the danish solution of the nrf benchmark problem 1980 ... · pdf filethe danish solution of...

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