the TMAX criterion. The most influent parameters for the NC performance
and reliability are the same as in the reference case (i.e., T2DHR, FRPLAQ, and
REPLAQ).


## 6. Conclusions and Impact for the GFR Design and Probabilistic Engineering Assessment

In the frame of the
ongoing probabilistic safety assessment in support to the 2400 MWth GFR design
(called “probabilistic engineering assessment”), the RMPS methodology has been
applied in order to assess the performance and the reliability of the natural
circulation DHR in pressurized situations (i.e., for intact helium pressure
boundary). So far, the gaseous NC process is foreseen:(i)
for pressurized situations in the early
phase (i.e., first 24 hours) of transients characterized by the integrity of
primary circuit;(ii)
for the transient termination (here called
“late phase,” starting around one day after the initiating event) of
depressurized situations.
Owing to the
DHR system features (dedicated loops for forced or natural circulation of gas,
with passive water-filled secondary circuit), the primary gaseous coolant NC
performance is directly related to the natural circulation capability in the
secondary side pressurized water circuit, which is thermally linked to a
ternary pool. Then, the frame of RMPS exercise for the GFR DHR system is
involving a “two-in-one” exercise: one for gaseous coolant, the second for
pressurized water natural circulation. This interdependency of physical
processes had lead to a methodology proposal in order to define the critical
parameters for the RMPS exercise. This proposal is to determine the critical
parameters according to “engineering judgment” based on a simplified “deductive analysis” (or
cause-consequence analysis). Two classes of critical parameters were determined
for the pressurized situation: the first addresses the specific uncertainties
associated with factors on which the magnitude of the engaged forces and
counter forces depends (values of heat transfer coefficients and pressure
losses), where the second relates to uncertainties associated with the
potential discrepancy of T-H parameters at “transient” initiation.Correlatively,
sensitivity studies were performed with the CATHARE 2 code to check the
influence of the time delay before the forced circulation is lost (FC being the
first line of defense) on T-H conditions at NC actuation. The results obtained
are exhibiting that the
core decay heat and primary pressure levels at NCDHR actuation do not appear as
critical parameters for the reliability and performance assessment of this
passive system. Translated for the GFR PEA, it validates the event
representation in a Boolean model, as all active systems failures during the
first 24 hours are aggregated as they occur at initiating event (“static” probabilistic
model).Owing to the precision required for this first NCDHR
performance and reliability assessment and compared to the magnitude of other
sources of uncertainties in the PEA model, the number of calculations is first
limited at 100. However, a linear correlation between TMAX and input
parameters, and based only on 6 input parameters, has been determined. The
linear standard regression coefficients were applied in order to rank the most
influent parameters. For the maximum temperature of materials in the core
region, the most influent parameters are according to importance:(i)
FRPLAQ
(multiplicative factor for laminar NC pressure drop in the core region);(ii)
REPLAQ
(Reynolds number for turbulent to laminar transition in the core region);(iii)
T2DHR
(ternary pool and secondary circuit temperature level at DHR initiation).
Compared to the failure/success criteria fixed at
1600°C as mentioned earlier in this document, the results obtained with the
CATHARE 2 code are exhibiting the safety margin conferred by the DHR loop
structural and thermodynamical design. According to the above-mentioned linear
regression, 106 simulations were performed to increase the number of
calculations (compared to the 100 ones performed with CATHARE 2) and then to
improve the probability value of the NC reliability assessment in the PEA
model. The results are providing an NCDHR unreliability upper bounded by 5.10−6 for the reference case. This result should be regarded knowing that previous
parametric studies on the NCDHR reliability value in the GFR PEA model (from 10−1,
as reference value, to 0) were leading to a weak reduction of the core damage
frequency of about 3% (for the initiating event families retained for this
first model and according to the assumption that the same level of NCDHR
reliability will be obtained for depressurized situations).On the other hand, the sensitivity study performed
upon the additional singular pressure drop in the NC loop (through the DHR
system isolating valve opening fraction) exhibits that the process
unreliability ranges from5.10−6 (reference) to 2,3.10−3 ( ΔP≈0.1 MPa) in pressurized situations. At this
stage, it should be mentioned that the valve opening fraction was not retained
as critical parameter (i.e., with distribution attached on this parameter) due
first to its influence on temperature results (potentially masking the effects
of others parameters) and also in relation with the common practice in PSA, in
which partially opened valves
are not depicted. These results should be weighted against the mean reliability
value of an active system which is near 10−3.Nevertheless, the effect of additional pressure drop
in the NC loop may be translated to insights for reactor design team and is
potentially combining a broad range of uncertainties. Indeed, as the GFR design
is still in progress, the improvements of the concept and of specific
components (DHR heat exchanger, core) may lead to a reduction of margin compared
to the present design. In addition, the CATHARE 2 model for GFR, even detailed,
is not representing all the sources of counter forces potentially challenging
the NC process. Then, for the design team, it defines margin for overall
pressure drop increase in the primary NC loop. Another way to interpret this
result could be linked to a reliability allocation for the NCDHR process in
order to guaranty a defined core damage frequency. Then, it fixes the overall
NC loop pressure drop potential in order to respect the, to date, success/failure
criteria.The pursuit of this work is now related to the study
of depressurized situations where the primary circuit is linked to the guard containment
and to T-H involved in it (natural leakage, exchange with a large amount of
structures, etc.).Nomenclature
f:Friction factor;Re:Reynolds number;Nu:Nusselt number;Pr:Prandtl number;Cv:Valve flow Coefficient;Pu:Stem position for a valve;q:Mass flow in kg/s;Pa:Upstream pressure in Pa;ρa:Upstream gas density.



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*Source: 287376-2008-03-17.xml*