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Control systems and transient analysis
NUCLEAR ENGINEERINGAND DESIGN 10 (1969) 231-242. NORTH-HOLLANDPUBLISHINGCOMPANY,AMSTERDAM
CONTROL SYSTEMS AND TRANSIENT ANALYSIS Yoichi FUJI-I-E
Department of Nuclear Engineering, Osaka University, Osaka, Japan Received 24 April 1969
Characteristics governinga marine reactor operation include: (1) occurrence of abrupt load changes in association with maneuvering operations; (2) subjection to ship motion such as rolling, heaving and pithing. The effects of abrupt load changesappear on the reactor primary system as well as on the secondary steam generator. However, the effects of ship motion appear only on the steam generator since enough subcoolingis given to primary coolant and no steam void is found in the primary coolant. This paper contains the following subjects: (1) description of the part of the reactor system which has an intimate relation to reactor operation; (2) description of the functions of the control system and the safety system; (3) transient behaviour of the reactor and the steam generator under load change;(4) transient behaviour of the steam generator due to ship motion.
1. Introduction In the coolant system of the First Nuclear Ship of Japan, heat generated in the reactor is transported to the steam generators by means of two similar closed loops. Each loop contains a main circulating pump, a steam generator, valves and the associated piping. The flow of cooling water in each of the two loops is from the discharge side of the pump to the reactor, through the steam generator, and back to the suction side of the pump. The coolant system is designed to transfer 36 megawatts of heat from the reactor core at the rated power with flow rate of 2 X 900 tons per hour. At this power level, the inlet temperature to the reactor core is 271°C and the outlet temperature is 285°C, and the primary system pressure is about 110 kg/cm 2. Though the circulating pump can be operated at half speed, the flow rate is held constant during normal operation. The heat added to the coolant is given off in the steam generators where the primary water generates saturated steam from feedwater entering the steam generator at 160°C. For full load conditions, the steam generated is 2 X 30 tons per hour and also for the base load conditions the steam generated is about 2 X 54 tons per hour.
The heat transport system is designed to meet the following variations in steam demands. 1. Rapid power decrease: 100-18% of full load in 1 second. 2. Rapid power increase: 18-90% of full load in 30 seconds. 3. Ahead-astern operation: 100-18% of full load in 5 seconds staying at 18% of full load for 50 seconds and 18-80% of full load in 30 seconds. 4. Astern-ahead operation: 80-18% of full load in 5 seconds staying at 18% of full load for 50 seconds and 18-100% of full load in 30 seconds. It is worthwhile to mention about thermal and hydraulic design criteria for the First Nuclear Ship of Japan; The basic thermal and hydraulic criteria are as follows: a) The maximum value of the internal temperature of the oxide fuel shall not exceed the melting temperature even at the hot spot during normal operation. b) The local heat flux at the fuel element cladding surface shall not exceed designed DNB heat flux (Departure from Nucleate Boiling heat flux) either during the steady-state operation or during any transient operation.
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Y.FUJ/-I-E
c) Bulk boiling shall not occur so much as to induce some hydraulic instability. To meet the criteria mentioned above, the following operation limits are imposed on the reactor operation. 1. The reactor power level shall not exceed 130% of the rated power either during the steady-state operation or during any transient operation. The maximum fuel temperature at the center of the hot spots is about 2100°C at 130%-power, which is much less than the melting point of oxide fuel, therefore the criterion (1) can be satisfied easily for any operation pattern. 2. Since DNB heat flux may be a function of flow rate, hydraulic diameter, inlet enthalpy, steam quality and so forth, some correlation formula is introduced to determine the maximum heat flux and minimum heat flux ratio. The minimum heat flux ratio means the minimum value of the ratios between the design heat flux at the hot channel and the limiting heat flux along the axial direction. The minimum heat flux ratio is determined to be 1.30, however, since ship motion may cause some aggravation to the hydraulic properties, a 15% margin is added to the limiting heat flux ratio to give the consequent DNB ratio of 1.53. With this DNB ratio, the maximum core inlet temperature permitted is given as a function of other reactor process parameters (pressure and the reactor power level). 3. The last criterion is different from the other two in its character. Bulk boiling, when it occurs, does not directly cause hydraulic instability or any unstable state on the reactor and the criterion 2), though not thoroughly, suppresses the rate of bulk boiling as is clear from fig. 1. Therefore this criterion can be considered to be set up to avoid unknown instability or unstable condition which might be induced by ship motion. To meet this criterion, the minimum operating pressure permitted is determined as a function of the power level and core inlet temperature. To follow the load change quickly and stably, several control systems are provided and a constant average primary temperature control is adopted in the reactor system. From the point of view of selfregulability of the reactor, although the pressure coefficient of reactivity is positive, its magnitude is
Low Pressure Scrota High Temperoture Scrom Over Power Scrota
320 ......... Pressure 510
:300 o v
290
% •
'
E
cp
280 c
0 (,.)
270
260
25c~'0-9
~ I00
I I10
I 120
; 130
Power (%)
Fig. 1. Operation limit. not large and the moderator temperature coefficient of reactivity and the Doppler coefficient of reactivity are negative and large throughout the temperature range of operation, so that the power coefficient of reactivity is negative and the reactor can follow the load change by itself. However, since severe load change is required for nuclear ship reactor when compared to usual land based reactor, control systems are provided to improve the transient responses and therefore the reactor operations. To design the control systems, the following criteria are postulated: a) For any load change, if the control systems operate normally, the reactor should not be scrammed, and the relief valve of the primary system and the safety valve in the secondary system do not open. b) For any load change, the reactor can be operated safely and stably and no unstable state occurs at any parts in the plant.
CONTROL SYSTEMS AND TRANSIENT ANALYSIS
233
Table 1 Ship condition. The rated power Rolling Pitching
100% 30° (3"9 cpm) 10° (4~15 cpm)
50% 45 ° (3"9 cpm)
Vertical acceleration Abrupt change of vertical acceleration
(1+0.6) go (4"q5 cpm)
(1+0.6) go (4~15 cpm)
c) Even under the ship conditions listed in table 1, safe and stable operation of the reactor can be continued.
2. Control systems Reactor system control and instrumentation consist of nuclear instrumentation, reactor automatic control system, safety and process instrumentation. Operation of the reactor plant is monitored and controlled at the main control console and the following functions are provided: 1. To maintain safe and stable operation. 2. Informations concerning the operation will be indicated and/or recorded on the console. 3. Safety action is rapidly and properly fulfdled automatically and/or manually when something unusual happens in the reactor system. Reactor start up is manually operated until the reactor power level increases up to about 10% of the rated power and then it is possible to operate the reactor automatically or manually and also the reactor shut down operation is made either automatically :or manually. 2.1. Nuclear instrumentation The function of the nuclear instrumentation system is to measure continuously the neutron flux level ranging from the source range up to 150% of the rated power, to indicate and/or to record on the main control console and, if necessary for the reactor safety operation, to feed signals to reactor control system and/or to safety system.
15° (4~15 cpm)
(1-+0.82) go
2.2. Reactor control system 2.2.1. Reactor power control system To control the reactor power level, constant average primary temperature control is adopted and the primary coolant temperature variation during load change to a region which is compatible with the capacity of the pressurizing system. The reactor power control system is operated either manually or automatically. Control signals to be fed to the control rod driving system are composed from two components. One of them is a temperature error signal given as the difference between the average temperature of the primary coolant and the reference temperature. As the average temperature the higher one of two primary 10op average temperatures is selected at the auctioneer circuit. Another signal is given as the error signal between the normalized steam flow and the normalized neutron flux. This signal is used to improve transient responses to load change. The control rods operated for reactivity regulation during load change are inner positioned two, and therefore there are two reactivity compensation speeds with one rod speed as is shown in fig. 2. The control rods are driven in group, however, the rods for reactivity compensation can be moved either individually or in group. The two rods in diagonal position among the inner_four rods make one group, and either of the two groups can be used as the control rod group for reactivity compensation during normal operation and the other group is used as shim rods. 1 +
rlS
e = I + r2--1-~(Tav-rref)
(1)
r3S +~
kg (~:-:~'s)
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Y.FUJI-I-E
21fliii......... V ; one rod operation 2V ; two rodsoperation D ; dead band H~ ; hysteresis H2 ; Fig. 2. Control rod drive speed.
where e = error signal Tw = average coolant temperature Tref =reference temperature E = normalized neutron flux ~s = normalized steam flow kg = gain
loops. The pressurization method of the primary coolant is similar to the ordinary pressurized water reactor and the pressurizer keeps the primary pressure to give enough sub-cooling to the coolant and also absorbs volume change of the coolant and then holds the plant parameters in permitted ranges. The pressure control components are: (a) steady heater; (b) transient heater; (c) continuous water spray; (d) transient water spray; (e) relief valve and (0 safety valve, a volume control system is also attached to the pressurizer. In ease of positive pressure surge caused by power decrease, the transient spray is driven to condense steam in the pressurizer to lower the system pressure and in case of negative pressure surge caused by power increase transient, water in the pressurizer is evaporated by the transient heater to absorb the surge. 2.2.3. Steam dump control system In the secondary steam loop, a steam dump system with its capacity of 18 tons per hour (30% of the rated steam flow) is provided to bypass steam to the main condenser. This steam dump system acts to weaken the effects which are to appear in the secondary system as well as in the primary system during load change especially during rapid load decrease and the system also favorably acts during pressure increase transient in the secondary system. The control
The block diagram of reactor power control system is shown in fig. 3. 2.2.2. Pressure control system Pressure control of the primary system is made at the pressurizer settled on the one of the two primary
RODNol p o s i t i o n ~ RO01~ position,n!_+ ~ Detector
Aver.ogiI.ng
"
Tc
TH
~---
+
clr
IT
~
,o~x;to~" Vno~ Averag.ing I
-L~,Sl
l+ P-~' I
Two rods
I
I
~.~
insert,0n insertion/
RICONo.Iwithdrawal
2r~
circuit _
Detector
_
~ain Tworods x~ldrawal
One rod withdm~f
Fig. 3. Block diagram or reactor power control system.
CONTROL SYSTEMS AND TRANSIENT ANALYSIS
I SteamPressure Ps
+ ~
235
~ t e r level
2- IT~ of swirevane 1
.5"~ . . . . . . . . . . . . . . . . ~ . . ~
_,o°
,00%
-3~T~of
l..ood
tube ~ l e
Fig. 5. programmed water level Operation mode " R u n " interlock
I--I-o,,
Man. - A u t ~ selector
~nuol Main condenser vacuum i n t e r l o c k Main
steam flow I n t e r l o c k
Dump valve
inside of which primary coolant flows might not be dried out during load change. The feed water control system keeps the programmed water level automatically. Control elements, steam flow, feed water and water level are selected to form a usual three-element control system. The programmed water level is shown in fig. 5 as a function of the reactor power level and the block diagram of the feed water control system is also shown infig. 6.
Fig. 4. Block diagram of dump control system. signal to be fed to the steam dump control system is given as the difference between steam pressure and the reference dump pressure. The block diagram of the system is shown in fig. 4. 2.2.4. Feed water control system In the secondary side of the steam generator, natural circulation of water is formed and the water level in the steam generator varies during load change. The water level in the steam generator is programmed with the reactor power level to conf'me the level in a ftxed region so that the steam separator in the riser might not be immersed and the top of the tube bundle,
2.3. Safety system The reactor safety system has the following functions: One of which is an interlocking function. Reactor operation modes are stop, start up and operation and one of the operation modes is selected with the mode selection switch. Corresponding to each mode several interlocks are settled, for example, in the start up mode the following conditions must be satisfied before operation. 1. The mode selection switch is at the start up mode position. 2. Logarithmic counting rates of the two start up channels of the nuclear instrumentation should be larger than the reference value.
J
Fs
I , . '-._ ~ I . . . . .
,Turbine PumP.I~
- ~ o FILTER
H I - Lo LEVEl_ / ~ N U N C IATOR
JSystem '.* ~,~) log
I' ~. . . . . .s~.~l'
Fig. 6. Block diagram of feedwater control system.
236
Y.FUJI-I-E Table 2 Scram conditions. Scram signal
Detector
Trip level
Start up rate
Intermediate range
5 DPM
Power range Neutron flux
Neutron detector
25% of the rated power (start up mode) 123% of the rated power (operation mode)
Primary coolant pressure
Pressure switch
Variable
Primary coolant temperature
Temperature switch
Variable
Pressure switch Pressure difference switch
Not fixed
Pressurizer water level
Pressure difference switch
Not fixed
Primary coolant flow
flow switch Voltage switch
Not fixed
SIS action
Rod drop
Position switch
Position difference in each control rod group
Position switch
Not fixed
Ship inclination
Position switch
Not fixed
Manual
Botan
3. All the control rods should be at the lower most positions. Another function is safety action concerning the rod motion. When reactor plant parameters leave from their normal ranges or some mechanical failure which might cause some unsafe state of the reactor, safety actions such as an alarm, control rod stop or scram action occur to avoid the reactor from entering into crisis and to hold the reactor in safe. The last feature is safety and protection function such as safety injection and boron injection. All the safety circuits are multichannel circuits with fail-safe principle and logical circuits o f 1 out o f 2 or 2 out o f 4 are employed to improve the reliability o f the signals. Signals such as rod stop and scram are fed to the control rod drive system with alarm annunciation and with indication and/or record on the main control console. Scram conditions are listed in table 2. Among the scram conditions, over-power scram, high-temperature scram and low-pressure scram are worthy o f mentioning in details.
2.3.1. Over power scram To limit reactor power level to less than 130% o f the rated power, the neutron flux is taken as the reactor power and over-power scram action is made by monitoring the neutron flux level. Taking the errors due to neutron flux m e a s u r ~ e n t into account the scram level set point is determined to be 123% o f the rated power. So the reactor m a y be scammed within the neutron flux range between 1 1 7 - 1 3 0 % o f the rated power. A t 115% o f the rated power, rod stop action will occur. 2.3.2. High temperature scram The high temperature protection limit calculated from thermal design is here linearized for ease to the control circuitry and is given as a function of the reactor percent power(q): (Tci)limit = (Tci)o -
A(q- 1.3),
where Tci = core inlet temperature and q = percent power.
(2)
CONTROLS SYSTEMS AND TRANSIENT ANALYSIS When the core inlet temperature rises up to the limit temperature calculated from eq. (2), the reactor is to be scrammed, however, from the point of view of transient behavior of the reactor, the temperature responses to transients are similar whether they are at the average channel or at the hot channel when the reactor is in steady state or slow transient state, but they do not show similar behavior when some rapid transient may be introduced; besides, in such a rapid transient, time delay of scram action may be taken into account. Therefore the protection limit is 10°C lowered and also a few second of time delay is corrected circuitly to compensate the difference of the fuel heat transfer time constants between hot channel and average channel. 2.3.3. Low pressure scram The protection limit of the reactor primary pressure is also linearized and is given as a function of the core inlet temperature and the reactor percent power: Pminl = aTci - bq - c ; where Pminl = limit pressure. When the primary pressure of the reactor decreases down to Pminl the reactor will be scrammed. As mentioned before, the low-pressure scram is not so critical as the high-temperature scram, therefore only the error due to pressure measurement is taken into account for the determination of the protection limit.
3. Transient analysis For operating conditions or load change requirement mentioned before, the transient behaviors of the reactor plant are simulated. Since reactivity coefficients, control rod worth and other reactor parameters will change with fuel temperature, moderator temperature, primary pressure and integral of operation time or fuel burn-up, they have ranges in their value as is shown in table 3. The maximum and minimum values of them are taken in simulation, and the combination of these parameters is determined in such a way that the transient behaviors of the plant should not become moderate by their combination, however, and that only physically plausible combinations are selected. 3.1. Plant transient response to a main turbine trip
When the main turbine trips and steam flow decreases rapidly, secondary temperature increases, then heat to be removed in the secondary system decreases and consequently the primary temperature increases to introduce negative reactivity to the core. As for control signal to be fed to the control rod drive system, error signal from the difference between steam flow and neutron flux dominates initially, therefore rod insertion does not get behind the load change so much, then the core inlet temperature rises up and introduces negative reactivity which lowers the reactor power level and the reactor power variation becomes moderate because of reactivity compensation
Table 3 Reactivity coefficient and other constants. Neutron lifetime (sec)
Nearly 1.8 X 10-s
Delayed neutron fraction (%) Moderator temperature coefficient
Nearly 0.64
(~lrl°o Fuel temperature coefficient
(arlrl°c)
237
Nearly -3.0 X 10"~ "Nearly -7.8 X 10--4 Nearly -2.1 X 10-s "Nearly -3.2 X 10-s
Pressure coefficient ( a x / g /at)
Nearly + 3.6 X 10-s ~Nearly + 5.8 X 10-s
Control rod worth (%AK/K /cm/group )
Nearly 0.033 ~Nearly 0.095
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Y.FUJI-I-E
due to moderator temperature rise. In this state the error signal from the temperature difference becomes dominant and the transient will be over with the reactivity balanced. In this load change, if the reactor power control system is not operated the plant transient does not cause reactor scram, however, the safety valve in the secondary loop opens because of the pressure rise in the secondary loop. In case when the steam dump control system does not dump steam to the main condenser, the safety valve also opens to lower steam pressure in the secondary loop, however, reactor scram does not occur. As for the transient response of the water level in the steam generator, when steam flow decreases suddenly steam quantity in the drum increases and therefore steam pressure in the drum increases. With this increase of steam pressure, condensation of steam occurs to lift the boiling surface to some upper point. Since the flow resistance due to friction at the swirl vane in the riser is large compared with the flow resistance in the downcomer, when condensation occurs, flow in the downcomer increases and water
flows into the boiling section. This transient behavior lasts for only a few seconds. The water level in the steam generator descends rapidly because of water flow-in to the boiler and the inverse response of the water level appears. The simulated results are shown in figs. 7 and 8.
3.2. Plant transient response to rapid load increase When the steam flow in the secondary loop increases rapidly, heat being removed increases and causes the temperature decrease in the primary coolant and moderator which introduces positive reactivity due to the moderature temperature reactivity effect. As is explained in the previous case, the control rod drive signal is dominantly from power-steam flow difference at first, then the control signal from temperature difference follows. In this load change, if rod stop motion occurs by control rod stop signal at 110% of the rated power the reactor power level fluctuates like sawtooth wave and power overshoot lasts for a long time. Without rod stop motion reactor scram does not occur, however,
Full temp~coeff. ;-3.2x10 -m A K / K / ° C Moderator temp, coeff. ; -~LOxK)"4 ~ K / K / ' C Pree~re
coeff.; 5.6xK)-e A K / K / k g / c m e
Control rod worth ; 0.055% AK/Klcm/group
o
.oo ff,,(
f ff,
I fff f
FS ;Steam flow rate ON ;Neutron flux
_,o
TAN; Coolant avera(~e temp. P
; Primary system pressure
ZR ; Rod
~,~
11,!, [ / ±/ / / / / P/
Position -2o
PS ; Secondary
L
system pressure
Fig. 7. Transient responses to rapid power decrease.
/ s' f
CONTROLS SYSTEMS AND TRANSIENT ANALYSIS
239
%
ioo '~',,,y'Fh,
F, /
50
t/
-'-
T I M E (MIN.)
l;;) .... ,o~ o,..,r,--
_40~--Top
of tube bundle
Fig. 8. Feedwater flow and steam generator water level transients to main turbine trip.
Fuel temp. cueff. ; - 3 . 2 x I 0 "6 ~ K / K / e C
%1 I/ 2oo Iti '°°i ~!
F,
r
Moderotor temp. coeff. ~-3.0xlO-" ~K/K/eC Pressure coeff. ; ~6xlO -~ ~ K / K l k g l c m ~
iI
Control rod worth ; 0 0 3 3 % A K I K / c m / g r o u p
o
~
l//// I
-20
'1
0 -20
o
li
~ "
~
Fig. 9. Transient responses to rapid power increases.
L
/
: ,
240
Y.FUJI-I-E
%
Fs
/
II
"
isl
50
g-~0
I=
I
/
I
/'~" F f w
2
3
4
,5 6 7 TIME (MIN.)
8
9
tO
II
8
9
I0
II
op at swirl vane
7 TIME (MIN.)
-2G Top of tube bundle
-4(
Fig. 10. Feedwater flow and steam generator level transients to power increase to 90%. about 10% power o~,ershoot lasts for more than a few minutes. Rapid increase in steam flow causes temporary decrease in steam pressure and the flashing of water in the steam generator occurs in the heated section due to pressure decrease, then the inverse response appears and the water level swells up rapidly. In the transient, liquid-vapor separator is sometimes immersed into water for a minute, however, it is considered that no severe trouble happens with the main turbine because of water drop transport to the turbine. The stimulated results for this load change are shown in figs. 9 and I 0.
3.3. Plant transient response to ahead-astern and astern-ahead operation Steam flow variation in Ahead-Astern and AsternAhead operations are rapid but it recovers to the similar value corresponding to the previous power level (100%-80% or 80%-100%) in a short time. The time lag for disturbance transfer from the secondary system to the primary system through primary coolant and control systems and heat capacity of the primary system make transient behavior moderate and absorb such short time load change without large effects on the primary system parameters. Therefore, reactor operation can be continued without scram even when Ahead-Astern and/or Astern-Ahead opera-
tions are necessary to escape from a ship crash accident. Transient behavior of the primary system parameters becomes moderate with shortening the staying time of the reactor power level at the base load. Simulation results for this load change are shown in figs. 11, 12, 13 and 14. 3.4. Variation of steam generator water level during ship motion In the primary system of the reactor, though free water surface is present in the pressurizer, no bulk boiling occurs in the coolant channel during the normal operation and enough subcooling is kept even at the hot channel exit. Therefore effects of ship motion on the primary system of the reactor can be considered small and the analysis of the effects, though not given here, shows that primary system parameters deviate less than a few percent from their normal values. In the secondary system, natural circulation is formed and free water surface is present in the steam generator. Accordingly, effects of ship motion on thermal and hydraulic properties are not negligible and the prominent effect will appear on the water level in the steam generator. To limit the range of the water level variation due to ship motion, the steam generator is designed with
16 cm
16
0
I
j
1
\
\
,
j
j
\
1
\
\
j
j
\
j
\
1
,
\
[
j
\
,
ol
1
I1
I
I TIr&
00
\
Fig. 13. Transient responses to astern-ahead operation.
Fig. 11. Transient responses to Ahead-Astern operation.
5
I R
/-\_
40-
5
I
I
a10
I
2
3
4
I
I
I
I
I
7
8
9
IO
*Loo
I
2
dN.1
Fig. 12. Feedwater
I 4
I 5
, 6 TIME
, , 7 8 (MIN.1
I 9
I IO
I II
f.. -Top
-4oF
I 3
of swirl vane
-4oc
and water level transients to AheadAstern operation.
flow
Fig. 14. Feedwater flow and steam generator water level transients to Astern-Ahead operation.
I 12
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Y.FUJI-I-E
paying attention to following items: 1. Large circulation ratio. 2. Large steam drum cross section. 3. Small pressure loss in the heat exchanger and the moisture separator. To analyze the water level variation, ship motion is simulated with vertical gravity change
time (see)
0
8 16 24 32 40 48 Water level variation to ship motion el (1 +O,6)g
15 (cm)-
in 100% ~.ower operation water
0 1.6g ~
.
lg 0.4 g
g = go [ 1 + A sm
56
graviw
t)] , 10 i-
water level
~
where go = gravity, 9.8 m/sec 2 0.4g
gravity
A = amplitude of gravity change Tg = oscillation period
10 (cmi 5 water level
0
4 sec period
1.6 q
Assumptions made for analysis are: 1. Constant slippage between liquid and vapor in the boiling section 2. Two phase pressure loss is given by Martinelli and Nelson formula:
1 0.4
I
i 8
I
I 116
, gravity 24
I 32
i 40
i
I 48
t
I
I
56
time (see)
= ~bo (I+~xX#),
Fig. 15. Variation of steam generator water level due to ship 3. In the non-boiling region, the linear increase in enthalpy along the axial direction and in the boiling region, the linear increase in steam quality along the axial direction of the steam generator. In fig. 15 shown is the water level variation in the steam generator when the largest gravity change (A=0.6) with the oscillation periods of 4, 10 and 15 sec is encountered at the rated power operation. As is clear from fig. 15, the amplitude of the water level variation increases with the increase of oscillation period, however, no more than 8 cm deviation from the programmed level was seen. The time period of ship motion expected for the First Nuclear Ship of Japan is ranging from 3 sec to 15 see and no control system for the regulation of the water level variation is provided because there may be no severe trouble caused by the water level variation due to ship motion and there is no effective control system to follow such a rapid transient without time lag. In the feed-water control system with which the water level variation is controlled has a high pass filter not to follow the water level variation due to ship motion.
motion. As mentioned above, effects of ship motion on the primary system parameters are small and negligible, therefore, even if ship motion is superposed on some load change the magnitude of the water level variation in the steam generator is at most sum of amplitudes of them. Consequently, it is said that no severe conditions appear on the secondary system as well as on the primary system during ship motion. The transient analysis is performed with the parameters based on the preliminary design.
Acknowledgements This paper summarizes the studies concerning the reactor kinetics of the First Nuclear Ship of Japan. The author wishes to thank the design team members who were engaged in these works. The references are all written in Japanese. One of them is "Safety assessment of First Nuclear Ship of Japan".
CONTROL SYSTEMS AND TRANSIENT ANALYSIS Yoichi FUJI-I-E
Department of Nuclear Engineering, Osaka University, Osaka, Japan Received 24 April 1969
Characteristics governinga marine reactor operation include: (1) occurrence of abrupt load changes in association with maneuvering operations; (2) subjection to ship motion such as rolling, heaving and pithing. The effects of abrupt load changesappear on the reactor primary system as well as on the secondary steam generator. However, the effects of ship motion appear only on the steam generator since enough subcoolingis given to primary coolant and no steam void is found in the primary coolant. This paper contains the following subjects: (1) description of the part of the reactor system which has an intimate relation to reactor operation; (2) description of the functions of the control system and the safety system; (3) transient behaviour of the reactor and the steam generator under load change;(4) transient behaviour of the steam generator due to ship motion.
1. Introduction In the coolant system of the First Nuclear Ship of Japan, heat generated in the reactor is transported to the steam generators by means of two similar closed loops. Each loop contains a main circulating pump, a steam generator, valves and the associated piping. The flow of cooling water in each of the two loops is from the discharge side of the pump to the reactor, through the steam generator, and back to the suction side of the pump. The coolant system is designed to transfer 36 megawatts of heat from the reactor core at the rated power with flow rate of 2 X 900 tons per hour. At this power level, the inlet temperature to the reactor core is 271°C and the outlet temperature is 285°C, and the primary system pressure is about 110 kg/cm 2. Though the circulating pump can be operated at half speed, the flow rate is held constant during normal operation. The heat added to the coolant is given off in the steam generators where the primary water generates saturated steam from feedwater entering the steam generator at 160°C. For full load conditions, the steam generated is 2 X 30 tons per hour and also for the base load conditions the steam generated is about 2 X 54 tons per hour.
The heat transport system is designed to meet the following variations in steam demands. 1. Rapid power decrease: 100-18% of full load in 1 second. 2. Rapid power increase: 18-90% of full load in 30 seconds. 3. Ahead-astern operation: 100-18% of full load in 5 seconds staying at 18% of full load for 50 seconds and 18-80% of full load in 30 seconds. 4. Astern-ahead operation: 80-18% of full load in 5 seconds staying at 18% of full load for 50 seconds and 18-100% of full load in 30 seconds. It is worthwhile to mention about thermal and hydraulic design criteria for the First Nuclear Ship of Japan; The basic thermal and hydraulic criteria are as follows: a) The maximum value of the internal temperature of the oxide fuel shall not exceed the melting temperature even at the hot spot during normal operation. b) The local heat flux at the fuel element cladding surface shall not exceed designed DNB heat flux (Departure from Nucleate Boiling heat flux) either during the steady-state operation or during any transient operation.
232
Y.FUJ/-I-E
c) Bulk boiling shall not occur so much as to induce some hydraulic instability. To meet the criteria mentioned above, the following operation limits are imposed on the reactor operation. 1. The reactor power level shall not exceed 130% of the rated power either during the steady-state operation or during any transient operation. The maximum fuel temperature at the center of the hot spots is about 2100°C at 130%-power, which is much less than the melting point of oxide fuel, therefore the criterion (1) can be satisfied easily for any operation pattern. 2. Since DNB heat flux may be a function of flow rate, hydraulic diameter, inlet enthalpy, steam quality and so forth, some correlation formula is introduced to determine the maximum heat flux and minimum heat flux ratio. The minimum heat flux ratio means the minimum value of the ratios between the design heat flux at the hot channel and the limiting heat flux along the axial direction. The minimum heat flux ratio is determined to be 1.30, however, since ship motion may cause some aggravation to the hydraulic properties, a 15% margin is added to the limiting heat flux ratio to give the consequent DNB ratio of 1.53. With this DNB ratio, the maximum core inlet temperature permitted is given as a function of other reactor process parameters (pressure and the reactor power level). 3. The last criterion is different from the other two in its character. Bulk boiling, when it occurs, does not directly cause hydraulic instability or any unstable state on the reactor and the criterion 2), though not thoroughly, suppresses the rate of bulk boiling as is clear from fig. 1. Therefore this criterion can be considered to be set up to avoid unknown instability or unstable condition which might be induced by ship motion. To meet this criterion, the minimum operating pressure permitted is determined as a function of the power level and core inlet temperature. To follow the load change quickly and stably, several control systems are provided and a constant average primary temperature control is adopted in the reactor system. From the point of view of selfregulability of the reactor, although the pressure coefficient of reactivity is positive, its magnitude is
Low Pressure Scrota High Temperoture Scrom Over Power Scrota
320 ......... Pressure 510
:300 o v
290
% •
'
E
cp
280 c
0 (,.)
270
260
25c~'0-9
~ I00
I I10
I 120
; 130
Power (%)
Fig. 1. Operation limit. not large and the moderator temperature coefficient of reactivity and the Doppler coefficient of reactivity are negative and large throughout the temperature range of operation, so that the power coefficient of reactivity is negative and the reactor can follow the load change by itself. However, since severe load change is required for nuclear ship reactor when compared to usual land based reactor, control systems are provided to improve the transient responses and therefore the reactor operations. To design the control systems, the following criteria are postulated: a) For any load change, if the control systems operate normally, the reactor should not be scrammed, and the relief valve of the primary system and the safety valve in the secondary system do not open. b) For any load change, the reactor can be operated safely and stably and no unstable state occurs at any parts in the plant.
CONTROL SYSTEMS AND TRANSIENT ANALYSIS
233
Table 1 Ship condition. The rated power Rolling Pitching
100% 30° (3"9 cpm) 10° (4~15 cpm)
50% 45 ° (3"9 cpm)
Vertical acceleration Abrupt change of vertical acceleration
(1+0.6) go (4"q5 cpm)
(1+0.6) go (4~15 cpm)
c) Even under the ship conditions listed in table 1, safe and stable operation of the reactor can be continued.
2. Control systems Reactor system control and instrumentation consist of nuclear instrumentation, reactor automatic control system, safety and process instrumentation. Operation of the reactor plant is monitored and controlled at the main control console and the following functions are provided: 1. To maintain safe and stable operation. 2. Informations concerning the operation will be indicated and/or recorded on the console. 3. Safety action is rapidly and properly fulfdled automatically and/or manually when something unusual happens in the reactor system. Reactor start up is manually operated until the reactor power level increases up to about 10% of the rated power and then it is possible to operate the reactor automatically or manually and also the reactor shut down operation is made either automatically :or manually. 2.1. Nuclear instrumentation The function of the nuclear instrumentation system is to measure continuously the neutron flux level ranging from the source range up to 150% of the rated power, to indicate and/or to record on the main control console and, if necessary for the reactor safety operation, to feed signals to reactor control system and/or to safety system.
15° (4~15 cpm)
(1-+0.82) go
2.2. Reactor control system 2.2.1. Reactor power control system To control the reactor power level, constant average primary temperature control is adopted and the primary coolant temperature variation during load change to a region which is compatible with the capacity of the pressurizing system. The reactor power control system is operated either manually or automatically. Control signals to be fed to the control rod driving system are composed from two components. One of them is a temperature error signal given as the difference between the average temperature of the primary coolant and the reference temperature. As the average temperature the higher one of two primary 10op average temperatures is selected at the auctioneer circuit. Another signal is given as the error signal between the normalized steam flow and the normalized neutron flux. This signal is used to improve transient responses to load change. The control rods operated for reactivity regulation during load change are inner positioned two, and therefore there are two reactivity compensation speeds with one rod speed as is shown in fig. 2. The control rods are driven in group, however, the rods for reactivity compensation can be moved either individually or in group. The two rods in diagonal position among the inner_four rods make one group, and either of the two groups can be used as the control rod group for reactivity compensation during normal operation and the other group is used as shim rods. 1 +
rlS
e = I + r2--1-~(Tav-rref)
(1)
r3S +~
kg (~:-:~'s)
234
Y.FUJI-I-E
21fliii......... V ; one rod operation 2V ; two rodsoperation D ; dead band H~ ; hysteresis H2 ; Fig. 2. Control rod drive speed.
where e = error signal Tw = average coolant temperature Tref =reference temperature E = normalized neutron flux ~s = normalized steam flow kg = gain
loops. The pressurization method of the primary coolant is similar to the ordinary pressurized water reactor and the pressurizer keeps the primary pressure to give enough sub-cooling to the coolant and also absorbs volume change of the coolant and then holds the plant parameters in permitted ranges. The pressure control components are: (a) steady heater; (b) transient heater; (c) continuous water spray; (d) transient water spray; (e) relief valve and (0 safety valve, a volume control system is also attached to the pressurizer. In ease of positive pressure surge caused by power decrease, the transient spray is driven to condense steam in the pressurizer to lower the system pressure and in case of negative pressure surge caused by power increase transient, water in the pressurizer is evaporated by the transient heater to absorb the surge. 2.2.3. Steam dump control system In the secondary steam loop, a steam dump system with its capacity of 18 tons per hour (30% of the rated steam flow) is provided to bypass steam to the main condenser. This steam dump system acts to weaken the effects which are to appear in the secondary system as well as in the primary system during load change especially during rapid load decrease and the system also favorably acts during pressure increase transient in the secondary system. The control
The block diagram of reactor power control system is shown in fig. 3. 2.2.2. Pressure control system Pressure control of the primary system is made at the pressurizer settled on the one of the two primary
RODNol p o s i t i o n ~ RO01~ position,n!_+ ~ Detector
Aver.ogiI.ng
"
Tc
TH
~---
+
clr
IT
~
,o~x;to~" Vno~ Averag.ing I
-L~,Sl
l+ P-~' I
Two rods
I
I
~.~
insert,0n insertion/
RICONo.Iwithdrawal
2r~
circuit _
Detector
_
~ain Tworods x~ldrawal
One rod withdm~f
Fig. 3. Block diagram or reactor power control system.
CONTROL SYSTEMS AND TRANSIENT ANALYSIS
I SteamPressure Ps
+ ~
235
~ t e r level
2- IT~ of swirevane 1
.5"~ . . . . . . . . . . . . . . . . ~ . . ~
_,o°
,00%
-3~T~of
l..ood
tube ~ l e
Fig. 5. programmed water level Operation mode " R u n " interlock
I--I-o,,
Man. - A u t ~ selector
~nuol Main condenser vacuum i n t e r l o c k Main
steam flow I n t e r l o c k
Dump valve
inside of which primary coolant flows might not be dried out during load change. The feed water control system keeps the programmed water level automatically. Control elements, steam flow, feed water and water level are selected to form a usual three-element control system. The programmed water level is shown in fig. 5 as a function of the reactor power level and the block diagram of the feed water control system is also shown infig. 6.
Fig. 4. Block diagram of dump control system. signal to be fed to the steam dump control system is given as the difference between steam pressure and the reference dump pressure. The block diagram of the system is shown in fig. 4. 2.2.4. Feed water control system In the secondary side of the steam generator, natural circulation of water is formed and the water level in the steam generator varies during load change. The water level in the steam generator is programmed with the reactor power level to conf'me the level in a ftxed region so that the steam separator in the riser might not be immersed and the top of the tube bundle,
2.3. Safety system The reactor safety system has the following functions: One of which is an interlocking function. Reactor operation modes are stop, start up and operation and one of the operation modes is selected with the mode selection switch. Corresponding to each mode several interlocks are settled, for example, in the start up mode the following conditions must be satisfied before operation. 1. The mode selection switch is at the start up mode position. 2. Logarithmic counting rates of the two start up channels of the nuclear instrumentation should be larger than the reference value.
J
Fs
I , . '-._ ~ I . . . . .
,Turbine PumP.I~
- ~ o FILTER
H I - Lo LEVEl_ / ~ N U N C IATOR
JSystem '.* ~,~) log
I' ~. . . . . .s~.~l'
Fig. 6. Block diagram of feedwater control system.
236
Y.FUJI-I-E Table 2 Scram conditions. Scram signal
Detector
Trip level
Start up rate
Intermediate range
5 DPM
Power range Neutron flux
Neutron detector
25% of the rated power (start up mode) 123% of the rated power (operation mode)
Primary coolant pressure
Pressure switch
Variable
Primary coolant temperature
Temperature switch
Variable
Pressure switch Pressure difference switch
Not fixed
Pressurizer water level
Pressure difference switch
Not fixed
Primary coolant flow
flow switch Voltage switch
Not fixed
SIS action
Rod drop
Position switch
Position difference in each control rod group
Position switch
Not fixed
Ship inclination
Position switch
Not fixed
Manual
Botan
3. All the control rods should be at the lower most positions. Another function is safety action concerning the rod motion. When reactor plant parameters leave from their normal ranges or some mechanical failure which might cause some unsafe state of the reactor, safety actions such as an alarm, control rod stop or scram action occur to avoid the reactor from entering into crisis and to hold the reactor in safe. The last feature is safety and protection function such as safety injection and boron injection. All the safety circuits are multichannel circuits with fail-safe principle and logical circuits o f 1 out o f 2 or 2 out o f 4 are employed to improve the reliability o f the signals. Signals such as rod stop and scram are fed to the control rod drive system with alarm annunciation and with indication and/or record on the main control console. Scram conditions are listed in table 2. Among the scram conditions, over-power scram, high-temperature scram and low-pressure scram are worthy o f mentioning in details.
2.3.1. Over power scram To limit reactor power level to less than 130% o f the rated power, the neutron flux is taken as the reactor power and over-power scram action is made by monitoring the neutron flux level. Taking the errors due to neutron flux m e a s u r ~ e n t into account the scram level set point is determined to be 123% o f the rated power. So the reactor m a y be scammed within the neutron flux range between 1 1 7 - 1 3 0 % o f the rated power. A t 115% o f the rated power, rod stop action will occur. 2.3.2. High temperature scram The high temperature protection limit calculated from thermal design is here linearized for ease to the control circuitry and is given as a function of the reactor percent power(q): (Tci)limit = (Tci)o -
A(q- 1.3),
where Tci = core inlet temperature and q = percent power.
(2)
CONTROLS SYSTEMS AND TRANSIENT ANALYSIS When the core inlet temperature rises up to the limit temperature calculated from eq. (2), the reactor is to be scrammed, however, from the point of view of transient behavior of the reactor, the temperature responses to transients are similar whether they are at the average channel or at the hot channel when the reactor is in steady state or slow transient state, but they do not show similar behavior when some rapid transient may be introduced; besides, in such a rapid transient, time delay of scram action may be taken into account. Therefore the protection limit is 10°C lowered and also a few second of time delay is corrected circuitly to compensate the difference of the fuel heat transfer time constants between hot channel and average channel. 2.3.3. Low pressure scram The protection limit of the reactor primary pressure is also linearized and is given as a function of the core inlet temperature and the reactor percent power: Pminl = aTci - bq - c ; where Pminl = limit pressure. When the primary pressure of the reactor decreases down to Pminl the reactor will be scrammed. As mentioned before, the low-pressure scram is not so critical as the high-temperature scram, therefore only the error due to pressure measurement is taken into account for the determination of the protection limit.
3. Transient analysis For operating conditions or load change requirement mentioned before, the transient behaviors of the reactor plant are simulated. Since reactivity coefficients, control rod worth and other reactor parameters will change with fuel temperature, moderator temperature, primary pressure and integral of operation time or fuel burn-up, they have ranges in their value as is shown in table 3. The maximum and minimum values of them are taken in simulation, and the combination of these parameters is determined in such a way that the transient behaviors of the plant should not become moderate by their combination, however, and that only physically plausible combinations are selected. 3.1. Plant transient response to a main turbine trip
When the main turbine trips and steam flow decreases rapidly, secondary temperature increases, then heat to be removed in the secondary system decreases and consequently the primary temperature increases to introduce negative reactivity to the core. As for control signal to be fed to the control rod drive system, error signal from the difference between steam flow and neutron flux dominates initially, therefore rod insertion does not get behind the load change so much, then the core inlet temperature rises up and introduces negative reactivity which lowers the reactor power level and the reactor power variation becomes moderate because of reactivity compensation
Table 3 Reactivity coefficient and other constants. Neutron lifetime (sec)
Nearly 1.8 X 10-s
Delayed neutron fraction (%) Moderator temperature coefficient
Nearly 0.64
(~lrl°o Fuel temperature coefficient
(arlrl°c)
237
Nearly -3.0 X 10"~ "Nearly -7.8 X 10--4 Nearly -2.1 X 10-s "Nearly -3.2 X 10-s
Pressure coefficient ( a x / g /at)
Nearly + 3.6 X 10-s ~Nearly + 5.8 X 10-s
Control rod worth (%AK/K /cm/group )
Nearly 0.033 ~Nearly 0.095
238
Y.FUJI-I-E
due to moderator temperature rise. In this state the error signal from the temperature difference becomes dominant and the transient will be over with the reactivity balanced. In this load change, if the reactor power control system is not operated the plant transient does not cause reactor scram, however, the safety valve in the secondary loop opens because of the pressure rise in the secondary loop. In case when the steam dump control system does not dump steam to the main condenser, the safety valve also opens to lower steam pressure in the secondary loop, however, reactor scram does not occur. As for the transient response of the water level in the steam generator, when steam flow decreases suddenly steam quantity in the drum increases and therefore steam pressure in the drum increases. With this increase of steam pressure, condensation of steam occurs to lift the boiling surface to some upper point. Since the flow resistance due to friction at the swirl vane in the riser is large compared with the flow resistance in the downcomer, when condensation occurs, flow in the downcomer increases and water
flows into the boiling section. This transient behavior lasts for only a few seconds. The water level in the steam generator descends rapidly because of water flow-in to the boiler and the inverse response of the water level appears. The simulated results are shown in figs. 7 and 8.
3.2. Plant transient response to rapid load increase When the steam flow in the secondary loop increases rapidly, heat being removed increases and causes the temperature decrease in the primary coolant and moderator which introduces positive reactivity due to the moderature temperature reactivity effect. As is explained in the previous case, the control rod drive signal is dominantly from power-steam flow difference at first, then the control signal from temperature difference follows. In this load change, if rod stop motion occurs by control rod stop signal at 110% of the rated power the reactor power level fluctuates like sawtooth wave and power overshoot lasts for a long time. Without rod stop motion reactor scram does not occur, however,
Full temp~coeff. ;-3.2x10 -m A K / K / ° C Moderator temp, coeff. ; -~LOxK)"4 ~ K / K / ' C Pree~re
coeff.; 5.6xK)-e A K / K / k g / c m e
Control rod worth ; 0.055% AK/Klcm/group
o
.oo ff,,(
f ff,
I fff f
FS ;Steam flow rate ON ;Neutron flux
_,o
TAN; Coolant avera(~e temp. P
; Primary system pressure
ZR ; Rod
~,~
11,!, [ / ±/ / / / / P/
Position -2o
PS ; Secondary
L
system pressure
Fig. 7. Transient responses to rapid power decrease.
/ s' f
CONTROLS SYSTEMS AND TRANSIENT ANALYSIS
239
%
ioo '~',,,y'Fh,
F, /
50
t/
-'-
T I M E (MIN.)
l;;) .... ,o~ o,..,r,--
_40~--Top
of tube bundle
Fig. 8. Feedwater flow and steam generator water level transients to main turbine trip.
Fuel temp. cueff. ; - 3 . 2 x I 0 "6 ~ K / K / e C
%1 I/ 2oo Iti '°°i ~!
F,
r
Moderotor temp. coeff. ~-3.0xlO-" ~K/K/eC Pressure coeff. ; ~6xlO -~ ~ K / K l k g l c m ~
iI
Control rod worth ; 0 0 3 3 % A K I K / c m / g r o u p
o
~
l//// I
-20
'1
0 -20
o
li
~ "
~
Fig. 9. Transient responses to rapid power increases.
L
/
: ,
240
Y.FUJI-I-E
%
Fs
/
II
"
isl
50
g-~0
I=
I
/
I
/'~" F f w
2
3
4
,5 6 7 TIME (MIN.)
8
9
tO
II
8
9
I0
II
op at swirl vane
7 TIME (MIN.)
-2G Top of tube bundle
-4(
Fig. 10. Feedwater flow and steam generator level transients to power increase to 90%. about 10% power o~,ershoot lasts for more than a few minutes. Rapid increase in steam flow causes temporary decrease in steam pressure and the flashing of water in the steam generator occurs in the heated section due to pressure decrease, then the inverse response appears and the water level swells up rapidly. In the transient, liquid-vapor separator is sometimes immersed into water for a minute, however, it is considered that no severe trouble happens with the main turbine because of water drop transport to the turbine. The stimulated results for this load change are shown in figs. 9 and I 0.
3.3. Plant transient response to ahead-astern and astern-ahead operation Steam flow variation in Ahead-Astern and AsternAhead operations are rapid but it recovers to the similar value corresponding to the previous power level (100%-80% or 80%-100%) in a short time. The time lag for disturbance transfer from the secondary system to the primary system through primary coolant and control systems and heat capacity of the primary system make transient behavior moderate and absorb such short time load change without large effects on the primary system parameters. Therefore, reactor operation can be continued without scram even when Ahead-Astern and/or Astern-Ahead opera-
tions are necessary to escape from a ship crash accident. Transient behavior of the primary system parameters becomes moderate with shortening the staying time of the reactor power level at the base load. Simulation results for this load change are shown in figs. 11, 12, 13 and 14. 3.4. Variation of steam generator water level during ship motion In the primary system of the reactor, though free water surface is present in the pressurizer, no bulk boiling occurs in the coolant channel during the normal operation and enough subcooling is kept even at the hot channel exit. Therefore effects of ship motion on the primary system of the reactor can be considered small and the analysis of the effects, though not given here, shows that primary system parameters deviate less than a few percent from their normal values. In the secondary system, natural circulation is formed and free water surface is present in the steam generator. Accordingly, effects of ship motion on thermal and hydraulic properties are not negligible and the prominent effect will appear on the water level in the steam generator. To limit the range of the water level variation due to ship motion, the steam generator is designed with
16 cm
16
0
I
j
1
\
\
,
j
j
\
1
\
\
j
j
\
j
\
1
,
\
[
j
\
,
ol
1
I1
I
I TIr&
00
\
Fig. 13. Transient responses to astern-ahead operation.
Fig. 11. Transient responses to Ahead-Astern operation.
5
I R
/-\_
40-
5
I
I
a10
I
2
3
4
I
I
I
I
I
7
8
9
IO
*Loo
I
2
dN.1
Fig. 12. Feedwater
I 4
I 5
, 6 TIME
, , 7 8 (MIN.1
I 9
I IO
I II
f.. -Top
-4oF
I 3
of swirl vane
-4oc
and water level transients to AheadAstern operation.
flow
Fig. 14. Feedwater flow and steam generator water level transients to Astern-Ahead operation.
I 12
242
Y.FUJI-I-E
paying attention to following items: 1. Large circulation ratio. 2. Large steam drum cross section. 3. Small pressure loss in the heat exchanger and the moisture separator. To analyze the water level variation, ship motion is simulated with vertical gravity change
time (see)
0
8 16 24 32 40 48 Water level variation to ship motion el (1 +O,6)g
15 (cm)-
in 100% ~.ower operation water
0 1.6g ~
.
lg 0.4 g
g = go [ 1 + A sm
56
graviw
t)] , 10 i-
water level
~
where go = gravity, 9.8 m/sec 2 0.4g
gravity
A = amplitude of gravity change Tg = oscillation period
10 (cmi 5 water level
0
4 sec period
1.6 q
Assumptions made for analysis are: 1. Constant slippage between liquid and vapor in the boiling section 2. Two phase pressure loss is given by Martinelli and Nelson formula:
1 0.4
I
i 8
I
I 116
, gravity 24
I 32
i 40
i
I 48
t
I
I
56
time (see)
= ~bo (I+~xX#),
Fig. 15. Variation of steam generator water level due to ship 3. In the non-boiling region, the linear increase in enthalpy along the axial direction and in the boiling region, the linear increase in steam quality along the axial direction of the steam generator. In fig. 15 shown is the water level variation in the steam generator when the largest gravity change (A=0.6) with the oscillation periods of 4, 10 and 15 sec is encountered at the rated power operation. As is clear from fig. 15, the amplitude of the water level variation increases with the increase of oscillation period, however, no more than 8 cm deviation from the programmed level was seen. The time period of ship motion expected for the First Nuclear Ship of Japan is ranging from 3 sec to 15 see and no control system for the regulation of the water level variation is provided because there may be no severe trouble caused by the water level variation due to ship motion and there is no effective control system to follow such a rapid transient without time lag. In the feed-water control system with which the water level variation is controlled has a high pass filter not to follow the water level variation due to ship motion.
motion. As mentioned above, effects of ship motion on the primary system parameters are small and negligible, therefore, even if ship motion is superposed on some load change the magnitude of the water level variation in the steam generator is at most sum of amplitudes of them. Consequently, it is said that no severe conditions appear on the secondary system as well as on the primary system during ship motion. The transient analysis is performed with the parameters based on the preliminary design.
Acknowledgements This paper summarizes the studies concerning the reactor kinetics of the First Nuclear Ship of Japan. The author wishes to thank the design team members who were engaged in these works. The references are all written in Japanese. One of them is "Safety assessment of First Nuclear Ship of Japan".