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Sample calculations on fuel rod behaviour during a LOCA with the code system SSYST-mod 1
Nuclear Engineering and Design 43 (1977) 455-462 © North-Holland Publishing Company
455
SAMPLE CALCULATIONS ON FUEL ROD BEHAVIOUR DURING A LOCA WITH THE CODE SYSTEM SSYST-MOD 1 R. MEYDER, S. R A F F and W. SENGPIEL lnstitut fur Reaktorentwicklung, Gesellschaft far Kernforschung m.b.H., Postfach 3640, D-7500 Karlsruhe, Federal Republic of Germany Received 29 March 1977
The present paper shows results generated with SSYST, a program system developed for the analysis of the LWR fuel rod behaviour during a LOCA. A blowdown experiment in an out-of-pile test facility is analysed. The aim of the calculations is to demonstrate the influence of the various separate models, each describing a particular phenomenon such as rod internal pressure or rod mechanics on the behaviour of a hot rod by switching on these models sequentially. Calculations showed that the models presently included in the SSYST-system are able to describe the thermal and mechanical rod behaviour qualitatively in a correct way and that they may well be used to analyse the rod behaviour in a LWR during a LOCA.
1. Introduction Since several years calculations were made for loss of coolant accidents (LOCA) in light water reactors (LWR). Especially for the thermohydraulic analysis o f primary systems a number o f computer codes is available. These codes consider either the blowdown phase of a LOCA or the refill and reflood phase or all three of those phases. All these codes include fuel rod models which are more or less detailed only with respect to a thermal fuel rod analysis. But since January 1974 the US Atomic Energy Commission announced officially their acceptance criteria for emergency core cooling systems (ECCS) for LWR, which with some minor changes were also adopted by the German Reactor Safety Commission, it is clear that only a thermal analysis of a fuel rod during accident conditions is no more sufficient. Especially the questions on fission product release and on cladding deformation show that also a mechanical analysis must be included for the fuel rods. The code system SSYST, discussed in this paper is designed to do the mechanical and thermal fuel rod analysis as well. SSYST aimes at this time particularly on prediction o f response o f fuel rods during a LOCA. The system has been developed in close cooperation
between Institut fiir Kernenergetik at University o f Stuttgart and Institut fiir Reaktorentwicklung at Gesellschaft fiir Kernforschung Karlsruhe (GfK) under sponsorship o f Projekt Nukleare Sicherheit at GfK. This paper gives a short description of the present stage of the SSYST system. The calculations reported here are to demonstrate the influence of the various separate models, each describing a particular phenomenon, such as rod internal pressure or rod mechanics on the behaviour of a hot rod during the blowdown phase of a LOCA. A loss of coolant accident leads to a situation where the cladding is exposed for some time to internal overpressure at increased temperatures. This load, dependent on internal pressure and cladding temperature, leads to deformation of the cladding as shown in fig. 1. From this it can be seen that, depending on internal pressure and test temperature, the cladding can reach strains of 100% and more. Keeping in mind that for the pitch to diameter ratio of present-day reactor cores a cladding contact is reached at strains of 30%, assuming that all neighbouring rods deform in a similar way, we see that cooling of the rods can be locally disturbed. The term "locally" is used, since the rods in a reactor differ in power and burnup, and therefore in temperature levels and internal pressure
456
R. Meyder et aL / Fuel rod behaviour during a LOCA
Circumferential Strain E Ruptureat t < 90s to Rupture t H=905 £.- ~D/Oo Burst Strain Envelope:} ~ l/...,._~ Ruptured ~.------80bar ~
--
100 Best Fit ~ 8C at t H=90s ~ . ~ , ~ / ' ~ / ~ j 6(3 ,(3
~ P
! i~
I~'~ ~ ' ~
,,':i ./ ?,,-
Prior
1-- S01)or
IlL--t.-Z.
t H =gO5
t
.,
O
sss
600
J'
700
"'~ 800
900
1000 °C 1100
MaximumTeperature Fig. l. Circumferential strain versus maximal temperature of
creep burst tests at varied inner pressure from [ 1 ].
during the transient. Even small differences have a strong influence on final strain, as can be seen in fig. 1.
2.
Approach
Under the licensing process, the determination of the number of rods which may reach strains of 30% and more is done at present in two steps. First, the temperature transient of the cladding is calculated for the transient without feedback of clodding deformation on rod behaviour. To assess the feedback, experiments with rod simulators are used, which show a comparable temperature history to that of the cladding. From these experiments the final strain is deduced. To evaluate the behaviour of a whole core, the rods in the reactor are grouped in classes which differ in power and internal pressure. It is assumed that the deformation of one rod of a class is representative for all rods of its class. Mean values and variations of power and internal pressure are chosen in such a way that the region of large strains (see fig. 1) particularly is represented in a satisfactory manner. SSYST follows the same philosophy by considering single rods from different classes. In comparison to the usual procedure SSYST is characterized by a number of improved models i.e.: a) describing the physical processes in a rod, such as - thermo- and fluiddynamics in the subchannel - heat transfer in the rod - gap conductance
- oxidation of the cladding - rod internal pressure - mechanics of fuel and cladding in their mutual interactions. b) improving the class concept mentioned by introduction of probabilistic methods. After verification of the code system against inpile and out-of-pile experiments, peak cladding temperature and maximum deformation can be calculated with an improved reliability. To match these goals, SSYST was set up. It has models of all the processes mentioned under a) and, by its conception as a modular code-system, allows to investigate the influence and the interaction of single models in a simple manner.
3. Models A loss of coolant accident can be divided into three parts, i.e. blowdown, refill and reflood phases, or, in other words, into the depressurization phase of the primary system until containment pressure is reached, the refill phase until the water level reaches the bottom of the core and the reflood phase until the whole core is filled with water. For the deformation of cladding, the end of the blowdown and the refill phase are very important, since during this time the rod has full internal pressure and only poor cooling. The cladding temperatures which can be reached during this time depend on the cooling rate during the blowdown phases, i.e. the reduction in stored energy, and as can be seen from fig. 1 even small differences in temperature can lead to considerable differences in strain. To analyse the primary system the assumption is made that the reactor core may be characterized by an average fuel rod during the whole accident, i.e. the conditions of coolant in the reactor plena are not disturbed by deforming fuel rods. To get the boundary conditions for SSYST-mod I, i.e. temperature and pressure in the subchannel as well as the heat transfer coefficient from fuel rod to coolant, the thermal-hydraulics of the subchannel, using a model of fuel rods with rigid geometry, are calculated. This calculation is based on the plenums conditions of the primary system. Even in the analysis of subchannel the feedback effects of deforming
R. Meyder et al. / Fuel rod behaviour during a LOCA
fuel rods on subchannel behaviour is not included. In separating the subchannel behaviour from that of the primary system in this manner, we may analyse very different subchannels on the basis of one analysis of the primary system. To summarize, we do our fuel rod analysis in four steps: 1. Calculation of the thermo-hydraulic boundary conditions at the reactor plena (with a fuel rod of average power) for the whole LOCA. 2. Calculation of the boundary conditions in the subchannel. 3. Calculation of the initial conditions of a chosen type of fuel rod to get the initial conditions for the LOCA analysis. 4. Fuel rod analysis for LOCA with SSYST. To analyse the hydraulics of the primary system, we use the code RELAP [2] for blowdown and the code WAK [3] for the refill- and reflood phases. For the fuel rod and the subchannel analysis a number of modules have been developed. In doing this, the primary aim has been to determine the interaction, i.e. the feedback effects of the physical processes by simple models with short calculation times. The models of SSYST-mod 1 perform the single rod analysis as mentioned before. We assume rotational symmetry (r-z-analysis). During the transient processes the changing geometry is described by a varying grid. A detailed description of the models is given in [4]. Therefore in this paper we only intend to summarize them: - heat conductance in the fuel rod. The equation for heat conductance is solved in the module STT-2D for steady state conditions and in the modules ZET-1D and ZET-2D for transient conditions in one and two dimensions respectively. - heat transfer in the gap. The module WUEZ is calculating the heat transfer in the gap, accounting for heat conduction of the mixture of gases in the gap and heat transfer by radiation. In the case of contact between fuel and cladding, the theory of Ross and Stout [5] is being used. - internal pressure of the fuel rod. The internal pressure is calculated in the modul SPAGAD assuming the law of ideal gases. Beyond the pressurization by helium, the gaseous fission products are also taken into account. The module ODRUSPA calculates the
457
local pressure in the gap, considering gas flow between the fission gas plena and local deforming cladding. - fuel rod mechanics. The module STADEF or HRODE2, respectively, model the deformation of the fuel assuming unrestrained thermal expansion. The mechanics of the cladding is modelled by shell theory allowing coupling of the axial segments if desired (STADEF). The creep of the cladding is modelled by Norton's law, at present with parameters given by Emmerich [6]. - oxidation of the cladding. The rate of oxidation of the cladding is calculated in accordance with the Baker-Just relation. The oxidation causes heat production in the cladding and reduces its conductance. To prove that these models describing separate effects will be sufficient to simulate the integral fuel rod behaviour, we have to verify our models by means of experiments (separate effect tests and integral tests).
4.
Code
system
The idea of the code system is that each physical model may be used in the code system as a standardized module in a special chain of modules defined by the user. Due to the standardized flow of data, which is defined in such a manner, that each module is corresponding to the common data bank, the modules are mutually independent. Both features, the modular developed code system together with the standardized flow of data, allow the user: 1. to test different physical models in the integral system 2. to study the influence of the different modules by swith-on or switch-off of the modules 3. to verify models by using data from experiments as input for modules 4. to take into consideration special characteristics of components (e.g. heating of out-of-pile simulators by electrical resistance) by defining a chain of modules containing one module specially programmed for that purpose. The integration of the transient processes is performed by an explicit procedure. The sequence of modules defined for any problem is covered time step by time step, allowing iterations within the modules.
458
R. Meyder et al. / Fuel rod behaviour during a LOCA
tion of separate models are presently analysed. Some of the models have been verified by means of experiments. An extensive comparison of SSYST-Mod 1 with FRAPT [7] (FRAPT, developed at ANC, is supported by the US NRC) with regard to the description of fuel behaviour during accident conditions showed good agreement between results.
An example of a possible sequence of modules is shown in fig. 2. Time step control is performed by the module STEP, which determines the time step by extrapolation of certain values e.g. rate of temperature change. The present status of SSYST is as follows: SSYST-Mod 1, the first version of the program system, is in application. The influence and the interac-
Ke rne I
Data-
Modules
storage
J, 1
RE LAP
B lowdown
WAK
Primary
'
System
I Re flood
thermohydr auli cs
DataTransfer time STEP
RAN DM
preparing of boundary conditions for the time step
--tr Control Input Sequence
[ I
I I I i I
step
controler
WUET.
gap conductance
heat conduction fuel and cladding
ZET-ID
SPAGAD pressure
in
ODRUSPA
the gap
M RODE 2
rod deformation
ZIRKOX
oxidation of cladding
I
I I I
Datatrensfer Control
Fig. 2. StructureofSSYST.
rod>
analysis
459
R. Meyder et aL / Fuel rod behaviour during a LOCA
5. Evaluations of fuel rod behaviour during the blowdown phase of a LOCA
it is adequate to give results only for one definite axial position.
Beginning with a simple analysis of the temperature field, all models of SSYST-Mod 1 are added successively. With this method the relation between the various separate models can be shown clearly. Those models, not used during the transient phase are only included for the determination of their steady state results, which are kept constant throughout the transient phase. A review of the calculations is given in table 1.
5.2. Results
5.1. Boundary conditions and input data
The response of a rod simulator, similar to that used in the out-of-pile blowdown experiments PNS 4236 [8] will be analysed. The heated length of the rod simulator is 50 cm, it has a lower gas plenum of 16 cm 3 and an upper gas plenum of 9 cm 3. The cold radial gap width is 50 Ore. The steady state gas pressure is 70 bars. Rod power is assumed to be 600 W/cm with a flat power profile. It should be mentioned, that the results of these calculations are not representative for the LWR, since this specific rod power is higher than in a reactor. This rod power has been selected higher in order to accentuate the effects of the various parameters to be calculated and to be experienced in the test facility. The transient boundary conditions in the subchannel used for SSYST analysis have been determined by RELAP4. Since the axial distributions of coolant temperature, pressure and heat transfer coefficients are nearly constant, we defined mean values and considered them constant along the rod length. Because of the constant boundary conditions in axial direction,
Fig. 3 shows the transient central temperature and the mean cladding temperature for case 1 assuming only heat conduction in the rod with time-independent gap size. After the beginning of the blowdown phase there is a steep increase of cladding temperature due to DNB and reduction of heat transfer coefficient by a factor of about 0.01. Since the power in the rod at the same time decreases to the value of the decay heat rate, the radial temperature gradient decreases from 2000 K initially to 200 K. The peak cladding temperature of 1350 K is reached after about 5 seconds. At the end of the blowdown phase the cladding temperature is 1000 K. In case 2 the models describing the mechanical behaviour of fuel and cladding are switched on. The relation between gap conductance and change of gap width is omitted during the transient. For that reason the transient temperatures of cases 1 and 2 are almost identical. Fig. 4 shows the transient behaviour of gap size, i.e. the difference between inner cladding radius and outer fuel radius. The radius of fuel decreases slightly due to the decrease of the mean fuel temperature. The inner radius of cladding initially increases due to thermal expansion. As the material properties of Zircaloy change with increasing temperature, the presmodel I
h.t.
T[OK]
Table 1List of calculations. 2100 ---=--model
case 1
case1
~*
deform, gap c. -
-
r.i.p. -
[~
900 /r
"Tclad ,
case2
case 3 ¢Qse 4
~
•
global
case 5
~
M
global
-
0
10
---tm ie 20
[sec]
Fig. 3. Temperature of center line and cladding for case 1.
460
R. Meyder et al. / Fuel rod behaviour during a LOCA
= model
• model
t
h.t.
radii •--caset I0-3[m] ---case 2
d e f o r m . g a p c.
-
~-
r.i.p.
-
OX.
t
-
'"7
h.t.
T[°K] ---case;
w
- - -'cQse."
r.i.p,
ox.
w ,iw
I
-
I
-
i.c.:cladding internal surface
5.7
f.s. : fuel surface
5.3
/
/ 1150
IL~Lc. /
4.9 /
f.s.
lb
0
~o ------time
[sec]
650
Fig. 4. Gap width for case l and 2.
sure in the subchannel is sufficiently high to press the cladding onto the fuel after 2 seconds. After the 7th second the cubchannel pressure has decreased below that of the inner gas pressure. From this point, a steep increase in cladding strain occurs due to the increasing pressure difference. In case 3, the influence of the variable heat transfer coefficient in the gap due to changing gap size on heat transport in the rod is considered. Fig. 5 shows the large decrease of the gap heat transfer coefficient
• model
t Clgap
h.t.
toZ [m~
--case2
w
--case3
w
deform gap c.
ti.p.
ox.
0
~o
~
~time [sec] Fig. 6. Influence of heat transfer in the gap on cladding temperature.
beginning at about 12 seconds. As a result of the thermal decoupling of fuel and cladding the cladding temperature decreases clearly in the time interval under regard, as shown in fig. 6. The difference in cladding temperatures between cases 2 and 3 is 40 K. Because the deformation of the cladding is strongly dependent on temperature, the final strain is reduced to about one third in comparison to case 2 (fig. 7). The results illustrated so far were obtained by assuming a constant gap pressure of 70 bars. In case 4 the gas pressure is evaluated corresponding to the acmodel
I
"
I
"
I
I
h.t.
radii 20
\ l
--case2
w
10-3[m] - - c a s e 3
w
5."/
l
deform gap c. r.i.p, I
w
I
-
ox. -
w
Lc. =cladding internal surface f.s. =fuel surface
l l, l\ \
1oo
52 \ \
o
,b
~
i.c.
/...9
\ ,%
f.s.
~o • t i m e [sec]
Fig. 5. Influence of gap width on heat transfer in the gap.
---,,.- time [sec] Fig. 7. Influence of heat transfer model in the gap on cladding deformation.
R. Meyder et al.
1 --co..se~
461
,- model
model
h't'
pressure "--CcLse3[bar]
/ Fuel rod behaviour during a LOCA
def°rrrt gap c" ti'P"
"lW/ w
OX.
H I -
w
I -.-pressure in subchonnel
ri.p.
deform gap c.
h.t.
IOZ [ - ~ K]
global
w
t Ggop
~se3
w
N
-.-case/.
M
M
OX.
M
global
20C
1201.~
10c
\.
~0
~
o
,b
• ,...,,~
5o
2b • time
[see] ib
Fig. 8. Influence of model for inner pressure on pressure history.
----,--time [sec] Fig. 10. Influence of inner pressure on heat transfer in the gap.
tuat gas volume, taking into account the deformation of the rod, and the mean gas temperature. Fig. 8 shows the transient pressures in the subchannel and in the gap for cases 3 and 4. It can be seen that the onset of inner overpressure in both cases is reached at the same time. However in case 4 the feedback from deformations of the cladding on gas pressure results in a gas pressure reduction of about 10 bars. The decrease of the pressure difference between gap and subchannel pressure leads to a reduction of cladding
strain, as shown in fig. 9. Of course a smaller gap size means a better gap heat transfer and consequently an increase in cladding temperature, as was demonstrated in case 3. However the influence of this chain of events on the cladding temperature is apparently small. In comparison to case 4, cladding oxidation was additionally considered in case 5. It forms an additional source of heat and affects heat transfer into the coolant due to different conductance of Zircaloy
=
model
- model
t
h.t
deform, gap c.
r.i.p.
OX,
radii
10-3[ml
-
53
'-,case4
r Lp.
deform g a p c. T
W [ W w i.c. = cladding internal f.s. = fuel surface
---ca~3
x
--case/,
w
w
~
OX.
global
global surface
1150 5.!
.
.
.
.
4.9
0
650
ib = time
[sec]
Fig. 9. Influence of inner pressure history on gap width.
o - time
[sec]
Fig. 11. Influence of inner pressure on cladding temperature.
462
R. Meyder et al. / Fuel rod behaviour during a LOCA
and zirconium oxide. Some influence of cladding oxidation on deformation and reduction of gap heat transfer could be found, but differences were too small to allow representation in a diagram.
the core of a PWR during a LOCA according to the concept of characteristic classes mentioned above.
References
6.
Conclusions
A general statement concerning the importance of the modules describing cladding strain is not possible since physical phenomena during the refill and reflood phases have not been considered in the parametric study presented here. However with respect to the blowdown phase the following remarks can be made: - The models show the expected influence on rod behaviour. - Cladding temperature with and without rod mechanics is not very different, but clad deformation is sensitive even to those small changes. - Rod internal pressure reduces at the end of blowdown by about 10 bars. - Oxidation rate during the transient is negligible. Encouraged by these results we are currently performing an accident analysis with SSYST-mod 1 for
[ 1] H.G. Weidinger, G. Cheliotis, H. Watzinger, H. Stehle, LOCA Fuel Rod Behaviour of KWU Pressurized Water Reactors Specialist Meeting Sp]tind, Nord Torpa (norway), 13-16 September 1976. [2] K.V. Moore, W.H. Rettig, Relap4 - A Computer Program for Transient Thermal-hydraulic analyses, ANCR-1127, December 1973. [3] E. Seidelberger, Berechnung des Kernflutens bet gleichzeitiger Heiss- und Kalteinspeisung mit WAK 2, Reakter'tagung 1976, DUsseldorf. I41 W. Gulden et al., SSYST-1 - Ein Programmsystem zur Beschreibung des LWR-Brennstabverhaltensbet KtlhlmittelverluststOrfallen, KFK 2349 (1977). [5] A.M. Ross, R.L. Stoute, Heat transfer coefficient between UO2 and zircaloy, AECL-1552 (1962). [6] K.M. Emmerich, E.F. Juenke, J.F. White, Failure of Pressurized Zircaloy Tubes During Thermal Excursions in Steam and Inert Atmospheres, ASTM-STP458. [7] I.A. Dearien et al., FRAPT 3 - A Computer Code for the Transient Analysis of Oxide-Fuel Rods. Vol. 1, RE-S-76-169. [8] 1. PNS-Halbjahresbericht, Aug. 1974, KFK 2050.
455
SAMPLE CALCULATIONS ON FUEL ROD BEHAVIOUR DURING A LOCA WITH THE CODE SYSTEM SSYST-MOD 1 R. MEYDER, S. R A F F and W. SENGPIEL lnstitut fur Reaktorentwicklung, Gesellschaft far Kernforschung m.b.H., Postfach 3640, D-7500 Karlsruhe, Federal Republic of Germany Received 29 March 1977
The present paper shows results generated with SSYST, a program system developed for the analysis of the LWR fuel rod behaviour during a LOCA. A blowdown experiment in an out-of-pile test facility is analysed. The aim of the calculations is to demonstrate the influence of the various separate models, each describing a particular phenomenon such as rod internal pressure or rod mechanics on the behaviour of a hot rod by switching on these models sequentially. Calculations showed that the models presently included in the SSYST-system are able to describe the thermal and mechanical rod behaviour qualitatively in a correct way and that they may well be used to analyse the rod behaviour in a LWR during a LOCA.
1. Introduction Since several years calculations were made for loss of coolant accidents (LOCA) in light water reactors (LWR). Especially for the thermohydraulic analysis o f primary systems a number o f computer codes is available. These codes consider either the blowdown phase of a LOCA or the refill and reflood phase or all three of those phases. All these codes include fuel rod models which are more or less detailed only with respect to a thermal fuel rod analysis. But since January 1974 the US Atomic Energy Commission announced officially their acceptance criteria for emergency core cooling systems (ECCS) for LWR, which with some minor changes were also adopted by the German Reactor Safety Commission, it is clear that only a thermal analysis of a fuel rod during accident conditions is no more sufficient. Especially the questions on fission product release and on cladding deformation show that also a mechanical analysis must be included for the fuel rods. The code system SSYST, discussed in this paper is designed to do the mechanical and thermal fuel rod analysis as well. SSYST aimes at this time particularly on prediction o f response o f fuel rods during a LOCA. The system has been developed in close cooperation
between Institut fiir Kernenergetik at University o f Stuttgart and Institut fiir Reaktorentwicklung at Gesellschaft fiir Kernforschung Karlsruhe (GfK) under sponsorship o f Projekt Nukleare Sicherheit at GfK. This paper gives a short description of the present stage of the SSYST system. The calculations reported here are to demonstrate the influence of the various separate models, each describing a particular phenomenon, such as rod internal pressure or rod mechanics on the behaviour of a hot rod during the blowdown phase of a LOCA. A loss of coolant accident leads to a situation where the cladding is exposed for some time to internal overpressure at increased temperatures. This load, dependent on internal pressure and cladding temperature, leads to deformation of the cladding as shown in fig. 1. From this it can be seen that, depending on internal pressure and test temperature, the cladding can reach strains of 100% and more. Keeping in mind that for the pitch to diameter ratio of present-day reactor cores a cladding contact is reached at strains of 30%, assuming that all neighbouring rods deform in a similar way, we see that cooling of the rods can be locally disturbed. The term "locally" is used, since the rods in a reactor differ in power and burnup, and therefore in temperature levels and internal pressure
456
R. Meyder et aL / Fuel rod behaviour during a LOCA
Circumferential Strain E Ruptureat t < 90s to Rupture t H=905 £.- ~D/Oo Burst Strain Envelope:} ~ l/...,._~ Ruptured ~.------80bar ~
--
100 Best Fit ~ 8C at t H=90s ~ . ~ , ~ / ' ~ / ~ j 6(3 ,(3
~ P
! i~
I~'~ ~ ' ~
,,':i ./ ?,,-
Prior
1-- S01)or
IlL--t.-Z.
t H =gO5
t
.,
O
sss
600
J'
700
"'~ 800
900
1000 °C 1100
MaximumTeperature Fig. l. Circumferential strain versus maximal temperature of
creep burst tests at varied inner pressure from [ 1 ].
during the transient. Even small differences have a strong influence on final strain, as can be seen in fig. 1.
2.
Approach
Under the licensing process, the determination of the number of rods which may reach strains of 30% and more is done at present in two steps. First, the temperature transient of the cladding is calculated for the transient without feedback of clodding deformation on rod behaviour. To assess the feedback, experiments with rod simulators are used, which show a comparable temperature history to that of the cladding. From these experiments the final strain is deduced. To evaluate the behaviour of a whole core, the rods in the reactor are grouped in classes which differ in power and internal pressure. It is assumed that the deformation of one rod of a class is representative for all rods of its class. Mean values and variations of power and internal pressure are chosen in such a way that the region of large strains (see fig. 1) particularly is represented in a satisfactory manner. SSYST follows the same philosophy by considering single rods from different classes. In comparison to the usual procedure SSYST is characterized by a number of improved models i.e.: a) describing the physical processes in a rod, such as - thermo- and fluiddynamics in the subchannel - heat transfer in the rod - gap conductance
- oxidation of the cladding - rod internal pressure - mechanics of fuel and cladding in their mutual interactions. b) improving the class concept mentioned by introduction of probabilistic methods. After verification of the code system against inpile and out-of-pile experiments, peak cladding temperature and maximum deformation can be calculated with an improved reliability. To match these goals, SSYST was set up. It has models of all the processes mentioned under a) and, by its conception as a modular code-system, allows to investigate the influence and the interaction of single models in a simple manner.
3. Models A loss of coolant accident can be divided into three parts, i.e. blowdown, refill and reflood phases, or, in other words, into the depressurization phase of the primary system until containment pressure is reached, the refill phase until the water level reaches the bottom of the core and the reflood phase until the whole core is filled with water. For the deformation of cladding, the end of the blowdown and the refill phase are very important, since during this time the rod has full internal pressure and only poor cooling. The cladding temperatures which can be reached during this time depend on the cooling rate during the blowdown phases, i.e. the reduction in stored energy, and as can be seen from fig. 1 even small differences in temperature can lead to considerable differences in strain. To analyse the primary system the assumption is made that the reactor core may be characterized by an average fuel rod during the whole accident, i.e. the conditions of coolant in the reactor plena are not disturbed by deforming fuel rods. To get the boundary conditions for SSYST-mod I, i.e. temperature and pressure in the subchannel as well as the heat transfer coefficient from fuel rod to coolant, the thermal-hydraulics of the subchannel, using a model of fuel rods with rigid geometry, are calculated. This calculation is based on the plenums conditions of the primary system. Even in the analysis of subchannel the feedback effects of deforming
R. Meyder et al. / Fuel rod behaviour during a LOCA
fuel rods on subchannel behaviour is not included. In separating the subchannel behaviour from that of the primary system in this manner, we may analyse very different subchannels on the basis of one analysis of the primary system. To summarize, we do our fuel rod analysis in four steps: 1. Calculation of the thermo-hydraulic boundary conditions at the reactor plena (with a fuel rod of average power) for the whole LOCA. 2. Calculation of the boundary conditions in the subchannel. 3. Calculation of the initial conditions of a chosen type of fuel rod to get the initial conditions for the LOCA analysis. 4. Fuel rod analysis for LOCA with SSYST. To analyse the hydraulics of the primary system, we use the code RELAP [2] for blowdown and the code WAK [3] for the refill- and reflood phases. For the fuel rod and the subchannel analysis a number of modules have been developed. In doing this, the primary aim has been to determine the interaction, i.e. the feedback effects of the physical processes by simple models with short calculation times. The models of SSYST-mod 1 perform the single rod analysis as mentioned before. We assume rotational symmetry (r-z-analysis). During the transient processes the changing geometry is described by a varying grid. A detailed description of the models is given in [4]. Therefore in this paper we only intend to summarize them: - heat conductance in the fuel rod. The equation for heat conductance is solved in the module STT-2D for steady state conditions and in the modules ZET-1D and ZET-2D for transient conditions in one and two dimensions respectively. - heat transfer in the gap. The module WUEZ is calculating the heat transfer in the gap, accounting for heat conduction of the mixture of gases in the gap and heat transfer by radiation. In the case of contact between fuel and cladding, the theory of Ross and Stout [5] is being used. - internal pressure of the fuel rod. The internal pressure is calculated in the modul SPAGAD assuming the law of ideal gases. Beyond the pressurization by helium, the gaseous fission products are also taken into account. The module ODRUSPA calculates the
457
local pressure in the gap, considering gas flow between the fission gas plena and local deforming cladding. - fuel rod mechanics. The module STADEF or HRODE2, respectively, model the deformation of the fuel assuming unrestrained thermal expansion. The mechanics of the cladding is modelled by shell theory allowing coupling of the axial segments if desired (STADEF). The creep of the cladding is modelled by Norton's law, at present with parameters given by Emmerich [6]. - oxidation of the cladding. The rate of oxidation of the cladding is calculated in accordance with the Baker-Just relation. The oxidation causes heat production in the cladding and reduces its conductance. To prove that these models describing separate effects will be sufficient to simulate the integral fuel rod behaviour, we have to verify our models by means of experiments (separate effect tests and integral tests).
4.
Code
system
The idea of the code system is that each physical model may be used in the code system as a standardized module in a special chain of modules defined by the user. Due to the standardized flow of data, which is defined in such a manner, that each module is corresponding to the common data bank, the modules are mutually independent. Both features, the modular developed code system together with the standardized flow of data, allow the user: 1. to test different physical models in the integral system 2. to study the influence of the different modules by swith-on or switch-off of the modules 3. to verify models by using data from experiments as input for modules 4. to take into consideration special characteristics of components (e.g. heating of out-of-pile simulators by electrical resistance) by defining a chain of modules containing one module specially programmed for that purpose. The integration of the transient processes is performed by an explicit procedure. The sequence of modules defined for any problem is covered time step by time step, allowing iterations within the modules.
458
R. Meyder et al. / Fuel rod behaviour during a LOCA
tion of separate models are presently analysed. Some of the models have been verified by means of experiments. An extensive comparison of SSYST-Mod 1 with FRAPT [7] (FRAPT, developed at ANC, is supported by the US NRC) with regard to the description of fuel behaviour during accident conditions showed good agreement between results.
An example of a possible sequence of modules is shown in fig. 2. Time step control is performed by the module STEP, which determines the time step by extrapolation of certain values e.g. rate of temperature change. The present status of SSYST is as follows: SSYST-Mod 1, the first version of the program system, is in application. The influence and the interac-
Ke rne I
Data-
Modules
storage
J, 1
RE LAP
B lowdown
WAK
Primary
'
System
I Re flood
thermohydr auli cs
DataTransfer time STEP
RAN DM
preparing of boundary conditions for the time step
--tr Control Input Sequence
[ I
I I I i I
step
controler
WUET.
gap conductance
heat conduction fuel and cladding
ZET-ID
SPAGAD pressure
in
ODRUSPA
the gap
M RODE 2
rod deformation
ZIRKOX
oxidation of cladding
I
I I I
Datatrensfer Control
Fig. 2. StructureofSSYST.
rod>
analysis
459
R. Meyder et aL / Fuel rod behaviour during a LOCA
5. Evaluations of fuel rod behaviour during the blowdown phase of a LOCA
it is adequate to give results only for one definite axial position.
Beginning with a simple analysis of the temperature field, all models of SSYST-Mod 1 are added successively. With this method the relation between the various separate models can be shown clearly. Those models, not used during the transient phase are only included for the determination of their steady state results, which are kept constant throughout the transient phase. A review of the calculations is given in table 1.
5.2. Results
5.1. Boundary conditions and input data
The response of a rod simulator, similar to that used in the out-of-pile blowdown experiments PNS 4236 [8] will be analysed. The heated length of the rod simulator is 50 cm, it has a lower gas plenum of 16 cm 3 and an upper gas plenum of 9 cm 3. The cold radial gap width is 50 Ore. The steady state gas pressure is 70 bars. Rod power is assumed to be 600 W/cm with a flat power profile. It should be mentioned, that the results of these calculations are not representative for the LWR, since this specific rod power is higher than in a reactor. This rod power has been selected higher in order to accentuate the effects of the various parameters to be calculated and to be experienced in the test facility. The transient boundary conditions in the subchannel used for SSYST analysis have been determined by RELAP4. Since the axial distributions of coolant temperature, pressure and heat transfer coefficients are nearly constant, we defined mean values and considered them constant along the rod length. Because of the constant boundary conditions in axial direction,
Fig. 3 shows the transient central temperature and the mean cladding temperature for case 1 assuming only heat conduction in the rod with time-independent gap size. After the beginning of the blowdown phase there is a steep increase of cladding temperature due to DNB and reduction of heat transfer coefficient by a factor of about 0.01. Since the power in the rod at the same time decreases to the value of the decay heat rate, the radial temperature gradient decreases from 2000 K initially to 200 K. The peak cladding temperature of 1350 K is reached after about 5 seconds. At the end of the blowdown phase the cladding temperature is 1000 K. In case 2 the models describing the mechanical behaviour of fuel and cladding are switched on. The relation between gap conductance and change of gap width is omitted during the transient. For that reason the transient temperatures of cases 1 and 2 are almost identical. Fig. 4 shows the transient behaviour of gap size, i.e. the difference between inner cladding radius and outer fuel radius. The radius of fuel decreases slightly due to the decrease of the mean fuel temperature. The inner radius of cladding initially increases due to thermal expansion. As the material properties of Zircaloy change with increasing temperature, the presmodel I
h.t.
T[OK]
Table 1List of calculations. 2100 ---=--model
case 1
case1
~*
deform, gap c. -
-
r.i.p. -
[~
900 /r
"Tclad ,
case2
case 3 ¢Qse 4
~
•
global
case 5
~
M
global
-
0
10
---tm ie 20
[sec]
Fig. 3. Temperature of center line and cladding for case 1.
460
R. Meyder et al. / Fuel rod behaviour during a LOCA
= model
• model
t
h.t.
radii •--caset I0-3[m] ---case 2
d e f o r m . g a p c.
-
~-
r.i.p.
-
OX.
t
-
'"7
h.t.
T[°K] ---case;
w
- - -'cQse."
r.i.p,
ox.
w ,iw
I
-
I
-
i.c.:cladding internal surface
5.7
f.s. : fuel surface
5.3
/
/ 1150
IL~Lc. /
4.9 /
f.s.
lb
0
~o ------time
[sec]
650
Fig. 4. Gap width for case l and 2.
sure in the subchannel is sufficiently high to press the cladding onto the fuel after 2 seconds. After the 7th second the cubchannel pressure has decreased below that of the inner gas pressure. From this point, a steep increase in cladding strain occurs due to the increasing pressure difference. In case 3, the influence of the variable heat transfer coefficient in the gap due to changing gap size on heat transport in the rod is considered. Fig. 5 shows the large decrease of the gap heat transfer coefficient
• model
t Clgap
h.t.
toZ [m~
--case2
w
--case3
w
deform gap c.
ti.p.
ox.
0
~o
~
~time [sec] Fig. 6. Influence of heat transfer in the gap on cladding temperature.
beginning at about 12 seconds. As a result of the thermal decoupling of fuel and cladding the cladding temperature decreases clearly in the time interval under regard, as shown in fig. 6. The difference in cladding temperatures between cases 2 and 3 is 40 K. Because the deformation of the cladding is strongly dependent on temperature, the final strain is reduced to about one third in comparison to case 2 (fig. 7). The results illustrated so far were obtained by assuming a constant gap pressure of 70 bars. In case 4 the gas pressure is evaluated corresponding to the acmodel
I
"
I
"
I
I
h.t.
radii 20
\ l
--case2
w
10-3[m] - - c a s e 3
w
5."/
l
deform gap c. r.i.p, I
w
I
-
ox. -
w
Lc. =cladding internal surface f.s. =fuel surface
l l, l\ \
1oo
52 \ \
o
,b
~
i.c.
/...9
\ ,%
f.s.
~o • t i m e [sec]
Fig. 5. Influence of gap width on heat transfer in the gap.
---,,.- time [sec] Fig. 7. Influence of heat transfer model in the gap on cladding deformation.
R. Meyder et al.
1 --co..se~
461
,- model
model
h't'
pressure "--CcLse3[bar]
/ Fuel rod behaviour during a LOCA
def°rrrt gap c" ti'P"
"lW/ w
OX.
H I -
w
I -.-pressure in subchonnel
ri.p.
deform gap c.
h.t.
IOZ [ - ~ K]
global
w
t Ggop
~se3
w
N
-.-case/.
M
M
OX.
M
global
20C
1201.~
10c
\.
~0
~
o
,b
• ,...,,~
5o
2b • time
[see] ib
Fig. 8. Influence of model for inner pressure on pressure history.
----,--time [sec] Fig. 10. Influence of inner pressure on heat transfer in the gap.
tuat gas volume, taking into account the deformation of the rod, and the mean gas temperature. Fig. 8 shows the transient pressures in the subchannel and in the gap for cases 3 and 4. It can be seen that the onset of inner overpressure in both cases is reached at the same time. However in case 4 the feedback from deformations of the cladding on gas pressure results in a gas pressure reduction of about 10 bars. The decrease of the pressure difference between gap and subchannel pressure leads to a reduction of cladding
strain, as shown in fig. 9. Of course a smaller gap size means a better gap heat transfer and consequently an increase in cladding temperature, as was demonstrated in case 3. However the influence of this chain of events on the cladding temperature is apparently small. In comparison to case 4, cladding oxidation was additionally considered in case 5. It forms an additional source of heat and affects heat transfer into the coolant due to different conductance of Zircaloy
=
model
- model
t
h.t
deform, gap c.
r.i.p.
OX,
radii
10-3[ml
-
53
'-,case4
r Lp.
deform g a p c. T
W [ W w i.c. = cladding internal f.s. = fuel surface
---ca~3
x
--case/,
w
w
~
OX.
global
global surface
1150 5.!
.
.
.
.
4.9
0
650
ib = time
[sec]
Fig. 9. Influence of inner pressure history on gap width.
o - time
[sec]
Fig. 11. Influence of inner pressure on cladding temperature.
462
R. Meyder et al. / Fuel rod behaviour during a LOCA
and zirconium oxide. Some influence of cladding oxidation on deformation and reduction of gap heat transfer could be found, but differences were too small to allow representation in a diagram.
the core of a PWR during a LOCA according to the concept of characteristic classes mentioned above.
References
6.
Conclusions
A general statement concerning the importance of the modules describing cladding strain is not possible since physical phenomena during the refill and reflood phases have not been considered in the parametric study presented here. However with respect to the blowdown phase the following remarks can be made: - The models show the expected influence on rod behaviour. - Cladding temperature with and without rod mechanics is not very different, but clad deformation is sensitive even to those small changes. - Rod internal pressure reduces at the end of blowdown by about 10 bars. - Oxidation rate during the transient is negligible. Encouraged by these results we are currently performing an accident analysis with SSYST-mod 1 for
[ 1] H.G. Weidinger, G. Cheliotis, H. Watzinger, H. Stehle, LOCA Fuel Rod Behaviour of KWU Pressurized Water Reactors Specialist Meeting Sp]tind, Nord Torpa (norway), 13-16 September 1976. [2] K.V. Moore, W.H. Rettig, Relap4 - A Computer Program for Transient Thermal-hydraulic analyses, ANCR-1127, December 1973. [3] E. Seidelberger, Berechnung des Kernflutens bet gleichzeitiger Heiss- und Kalteinspeisung mit WAK 2, Reakter'tagung 1976, DUsseldorf. I41 W. Gulden et al., SSYST-1 - Ein Programmsystem zur Beschreibung des LWR-Brennstabverhaltensbet KtlhlmittelverluststOrfallen, KFK 2349 (1977). [5] A.M. Ross, R.L. Stoute, Heat transfer coefficient between UO2 and zircaloy, AECL-1552 (1962). [6] K.M. Emmerich, E.F. Juenke, J.F. White, Failure of Pressurized Zircaloy Tubes During Thermal Excursions in Steam and Inert Atmospheres, ASTM-STP458. [7] I.A. Dearien et al., FRAPT 3 - A Computer Code for the Transient Analysis of Oxide-Fuel Rods. Vol. 1, RE-S-76-169. [8] 1. PNS-Halbjahresbericht, Aug. 1974, KFK 2050.