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R e s e a r c h E s t a b l i s h m e n t R i S 0
Depar tment o f R e a c t o r Technology
DYN-1-81
March 1 9 8 1
AML/ i k- 2
THE DANISH SOLUTION OF THE NRF BENCHMARK PROBLEM 1980:
CONTROL ROD EJECTION I N A PWR
A.M. H v i d t f e l d t L a r s e n
E . Nonberl
B. T h o r l a k s e n
T h i s is a n i n t e r n a l r e p o r t . I t may c o n t a i n r e s u l t s or con-
c l u s i o n s t h a t a r e o n l y p r e l i m i n a r y and s h o u l d t h e r e f o r e be
t r e a t e d a c c o r d i n g l y . I t is n o t t o be r e p r o d u c e d n o r q u o t e d
i n p u b l i c a t i o n s o r fo rwarded t o p e r s o n s u n a u t h o r i z e d t o re-
c e i v e it.
TRYK: R I S 0 REPRO
CONTENTS
Page
1 . INTRODUCTION ..................................... 3
2 . COMMON FEATURES FOR THE THREE CASES .............. 4
................................ 3.1. ANTI CALCULATIONS 7
3.2. RESULTS OF THE ANTI CALCULATIONS ................. 10
4.1. PWR/ONE CALCULATION .............................. 14
............... 4.2. RESULTS OF THE PWR/ONE CALCULATION 16
5 . CONCLUSION ....................................... 20
........................................ 6 . REFERENCES 21
............................................... Table 1 22
............................................... Figures 23
APPENDIX: NRF BENCHMARK PROBLEM 1980 .................. 63
1. INTRODUCTION
The NRF benchmark problem was originally formulated as a control
rod ejection transient represented in one space dimension (axial),
see appendix 1. At Riser we have made three different approaches
to the problem:
a. A calculation with the one-dimensional finite element program'
b. A calculation with the three-dimensional nodal program ANTI,
but with one-dimensional features, as the hydraulics is
represented by only one average channel and with the ejected
rod covering the entire radial cross section of the reactor
core.
c. An ANTI calculation with three hydraulic channels and the
control rod concentrated at the center of the core.
The PWR/ONE is similar to the Finnish TRAWA program which the
benchmark problem was defined for, so in case a. above the
@ original formulation could be used with only slight modifications. -. The cases b. and c. were studied for comparison of ID and 3D
calculations. For these cases it was necessary to add some new
conditions to the original benchmark formulation.
A preliminary report on the Danish results was distributed at
the NRF meeting in Loviisa, November 1980, reference 1. The
present report is more detailed and the problem has been modified
compared to the preliminary edition. Descriptions of the
computer programs used for the calculations are given in
references 2 and 3.
2. COMMON FEATURES FOR THE. THREE CASES
Core Geometry
H e i g h t o f a c t i v e c o r e
T o t a l c r o s s - s e c t i o n a l a r e a
T o t a l c o o l a n t f l o w a r e a
-
- @ F u e l r o d
Number o f r o d s
C o o l a n t f l o w a r e a p e r r o d
R a d i u s o f t h e f u e l p e l l e t
O u t e r r a d i u s o f t h e c l a d d i n g
Number o f mesh-poin ts i n f u e l p e l l e t
Number o f mesh-poin ts i n c l a d d i n g
N e u t r o n i c s
-
@ The a c t i v e c o r e is s e p a r a t e d i n t o 5 a x i a l r e g i o n s w i t h -
d i f f e r e n t f u e l c o m p o s i t i o n s ; t h e h e i g h t o f e a c h r e g i o n i s
0 . 5 m .
The n u c l e a r p a r a m e t e r s are f u n c t i o n s o f t h e f u e l t e m p e r a t u r e
T and t h e m o d e r a t o r d e n s i t y p :
= D(: - 0.72 A p ( c m )
The reference values below are used:
Bottom of core 1 1 . 3 8 8 .3646 .01536 . 0 1 0 4 3 .07582 . 0 0 4 6 9 5 . I 1 1 2 0
2 1 .391 . 3 6 3 5 .01521 . 0 1 0 4 5 .07681 . 0 0 4 5 9 5 . I 1 1 3 0
3 1 . 3 9 2 . 3 6 3 4 . 0 1 5 2 0 . 0 1 0 5 4 .07691 .004494 . I 1 1 4 0
4 1 . 3 9 1 .3640 .01525 . 0 1 0 1 3 .07646 .004786 . I 1 1 6 5
If a control rod is inserted, the absorption cross sections are
modif ied as follows:
where f should be 1 . 0 0 for 3D calculations. For I D calculations it is
recommended to use f = 0 . 1 5 for the ejected rod and f = 0 . 6 0 for the
scram rods.
The neutron flux is only calculated in one energy group and
the following relationship is applied:
Energy Production and Deposition
Total thermal power 3000 MW
Energy released per fission 330 . 10-13 J The fission energy is released promptly, 97% is deposited in the
I ) fuel and 3% in the moderator. -
Neutron velocity 3922 m/s
Delayed Neutron Grou~s
Group no. Decay constant Fraction of total number
s-I of neutrons per fission
Hydraulics
System pressure at core inlet (steady state) 150 bar
Coolant inlet temperature
Total coolant flow
Hydraulic diameter
Single-phase friction coefficient
Thermo-dynamics of Fuel Rod
Radial thermal conductivity of the fuel pellet
of the cladding
The axial conductivity is neglected
Heat capacity
of the fuel pellet
of the cladding
Thermal resistance of the gas gap
(T is the average fuel temperature)
(I) T < 800 K
T > 1400 K 800 < T < 1400 K
Control Rod Positions
Ejected rod
Steady-state position
(distance from top) 1 .OO m
Time for start of travel 0.00 s
Time for stop of travel 0.05 s
i ) Velocity -20.00 m/s
Final rod position 0.00 m
5.0 K cm2/w
0.5 K cm2/w
linear interpolation
between the values above
Scram rods
3.1 ANTI CALCULATIONS
For the ANTI calculations the geometry of the one-dimensional
problem was extended to three dimensions in two different ways - ANTI-ID, an essentially one-dimensional calculation, and ANTI-3D
with three-dimensional effects included.
Core Geometry
A s shown i n F i g . 3 . 1 t h e r e a c t o r c o r e was composed o f 305
i d e n t i c a l f u e l e l e m e n t s o f s q u a r e c r o s s s e c t i o n . The f u e l
e l e m e n t s i z e was d e t e r m i n e d by t h e known t o t a l c r o s s s e c t i o n
a r e a o f 14 m 2 . To r e d u c e t h e s i z e o f t h e problem t h e c a l c u l a t i o n
was done f o r o n l y 1/8 o f t h e c o r e a s i n d i c a t e d by t h e d o t t e d
l i n e i n F i g . 3 .1 , g i v i n g 47 nodes h o r i z o n t a l l y . A x i a l l y t h e c o r e
was d i v i d e d i n t o 10 nodes .
Node d imens ions :
DX = DY = 0.214 m
(L) DZ = 0.250 in
C o n t r o l Rods
I n t h e ANTI-ID c a s e t h e c o n t r o l r o d was i n s e r t e d i n a l l f u e l
e l e m e n t s i n i t i a l l y and i ts a b s o r p t i o n c r o s s s e c t i o n m u l t i p l i e d
by t h e f a c t o r 0'.015 g i v e n i n t h e o r i g i n a l problem f o r m u l a t i o n .
C o r r e s p o n d i n g l y t h e scram r o d s were i n s e r t e d i n a l l e l e m e n t s ,
b u t w i t h t h e f a c t o r 0.060. I n ANTI-3D t h e c o n t r o l r o d t o be
e j e c t e d w a s c o n c e n t r a t e d i n t h e c e n t r a l p a r t o f t h e r e a c t o r
core a s shown i n F i g . 3 .1 , and t h e c o n t r o l r o d c r o s s s e c t i o n s are
a p p l i e d w i t h o u t - m o d i f i c a t i o n . The number o f f u e l e l e m e n t s
@ i n c l u d e d i n t h e c o n t r o l r o d a r e a was c h o s e n t o g i v e a s t e a d y -
s t a t e k e f f a s c l o s e a s p o s s i b l e t o t h e k e f f v a l u e o f t h e ANTI-ID
c a l c u l a t i o n . I n t h e ANTI-3D c a s e o n l y t h e f u e l e l e m e n t s o u t s i d e
t h e c o n t r o l r o d a r e a had scram r o d s i n s e r t e d , a s it is assumed t h a t
t h e e j e c t e d r o d s w i l l be o u t o f u s e a t r e a c t o r scram. The f a c t o r
0.060 f o r t h e scram r o d c r o s s s e c t i o n s w a s u sed a l s o i n ANTI-3D.
Ref l e c t o r
Albedo, t o p and bot tom r e f l e c t o r : 0.66667
( c o r r e s p o n d i n g t o t h e y -ma t r ix :::I )
Albedo, r a d i a l r e f l e c t o r :
( t h e r a d i a l b u c k l i n g was n o t u s e d )
H y d r a u l i c s
Dur ing t h e t r a n s i e n t t h e c o r e o u t l e t p r e s s u r e and t h e i n l e t
mass f l u x were k e p t c o n s t a n t . The p r e s s u r e b a l a n c e g i v e n i n t h e
problem d e f i n i t i o n was t h e r e f o r e n e g l e c t e d .
System p r e s s u r e ( c o r e o u t l e t )
I n l e t p r e s s u r e i n t h e s t e a d y s t a t e
I ) I n l e t e n t h a l p y
I n l e t mass f l u x
149.4 b a r
150.0 b a r
1.349 . 106 J / k g
2382 k g / ( s m 2 )
The h y d r a u l i c submodels u s e d i n ANTI a r e somewhat d i f f e r e n t
f rom t h o s e recommended f o r t h e benchmark. Steam i s s a t u r a t e d ,
b u t w a t e r may be s u p e r h e a t e d o r s u b c o o l e d . C o n d e n s a t i o n o r
f l a s h i n g r a t e is e x p r e s s e d a s
[ 5 1 0 ' f o r ~h~ > 0
D r i f t f l u x model: Zuber
Pf Two-phase f r i c t i o n f a c t o r : $2 = 1 + (- - 1 ) X
Heat t r a n s f e r : D i t t u s - B o e l t e r ( s u b c o o l e d ) ,
Thom ( n u c l e a t e ) ,
Dougall-Rohsenow ( f i l m ) .
In ANTI-ID only one hydraulic channel was used, representing
the average fuel element. ANTI-3D had three hydraulic channels,
one covering the control rod area in the center, one for the adjacent ring (two fuel elements thick)' and one for the remainder
of the core. The channel geometry is shown in Fig. 3.1. No cross
flow between the channels was allowed.
3.2. RESULTS OF THE ANTI CALCULATIONS
The maximum values of some key parameters of the calculation
and the times of occurrence are shown in Table 1 together with
the steady-state values. The table contains the results from
all of the four calculations, TRAWA, PWR/ONE, ANTI-ID and ANTI-3D.
Figs. 3.2 - 3.13 show the main results of the ANTI-ID and ANTI-3D
calculations as functions of time. The TRAWA results are included
for comparison.
In Figs. 3.14 - 3.20 the axial distributions of power, fuel and
coolant temperatures and void are shown and compared to the
TRAWA results.
Fig. 3.21 shows the development
ANTI-3D for the first 0.11 s of
of the radial power shape of
the transient.
Figs. 3.2 and 3.3. Total Power
Fig. 3.2 shows the power development during the first 2 seconds
of the transient, and Fig. 3.3 includes all 10 seconds calculated.
The power peak of ANTI-1D is somewhat higher than the peaks of
ANTI-3D and TRAWA. The waves seen on the ANTI powers between
1.5 and 7.75 s are caused by the non-linearity in the worth of
a control rod as it passes through a node. A smoothing function
exists in the program to correct this, but we did not spend the
effort required to find the proper value of a fitting constant,
which depends on the node height.
Figs. 3.4 and 3.5. Maximum Fuel Temperatures
In Fig. 3.4 the fuel center temperature is shown as a function
of time. The ANTI results are average temperatures of the
central mesh in the fuel rod. Even in steady state the ANTI
temperature is considerably higher than the temperature found
by TRAWA. The same is true for the radially averaged values in
# Fig. 3.5.
The difference between the two ANTI calculations is easily
explained by the fact that the hot channel in the 3D case is
hotter than the one and only channel in the ID case.
In the benchmark formulation the gas gap thermal resistance is
given as a constant value below the temperature 8 0 0 K and a
different constant value above 1 4 0 0 K. In our fuel model we
have assumed linear interpolation in the thermal resistance for
fuel temperatures between 8 0 0 and 1 4 0 0 K. In a preliminary ANTI
calculation, however, we by mistake interpolated the conductivity 1 . of the gas gap linearly (5 Instead of x). This calculation gave
d steddy-state fuel tempeiatures very close to the TRAWA results.
Figs. 3.6 and 3.7. Total Power to Coolant
The total power to coolant is shown as a function of time in
Figs. 3.6 and 3.7. The first peak of the ANTI-1D case is high
corresponding to the high total power peak. The second power
peak tends to be lower and to occur later in both ANTI cases
than in the TRAWA case.
Figs. 3.8 and 3.9. Reactivity
The reactivity as a function of time is shown in Figs. 3.8 and
3.9. In Fig. 3.9 the wavy shape of the ANTI curves is again due
to the non-linearity of the scram rod worth as explained for
the total power. The difference in reactivity at the end of the
transient between ANTI-ID and ANTI-3D may be explained by the
smaller number of scram rods in the 3D case.
Fig. 3.10. Outlet Water Temperature
a In Fig. 3.10 the outlet water temperature as a function of time
is shown.
Fig. 3.11. Outlet Void Fraction
Fig. 3.11 shows the outlet void fraction as a function of time.
The difference between TRAWA and ANTI-ID probably reflects the
differences in the hydraulic models. The comparison of the two
ANTI calculations shows the difference between the one-dimensional
and the three-dimensional representation.
In ANTI-3D the steady-state outlet void fraction is 0.02. Because
d of the control rod the power of the central channel is relatively
low, and therefore, in order to have the same total power,
channel no. 2 becomes so hot that it is boiling already in the
steady state.
Fig. 3.12. Outlet Steam Quality
The outlet steam quality shown in Fig. 3.12 has the same shape
as the outlet void as function of time.
Fig. 3.1 3. Outlet Pressure
Fig. 3.13 shows the constant outlet pressure used in the ANTI
calculations compared to the varying pressure of TRAWA.
Figs. 3.14 - 3.17. Axial Power Shapes
The normalized axial power shapes of ANTI-ID, ANTI-3D and TRAWA
are compared in steady state in Fig. 3.14, at 0.05 s in Fig.
3.15, at 1.0 s in Fig. 3.16 and at the end of the transient
calculation in Fig. 3.17. The last TRAWA power shape available
for comparison is taken at the time 6.8 s, and it is shown in
@ Fig. 3.17 together with ANTI results from the time 10.0 s. The
TRAWA shape is moving in the direction of the ANTI results,
and it seems likely that the agreement at 10 s would have been
quite good.
Figs. 3.18 - 3.20. Axial Distributions of Fuel and Coolant
Temperatures
The axial distributions of average fuel temperature and coolant
temperature are shown in Fig. 3.18 for the steady state and in
Fig. 3.19 at 1.0 s into the transient. The coolant temperatures
are in perfect agreement. The fuel temperatures, however, are
@ quite a lot higher in the ANTI cases than in TRAWA, except for the top and bottom nodes of the core.
Fig. 3.20. Axial Void Distribution
The axial distribution of the void fraction is shown in Fig.
3.20 at the time 1.0 s. On the average the void content in the
three-channel ANTI-3D calculation is lower than in ANTI-ID and
TRAWA, but the void contents of the three individual channels
are very different, as it is shown by the dotted curves.
Fig. 3.21. Horizontal Power Distribution
In order to give an impression of the change in horizontal
power distribution during the first part of the transient, the
normalized power distribution calculated in ANTI-3D was plotted
at time intervals of 0.01 s in Fig. 3.21. The plots represent
one quarter of the core. The steady-state power is low in the
center of the core because of the control rod, but when the rod
is ejected the central power increases rapidly.
The program PWR/ONE is a modification of the program BWRPLANT
described in ref. 3 . The hydraulic part is originally based on
the RAMONA code whereas a new technique is introduced in the
one-dimensional neutronic part. This technique is called the
improved quasi-static method, which means factorizing the
neutron flux into an amplitude part and a power shape part, the
former with complete dependence on time but not on space and
the latter with only a minor dependence on time but complete
dependence on space. Both the amplitude equation and the shape
J) equation are solved by using finite elements of the Hermite
type. A report describing the method is in preparation.
Geometry
For the calculation of the benchmark the core was divided into
1 8 axial sections with 1 4 sections to the fuel part and 2 x 2 sections to the reflector. The fuel rod was divided into 4
radial zones + 1 cladding zone.
Nuclear Data
The code is prepared for 2-energy group calculation but in its
present version, the fast group is condensed to the thermal
group in the following way
The nuclear data from the benchmark are fully applied as well
as the radial buckling. Also the control rod representation is
identical to the problem formulation. As far as the reflector
@ is concerned PWR/ONE treats these sections in the same way as
the fuel sections. f here fore I-group crosssections for the reflector corresponding to an albedo of 0.66 were made:
1 .693 cm; la,R = 0.0558 cm-I
Hydraulics
The pressure balance given in the problem formulation was not
taken into account. Instead the pressure drop across the core
was kept constant. Non-equilibrium model, saturated steam and
subcooled or superheated water was applied like in the RAMONA
code together with the evaporation and condensation model.
Slip ratio: Bankof •’-Jones
Two-phase multiplier: Becker correlation
Heat transfer: Dittus-Boelter and Jens-Lottes
In table 1 are shown maximum values and steady state values of
some key parameters of the calculation. Generally the maximum
values from the PWR/ONE calculation lie between the ANTI-3D
calculation and the TRAWA calculation while the times of
occurrence of the PWR/ONE calculation are delayed compared to
the TRAWA calculation.
Figs. 4.1 - 4.10 show the main results of the PWR/ONE calculation
as function of time with the TRAWA results included for comparison.
Figs. 4.11 - 4.18 show the axial distribution of thermal neutron
fluxes at different times during the transient together with
the mean fuel temperature distribution and the void distribution.
Also here the TRAWA results are included for comparison.
Finally Fig. 4.19 shows the development of the axial power
shape during the rod ejection calculated with PWR/ONE.
The PWR/ONE results are designated by a multiplication sign "x"
while the TRAWA results are designated by a plus sign "+".
Figs. 4.1 and 4.2. Total Nuclear Power
Fig. 4.1 shows the nuclear power development during the first 2
seconds while Fig. 4.2 includes all 1 0 seconds calculated. The
power peaks of PWR/ONE and TRAWA are almost identical, but the
time occurrence of the PWR/ONE peak is somewhat delayed compared
to the TRAWA peak. Also the PWR/ONE power peak decrease is
delayed. The waves are explained in the same way as for the
ANTI calculations.
Figs. 4.3
- 1 7 -
and 4.4. Total Heat to Coolant
In Figs. 4.3 and 4.4 are shown the total heat transport to the
coolant as function of time. The first peak of the PWR/ONE
calculation is a bit higher than the TRAWA result corresponding
to a higher nuclear power as shown in Fig. 4.1, while the second
peak is both lower and delayed compared to the TRAWA calculation.
The ANTI results showed the same tendency. A calculation was
made with PWR/ONE ignoring the cladding region in the fuel rod
model. This made the second peak of the heat to coolant curve
disappear.
Figs. 4.5 and 4.6. Excess Reactivity
The excess reactivity as function of time is shown in Fig. 4.5
and Fig. 4.6. The results of PWR/ONE and TRAWA are almost
identical for the first 0.1 s, whereas the PWR/ONE calculation
again is delayed compared to the TRAWA calculation beyond the
0.1 s. The difference in reactivity from 7.0 s to 10.0 s
corresponds to the difference of the nuclear power in Fig. 4.2.
Fig. 4.7. The Water Temperature at Core Outlet
Fig. 4.7 shows the water temperature ?t core outlet as function
of time. The two calculations correspond reasonably.
Fig. 4.8. The Void Fraction at Core Outlet
Fig. 4.8 shows the void fraction at core outlet. Again the
results of both the PWR/ONE and the TRAWA calculation are almost
identical.
Figs. 4.9 and 4.10. Fuel Temperatures at Core Height 1.75 m
Fig. 4.9 shows the fuel center temperature at the core height
1 .75 m as function of time and Fig. 4.10 shows the corresponding
average fuel temperature as function of time. Here appears the
largest disagreement of all results between the PWR/ONE
calculation and the TRAWA calculation. The shape of the two
curves is almost identical whereas the absolute level is about
1000 C higher for the PWR/ONE calculation compared with the
TRAWA calculation. The same is the case for the average fuel
temperature distribution at steady state and at time = 1.0 s
shown in Figs. 4.16 and 4.17.
The fuel model in the PWR/ONE code uses the same linear
interpolation in the thermal resistance between the temperatures
800 and 1400 K as mentioned in section 3.2, the ANTI calculations.
Thus the temperature level and shape at steady state correspond
very well for the ANTI calculation and the PWR/ONE calculation.
Fig. 4.11. Steady-State Power Distribution
Fig. 4.11 shows the power distribution at steady state and the
two calculations seem to agree very closely despite the difference
in the fuel temperature level. At steady state the PWR/ONE code
calculates the effective multiplication factor to
with the radial buckling = 6 . ~ m - ~ .
Ak for the ejected rod is calculated to 0.00881 compared with
0.00928 in the problem formulation, and Ak for the shut down
rods is calculated to 0.061 compared with 0.060 in the problem
formulation.
Figs. 4.12 - 4.15. The Thermal Neutron Flux Distribution at
Different Times
Fig. 4.12 shows the thermal neutron flux distribution at steady
state, Fig. 4.13 the thermal neutron flux at t = 0 .05 s, Fig.
4.14 the thermal neutron flux at t = 1.0 s and Fig. 4.15 the
thermal neutron flux at t = 10.0 s.
The results of TRAWA and PWR/ONE correspond rather well at
steady state and t = 10.0 s but at t = 0 .05 s and t = 1 .0 s the
level of the thermal neutron flux of PWR/ONE is decreased
compared with the TRAWA results. This disagreement can be
explained from the delay in the nuclear power development in
Fig. 4.1.
Figs. 4.16 and 4.17. The Average Fuel Temperature Distribution
Fig. 4.16 shows the average fuel temperature distribution at
steady state and Fig. 4.17 the average fuel temperature
distribution at t = 1 .0 s. Again the earlier mentioned level
disagreement is quite clear.
Fig. 4.18. The Void Distribution
Fig. 4.18 shows the void distribution at t = 1.0 s . The two
results seem to agree very well.
Fig. 4.19. The Power Distribution during the Rod Ejection
Finally Fig. 4.19 shows the power distribution development
during the rod ejection calculated with PWR/ONE.
5. CONCLUSION
Three different versions of the NRF benchmark 1980 have been
calculated and compared to the Finnish TRAWA calculation. As
expected the PWR/ONE calculation gave the results that were
closest to the TRAWA results. The main reason to include the
two ANTI calculations (in addition to the purpose of validating
the ANTI program) was to show the difference between a one-
dimensional and a three-dimensional calculation for this type
of problem.
Although the results of the programs differ in a number of
details their overall agreement is as good as could be expected
and surely good enough to make a comparison meaningful. The
results show clearly that the treatment of the fuel rod is very
important and that some difference unknown to us between the
Finnish and the Danish model must be present.
As to the ID - 3D comparison, the power transient in the 3D case for the core as a whole is milder than in the ID case, but
naturally the local fuel temperature and void content are highest
- in the 3D case. The benchmark problem, however, is not very
- well suited for conversion to three dimensions in the way attempted by us; because of the power reduction in tlhe channel
containing the control rod the power of the neighbouring channel
had to be so high to keep the total power that boiling took
place already in the steady state.
We have found this benchmark calculation very interesting and
also very useful for the validation of our transient programs.
We think it would be worth-while to discuss the calculations
further at a future meeting in order to clear up the reasons
behind the discrepancies.
6. REFERENCES
1. A.M. LARSEN, B. THORLAKSEN. "Forslaq ti1 lasning a•’ NRF
benchmark problem 1980: Kontrolstavsudskydninq i en PWR".
DYN-3-80, 1980-11-10.
2. E. FALCON NIELSEN, A.M. HVIDTFELDT LARSEN."Input Description
for the Three-Dimensional PWR Transient Code ANTI", RISQ-M-2256,
November 1980.
3. E. NONBQL. "Development of a Dynamic Model of a BWR Nuclear
Power Plant", Risa Report No. 336, December 1975.
T a b l e 1
Maximum v a l u e and i ts t i m e and s t a t i o n a r y v a l u e f o r some k e y p a r a m e t e r s
Maximum Time S t a t i o n a r y
T o t a l power
T o t a l h e a t t o c o o l a n t 1 s t peak
R e a c t i v i t y
2nd peak
TRAWA PWR/ONE ANTI-I D ANTI-3D
TRAWA PWR/ONE ANTI- I D ANTI-3D
TRAWA PWR/ONE ANTI-1 D ANTI-3D
TRAWA PWR/ONE ANTI-1 D ANTI-3D
F u e l c e n t e r t e m p e r a t u r e TRAWA PWR/ONE ANTI-1 D ANTI-3D
F u e l a v e r a g e t e m p e r a t u r e TRAWA PWR/ONE ANTI-I D
O u t l e t v o i d f r a c t i o n TRAWA PWR/ONE ANTI-1 D ANTI-3D
O u t l e t s t e a m q u a l i t y TRAWA PWR/ONE
820 pcm 824 - 820 - 814 -
Fuel element with control rod
[7 Fuel element without control rod - ~oundar; between, hydraulic channels
Fig. 3.1. Horizontal section of the reactor core
10 15 Fig. 3 . 2 . TOTFlL RERCTOR POWER
ANTI-ID'
6 8 TOTAL RERCTOR POVER
2 4 6 8 Fig. 3 . 4 . MFIXIMUM FUEL TEMPERFlTURE
DEG. .C
2 4 6 8 Fig. 3 . 5 . MRXIMUM RVERRGE FUEL TEMPERRTURE
5 10 15 Fig. 3 :6. TOTAL POWER TO COOLANT
4 6 8 Fig. 3.7. TOTFlL POWER TO COOLFINT
4 6 Fig. 3 . 9 . REflCTIVITY
Fig. 3 . 1 0 . OUTLET VRTER TEMPERRTURE
I I I I 1 0 -
-
-
-
-
-
S I I 1 I I I ,
0 2 4 6 8 10 x lo0
I
W W
I
Fig. 3 . 1 1 . OUTLET VOID FRRCTION
Fig. 3 . 1 2 . OUTLET STERM QURLITY
TRAWA
ANTI
4 6 Fig. 3 . 1 3 . OUTLET PRESSURE
Fig. 3.21. Development of the normalized horizontal power
distribution of ANTI-3D during the initial
0.11 s of the transient (1/4 of the core).
TINE ( S )
1 FIG,4.1:TOTRL NUCLEQR POWER
TIME I S ) -.
>.
F I G. 4.2: TOTFIL NUCLEQR POWER
TINE CSI
F I G. 4,3 : TOTRL HERT TO COOLRNT
FIG,4.4:TOTRL HERT TO COOLRNT
TINE IS )
FIG. 4,s: EXCESS REQCTIVITY
S I GNRTURE x PWR/WE
-+ TRFIWR
FIGn4. 6: EXCESS RERCTIVITY
S I GNFITURE x PWR/ONE + TRQWQ
6.0 7.0 8
TIME CSI
F I G. 4.7 h WRTER TEMP. T CORE OUTLET
TIME CS)
FIG.4.8:VOID FRFICTION FIT OUTLET
TIME CSI
S I GNRTUQE X PWR/ONE + TRAWA
,. . .. FIG.4.9tFUEL CENTER TEMP FIT H=l,75 M
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7. C
TIME CS)
..!* FIG.4 . 10:FIVE.FUEL TEMP. QT Hz1 =,75 M
POWER DISTR.
HEIGHT FROM THE BOTTOM
FIGO4,12:THERMQL FLUX RT T=O.O CSI
HEIGHT FROM THE BOTTOM
F I G . 4 . 13:THERMRL FLUX QT T=0.05 CSI
1 SIGNRTURE
HEIGHT FROM THE BOTTOM
FIG.4.14:THERMQL FLUX QT T-1 .O CSI
0.00 t 0.0 SO.
x PWWONE .b TRRWR
HEIGHT FROM THE BOTTOM
FIG.4,lS:THERMfiL FLUX fiT T = l O a O CSI
S I GNRTURE x PWR/ONE + TRQWR
HEIGHT FROM THE BOTTOfl
I
'FIG.4.16SVERQGE FUEL TEMP.DISTRB,fIT T=O.O CSI
HEIGHT FROM THE BOTTOM
FIGa4,17;FIVERFIGE FUEL TEMP,DISTRB,FIT T=l , O CS3
150.0 200.0
HEIGHT FROM THE BOTTOM
FIG. 4 . 18: V O I D DISTRB.QT T= 1.0 CSI
HEIGHT FROM THE BOTTOM
FIG.4.19:POWER DISTRB. DURING ROD EJECTION
TECHNICAL RESEARCH CENTRE OF FINLAX0 V U C L E A R E N G I N E E R I N G L A B O R A T O R Y
P O 3 159.SF-90181 HELSINKI 18. FINLAYO TEL. $0-G48931TTELEX 12-2972VmIN SF
R i i t t a Kyrki
APPENDIX
NRF BENCHMARK PROBLEM 1980
A c o n t r o l r o d e j e c t i o n a c c i d e n t was chosen as t h e NRF
benchmark p rob lem 1980.
I n t h e c o n t r o l , r o d e j e c t i o n t r a n s i e n t a l l t h e submodels o f a
r e a c t o r dynamics program, namely n e u t r o n i c s , h e a t t r a n s f e r
model i n t h e f u e l and h y d r a u l i c s , a r e e f f i c i e n t l y u t i l i z e d .
The r e a c t o r model i n t h i s benchmark problem d e s c r i b e s t h e
r e a l behaviout: o f s u b s y s t e m s b u t it d o e s n o t c o r r e s p o n d to
any t r u e r e a c t o r .
The c a l c u l a t i o n is made by one -d imens iona l reactor dynamics
program w i t h o n e a v e r a g e f l o w c h a n n e l and o n e f u e l rod . The
r e a c t o r is a p r e s s u r i z e d w a t e r reactor. The p r e s s u r e o f t h e
r e a c t o r i s 150 b a r and t h e t o t a l t h e r m a l power i s 3000 MW.
T r a n s i e n t
I n t h e s t a t i o n a r y s t a t e t h e r e is o n e top c p n t r o l rod i n t h e
c o r e . A t time t = 0. i t i s e j e c t e d . L a t e r t h e s h u t down is i n i t i t a t e d and t h e t o p c o n t r o l r o d s a r e i n s e r t e d i n t o t h e
core. The c a l c u l a t i o n o f t h e t r a n s i e n t is f i n i s h e d a t time
t = 10 seconds .
Neutronics
TWO-group diffusion theory 5 axial regions with different fuel compositions, the height
of each region 0.5 m Doppler feedback of the average fuel temperature is of the
form:
Moderator density feedback is of the form:
Fast and thermal absorption cross sections of control rods
' c R ~ ~ = 0.02583 l/cm
' c R ~ ~ = 0.006769 l/cm
Neutron velocities
l/vl = 5.3-1.0-~ s/cm
- 6 l/v2 = 2.55-10 s/cm
TABLE 1 Cross sections and feedback coefficients - - a
Bottom of core
region 1 2
3
4
5
Top of core
Whole core:
coefficient a
coefficient b
Geometry
Height of the core
Total cross-sect ional a r ea
Total cross-sect ional a rea
per t o t a l c ross-sect ional
a rea of the f u e l
Fuel rod:
Outer radius of the cladding
Thickness of the cladding '
Radius of the f u e l p e l l e t
Flow area i n the core
per one f u e l rod
Tota l number of the f u e l rods
T o t a l power o f t h e reactor 3000 MW
Average number o f n e u t r o n s
produced p e r f i s s i o n 2.6
Prompt e n e r g y r e l e a s e p e r f Ysion 330 lo
-13J
No d e l a y e d e n e r g y r e l e a s e
TABLE 2 Delayed n e u t r o n s
Groups Decay c o n s t a n t
( l/s) * . -
1 0 .0124
2 0 .0305
3 0 .111
4 0 .301
5 1.13
6 3.00
F r a c t i o n o f to ta l f i s s i o n
n e u t r o n number
Boundary c o n d i t i o n p a r a m e t e r s o f t he ' core:
R a d i a l b u c k l i n g
- * a t t o p and bo t tom r e f l e c t o r s
r
TABLE 3 Control Rod5
Ejected rod Shut down rods
Insertion in stationary state 1. m 0. m The beginning time of the rod 0. s 1.5 s motion
The end time of the rod motion 0.05 s 7.75 s Velocity of the rod - 20 m/s 0.40 m/s Insertion at the end of the 0. m 2.5 m transient
- @ Ak, rod in/rod out 0.00928 0.060
Absorption cross section 0 .015 0.060
coefficient calculated
by TRAWA
The absorption cross sections of the control rods are
multiplied by the absorption cross section coefficients given
in the Table 3.
Heat transfer in fuel rod
Radial thermal conductivity of 'fuel pellet 0.0357 W/Kcm
of cladding 0.215 W/Kcm
Axial conductivities
Thermal capacity
of fuel pellet of cladding
The thermal resistance of the gas gap:
average fuel temperature gas gap thermal resistance
(K) (KC~~/W) 400. 5 .
800. 5.
1400. 0.5
3000. 0.5
97% of power is released uniformly in fuel pellet
3 % oi power is released in coolant
Hydraulics
System pressure at the core inlet 150 bar
Coolant: inlet temperature 575 K
Total inlet mass flow 15000 kg/s
Equivalent hydraulic diameter
of the core channel 0.9 cm
Friction coefficient
of the core channel 1.9 l/m
The pressure balance in the dynamic state is determined by
- 4 - 4 Ap - = -4.10 (A - A - 7 1 0
where
Ap = pressure loss over the core (bar)
i = total mass flow (kg/s) S = total mass flow acceleration (kg/s2)
Subscript o means stationary values
,-
Recommended'hydraulic submodels in this benchmark problem:
I
Non-equilibrium model, subcooled or superheated water and
saturated steam
Evaporation and condensation model like RAMONA 11,
bulk boiling rate:
Slip ratio: Elankof f -Jones
Two-phase friction multiplier: Thom a2 = 1+ 7.8YX + 0.683X 2
Heat transfer: Dittus-Boelter and Jens-Lottes
R e s u l t s
As a f u n c t i o n o f t h e time:
- t h e t o t a l power o f t h e reactor - t h e t o t a l h e a t o f c o o l a n t
- t h e e x c e d s r e a c t i v i t y
- t h e c o o l a n t t e m p e r a t u r e a t t h e o u t l e t o f t h e core - t h e v o i d f r a c t i o n and t h e steam q u a l i t y a t t h e o u t l e t
o f t h e core
- t h e f u e l c e n t e r t e m p e r a t u r e and t h e a v e r a g e f u e l
t e m p e r a t u r e a t t h e h e i g h t 1 .75 m f rom bo t tom o f t h e core
The a x i a l d i s t r i b u t i o n s time ( s ) - f a s t and t h e r m a l . n e u t r o n f l u x e s O . , 0 .05, l., 1 0 .
- n e a n f u e l ' empera ture . ' O . , 1.
- c o o l a n t t e m p e r a t u r e O . , 1. - v o i d f r a c t i o n 1.
Maximum v a l u e and i t s time (and p o s i t i o n )
- t o t a l n e u t r o n power
- t o t a l h e a t t o c o o l a n t
- r e a c t i v i t y
- h e a t f l u x
- f u e l t e m p e r a t u r e
- o u t l e t steam q u a l i t y '
- mean v o i d f r a c t i o n