TUTKIMUKSIA
FORSKNINGSRAPPORTER 729
RESEARCH REPORTS
Hanna Raty, Riitta Kyrki-Rajamiiki & Markku Rajamak
Validation of the reactor dynamics code TRAB
VALTION TEKNILLINEN TUTKIMUSKESKUS STATENS TEKNISKA FORSKNINGSCENTRAL TECHNICAL RESEARCH CENTRE OF FINLAND E S P 0 0 1991
Valtion teknillinen tutkimuskeskus, Tutkirnuksia
Statens tekniska forskningscentral, Forskningsrapporter
Technical Research Centre of Finland, Research Reports 729
Validation of the reactor dynamics code TRAB
Hanna Raty
Riitta Kyrki-Rajamiiki Markku Rajamiiki
Nuclear Engineering Laboratory
Espoo, May 199 1
l83OOOO?
Copyright O Valtion teknillinen tutkimuskeskus ( V l T ) 1991
JULKAISIJA - UTGIVARE -PUBLISHER
Valtion teknillinen tutkimuskeskus 0 ,Vuorimiehentie 5,02150 Espoo puh. vaihde (90) 4561. teleksi 122972 vttha sf
Statens tekniska forskningscentral (VlT), Bergsmansvilgen 5,02150 Esbo tel. viixel(90) 4561, telex 122972 vttha sf
Technical Research Centre of Finland 0 ,Vuorimiehentie 5, SF42150 Espoo, Finland phone internat.
+
358 0 4561, telex 122972 vttha sfVTT, Ydinvoimatekniikan laboratorio, PL 208 (Tekniikantie 4). 02151 Espoo puh. vaihde (90) 4561, telekopio (90) 456 5000
VTT, K&nkraftstekniska laboratoriet, PB 208 (Teknikvilgen 4), 02151 Esbo tel. vaxel (90) 4561, telefax (90) 456 5000
VTT, Nuclear Engineering Laboratory, P.O.Box 208 (Tekniikantie 4), SF-02151 Espoo, Finland phone internat.
+
358 0 4561, telefax+
358 0 456 5000COVER ILLUSTRATION
Analysis of the initial part of the Chernobyl accident with TRAB; sudden flow reduction with axially double-humped initial power distribution.
From:
Vanttola, T. & Rajamiiki, M. One-dimensional considerations on the initial phase of the Chernobyl accident.
Nuclear Technology, Vol. 85(1989)1, pp. 33-47.
Tekninen toimitus Inkeri Heikkilil
V l T OFFSE'I'PAINO, ESP00 1991
UTY, Hanna, KYRKI-RAJAM&I. Riitta & R A J ~ ~ K I , Markku. Validation of the reactor dynamics code TRAB. Espoo 1991, Valtion teknillinen tutkimuskeskus, Tutkimuksia - Statens tekniska forskningscentral, Forskningsrapporter - Technical Research Centre of Finland, Research Reports 729.31 p.
UDC 621.039.5:519.87:53 1.3
Keywords validation, one-dimensional reactor dynamics, space-time kinetics, reactor safety analysis, reactor accidents, thermohydraulics, TRAB
ABSTRACT
The one-dimensional reactor dynamics code TRAB mansient Analysis code for W R s ) developed at VTT was originally designed for BWR analyses, but it can in its present version be used for various modelling purposes. The core model of TRAB can be used separately for LWR calculations. For
P W R
modelling the core model of TRAB has been coupled to circuit model SMABRE to form the SMATRA code. The versatile modelling capabilities of TRAB have been utilized also in analyses of e.g. the heating reactor SECURE and the RBMK-type reactor (Chernobyl).This report summarizes the extensive validation of TRAB. TRAB has been validated with benchmark problems, comparative calculations against independent analyses, analyses of start-up experiments of nuclear power plants and real plant transients.
Comparative RBMK type reactor calculations have been made against Soviet simulations and the initial power excursion of the Chernobyl reactor accident has also been calculated with TRAB.
TRAB has been extensively used for analyses of the TVO ABB Atom type BWR reactors and within SMATRA for
P W R
analyses of the Loviisa VVER-440 reactors and VVER-91 type reactors. TRAB is also used outside VTI' both for BWR analyses and, within SMATRA, for PWR analyses by the Finnish Centre for Radiation and Nuclear Safety (STUK) and the Imatran Voima Oy (IVO) power company.CONTENTS
ABSTRACT 3
1 INTRODUCTION
1.1 The reactor dynamical code system 1.2 Nuclear data
1.3 Fuel data
1.4 Thermohydraulic data
2 STEADY STATE VALIDATION
2.1 Comparison study of TRAWA and HEXBU-3D 2.2 Comparison of TRAB and HEXBU-3D results 2.3 Comparison of the 2-channel model of TRAB
with HEXBU-3D results
3 VALIDATION OF THE DYNAMIC CALCULATION 3.1 Reactor kinetic benchmark problem
3.2
NRF
benchmark calculations 3.3 Simulation of TVO start-up tests3.3.1 A-isolation test and load rejection test 3.3.2 Pump trip test
3.3.3 Stability test
3.4 Simulation of TVO overpressurization transient of 1985
3.5 Simulation of TVO oscillation incident of 1987
4 SIMULATION OF THE TOTAL FEED WATER LOSS IN RBMK AND
ANALYSIS OF THE INITIAL PART OF THE CHERNOBYL ACCIDENT 23
5 FURTHER VALIDATION PLANS 26
6 CONCLUSIONS 26
REFERENCES t 27
FIGURES
Reactor dynamical calculation system at
VTT
Axial fast neutron flux calculated by HEXBU-3D and TRAWA Rod ejection benchmark problem: total fission power
Rod ejection benchmark problem: total power transferred to coolant TVO overpressurization transient: relative power and system pressure calculated by TRAB compared to measured values
TVO overpressurization transient: total mass flow calculated by TRAB compared to measured values
TVO overpressurization transient: insertion of scram control rods calculated by TRAB compared to measured values
TVO oscillation incident: fission power calculated by TRAB
TVO oscillation incident: mass flow at inlet and outlet of core calculated by TRAB
Simulation of the total loss of feed water at full power in the RBMK reactor with TRAB: comparison of TRAB results with the Soviet curves 24 Analysis of the initial part of the Chernobyl accident with TRAB; positive
scram with double-humped power 25
1 INTRODUCTION
1.1 The reactor dynamical code system
The one-dimensional reactor dynamics code TRAB 114, 11-13, 15-28, 51 of VTT was originally designed for BWR analyses, but it can in its present version be used for versatile modelling purposes:
-
for BWR modelling; core, main circulation system inside the reactor vessel including steam dome with related systems, steam lines, incoming and outgoing flows as well as control and protection systems. TRAB has been extensively used for analyses of the ABB Atom type TVO reactors.-
as a separate core model TRAB-CORE for LWR calculations 191-
for PWR modelling: the core model of TRAB connected to circuit model SMABRE to form the SMATRA code /9/, which is used for the analyses of the Loviisa VVER-440 reactors and other VVER type reactors.- for exotic applications using the versatile capabilities of TRAB for modelling within input, e.g. the heating reactor SECURE, RBMK-type reactor (Chernobyl)
The core model of TRAB is based on an earlier model developed in VTI', TRAWA 112, 111. TRAWA has been transferred to the program library of OECD NEA from which it has been delivered to and is being used for PWR modelling in e.g. Germany (former GDR) and Yugoslavia.
The core model of TRAB has been combined with HEXBU-3D 141 to create a three-dimensional dynamics program HEXTRAN which is in its validation phase at present.
Neutronic parameters for the core model can be developed through the reactor physical calculation system of VTT which is described in fig. 1.
TRAB has been validated with benchmark problems, comparative calculations against independent analyses, start-up experiments of nuclear power plants and real transients.
The initial power excursion of the Chernobyl accident has also been calculated with TRAB 1331.
REACTOR DYNAMICAL CALCULATION SYSTEM AT VTT FOR TRANSIENT ANALYSES
1, Neutronic parameters
-Basic nuclear data
-Nuclear data processing
-Nuclear data libraries (25-70 energy groups)
-Calculation of
reactivity and reactivity HEXBU-3D coefficients, three-
dimensional power and -VVER code
burnup distributions etc.
t
-Data transfer and
integration for one- ODD
dimensional group constants
2. Thermohydraulic parameters
I
I
-fuel models (GAPCON- -hydraulic models
3. One-dimensional transient analysis codes
4 . Three-dimensional
transient analysis code
1
TRAB
-BWR core
and related systems
TAPP, SMATRA
-PWR core
and related systems
0
= programs developed by VTT0
= programs partly developed by VTT 0 = programs applied by VTTFig. 1 . Reactor dynarnical calculation system at W.
TRAB is used also outside VTT both for BWR analyses and within SMATRA for PWR analyses by the Finnish Centre for Radiation and Nuclear Safety (STUK) and the Imatran Voima Oy (NO) power company.
1.2 Nuclear data
One-dimensional group constants for the one-dimensional dynamics programs of
VTT
can be developed starting from the basic nuclear data libraries. Parallel program systems are used for BWR (rectangular) and
P W R
(VVER, hexagonal) calculations. The assemblywise two group constants and kinetic parameters are calculated with CASMO (rectangular) or CASMO-HEX (hexagonal). Three-dimensional power and burnup distributions, reactivities etc. are calculated with the three-dimensional simulator programs BOREAS (BWR) or HEXBU-3D (VVER). Results from both these calculations are transferred to the programs BROAD (BWR) and ODD (VVER) which perform the integrations for one-dimensional group constants and transfer the data for the dynamics programs. The ODD and BROAD codes are based on principles of ref. 19.1.3 Fuel data
Fuel parameters for the dynamic programs can be obtained from fuel models (e.g.
GAPCON-T-2) and checked against results in consistent linear powers and fuel temperatures in stationary calculations. Often these parameters are treated as variables in sensitivity studies (especially the heat conduction in the gas gap).
1.4 Thermohvdraulic data
A large selection of well-known thermohydraulic correlations for BWRs and PWRs are used and new dependencies based on separate tests can be included. In BWR calculations the thermal hydraulic correlations of the fuel suppliers are used as specified data of the fuel bundles. Often the parameters of the thermohydraulic models are treated as variables in sensitivity studies.
2 STEADY STATE VALIDATION
The purpose of the steady state comparisons is to validate the calculation of the axial distributions, reactivity coefficients, multiplication factor and the integration of the one-dimensional group constants with the condensing program.
One-dimensional calculations with the core model TRAWA have been extensively compared with three-dimensional HEXBU-3D calculations in a separate comparative study 13, 71. In connection with the Loviisa FSAR calculations with TRAB 1101 the steady state results of TRAB have been comprehensively compared to the results of HEXBU-3D calculations. HEXBU-3D has been thoroughly validated against Loviisa measurements.
2.1 Com~arison study of TRAWA and HEXBU-3D
Detailed comparative steady state calculations have been carried out between the one-dimensional dynamics core model TRAWA and the threedimensional stationary HEXBU-3D 13, 71 in order to verify and validate the neutronics model of TRAWA and the method of developing the neutronic input parameters.
The similarity of the performance of the solution methods of TRAWA and HEXBU-3D was initially verified with a very simple one-dimensional test case with fresh fuel, using HEXBU-3D as axially one-dimensional. The results of the two codes are in good agreement. The maximum difference in relative power is 1.1 % and the average difference is less than 0.6 %. The difference in the predicted multiplication factor is of the magnitude 10".
In a realistic test case comparative calculations were performed for the burnt VVER-440 core with different fuel types with three-dimensional HEXBU-3D geometry. The one- dimensional averaged group constant parameters for TRAWA including thermal hydraulic feedback parameters were condensed with the preprosessor program ODD from the HEXBU-3D results.
The results of TRAWA and HEXBU-3D are in good agreement also in the realistic test case. The differences between the results of the two codes are of the same magnitude or smaller than the differences between HEXBU-3D results and measurements. In fig. 2
the results for the axial distribution of the relative fast flux calculated by TRAB are compared to the transverse integrated HEXBU-3D results in a complicated two-peak case. The axial flux shape is well predicted. The maximum difference in the relative power is 1.8 % and the average difference is 1.0 %. These minor differences are due to the averaging procedure and the thermal hydraulic dissimilarities in the codes.
Full results of the comparisons with different variations are presented in ref. 7 (in Finnish). These comparisons confirm the calculation of the axial distributions and the correct operation of the condensing program ODD.
2.2 Comparison of TRAB and HEXBU-3D results
In connection with the Loviisa FSAR calculations 1101 the steady state results of TRAB and HEXBU-3D have been extensively compared in order to further validate the neutronic model of TRAB and the method for developing one-dimensional group constants.
The basic neutronic parameters of materials are described in TRAB with standard two-group diffusion theory parameters. They are based on parameters made for HEXBU-3D code by calculations with the CASMO-HEX code. The HEXBU-3D parameters are radially condensed into one-dimensional parameters for TRAB with the code ODD, the principles of which are described in ref. 19. The condensing is based on the burnup distribution and the power and neutron flux distributions, which had been calculated by HEXBU-3D for full power situation without control rods in core and with samarium and xenon in equilibrium. In addition to the parameters condensed from the HEXBU-3D input data, ODD also condenses parameters directly from the CASMO-HEX results for the dynamic calculation: the inverse velocities of neutrons in the fast and thermal group and the fractions of delayed neutrons in six groups. This condensing is also based on the HEXBU-3D distributions. The TRAB neutronic parameters were calculated for ten axial burnup regions as in HEXBU-3D, but they were mathematically modified to be given at the 11 boundaries of the regions. TRAB interpolates the neutronic parameters for the mesh points inside the region. The radial buckling was treated as axially constant and its value was calculated on the basis of the average migration area assuming an average value for the radial leakage of neutrons. The axial boundary conditions are calculated from HEXBU-3D albedos.
0
?
1
oiliiiiiiiiiiiiii , I l l 1
0.00 0 . 1 0 0 . 2 0 0 . 3 0 0 . 4 0 0.60 0 . 6 0 0.70 0.80 0 . 9 0 1.00
H E I G H T F R R C T I O N FROM BOTTOM OF CORE
DRAW VTT/YOI 290280
Fig. 2 . Axial fast neutron
flux
calculated by HEXBU-3D and TRAWA 171.The axial dismbutions calculated by TRAB and HEXBU-3D were compared at different power levels and for different burnup. The results of the two codes are in very good agreement in all the cases, when the shorter control rod follower fuel rods were taken into account by a constant additional control rod. Transition from one state to another by means of changing the system parameters results in correct predictions without any tuning. The comparisons prove that axial distributions are well predicted with the condensed one-dimensional cross section data sets.
The results for multiplication factor and critical boron concentration calculated by TRAB and HEXBU-3D were also compared at different power levels and for different burnup.
Comparisons were made between different steady states to evaluate the calculation of reactivity effects. The comparisons c o n f i e d that all the reactivity effects which are connected to fuel or moderator feedback are predicted correctly with the sets of cross section data and are in good agreement with HEXBU-3D.
The reactivity coefficients predicted with the cross section data sets in TRAB were also close to the HEXBU-3D and the real Loviisa values.
2.3 Com~arison of the 2-channel model of TRAB with HEXBU-3D results
The applicability of TRAB in the calculation of asymmetric effects was studied in connection with Loviisa FSAR calculations /lo/. The core model of TRAB was used with two parallel axially one-dimensional channels, corresponding to 116 and 516 of the core. The transverse neutron flux shape function dynamics model of TRAB was used to take into account variations of the neutron flux in the radial direction. The weight factor parameters for the regionwise onedimensional group constants of TRAB were developed /27/ from flux integrals based on HEXBU-3D calculations. The results of the TRAB and HEXBU-3D were compared in several symmetric and strongly asymmetric cases for relative power of the two regions and reactivity effects.
In the asymmetric cases the disturbance affects the 116-sector of the core. In the most extreme case the power of the disturbed sector is as high as 8 times the power of the undisturbed sector. Power peaking in the disturbed section is a little less pronounced in the TRAB calculation than in the HEXBU-3D calculation. Difference in the relative power of the disturbed region calculated with the two codes is about 10 %.
For asymmetric boron inlet disturbances the reactivity effect calculated by TRAB is predicted within 7 % of the HEXBU-3D value in the most extreme case. For asymmetric disturbances in the coolant inlet temperature the differences in the predictions of the two codes are somewhat larger but, when interfering factors in the data base are eliminated, are estimated to be within 10 % for the reactivity effect.
The reactivity effects of the asymmetric and symmetric disturbances were also studied with cross calculations (interpolation and extrapolation) with different data sets of TRAB. The results are in good agreement, further confirming both the method used for developing transverse shape function data and the correctness of the developed data sets.
Both the applicability of the two-channel model and neutronic shape function dynamics of TRAB and the method for developing the shape function parameters from the three-dimensional HEXBU-3D results in order to calculate radially asymmetric transients were confirmed. The two-region model of TRAB underestimates the relative power in the disturbed region by only about 10 % compared to HEXBU-3D in strongly asymmetric cases.
3 VALIDATION OF THE DYNAMIC CALCULATION
In order to validate the dynamic calculation, TRAB has been tested against benchmark calculations, independent analyses, start-up tests of nuclear power plants and real plant transients. The core model (TRAWA) has also been tested separately. Both reactivity transients and thermohydraulic transients as well as complicated and demanding combinations have been considered.
3.1 Reactor kinetic benchmark ~roblem
The dynamic performance of the core model TRAWA has been successfully compared with other codes using a one-dimensional reactor kinetic benchmark problem /29/. The benchmark problem DO/ consists of four test cases:
-
control rod withdrawal at 1 cm/s with negative fuel temperature feedback;- control rod withdrawal at 1 cm/s with positive fuel temperature feedback;
-
control rod blowout: rod withdrawal at 20 cm/s in 10 s and rod drop in 1 s;-
removal cross section reduced linearly during 200 s.In the case of control rod withdrawal with negative fuel temperature feedback the results of TRAWA differ by only about 2 % from the averaged results of nine codes. In the second test case the neutron flux and fuel temperatures increase exponentially because of the positive temperature feedback. The scattering in the results of the different codes is larger than in the first case. The results of TRAWA fall within 2-10 % of the results of the codes which solve the problem by the implicit method. Differences between TRAWA and the codes which solve the problem by the explicit method are much larger.
In the rod blowout test case the results of TRAWA and the averaged results of nine codes is less than 2 %. The last test case in which the removal cross section is reduced could not be solved by all the codes and the results differ significantly. The difference between TRAWA and the averaged results of other codes is about 16 % in this case.
3.2 NRF benchmark calculations
A control rod ejection accident in a PWR was presented as the NRF reactor dynamic benchmark problem at the 1980 Nordic Reactor Physics (NRF) Meeting 161. In the analysis of a control rod ejection transient all the essential submodels of a reactor
dynamics code, viz, neutronics, heat transfer model in the fuel and hydraulics must be efficiently utilized. For the same purpose e.g. the two-phase phenomena are exaggerated in comparison with a conventional PWR.
The benchmark problem has been analyzed with the one-dimensional reactor dynamics core model TRAWA and with Danish reactor dynamics codes 181. The behaviour of the fission power and the power transferred to the coolant calculated by TRAWA are presented in figs. 3 and 4, demonstrating the severity of the transient. The magnitude of the fission power peak calculated by TRAWA is 84874 MW, whereas the stationary value is 3000 MW. The TRAWA results closely agree with the results of the Danish programs. The maximum value of fission power is 861 10 MW with the one-dimensional code P W O N E and 79720 MW with the three-dimensional code ANTI-3D. The differences between the results are thus only about 6 % of the total magnitude of the power peak.
The maximum reactivities calculated with the different programs are very close to each other; the largest is the TRAWA result 829 pcm, the smallest the ANTI-3D result 814 pcm, the P W O N E result 820 pcm being almost identical to the TRAWA result.
Results for the fuel center temperature and the average fuel temperature are again almost identical with TRAWA and the one-dimensional PWR/ONE code. The temperatures calculated by the three-dimensional ANTI-3D code are some 10-15 % higher than the one-dimensional results. This is due to the fact that the channel with the highest power in the three-dimensional calculation is considerably hotter than the average channel in the one-dimensional calculation. Minor differences in the void fraction calculation reflect the differences between the differences in the hydraulic models, most probably the evaporation/condensation model.
The rod ejection benchmark problem places high demands on the reactor dynamics codes utilized in the comparative calculations. The results calculated with TRAWA are almost identical to the results of the one-dimensional dynamics code PWR/ONE and also closely agree with the results of the three-dimensional ANTI-3D code. The benchmark calculation demonstrates the applicability of TRAWA to the calculation of reactivity transients under extreme conditions.
N R F B E N C H M R R K 1 9 8 0 C O N T R O L R O O E J E C T I O N R C C I D E N T C R L C U L R T E D B Y T R R W R
V1
N R F B E N C H M R R K 1 9 8 0 C O N T R O L R O O E J E C T I O N R C C I D E N T C A L C U L R T E D B Y T R R W R
0 0
L
-
I
0 +
-
xII
-
-
t
0
4
CK -
0 I
I- 0 -
a -
W CY -
L L
-
0
"tl
CtL *-
W
-
3; 1
0 -
Q- -
I-
-
0 I-
N 0 +
~ ~ ~ . l l I l l l , , , ,
m
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1 - 4 0 1.60 1.80 2.00
T I M E ( S 1
-
-
1 1 1 1 1 i 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00
ORRW VTT/YOI 010781 I
T I M E ( S 1
ORRU V T T / Y O I 010781
Fig. 3 . Rod ejection benchmark problem: total fission power 181.
-
Ii
I
i
i
0
I
1
I
Fig. 4 . Rod ejection benchmark problem: total power transferred to coolant 181.
18300017
3.3 Simulation of TVO start-up tests
3.3.1 A-isolation test and load rejection test
Start-up tests of the TVO I BWR reactor have been simulated with TRAB for the Finnish Centre for Radiation and Nuclear Safety (STUK) in order to validate the TRAB code 1311. Extensive sensitivity studies were carried out to study the effects of less accurately known parameters. The A-isolation and load rejection tests were selected for the simulations.
In the A-isolation test the steam line isolation valves close resulting in a rapid rise in reactor pressure and power. Reactor scram occurs and the control and relief valves open in order to regulate reactor pressure. The recirculation pumps are mpped and the reduced flow results in increased core voidage, reducing reactor power. The most important results of the A-isolation test for the comparison were reactor pressure and water level as a function of time. During the simulation of the test, the maximum change in reactor pressure is about 3.5 bar and the maximum change in water level is about 1.2 m. The overall behaviour of these system parameters agrees well with the test results. The differences between results of the best estimate calculation and measured values are about 0.1 bar for the maximum pressure and less than 0.1 m for the maximum of the water level.
In the load rejection test, reactor power is reduced from the nominal value by reducing the main coolant flow to a level compatible with house-load turbine operation. The most important results for the comparison were the neutron power of the reactor and water level as a function of time. Reactor power is reduced from 100 % to about 20 % in about five seconds. The maximum change in the water level is about 1 m. The power decrease is very accurately predicted with the code and the calculated water level is reasonably compatible with measured data.
The analyses demonstrate that TRAB is capable of giving a correct quantitative presentation of the changes in reactor pressure, water level and fission power as a function of time. The calculated process parameter values are in close agreement with the test results. The simulations are discussed in detail in ref. 3 1.
3.3.2 Pump trip test
The pump trip test of TVO I BWR reactor has been simulated with TRAB in order to confirm the applicability of TRAB to loss-of-flow transients and the pump model described in ref. 15. The simulations show close agreement with the measurements with the most realistic assumptions and without any unphysical fittings.
3.3.3 Stability test
The start-up stability test of TVO I1 BWR reactor at the observed point of instability has been studied with TRAB. The results of the calculations are in reasonably good agreement with real plant data without elaborate tuning of the model. The applicability of TRAB to instability studies even in extreme conditions was confirmed. The description of the by-pass channel was found to be an important factor in the modelling.
3.4 Simulation of TVO ovemressurization transient of 1985
The overpressurization transient which took place in September 10 1985 in the TVO I BWR reactor has been simulated with the one-dimensional dynamics code TRAB, as a joint project of the Technical Research Centre of Finland (VTT) and the Finnish Centre for Radiation and Nuclear Safety (STUK). The transient was initiated by the closing of the turbine valves in about 0.5 s which was due to erroneous functioning of the pressure controller. A best estimate calculation was performed in order to validate the code. The steam line model of TRAB was used, including the option allowing steam to superheat in the upper plenum and steam lines 115, 181. Sensitivity studies were carried out for the key parameters, which can not be clearly defined from the measurements. The principal purpose was to describe the initial stage of the transient.
In the real plant all the identical systems do not operate exactly identically and the accurate test calculation would require much more detailed information than is needed for the safety calculations.
Calculated and measured values of fission power, pressure, main circulation flow and insertion time of scram control rods were compared. The results of the comparison are presented in figs. 5-7. The maximum value of fission power could not reliably be determined from the measurements. For the available data the overall behaviour of the fission power is well predicted and the calculated values are very close to the measured
Fig. 5 . TVO overpressurization transient: relative power (+) and system pressure ( X ) calculated by TRAB compared to measured values (circled dot, dot).
X i J . 6 - I I , , I I [ , I
O . W 1 . 0 0 2 . 0 0 3 . 0 0 4 . 0 0 5 . 0 0 6 . 0 0 7100 I a!oo I
T I M E ( 6 1
Fig. 6 .
TVO
overpressurization transient: total mass flow calculated by TRAB ( X ) compared to measured values (circled dots).Fig. 7. TVO overpressurization transient: insertion of scram control rods calculated by TRAB (+) compared to measured values (circled dots).
ones. The difference in the powers after the peak is caused by the safety-purpose reactivity value of shutdown in the TRAB calculation. Pressure was slightly overestimated in the calculations. The best estimate pressure values were however within half a bar from the measured values whereas the magnitude of the pressure rise was about 8 bars. The differences are believed to be caused mainly by the delays in the measurement system and the fact that the four steam lines were described with one steam line in the model. The main circulation flow is well predicted in the beginning of the transient. Later during the transient, the flow is slightly overestimated but, taking into account the accuracy of the measurement, the results are good. The behaviour of the scram control rods predicted by the hydraulic scram model of TRAB 1211 is identical with the measured values.
In summary, the results of the simulation are in good agreement with the measured values. In the sensitivity studies the scattering of the results is relatively small. The difference between the highest and lowest predicted values of maximum pressure is 0.65 bar.
3.5 Simulation of TVO oscillation incident of 1987
The oscillation incident which took place in February 22 1987 in the TVO 1 BWR reactor has been studied by the Finnish Centre for Radiation and Nuclear Safety (STUK) 1321. The event and its variations were studied with the three-dimensional BWR dynamics code RAMONA-3B 1341, developed by Brookhaven National Laboratory, and with the one-dimensional code TRAB. TRAB calculations were performed using only one core channel and a by-pass channel parallel to the core. The results show that both codes are capable of analyzing the oscillation incident. Agreement between measurements and calculations is reasonably good for both codes. TRAB analyses for different points in the powerlflow map are consistent with the results for channels with different power levels in the three dimensional RAMONA-3B calculation. For the conect prediction of instability behaviour with the one-dimensional model, reactor power in the one representative channel has to be increased by some 20 percent compared to the average power of the reactor. This can be compensated by increasing the flow of the by-pass channel. Results of one of the cases studied with TRAB are shown in figs. 8-9.
In the sensitivity analysis the heat conduction in the fuel rod and especially in the gas gap, affecting the time constant of fuel heat transfer, was found to be the most important of the studied parameters.
B W R O S C I L L R T I O N S _g r - ~ o a a i e z I I I
CASE 3 , P = 1408 MW, F = 2658 K G / S
SOUSCCI I . Tea0 I
Fig. 8. TVO oscillation incident: fission power calculated by TRAB 1321.
Fig. 9. TVO oscillation incident: muss flow at inlet and outlet of core calculated by TRAB 1321.
4 SIMULATION OF TOTAL FEED WATER LOSS IN RBMK AND ANALYSIS OF THE INITIAL PART OF THE CHERNOBYL ACCIDENT
Some of the most frequently presented scenarios for the initial power excursion of the Chernobyl accident have been evaluated based on simulations with TRAB 1331. The TRAB model of the Chernobyl reactor takes into account most of the essential features of the RBMK reactor type. The emphasis in the simulations was on the initiating mechanisms of the accident. The one-dimensional core description proved to be useful for evaluating credibility of different accident scenarios.
As a test case for the RBMK model of TRAB the total feed water loss transient from full power was simulated with TRAB. The results of the simulation are presented in fig. 10 where they are compared to the Soviet simulation data Dl. The results of TRAB agree reasonably well with the Soviet curves, taking into account the uncertainties due to the incomplete initial data.
In the analyses of the Chernobyl accident the axial flux behaviour proved to be very important. The results tend to support the occurence of the so called "positive scram", even though the scenarios with some type of sudden flow reduction are not totally excluded. Examples of the results of the simulation calculations are presented in fig. 11 for the case with "positive scram" and double humped initial axial power dismbution, using two different values for void coefficient of reactivity, the origin of which is the following. When the chopped cosine initial shape was modified into the double humped initial shape with the power fitting procedure of TRAB 1161, the void coefficient changed from 30.10-'1% void into l610-~/% void. These values were used in the analyses. Subsequently the corresponding void coefficient values in the three-dimensional static calculations 111 were published to be 27.5.10-51% void and 16.5.10-~/% void, respectively.
0 15 30 45 60
Time (s)
0 15 30 45 60
rime (s)
Fig. 10. Simulation of the total loss of feed water at full power in the RBMK reactor with TRAB 1331: comparison of TRAB results (-
-
-) with the Soviet curves 121 (-).I = Nuclear power, 2 = Power to the coolant, 3 = Mass flow, 4 = Liquid in the steam drums, 5 = System pressure.
C
3 100000 :
x - Fission p.
w -
I-. 10000
g
-[L -
1000 j P. to cool.
-
100 I I I
Time (s)
i
#
Core out
e
0 15 30 45 60
Time (s)
0 15 30 45 60
Time (s)
1000000
n 3 100000
x
Fission p.w
&I
a, 10000
a
5 -
1000 g i P. to cool.
-
100 I I I
Time (s)
I Core out
vl 20000
2
~ O O O O
L-,
core in0 15 30 45 60
Time (s)
0 15 30 45 60
nme (s)
Fig. 11. Analysis of the initial pan of the Chernobyl accident with TRAB 1331;
positive scram with double-humped power.
Left side with the smaller void coefficient; right side with the larger void coefficient.
5 FURTHER VALIDATION PLANS
Further validation plans for TRAB include
-
the simulation of Loviisa start-up tests with the SMATRA code;-
further comparisons between TRAB and the three dimensional RAMONA-3B code in order to study the multi-channel (two or three channel) modelling in TRAB;- comparisons between TRAB and the new three dimensional dynamics code
HEXTRAN
in order to study the multi-channel (two or three channel) modelling in TRAB.6 CONCLUSIONS
TRAB provides mainly one-dimensional modelling of the dynamics of both the power generation and the thermal hydraulic phenomena occuring in the reactor core, in the interior of the pressure vessel and in related subsystems of an undamaged BWR. Within the scope of the mathematical descriptions, TRAB has been shown to function correctly.
As a model of a real nuclear power plant, TRAB has been shown to simulate with good accuracy dynamical behaviour which is characterized by reactivity insertions, mass flow alterations and pressure rise. Reasonable results are also achieved in instability transients. In addition, it has been possible to include clearly multidimensional reactor core effects correctly in the TRAB description.
REFERENCES
Chan, P.S. & Dastur, A.R. The physical basis for the void reactivity effect and its dependence on absorber rod configuration in the RBMK-1000. Nuclear Science and Engineering, 103(1989)3, pp. 283-288.
Emel'yanov, Ya., Kuznetsov, S.P. & Cherkasov, Yu.M. Design provisions for operational capability of a nuclear power plant with a high-powered water-cooled reactor in emergency regimes. Translated from Atomnaya Energiya, 50(198 1 )4, pp.
25 1-254.
Kaloinen, E. & Rajarntiki, M. The numerical accuracy of the HEXBU-3D code for application to the reactor consisting of large homogeneous nodes. Helsinki 1984.
Technical Research Centre of Finland, Nuclear Engineering Laboratory, Technical Report REP- 12/84. 22 p. (for the XI11 Symposium on WWER Physics of the VMK, Curtea de Arges, Romania 30.9.-6.10.1984).
Kaloinen, E., Teriisvirta, R. & Siltanen, P. HEXBU-3D, a three-dimensional PWR-simulator program for hexagonal fuel assemblies. Helsinki 1981. Technical Research Centre of Finland, Nuclear Engineering Laboratory, Research Report 7.
148 p
+
app. 5 p.Keinanen, S. BINPUT. Espoo 1971. RKR Memo 13. 14 p. (in Finnish).
Kyrki, R. (currently Kyrki-Rajamiiki, R.). NRF Benchmark Problem 1980, specifications and results of Finland. Helsinki 1980. Technical Research Centre of Finland, Nuclear Engineering Laboratory, Technical Report REP-14/80. 36 p.
Also: NEACRP-L-328, OECDINEA, Paris 1991.
Kyrki, R. (currently Kyrki-Rajamiiki, R.). Dynamiikkaohjelman TRAWA neutroniikkamallin verifiointi painevesireaktorin stationaaritilassa (Verification of the neutronics model of dynamics program TRAWA in the stationary state of a PWR). Helsinki 1980. Technical Research Centre of Finland, Nuclear Engineering Laboratory, Technical Report REP-17/80. 11 p.
+
app. 21 p. (in Finnish).Kyrki-Rajamiiki, R. Results of Finland for NRF Benchmark Problem 1980 with modified gas gap conductivity. Helsinki 1981. Technical Research Centre of Finland, Nuclear Engineering Laboratory, Technical Report REP- 1318 1. 27 p.
Also: NEACRP-L-329, OECDINEA, Paris 199 1.
Kyrki-RajamZiki, R. The use of program SMATRA (PWR) with parallel core channels and the use of program TRAB-CORE (PWR+BWR). Helsinki 1990.
Technical Research Centre of Finland, Nuclear Engineering Laboratory, Technical Report RFD- 11'90. 17 p.
Kyrki-Rajamiiki, R. Reactivity initiated accident analyses for Loviisa FSAR with reactor dynamical computation system of V'IT. Proceedings of the 19. Symposium on WWER Physics of the VMK. Siofok, Hungary, 30.9.
-
6.10.1990. Budapest, 1990.KFKI
(Central Research Institute for Physics of Hungarian Academy of Sciences). P. 505-
519.Raiko, R. (currently Kyrki-Rajamiiki, R.) & Rajama, M. TRAWA, a transient analysis code for water reactors, Supplementary part 1. Helsinki 1978. Technical Research Centre of Finland, Nuclear Engineering Laboratory, Report 33. 54 p.
RajamZiki, M. TRAWA, a transient analysis code for water reactors. Espoo 1976.
Technical Research Centre of Finland, Nuclear Engineering Laboratory, Report 24.
149 p
+
app. 31 p.Rajarniiki, M. BINPUT-sisWnlukuohjelman soveltarnisesta (On the application of the input reading program BINPUT). Espoo 1978. Technical Research Centre of Finland, Nuclear Engineering Laboratory, SR-6/78. 10 p. (in Finnish).
Rajarniiki, M. TRAB, a transient analysis program for BWR, Part 1. Principles.
Helsinki 1980. Technical Research Centre of Finland, Nuclear Engineering Laboratory, Report 45. 101 p
+
app. 9 p.Rajamaki, M. Extensions of TRAB-program, plant submodels. Helsinki 1981.
Technical Research Centre of Finland, Nuclear Engineering Laboratory, Technical Report REP-15/81. 17 p.
Rajamiilci, M. Tietokonemenetelmii lasketun reaktorin tehojakauman sovittarniseksi halutun kaltaiseksi (A computer method for fitting of the calculated power distribution of a reactor to a desired distribution). Helsinki 1982. Technical Research Centre of Finland, Nuclear Engineering Laboratory, Technical Report REP-13/82. 15 p. (in Finnish).
Rajamiiki, M. Acceleration method for neutronic and thermohydraulic iterations.
Helsinki 1983. Technical Research Centre of Finland, Nuclear Engineering Laboratory, Technical Report REP-3/83. 4 p.
Rajamaki, M. TRAB-model for wet or superheated steam in the steam dome and steam lines of BWR. Helsinki 1983. Technical Research Centre of Finland, Nuclear Engineering Laboratory, Technical Report REP-4/83. 14 p.
Rajamiiki, M. One-dimensional group constants. Helsinki 1983. Technical Research Centre of Finland, Nuclear Engineering Laboratory, Technical Report REP-19/83. 34 p.
Rajamtki, M. Reaktorifysikaalisten parametrien mW&ninen tehojakauman avulla (Determining of the reactor physical parameters from the power distribution).
Helsinki 1983. Technical Research Centre of Finland, Nuclear Engineering Laboratory, Technical Report REP-24/83. 12 p. (in Finnish).
Rajamiiki, M. Hydraulic scram system of BWR in TRAB program. Helsinki 1986.
Technical Research Centre of Finland, Nuclear Engineering Laboratory, Technical Report RFD-6/86. 13 p.
Rajamiiki, M. Poikittaisten jakautumien muuttumisen huomioonottaminen yksiulotteisissa ryhmavakioissa (Taking the changing of transverse distributions into account in the one-dimensional group constants). Helsinki 1986. Technical Research Centre of Finland, Nuclear Engineering Laboratory, Technical Report RFD-7/86. 18 p. (in Finnish).
Rajamiki, M. & Raty, H. Collection of COMMON-variables of TRAB most useful to program users. Helsinki 1986. Technical Research Centre of Finland, Nuclear Engineering Laboratory, Technical Report RFD-12/86. 24 p
+
app. 5 p.Raty, H. Varoventtiilien avautumisen ja sulkeutumisen kuvaus TRABissa (Description of the opening and closing of relief valves in TRAB). Helsinki 1989.
Technical Research Centre of Finland, Nuclear Engineering Laboratory, Technical Report RFD-14/89. 7 p. (in Finnish).
Raty, H. & Rajamiiki, M. Separate hot channel calculations with TRAB. Helsinki 1988. Technical Research Centre of Finland, Nuclear Engineering Laboratory, Technical Report RFD-24/88. 8 p.
Raty, H. & Rajamiiki, M. TRAB, a transient analysis program for BWR, Part 2.
User's manual. Helsinki 1991. Technical Research Centre of Finland, Nuclear Engineering Laboratory, Research Notes 1232. 105 p
+
app. 46 p.Raty, H. & Rajamiiki, M. Utilization of the transverse neutron flux shape function dynamics of TRAB between two core states known from stationary 3-D calculations. Helsinki 1990. Technical Research Centre of Finland, Nuclear Engineering Laboratory, Technical Report REP-10/90.7 p.
Raty, H. & Rajamiiki, M. Utilization of the transverse neutron flux shape function dynamics of TRAB in stability calculations. Helsinki 1990. Technical Research Centre of Finland, Nuclear Engineering Laboratory, Technical Report RFD-15/90.
16 p.
Salminen, R. Onedimensional reactor kinetic benchmark problem computed by TRAWA and comparisons with some other programs. Helsinki 1977. Technical Research Centre of Finland, Nuclear Engineering Laboratory, Technical Report REP-1/77. 10 p
+
app. 60 p.Sidell, I. The analysis of one-dimensional reactor kinetic benchmark computations.
Dorchester, 1974. United Kingdom Energy Authority. 17 p
+
app. 9 p.Valtonen, K. Verification and tuning of computing codes for transient analysis using the results of power plant start-up experiments. Institute of Radiation Protection, Department of Reactor Safety. Finnish-Soviet Reactor Seminar, KTM-GKAE, Helsinki, Finland 15.-22.9.1980. (unpublished).
32. Valtonen, K. BWR Stability Analysis. Helsinki 1989. Finnish Centre for Radiation and Nuclear Safety, STUK-A-88. 48 p.
33. Vanttola, T. & R a j a e i , M. One-dimensional considerations on the initial phase of the Chernobyl accident. Nuclear Technology, Vol. 85(1989) 1, pp. 33-47.
34. Wulff, W., Cheng,
H.S.,
Diamond, D.J. & Khatib-Rahbar, M. A description and assessment of RAMONA-3B MOD.0 CYCLE 4: A computer code with three-dimensional neutron kinetics for BWR system transients. Upton 1984.Brookhaven National Laboratory, Department of Nuclear Energy, NUREGICR-3664, BNL-NUREG-5 1746. 392 p.
.
Published by Technical Research Centre of Finland Series title, number and report code of publicationVuorimiehentie 5 VlT Research Reports 729 FI+VTITUTK-9 ID29
S F 4 2 1 50 Espoo, Finland
phone internat. + 358 0 4561 Date Project number
telex 122972 vttha sf May 1991 YDI000537
ruthors
-9, I-hna
Kyrki-Rajamiiki, Riitta Rajamiiki, Markku
Name of project Reaktoridynarniikkamenetelmien tason varmista- minen ja dokumentointi
Commissioned by
VALIDATION OF THE REACTOR DYNAMICS CODE TRAB
bstract
The one-dimensional reactor dynamics code TRAB mansient Analysis code for BWRs) developed at V?T was originally designed for BWR analyses, but it can in its present version be used for various modelling purposes. The core model of TRAB can be used separately for LWR calculations. For PWR modelling the core model of TRAB has been coupled to circuit model SMABRE to form the SMATRA code. The versatile modelling capabilities of TRAB have been utilized also in analyses of e.g. the heating reactor SECURE and the RBMK-type reactor (Chernobyl).
This report summarizes the extensive validation of TRAB. TRAB has been validated with benchmark problems, comparative calculations against independent analyses, analyses of start-up experiments of nuclear power plants and real plant transients.
Comparative RBMK type reactor calculations have been made against Soviet simulations and the initial power excursion of the Chernobyl reactor accident has also been calculated with TRAB.
TRAB has been extensively used for analyses of the TVO ABB Atom type BWR reactors and within SMATRA for PWR analyses of the Loviisa VVER-440 reactors and VVER-91 type reactors. TRAB is also used outside V?T both for BWR analyses and, within SMATRA, for PWR analyses by the Finnish Centre for Radiation and Nuclear Safety (STUK) and the Imatran Voima Oy (NO) power company.
9ctivity unit
Nuclear E n g i n e e ~ g Laboratory, P.O.Box 208 (Tekniikantie 4). SF-0215 1 Espoo, Finland SSN and seriis title
0358-5077 Tutkimuksia - Valtion teknillinen tutkimuskeskus SBN
95 1-38-39761 lass (UDC)
621 .O39.S:S l9.87Sl.3
;old by Government Printing Centre P.O. Box 51 6
S F 4 0 1 01 HELSINKI
phone internat. + 358 0 56601
Language English Key words
validation, one-dimensional reactor dynamics, space-timc kinetics, reactor safety analysis, reactor accidents,
Pages 31 p.
Price group A
Note
VTT:N JULKAISUSARJAT VTT:N JULKAISUSAR- Kolnien vuottn vanhcmniat
JOJEN HANKINTA julkaisut toimitetaan kopioina
Valtion teknillisen tutkiniuskes- VTT:n inforniaatiopalvelu-
kuksen julkaisusarjat ovat VTT:n julkaisuja myy laitoksesta:
0 Technical Research Centre of Valtion painatuskeskus.
Finland Publications VTT
0 Valtion teknillinen tutkinius- keskus Tutkiniuksia -
Statens tekniska forsknings- central Forskningsrapporter - Technical Research Centre of Finland Research Reports
Postimyynti:
Valtion painatuskeskus PL 516
00101 Helsinki puh. (90) 566 0266 teleksi 123458 vapk sf telekopio (90) 566 0374
lnforniaatiopalvelulaitos PL 42
02151 Espoo
puh. (90) 4356 4402 teleksi 125175 vttin sf telekopio (90) 455 4073 0 Valtion teknillinen tutkimus-
keskus Tiedotteita - Kirjakaupat Helsingissl:
Statens tekniska forsknings- Annankatu 44 central Meddelanden - puh. (90) 1734 2012
Technical Research Centre of ~ t ~ l l ~ ~ ~ l ~ ~ ~ d i 4 Finland Research Notes puh. (90) 662 801
0 VTT Symposium
VTT'S PUBLIKATIONS- ANSKAFFNING AV Tre i r Gldre publikationer le-
SERlER VTT'S PUBLIKATIONER vereras som kopior fr5n VTTs Informat ionstjanst:
Statens tekniska forskningscentra- VTT's publikationer saljes av lens (VTT) publikationsserier iir Statens tryckericentral.
VTT 0 Technical Research Centre of
Finland Publications
Valtion teknillinen tutkinius- keskus Tutkimuksia - Statens tekniska forsknings- central Forskningsrapporter -
Technical Research Centre of Finland Research Reports 0 Valtion teknillinen tutkinius-
keskus Tiedotteita -
Statens tekniska forsknings- central Meddelanden -
Technical Research Centre of Finland Research Nctes 0 VTT Syniposiuni
Postforsaljning: lnformationstjlnst
Statens tryckericentral PB 42
PB 516 02151 Esbo
00101 Helsingfors tel. (90) 4356 4402 tel. (90) 566 0266 telex 125175 vttin sf telex 123458 vapk sf telefax (90) 455 4073 telefax (90) 566 0374
Bokhandlar i Helsingfors:
Annegatan 44 tel. (90) 1734 2012 Sodra esplanaden 4 tel . (90) 662 80 1
PUBLICATION SERIES O F V T T
T h e publication series of the Technical Research Centre of Finland (VTT) are
0 Technical Research Centre of Finland Publications
0 Valtion teknillinen tutkinius- keskus Tutkimuksia -
Statens tekniska forsknings- central Forskningsrapporter - Technical Research Centre of Finland Research Reports 0 Valtion teknillinen tutkinius-
keskus Tiedotteita -
Statens tekniska forsknings- central Meddelanden - ,
Technical Research Centre of Finland Research Notes 0 VTT Symposium
H O W T O OBTAIN VTT'S PUBLICATIONS
VTT's publications are sold by Government Printing Centre.
mail orders:
Government Printing Centre P.O. Box 516
SF-00101 Helsinki phone
+
358 0 566 0266 telex 123458 vapk sf telefax+
358 0 566 0374 Bookshops in Helsinki:Annankatu 44
phone
+
358 0 1734 2012 Etelaesplanadi 4phone
+
358 0 662 801Publications published more than three years ago are de- livered as copies from the Information Service at VTT:
VTT
Information Service P.O. Box 42
SF42151 Espoo, Finland phone
+
358 0 4356 4402 telex 125175 vttin sf telefax+
358 0 455 4073VALTION TEKNILLINEN TUTKIMUSKESKUS, TUTKIMUKSIA
STATENS TEKNISKA FORSKNINGSCENTRAL, FORSKNINGSRAPPORTER TECHNICAL RESEARCH CENTRE O F FINLAND. RESEARCH REPORTS
YDINVOIMATEKNIIKAN LABORATORIO - KA NUCLEAR ENGINEERING LABORATORY
RNKRAFTSTEKNISKA LABORATORIET -
Kjaldman, Lars. Numerical simulation of peat dust explosions. 1987. 85 p.
Pipatti, Riitta & Lautkaski, Risto. Vaarallisten aineiden varastointiin liittyvat vaaratilanteet. 1987.
110 s. + liitt. 12 s.
Rintamaa, Rauno, Torrijnen, Kari, Keinanen, Heikki, Sarkimo, Matti, Sundell. Henrik, Talja, Heli
& Ikonen, Kari. Prevention of catastrophic failure of pressure vessels and piping. Results of pressure test with a large vessel (HCI-test). 1988. 52 p.
Pipatti, Riitta. Teollisuusprosessien suuronnettomuusriskit. 1989. 155 s. + liitt. 12 s.
Ikonen, Kari, Saarenheimo, Arja & Talja, Heli. Paineastioiden ja putkistojen murtumisen lasken- nallinen arviointi. 1989. 109 s.
Silvennoinen, Eero, Juslin, Kaj, Hanninen, Markku, Tiihonen, Olli, Kurki, Jorma & Porkholm, Kari.
The APROS software for process simulation and model development. 1989. 106 p. + app. 19 p.
Kjaldman, Lars. Virtausten ja palamisen numeerinen laskenta tulipesissa. 1989. 68 s.
Leinonen, Mikko S. & Mikkola, Timo P. J. The ACR-program for automatic finite element model generation for part through cracks. 1989. 80 p.
Talja, Heli. Nordic numerical round robin for a side-grooved CT-specimen. 1989. 30 p. + app.
9 P.
Rintamaa, Rauno, Talja, Heli, Keinanen, Heikki & Saarenheimo, Arja. Prevention of catastrophic failure in pressure vessels and piping. Comparison of experimental and computational results of the pressure vessel test HC2. 1990. 33 p.
Keinanen, Heikki, Rintamaa, Rauno, berg, Tero, Sarkimo, Matti, Talja, Heli & Saarenheimo, Arja.
Evaluation of catastrophic failure risk in pressure vessels. Results of pressure vessel test with a large vessel (HC2-test). 1990. 62 p.
Pipatti, Riitta. Ammoniakkipaastot ja -1askeuma Suomessa. 1990. 41 s. + liitt. 3 s.
Raty, Hanna, Kyrki-Rajamiiki, Riitta & Rajamaki, Markku. Validation of the reactor dynamics code TRAB. 1991. 31 p.
Toto julkoisua myy Denno publikot~on solis This publ~cation IS
ovoiloble from
4 4
VALTION STATENS GOVERNMENT
PAINATUSI(ESI(US TRYCKERICENTRAL PRINTING CENTRE
POSTIMY YNTl POSTFURSALJNINGEN MAIL ORDERS
PL 516 PB 516 P O 0 516
00101 Helsmk! 00101 Helsmgfors SF40101 Hels~nk~ Fmlond
Puh (90) 566 0266 Tel (90) 566 0266 Phone tnternat
Vo~hde (90) 56601 Voxel (90) 56601 + 358 0 56601
Teleks~ 123458 vapk sf Telex 123458 vopk sf Telex 123458 vopk sf KIRJAKAUPAT HELSINGISSA BOKHANDLARNA I HELSINGFORS BOOKSHOPS I N HELSINKI
Annankotu 44 Annegoton 44 Annonkotu 44
IEt Routot~ekodun kulrnol (I hornet ov S Jarnvg ) Phone (90) 1734 2012 Puh (90) 1734 2012 Tel 190) 1734 2012
18300036
ISBN 95 1-38-39761
Etelaesplonod~ 4 Sodro esplonaden 4 Eteloesplonod~ 4 lSSN 03.58-5077
Puh (90) 662 801 Tel (90) 662 801 Phone (90) 662 801 UDC 62 1 .020 5 5 19.8753 I ;.
