LOAD FOLLOWING OPERATION OF A PRESSURIZED
WATER NUCLEAR POWER PLANT
by
GILBERTO GOMES DE ADRADE
B.S. in Chemical Engineering
at Universidade Federal de Minas Gerais
1968
M.S. in Nuclear Engineering
at Universidade Federal do Rio de Janeiro
1973
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
NUCLEAR ENGINEER
at the
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
January 1978
Signature redacted
Signature of the Author
Departm
"
,,--N 4
;'.-
-
t of' Nucj~ajEngineering
"-anuary 19, 1978
Signature redacted
Certified by
L..-'
hesis Supervi4r
Signature redacted
Certified by
Thesis Readek'
Accepted by
Signature redacted
Archives
JuN 9 1978
.
Chairman, Department/ Committee on
Graduate Students
2
ABSTRACT
LOAD FOLLOWING OPERATION OF PRESSURIZED
WATER NUCLEAR REACTORS
by
GILBERTO GOMES DE ANDRADE
Submitted to the
Department of Nuclear Engineering
on January 19, 1978 in partial fulfillment
of the requirements for the degree of
Nuclear Engineer
After considerations about the reasons that can lead
pressurized water nuclear reactors to a more
flexible
scheme than the usual base-load operation, this thesis
identifies three areas of concern if PWRs are to be used for
load-following: fuel element restrictions due pellet-clad
interactions; core reactivity control limitations due
difficulties with the use of part-length control rods;
and wet-steam high pressure turbine restrictions due
fatigue life
of the equipment.
Ramp rates for each one of the three areas selected
and overall ramp rates for the plant are analysed, which
show the difficulties presently existing to operate the
PWR taken as reference for this study, with ramp rates of
5%/min, considered representative of the load-following duty.
3
Thesis Supervisor:
John E. Meyer
Professor of Nuclear Engineering
Thesis Reader:
David D. Lanning
Professor of Nuclear Engineering
4
ACKNOWLEDGEMENTS
I wish to extend my gratitude to Professor John E. Meyer
for his interest and valuable criticism
throughout
this
thesis research and to Professor David D. Lanning who was
the Thesis Reader.
My appreciation to Furnas Centrais Eletricas S/A, whose
finantial support made possible this work.
The computer expenditures to this project were provided
via MIT Energy Laboratory by Northeast Utilities Service
Company, New England Electric System, Yankee Atomic Electric
Company, Public Service Electric and Gas Company (NJ) and
was appreciated
To
jy wife Elisete, who shared with me all the good and
hard times of this experience, my recognition.
5
TABLE OF CONTENTS
ABSTRACT
2
ACKNOWLEDGEMENTS
4
TABLE OF CONTENTS
5
CHAPTER I -
Approach to the Study of Load-Following
1.1. Introduction
7
1.2. Nuclear Power Plants on Load-Following
9
1.3. Method of Analysis Used
13
1.4. Limitations and Scope of the Analysis
19
CHAPTER II - General Plant Behavior on Load-Following
2.1. Introduction
21
2.2. Overall Effects of Power Changes
25
2.3. Selection of the Critical and
Limiting Components
40
CHAPTER III- Reactivity Control for Load-Following
3.1. Introduction
42
3.2. Operation Modes for the Reactivity
Control Systems
3.3. The Computer Code FOLLOW
CHAPTER IV-
45
49
Fuel Element Behavior in Load-Following
4.1. Introduction
63
4.2. Zircaloy Corrosion Behavior
66
4.3. Fatigue Analysis
70
4.4. Pellet-Clad Interactions
76
6
CHAPTER V
- Turbine Analysis
5.1. Introduction
82
5.2. Moisture Effects
83
5.3. Turbine Governing
87
5.4. Part Load Operation of the Turbine
90
5.5. High Pressure Turbine Model
93
5.6. The TURBINE Computer Code
104
CHAPTER VI - Ramp Rate Limitations
6.1. Introduction
111
6.2. Weekly Load Curves for Load-Following
111
6.3. Reactivity Control System Limitations
115
6.4. Fuel Element Limitations
119
6.5. Turbine Limitations
121
6.6. Ramp Rate Limitations for the Plant
128
CHAPTER VII- Conclusions and Recommendations
7.1. Conclusions
138
7.2. Considerations About Plant Capability
139
7.3. Recommendations
141
APPENDIX 1 -
Listing of Computer Code FOLLOW
143
APPENDIX 2 -
Listing of Computer Code TURBINE
153
APPENDIX 3 - Angra I Power Plant Data
171
LIST OF REFERENCES
173
7
Chapter I
Approach to the Study of Load-Following
1.1. Introduction.
It is a general rule for the electric utilities that
electricity should be
provided
within tight
specifications, in the quantity demanded
frequency
and when required
by the customers. The large investments involved in the
construction and operation of electric generating units and
the formal necessity to satisfy the demand,
assumed by the
utilities, make planning the expansion and operation of the
electric system a key point to the success
of the electric
utilities."Satisfy the demand"means that the company should
be able to meet the daily load-curve imposed on its electric
system, independent of the time of the day, week, month
year. It is important to list all such times because
variations in demand are expected to exist throughout
time scale. Another complication is that demand
only statically through previous experience
and
is
or
large
that
known
must be
projected many years into the future.
In order to describe the behavior of a power generating
unit connected to an electric grid during a specific interval
of time, some statistics of the plant can be used /41/. For
this purpose, the capacity factor of the unit is defined as
the ratio of the effective energy output for that time inter-
8
val to the total energy produced
if the plant
was used at
full power, the load-factor is the ratio of the average load
to the attained peak load during the time interval, and the
availability factor is the ratio of the number of hours that
the plant is available for operation to the total number
of
hours during the period.Based on these statistical indices,
it is possible to group the plants in at least three broad
classes /38/,
-
specifically:
base-loaded plants, which are used to produce energy
at a rate in excess to 4000 kWhr per year per kW
of in-
stalled capacity, implying reasonably continuous operation
of the unit with load factor greater than 50%.
-
cyclic-loaded plantswith power production
between
1000 and 4000 kWhr per year per kW installed, which normally
implies
a discontinuous operation of the plant during
say
2/3 of the year, with daily duration of 4 to 16 hours or an
equivalent production on a seasonal or other intermitent
basis with capacity factor in the range from 15% to 50%.
-
peak-loaded plants, with energy production smaller
than 1000 kWhr per year per kW installed.
Typical numbers for the distribution of load
respect to the total installed capacity for the
with
electric
utilities in the United States are to have about 65% as
base-loaded, 25% as cyclic-load and 10% as peaking-load/38/,
with the actual distribution between the three segments
varying from system to system, and presenting a relatively
9
constant value for the cyclic portion, with the base-load
and peaking being distributed depending on the load factor
of the system.
To handle the uncertainties associated with the demand
load curve and to optimize both operation of existing units
and
planning for new plants, is common practice to classify
the power generating units with respect to their
duties on the load curve. This
specific
classification, as well as
the other just presented, is by no means rigid, but instead,
dynamic, because depending on special requirements imposed
on the system, such as outages of other units
or seasonal
variations, a unit can quickly change its duties
in the
system. Figure 1.1 /40/ presents the different required ramp
rates for plants working either as cyclic-load or peakingload in a large interconnected system, where the first step
is a load-following operation with daily power variations
with required response up to rates of 5% of full power
per
minute, which will be taken here as typical for this cyclic
duty.
1.2. Nuclear Power Plants on Load-Following Operation.
Because of their low fuel cycle cost compared with other
energy production sources and due the relatively high capital
investment required,
nuclear power plants are best suited
and have been extensively used as base-loaded units. It may
10
Frequency
regulation
Tie-line
thermal
backup
Response
1000
Daily
load
I ~-,.following
Rate
(%MW/min)
100
Un it
co mmitment
*Full Power
10
'N
1
-I
I
0.1
1
I
10
'N
I\
100
1000
Time to Perform Load Change (min)
Figure 1.1
(From Ref. 40)
11
happen, though, depending on peculiarities of the
power
production system in which the nuclear plant will
be
integrated that load-following becomes interesting for those
plants, from the optimization of the system point of view.
for
To mention some reasons for load-following operation
nuclear power plants, we have:
a. Transition from almost pure hydroelectric power
supply system to a mixed thermal and hydro system,
with
pronounced seasonal variations due uncertainties on rainfall,
will have the tendency to operate the hydraulic plants
as
base-loaded units during the "wet" season in order to save
thermal generation. This will make the thermal units,
including the nuclear plants, to operate in a
more flexible
scheme, as load-following units for instance. This is
the
case for the first nuclear unit, the Angra I Nuclear Power
Plant, to be operated in South-East Brazil /42/, where the
hydroelectric plants account for more than 90% of the total
electricity production of the region. The optimization of
the operation of the system indicates that, ideally,
nuclear plant would operate as a cyclic-loaded unit
the
for
periods that could range from 6 month to 3 years, depending
on the rainfall. Specific load-curves for this operation
mode is presented in Chapter VI.
b. When thermal generation is responsible for most of
12
the energy produced, incentives for load-following would
come when new units take over all the base-load operation
and displace older units, generally with higher incremental
operating cost, to the more flexible operating region of the
load curve. This reasoning will be shown as not
applicable today /38/,
completly
which together with the
fact
that
nuclear units are, in general, new units in the system, and
even the relatively old nuclear plants operate with low fuel
cycle cost, make the possibility of displacement
feasible
only much later in time.
c. A reason for load-following with nuclear units much
closer in time and realistic for the thermal electric
systems, is the necessity to satisfy the cyclic-load demand,
which, as discussed before, grows with the total
demand
increase. It is pointed out by Swengel /38/ that units now
facing downgrading are reasonably efficient machines
and
were built at lower capital cost than any new facility; with
comparable fuel cost and lower capital cost, they can
produce electricity at lower
.or comparable cost and should
be kept as base loaded units. To satisfy the cyclic-load
demand, though, units must be bought for this
specific
duty.
Large oil-fired units have already been used for cyclic
duties /12,43/ and it can happen that the same eponomic
arguments that favour nuclear plants for base-load will make
13
them more attractive for cyclic duties also, as long as they
show their capability to cope with the ramp rates demanded
by the system. To reinforce the competitiveness of
nuclear
units with respect to alternative energy sources, Figure 1.2
/39/
shows a specific case where nuclear units could
be
considered as a better choice even for capacity factors as
low as 45%. Resulting either from the scarcity of
alter-
native fuel sources or from the increase in total installed
capacity of base-loaded nuclear plants, incentives exist to
consider the use of nuclear plants in a load-following
operation scheme.
This research covers the problems that can be
pated if a Pressurized Water Reactor nuclear plant,
anticias
presently designed, controlled and operated, were to be used
in a daily load-following operation pattern. The reference
design considered here is the Angra I Power Plant /19/,
a
626 MWe plant designed by Westinghouse and to go on line by
mid-1978 /42/.
1.3. Method of Analysis Used.
The first idea on how to develop this work was to take
the base-load operation as a reference case. When the plant
is changing power, several additional activities are carried
out in order to adjust and control the process variables to
14
20.0
Total
15.0
Generation
Co st
Western Coal
10*0
~
--
Nuclear
~
5.0
(mills/kWh)
0
ag
40
Mixed Coal
50
60
Capacity Factor, Percent
Figure 1.2
(From Ref. 39)
70
15
their new operating level, which will "waste" the plant
relatively to the reference case. We can then develop
a
statistical approach to assess this extra usage that the
load-following operation will impose on plant components.
Working this way, it would be possible to quantify the price
to be paid for load-following and to identify the important
components to be considered for extra maintenance. The above
considerations assume that fatigue is the feature contributing
most to the wastage of the plant in load-following operation
due the cyclic variation of the process variables.
Let's see now how it would be possible to define
a
reliability index to be used to compare the reference case,
base-load operation, with load-following.
We follow Green
and Bourne /50/ and define reliability as "that characteristic
of an item expressed by the probability that it
will
perform its required function in the desired manner, under
all the relevant conditions and on the occasions or during
the
time
intervals
when it is required so to perform".
We can consider that a single number defining a failed state
for an item exists and is associated with a failure probability function and is an unreliability index for that item.
The number associated with the
complementary probability,
in this case, is a reliability index.
Let's take now the case of fatigue failure.
If
consider whether is possible or not to characterize
we
the
state of fatigue of an item by a single number, the answer,
16
as is well known, is that the theories of cumulative damage
assume that this is possible /44/. To complete the approach,
we can associate a specific state of fatigue, now characterized by a single number, to a well defined loading
history, through the use
of a linear cumulative
damage
analysis /45/.
If a piece of equipment is subjected to a variety
of
stress cycles during its lifetime and fatigue failure occurs
when the cumulative usage factor is equal to one, as defined
in the ASME Code /30/,
of the
then we can use the calculated value
.cumulative usage factor as an unreliability
index
for that item subjected to a specific load history,
with
respect to its fatigue life. Of course this is not strictly
true and would be useful only as a comparative index
to
relate base-load and load-following, since if the calculated
cumulative usage factor is equal to one, the item will not
necessarily fail. Conservatisms introduced in the
design
criteria (e.g. introduction of a factor of two on the
stresses or a factor of twenty on the number of cycles
whichever is more conservative /45/),
prevent it to happen.
It however is plausible that bigger values of the
index
will characterize a more demanding fatigue life.
With the fatigue reliability index just defined,
can proceed to assess a comparative analysis
of
we
load-
following in respect to base-load, considering fatigue as
the failure mechanism. That is the whole idea behind the
17
previous discussion, where the linear cumulative usage factor
our unreliability index,
would be used to quantify
the two
conditions: base-load and load-following.
To check the validity of the approach above proposed,
we can refer to Table 2.2, where the fluctuations in surface
stresses for the pressure vessel of the reactor are shown in
respect to the design transients considered in the
fatigue
life analysis for that item. Table 1.1 is a list of
the
design transients considered.
From Table 2.2 we can conclude that the alternating
stresses associated with the loading and unloading
operations at 5% per minute are possibly smaller than
the
endurance limit of the material (11 ksi or 75 MPa). Another
point to be noted is that they are of the same order
of
magnitude as the stresses resulting from the steady state
fluctuations, for which a practically infinite number
cycles is considered. It is obvious, though, that
of
the
stresses resulting from loading and unloading the unit at
5% per minute, or in other words, resulting from
load-
following, do not add up in the cumulative damage
factor
of the item, in such way that, from the fatigue analysis
point of view, the reliability of the item is
not
affected at all if load-following is used or not. Those
conclusions will also be shown to be valid for several other
items with respect to fatigue failure, which means
effects of load-following are not seen in the
that the
cumulative
18
Table 1.1
(From Ref. 29)
Heatup and Cooldown at 10 0 1F/hr (50 0/ahr).
.
Loading and unloading at 5% per minute
.
0
0
*
0
0
.
.
*
fluctuations.
.
.
.
.
200
0
106
.
Steady-state
200 (each)
2000 (each)
.
.
Large step load with steam dump.
.
18400 (each)
*
.
.
0
.
Step Change of 10% in load . . .
.
.
Reactor Design Transients
0
.
.
.
.
.
.
.
.
from full power .
.
.
Turbine roll test. .
.
Cold
-
hydro test .
Hot hydro test .
.
.
.
..
.
.
0
.
.
- .* . .
. . . .
.
.
.
0
0
.
80
400
10
W
.
0
.
.
.
Reactor trip
.
.
flow
.
of
.
Loss
80
.
Loss of load . . . . . . . . . . .
.0
5
40
19
damage factor.
There are therefore no apparent fatigue effects in most
components when using a pressurized water reactor
nuclear
plant in load-following as compared to the regular practice
of base-load operation. There is however a much more
fundamental question which must be adressed: whether or not
is possible to use the pressurized water reactor as designed
and operated today, in load-following at all. This work will
try to answer this latter question.
1.4. Limitations and Scope of the Analysis.
It is important to recognize that in this work it
is
not intended to cover in depth all the implications of loadfollowing, but, instead, to develop a pathfinder research,
since no other general compilation involving the
primary
and secondary parts of the plant, as well as aspects
of
design, control, and operation of the Pressurized Water
Nuclear Power Plant is load-following is known by the author.
As mentioned before, the plant considered here
as
reference, is the Angra I Nuclear Power Plant /19/ designed
by Westinghouse. Different designers have small peculiarities
in their design concept, as the once-through steam-generator
and slightly superheated steam for the Babcock-Wilcox /17/,
and the two-loop concept of Combustion Engineering and Babcock
Wilcox as opposed to the four-loop design for the large plants
20
of Westinghouse. Those differences are not expected to affect
very much the conclusions of this work, because the essential
aspects of the pressurized water nuclear power plant concept
are not changed from one designer to another.
Load-following operation will be intended here as daily
load variation for the plant, with ramp rates of the order of
5% of full power per minute. Chapter II will cover the overall
effects of load-following on plant components in order
to
evaluate the potential areas of concern. Three aspects are
then selected for further analysis, the core reactivity control
covered in Chapter III, the fuel element behavior covered in
Chapter IV, and the turbine behavior analyzed in Chapter V.
Chapter VI presents the general results of the analysis
and
the final conclusions and recomendations are in Chapter VII.
21
Chapter II
General Plant Behaviour on Load-Following
2.1. Introduction.
The reactor control, the pressurizer control, the steam
dump control and the feedwater control are the systems
generally provided in a Pressurized Water Reactor (PWR) plant
to execute or to help the operator during the
complex task
of changing the power of the plant /26/. Manual or automatic
the
operation modes can be selected respectively when
control system works only as a monitor to the
executing the tasks by itself. For
operator or
both cases the
plant
protection system supervises the region of allowed operation
for the process variables. Figure 2.1 shows a
simplified
schematic of a PWR plant and Figure 2.2 is a block diagram of
the plant and of the control system that
will be active
during power changes.
the
If the plant is operated in automatic control,
reactor control system regulates the power of the reactor
via control rod movements.
turbine demanded power,
The
reactor
the
where the first stage pressure is
the process variable for the turbine
ion detectors current
follows
and
the
for the reactor /26/.
excore
The reactor
control philosophy is to maintain the average of the
hot
and cold leg coolant temperature varying in a prestated form
spray valve
R.1;ef Valve
I
R.Ocl-rrof
Va~ive
w 11
Vvm
N)3
23
ntrol
Core
Neutron
Po
Po~sition
Kinetics
Reactor
Control
System
Operator
Neutron
Populatio
Turbine
Load
Temp.
Fuel
Fissio
Produc
Ha
Cool at
Te mpj
Boriq
Cool
oCoolan
Coolant
Boron
Concent.
&CaICi
6j010
Chemical
and
Volume
Operator
Control
System
Heat
Steam
enerator
Steam
Contro
Turbine
Position
Plant
Turbine
Control
System
Control-,
Figure 2.2
Block Diagram of Reactor Plant
and Control (from Ref.26)
Operator
24
with load.
One possibility is to have a constant primary
pressure scheme with a linear coolant average temperature
variation imposed in the power range for automatic operation
(from 15% to 100% full power);
followed
in
this is the
pattern
the Angra I Power Plant /19/ and will
used here for the analysis.
For
be
this constant pressure
philosophy, the pressurizer pressure control has the task of
keeping the reactor coolant loop pressure constant with power
through the actuation of electrical heaters and water spray
from the reactor coolant cold leg, as is shown in Figure 2.1.
The chemical and volume control system handles
the soluble
boron concentration changes and provides storage space for
the reactor coolant volume changes due density variations
with temperature. The
options for reactivity changes and
neutron flux shaping, operated either through the actuation
of part-length and full-length control rods or through the
boron dilution and concentration mechanisms,will be discussed
with further detail in Chapter III.
Steam dump valves are provided to reduce the impact ofa
large turbine load reduction on the reactor coolant system
temperature. The steam dump control actuates a turbine bypass
to the steam,which is discharged directly into the condenser.
The feedwater control has the function of maintaining
the
water level of the steam generator within specified bounds
in both steady state and with power changes.
Following the above discussion we can see that several
25
changes are supposed to occur in the process variables when
the power of the plant is varied. The impact of the changes
in temperature, pressure, flows and levels on several plant
components will now be discussed.
2.2. Overall Effects of Power Changes.
The reactor coolant pumps of the PWR are generally of
the centrifugal type and operate with single speed, independent of the power level /34/.This implies in a practically
constant water flow rate with power through the pumpreactor,
pipes, and primary side of the steam generator /27/.
With
the constant pressure and variable coolant mean temperature
control scheme for the reactor coolant system, the total
heat production in the fuel elements, the cold and
legs temperature, the coolant boron concentration
hot
and
control rod positions, as well as the water level in the
pressurizer tank, are the process variables to be considered
here as power dependent in the primary side of the plant.
During power transients, the coolant temperature variation
changes the coolant density with consequent coolant volume
variation, which will produce a change in the water level of
the pressurizer and in the flow rate through the letdown
orifice between the reactor coolant system and the chemical
and volume control system. The chemical and volume control
system works also a backup system for the coolant volume
26
variations with power and provides the desired coolant
boron concentration.
system
The analysis of the steam and power conversion
behavior with power is focussed on the operation
of
the
secondary side of the steam generator, the feedwater heating
system, and the turbine-generator group.Beyong these, the
electrical generator and the feedwater heating system are
not different from those used in oil or coal fired plants
and no special attention will be dedicated to them. The
secondary side of the steam generator has its water level
controlled by the feedwater control system and, typically,
can be considered as operating with small pressure changes
with load, which will imply in correspondingly
small
temperature variations for the wet steam produced (it can
alternatively be operated with no pressure and temperature
variations at all). The turbine sees large flow
rate
variations with load, as well as pressure and temperature
changes due the throttling process of the steam. The flow
rate changes are executed by the turbine electro-hydraulic
control system, in order to keep constant rotational speed
in the turbine shaft. Careful operation is required for the
moisture separator reheater (MSR) when load is changed in
order to avoid overheating of the last stage blades of the
low pressure section of the turbine and also to protect the
reheater section tubes /2/; due those facts, the moisture
separator reheater operation is constrained with respect to
27
temperature and flow rate variations with load.
Table 2.1 presents an overall summary of the variations
considered here as relevant for the analysis of
load-
following operation of the PWR, and Figure 2.3 shows the
expected behavior, when automatic control is used, of
pressure and temperature with load for the cold and
hot
legs of the primary side and for the shell side of the steam
generator, where a pressure increase of 10% was supposed to
occur when load is reduced from full power to the hot zero
power condition /28/.
A brief discussion of the effects of process variable
changes with power will be made considering the equipment
presented in the schematic simplification of Figure 2.1. It
is important to remember that this study is intended to
define areas for further study but not to cover in detail
the structural analysis of
individual components.
2.2.1. Reactor Analysis.
Reactor core, structurals and pressure vessel
are
subjected to variations in temperature of the order of 3700,
and in neutron flux, about one decade. The control rod
positions and soluble boron concentration depend on
the
reactivity control strategy and on the core burnup level/19/,
The different options of reactivity control
and their
operational constraints are discussed with some detail in
Chapter III, because, as will be shown, special limitations
28
Table 2.1
Some Effects of Load-Following on Plant Components
Reactor Coolant System
Reactor:neutron flux or fuel heat generation
temperatures in hot and cold legs and fuel
control rods positioning
soluble boron concentration
Pressurizer: water level
soluble boron concentration
Pipes and Pumps: temperature
soluble boron concentration
Steam Generator
Primary side:temperature
soluble boron concentration
Secondary side: temperature
pressure
(steam and feedwater)
flow rates
water level
Steam and Power Conversion System
All components will see large variations in the flow rates
and variations in temperature and pressure.
Chemical and Volume Control System
Feed and Bleed Lines: flow rates
temperature
soluble boron concentration
29
330
Semperature
( 0)
0
Hot Leg
320
310
,--'o
Average
t
300
290
0
'mm
,--
.
.
mm M
Steam
280
20
60
40
80
100
Percent Load
Primary
15.5
Pressure
(MPa)
4
'" .
Secondary
*
6.0
'
20
*
'
7.0:
40
60
80
100
Percent Load
Figure 2.3
Temperature and Pressure Variations with Load
30
on the use of part-length control rods are imposed in today's
PWR, thereby making the reactivity control of the reactor
one of the limiting conditions for load-following.
Reactor internals and other components are designed to
withstand the stresses resulting from starup, steady-state
operation with any number of pumps running and
shutdown
conditions /19/. The internals are designed to maintain their
functional integrity even in the event of very severe
accidents. Fuel assemblies are designed to withstand
the
combined effects of flow induced vibrations, earthquake,
reactor pressure, fission gas pressure, fuel growth, thermal
strain, differential expansion and other effects associated
with fatigue due thermal cycling /19/. The thermal cycling
effect on the grid-clad support, for instance, is a slight
relative movement between the grid contact surfaces and
the
clad, which is gradual in nature and relatively important
during the heatup and cooldown cycles /19/,
and small for
temperature variations of the order of 3700 associated with
power cycling.
For the pressure vessel we can refer to the work
of
Riccardella and Mager /29/, where a fatigue evaluation of a
reactor pressure vessel using fracture mechanids
was
presented. From this work we have.the pressure vessel stress
analysis divided in four regions, as is shown in Figure 2.4
and in Table 2.2. The fluctuations in inside surface stress
for the reactor design transients are presented at selected
31
Control rod
drive mechanisms
Closure
Head
Region
Closure
flange
Outlet
nozzle
Core
1-~ \-*
Nozzle
Shell-Course
Region
Beltline
Region
Thickne ss
=22 cm
Radius
=220cm
Lower
Head
Region
In-core
instrumentation
penetration
* critical locations
Figure 2.4
Pressurized Water Reactor Vessel
(from Ref.29)
32
Table 2.2
(from Ref. 29)
Inside Surface Stress Ranges for Critical Loeations
(MPa)
Transients
Closure
Head
Nozzle
Shell
Beltline
Region
Lower
Head
Cooldown
426.4
393.3
205.6
133.2
Plant Loading and Unloading
12.4
43.5
31.7
12.4
Step Change in Power
66.9
55.9
71.0
59.3
Steam Dump
84.9
76.6
20.0
82.1
Steady State Fluctuations
31*7
61*4
12.4
37*3
Loss of Load
186.3
146.6
44.2
171.8
Loss of Flow
188.3
216.7
89.0
188.3
Reactor Trip
32.4
39.3
20.*0
26.9
Turbine Roll Test,
146.3
515.4
118.7
111.8
Cold Hydro Test
105.5
564.4
214.6
186.3
Hot Hydro Test
380.9
442.3
202.2
148.3
Heatup -
33
critical locations of each region. From this table it can be
seen that the expected stress fluctuations for unit loading
and unloading are at least one order of magnitude smaller
than the corresponding stresses for more critical transients.
If a linear cumulative damage concept is used, the cumulative
usage factor fraction due the unit loading and unloading at
the rate of 5% of full power per minute is practically zero
because the associated stress fluctuation is very small /30/.
This is an important point and is well worth emphasizing
again: the relatively small temperature variation due unit
loading and unloading, if compared to others much
more
severe transients considered during the design of the
equipment, results in an almost negligible fatigue effect
in the equipment, for the design ramp rate of 5% of full
power per minute, considered here as sufficient for the
duties of load-following, as explained in Chapter I.
The fuel elements have important variations with
the
power level and with burnup. Although they were manufactured
to support the design transients, which includes the ramp
rate of 5% per minute, unanticipated events have reduced
drastically the advisable ramp rates for commercial fuels
used in the PWR. The fuel behavior is today one of the
limiting condition for the plant operation in load-following
and will be discussed in Chapter IV.
34
2.2.2. Pressurizer Analysis.
The pressurizer is a cylindrical vessel with a surge
line penetration connected to the hot leg piping and
spray line connected to the cold leg piping /27/.
a
It
provides a surge chamber and water reservoir to accomodate
density changes in the reactor coolant during operation and
is built to maintain the steam and water inside the
pressurizer at the saturation temperature corresponding to
the desired reactor coolant system pressure, through
the
actuation of electrical heaters ans spray line.
For slow transients such as unit loading and unloading,
it can be considered that the pressurizer works all the time
in equilibrium with the reactor coolant system, which means
that pressure and temperature are kept constant inside
the
vessel and the only change with power will be the water
level, which will follow a prestated program controlled by
the pressurizer control system. Since no pressure
temperature variations are expected, no special
or
fatigue
problem is antecipated for the pressurizer.
2.2.3.
Steam Generator Analysis.
The steam generator uses pressurized water, heated in
the reactor core, as the hot fluid in the tube side, which
exchanges heat with a lower-pressure feedwater in the shell
side, where vapor is produced. For the tube side, constant
pressure and variable temperature will occur, and for
the
35
shell side a small pressure variation is considered with
load before the turbine stop valve, which will imply in an
equivalently small temperature change with load for
the
saturated steam. The shell side water level will change with
load in a prestated form controlled by the feedwater control
system.
Since the shell side will see a temperature variation
with power, the overall dimensions ofthe vessel are expected
to change slightly with load; fatigue stresses can
result from the tube side
also
temperature change. The structural
behavior of the thick perforated plate, called the tubesheetj
where the U-shapped tubes are supported, was analysed
by
Tichit /28/ with respect to fatigue failure due temperature
cycling during normal operation. It was concluded that
the
temperature changes do not appear to be sufficient to bring
any concern of fatigue damage to the tubesheet. The tubes
are supported radially and are free to expand axially, So,
no stress cycling is expected to be imposed on them by normal
operation, as long as they are free to expand. Recently some
concern has been shown with the occurence of tube
denting
along the tube support plate /31,32/, which prohibit
the
axial free expansion for the tubes and can bring the occurence
of stress cycling and fatigue problem. This is, however, a
case that concerns a special condition in the steam generator
and can not be considered as a normal operation case. This
kind of problem will not be covered here because it appears
36
that a convenient feedwater treatment associated with minimum
condenser leakage, can avoid the problem /32/, and no ramp
rate limitation is expected for the steam generator. Another
reported problem with steam generator is related to the crud
deposition on tube walls and the formation of sludge deposits
along the low flow areas of the tubesheet. The steam
generator acts like an evaporator and all nonvolatile
impurities, soluble or solids, brough into the steam generator
by the feedwater train, are therefore concentrated
boiler water and in the tube walls /33/.
in the
As the sludge piles
grow with time, the concentration of corrosive chemicals can
take place and the tube can corrode /33/.
There appears to
be a correlation between the flow atagnation positions in
the tubesheet and the sludge pile. Since the flow patterns
are expected to change with load, periodic reductions
part load operation may be favorable with respect to
to
this
problem.
2.2.4. Pumps and Pipes Analysis.
Each reactor coolant pump is a vertical, single-stage,
centrifugal, shaft-seal pump, with normal operating speed of
1189 rpm /34/.
Working in the cold leg of the reactor coolant
system, the pump is supposed to operate with constant pressure
and constant speed with load and it will see only the very
small temperature changes associated with the cold leg.
Stress levels in the pump are generally limited to one-half
37
the minimum yield strength of the materials used /34/ and
the small temperature cycling with load, about 500, is
expected to bring any special fatigue problem to
not
the
operation of the reactor coolant pumps.
The fatigue analysis of the reactor coolant loop piping
system during unit loading and unloading with the design ramp
rate of 5% of full power per minute, as in the pump analysis
just presented, will have only the temperature transient of
the coolant. Following the analysis presented in
/35/,
WCAP-8172
where all the normal, upset, and test transients
required by the ASIE Code for Class 1 components /30/ were
considered, it is pointed out that only a few of the many
transients considered have an appreciable effect on the
cumulative usage factor. Using a conservative technique to
calculate the alternating stress intensity range and
the
expected number of cycles for each transient, it was
concluded that the high values of the cumulative usage factor
occur only at equipment nozzle junctions with the pipe and
that the values at the elbows are at least one order
of
magnitude lower. The detailed stress analysis results
at
terminal points are presented for the governing load sets
and are here reproduced in Table 2.3. From these data it
can be seen that transients with big pressure and temperature
changes are the governing conditions and we conclude
that
the small temperature changes and no pressure variation
conditions imposed in the unit loading and unloading transient
38
Table 2.3
(from Ref. 35)
Detailed Stress Analysis Results for the Piping System
Values are for Terminal Points (Inside Surface)
Terminal
Points
Range
Governing
Set
(MPa)
(00)
Reactor Vessel
Outlet
15.5
140
215
Steam Generator
Inlet
12.9
Steam Generator
Outlet
17.2
Pump Inlet
Inside
Wall
Stresses
Transients
Axial
Hoop
Cooldown
Heatup
772
-103
300
300
Reactor Trip
Hydro Test
434
-186
305
572
-69
305
Loos of Load
Hydro Test
17.2
305
305
Loss of Load
Hydro Test
607
-55
Pump Outlet
17.2
305
305
Loss of Load
Hydro Test
483
-34
Reactor Vessel
Inlet
15.5
200
90
Heatup,
Cooldown
690
-124
39
are not expected to cause any trouble with respect to
the
fatigue life of the piping system. The secondary side piping,
where small pressure variations are also expected together
with the temperature, does not seem to present any special
problem either.
2.2.5. Turbine and Moisture Separator Reheater Analysis.
The turbine will see large pressure, temperature and
flow rate variations with load and will be analysed with
some detail in Chapter V, because they are expected
to pose
limitations on the ramp rates required for load-following
with the PWR plants.
Moisture separator reheater (MSR) are generally
associated with the wet-steam nuclear turbines because they
improve the cycle efficiency and reduce the erosioncorrosion problems resulting from the expansion of
high
wetness steam in the turbine /2/.
A MSR is a pressure vessel with an outer shell, moisture
separators of chevron type or wire mesh, and one or more
tube bundles to superheat the steam in the shell
transfering heat from high pressure steam.
side by
Test results
show that the steam should be admitted carefully
to
the
reheater section in order to avoid binding the tubes in the
support due uneven thermal expansion /2/.
Another problem is
the existance of temperature instabilities that are
apparently caused by tubes that flow filled with water,
40
which reduces the tube temperature and causes it to contract
and to bind in its supports /2/.
Similarly to the turbine, during power changes the MSR
flow rate
will have important pressure, temperature and
variations. These variations, associated with the fact that
the MSR can not be operated continuously
for
very low
turbine power levels (in order to avoir overheating the
last stage blades of the low-pressure turbine) generally
requires a careful operation for the MSR. But, as will be
shown in
Chapter V, the ramp rate limitations imposed by the
high pressure turbine rotor of the wet-steam turbine can be
considered as more demanding than those imposed by the MSR.
2.3. Selection of the Critical and Limiting Components.
As presented above, it can be concluded that the loadfollowing operation of the PWR using the design ramp rate of
5% of full power per minute, is already covered by
the
design structural analysis of the non-core equipment used in
the primary side of the plant. Fatigue problem due thermal
cycling was generally shown as not existing
for the unit
loading and unloading, since the temperature transient is
small if compared with others that are more demanding and that
have to be included
From the review
by the design
of
the
of the behavior of the primary
two specific problems were
equipment.
side,
selected to be covered with
41
greater detail because they represent conditions not covered
by the structural design considerations. First, the
core
reactivity control will reduce the expected allowable ramp
rates due the existance of special restrictions on the use
of part-length control rods /36/,
designed specifically for
power shaping and xenon feedback control during reactor
transients. Second, pellet-clad interaction mechanisms were
not sufficiently accounted in fuel design, resulting in fuel
element failures and in additional restrictions
on
allowable ramp rates for the reactor operation /37/.
the
Chapter
III will cover the core reactivity control limitations
and
Chapter IV the fuel element limitations.
For the steam and power conversion system, the operation
of the high pressure turbine in the wet-steam region will
also impose limitations on the ramp rates for safety
operation of the turbine unit. Those restrictions will be
analysed in Chapter V.
42
Chapter III
Reactivity Control for Load-Following Operation
3.1. Introduction.
Pressurized water reactors are generally provided with
two independent systems for core reactivity control,
control rods and a chemical shim in the form
the
of boric acid
dissolved in the reactor coolant.
The control rod assemblies in Angra 1 /19/ are of two
types, the full-length control rods made of an alloy
of
Ag-In-Cd sealed in stainless steel, and the part-length rods
made of the same alloy in the lower 25% and with an inert
material, Al203, in the upper 75%. Full-length rods
are
also provided as the shutdown group in order to assure a
safe operation of the plant under all the circunstances. The
Angra I power plant has 33 full-length rod clusters, 12 of
which are in the shutdown group and the others 21
are divided
in four control groups from A to D, which operate sequentially
when power is increased from 0 to 100% /19/.
Four part-length
assemblies are also provided, as is shown in Figure 3.1.
The reactor coolant boric acid concentration is controMled
by the boron thermal regeneration system, which process
the
reactor coolant letdown flow before it is returned
to the
volume control tank and the reactor coolant system
through
the chemical and volume control system charging pumps /27/.
43
0
0
@
0
o
0
00
@
0
0
0
A,B,C,D
-
Control Groups Full Length
PL
-
Control Group Part Leiagth
S
-
Shutdown Group
Figure 3.1
Control and Shutdown Groups Distribution
(from Ref. 19)
44
Alternative paths can be used to increase the dilution or
the boration capability of the plant through proper
operation
of the chemical and volume control system /47/.
One important aspect of the use of soluble boron
for
reactivity control is the considerable amount of tritium
produced by the B10(n,2 )H3 reaction, which will have to
be
considered in respect to the radioactive plant discharge /46/.
As will be discussed below, the load-following reactivity
control of the reactor will possibly result in an increase in
the boron concentration to be used throughout the life of the
core, with corresponding increase in the total tritium
production. Although important with respect to the dimensioning
and designing of the liquid and gaseous waste disposal system,
which.will have to be able to handle increased flow rates,
this problem will not be covered here nor will be considered
as a limiting factor with respect to the possible ramp rates
for the plant.
In the following material, first will be discussed the
way that the soluble boron and the control rods are actuated
with respect to the core reactivity control and
the
difficulties resulting fiom practical limitations on the
use of part-length control rods. Then, the computer
FOLLOW, written for this thesis, is presented.
code
A zero-
dimension mathematical model is built to analyse the
transient behavior of the reactivity control systems in order
to define what are the attainable ramp rates for the present
45
configuration of the control systems.
3.2. Operation Modes for the Reactivity Control Systems.
In order to minimize transient xenon feedback effects
on the axial power distribution, the normal procedure is to
keep constant, as much as possible, the axial power shape at
all power levels, with a pre-scheduled gradual change
throughout core life. This operation, regularly known as
constant axial offset control (CAOC) /47,48/, can
performed with or without the use of part-length
be
control
rods. In each case, the dynamic behavior of the plant will
be different, in such a way that we can identify
two
independent operation modes. If part-length rods are used,
the normal procedure is to have the full-length rods
to
compensate for the power defect, the part-length rods to
keep constant the axial offset, and the soluble boron system
handle the reactivity change associated with the transient
xenon. This is the basic operation scheme considered
in
early planning for the plant to give load-following
capability with respect to what
is there considered as the
typical load cycle, and will be called here as operation
mode 1.
Mode 2 will be the case when part-length rods are
not used at all. Under this circunstance, the full-length
rods have to be used to handle the constant axial offset
control, and the soluble boron system is used to overcome
46
the reactivity changes due
both the power defect and the
xenon transient /48/.
The maximum allowable ramp rate for power change
is
strongly dependent on the operation mode selected. In order
to keep the fast transient capability predicated in the plant
design, where the system is assured to support the design
reference load cycle with ramp rates of 5% per minute /48/,
operation mode 1 should be selected, which means that the
part-length rods have to be used. But the use of part-length
rods pose some potential problems and special care should be
exercised. One condition to be avoided
results
from a
bad positioning of the part-length rods with respect to the
full-length groups. The occurrence of a "pinched"
power
distribution with a high power peak in the center can result
/47/.
Since the constant axial offset criteria will
not
be violated, the adverse power distribution will not be
indicated by the ex-core detectors. To prevent this problem
from happening, a convenient overlap of the part-length and
full-length groups have to be considered in much the same
way as the one existing for the different full-length
rod
banks themselves. Figure 3.2 shows the recommended insertion
limit for the part-length control rods with power.
Other limiting condition to be avoided in case of partlength rods use, is the so called fuel burnup shadowing /48/,
resulting from long periods of operation at full power with
the part-length rods inserted half way, as indicated
in
0.
0.
I
I
I
I
I
I
I
I
I
I
I
K
-
jg.
4/0 "dion
10
30
-
30
40
SQ
ci- P.
0
bo.
(00.
CD
70IQ
-4000//
10
qo.
"00
C',
0
0
H
I
I
20.
40.
PL -A
I
Qo.to00.
I
INSECTilJ- MO]&-
|
0. 20.
o0 oo.
4
%PoWsvontN&e-
-
IV49'E-TiZTOJ
MOjE.
2
-
.
-
AmQ
1-b* 00
48
Figure 3.2, in order to avoid the "pinched" power distribution.
This insertion will cause adjacent fuel rods to have
a
relatively smaller neutron flux. Again, a high power peak
factor can result near the core center when the power
it
changed and the part-length rods removed from their previous
position, leaving the shadowed and relatively less burned
fuel at the core center to see now a higher neutron flux.
Studies have shown /48/ that no increase in the axial
peak
factor due shadowing is expected to occur if the core is
depleted at full-power with the part-length rods inserted for
no more than 60% of time. The recommended rule for operation
with the part-length control rods is to use them on no more
than 18 of every 30 equivalent full-power days /48/.
All the above limitations have strongly restricted
the
use of part-length control rods in today's pressurized water
reactor operation. Utilities that operate PWR nuclear power
plants keep the part-length rods out of the core as a normal
operating procedure /36/,
in order to avoid the axial
misalignment problem and the resulting safety related
consequences due higher than allowed axial power peaking.
Those practical limitations on the use of part-length
control rods bring us to consider mode 2 as a more realistic
option from a reactor operation standpoint, and we calculate
now the ramp rate limitations resulting from the fact that
mode 2 has to be used.
49
3.3. The Computer Code FOLLOW.
FOLLOW is a point model code with the built in capability
to simulate the reactivity control both by the part-length and
full-length control rod groups, as well as by the
soluble
power history
boron system, in order to follow a prestated
imposed on the plant. The reactivity required to overcome the
power defect and the xenon poisoning
is distributed to the
different control systems depending on the
operation mode
previously specified and on the reactivity characteristic of
each item involved. No allowance is made here
to
use
variations of the coolant temperature as an additional
mechanism to change core reactivity through the actuation
of the coolant temperature reactivity feedback effect, which
could account for a reduced demand on the boron dilution
system /51/.
All the reactor physics data defining the characteristics
of each control rod group, the soluble boron
reactivity
coefficient, the reactivity power defect and the hot
power critical boron concentration, must be specified
full
for
all burnup levels. Data related to the soluble boron system
model and the xenon poisoning model must also be provided.
Linear interpolation is generally used to obtain the values
for the variables in between those specified.
Practical operational procedures are used in order to
couple the insertion position of the control rod groups with
50
power. In mode 1 operation, a one-hundred step overlap (or
an overlap of 1.60m, with a full control rod travel of 3.80m)
is used for the three full-length control groups B,
C, and D,
that are active when power is increased from the hot zero
power condition to hot full power /19/, and the part-length
rod position is defined by the typical insertion curve
of
Figure 3.2. For mode 2 operation, the experience has shown
/48/ that only one control rod group has to be used for
constant axial offset operation, and the typical insertion
curve for this case is also presented in Figure 3.2.
To
account for the total reactivity effect of each control
group as function of its insertion in the core, a typical
integral control rod worth versus percent insertion curve is
used, and is shown in Figure 3.3. For the part-length
control rod, the integral worth relative to its 25% reactive
portion is calculated by the difference of the integral
worth relative to the position of the top of the rod and,
the beginning of its active length.
Figure 3.4 presents the block diagram of the code FOLLOW.
The xenon transient equations /49/ and the soluble boron
system model /41,46/ are discussed below, as well as the
input data preparation for the code. A complete listing of
the code with a sample problem is presented in Appendix I.
The resulting ramp rate limitations with respect to both
operation modes and core burnup level, is shown in Chapter VI,
together with the final conclusions of this work.
51
Figure 3.3
(from Ref. 19)
Normalized Control Rod Worth
100
Rod
Worth
(/M)
50
00
.LVV
:)u
Rod Insertion (%)
C7ED
Figure 3.4
Block Diagram
for code FOLLOW
READ CASE INPUT DATA
-operation mode
-burnup level
-power history
DETERMINE
-initial boron
-initial reactivity
-rod positions
-boron reactivity
-xenon concentration
NEXT TIME STEP
-cale. power
-calc. xenon
NO
PRINT
ES
CALCULATE AND PRINT
-critical boron
-maxmin boron cone.
-rod positions
-reactivities
_N FOLLOr
NO
YES
NO
AST
TI
ES
P=IN
WARNING MB365AGd
"OPERATION IMPOS."It
NO
T
CAS
ES
STOP
52
53
3.3.1. Transient Xenon Calculation /49/.
Due its very high absorption cross-section for thermal
neutrons, Xel35 is the most important of all the fission
products for control of the reactor during power transients.
It is part of a fission chain where it can be directly
produced with low yield fraction, or can be produced by beta
decay of Te 1 3 5 to 1135 and then to Xe1 3 5, with a higher yield
to
/49/. For practical purposes a simplified chain is used
analyse the transient behavior of the xenon poisoning, where
the I135 is assumed to be produced directly from fission and
the chain ends with the destruction either by neutron absorption
or by beta decay. This simplified chain representation, as
well as the resulting differential equations to be solved
by the code FOLLOW, are presented in Table 3.1. The numerical
values used in the model are in Table 3.3.
3.3.2. Soluble Boron System Model /41,46/.
The soluble boron model considers that the reactor
coolant system is a control volume which receives an inlet
flow with variable boron concentration, and from which
an
equivalent flow is taken with the same boron concentration
as the control volume itself and with the same flow rate as
the inlet flow. A mass balance is made for the boron with the
assumption that all the available boron is kept in solution,
in such way that the transient concentration for the soluble
boron in the reactor coolant system can be determined.
54
Table 3.1
Transient Xenon
fission------------------
Model
u
(SIMPLIFIED
L ........
1135
--- ~.
13 5 .---.
I>X1X
CHAIN)
Differential equations for the simplified xenon chain above:
dt
i
xI(t)
- TXec
z*!
i1
+
J I(t)
+
-
df1t) _
Xe
Xe(t)
Z;all1
If we consider a linear relation between neutron flux and power
and take
Xf1
and
x(t) = 6e Xet)
a 1f
we have:
d
_Xe IoP
_t)
xe Xe 0
.0 1, (-p0
e21T
+ 1 igt
-P
e~o (E
+
di (t)
Z/O
1 P0
) + AX
(t)
55
Table 3.2
Soluble Boron System
Model
V M -
VT
(C)
R - flow rate (mass)
C - boron concentration
t - time
- C R
I
volume
mass
.
-
coolant density
Mass balance for soluble boron in VT assuming
perfect mixing of all
boron:
dMS=
CinR - C R
Supposing constant volume for the primary:
Tt
dc
+
C ) R
( Cin -
=
R
t=
s
R
Where the solution for the initial concentration C
is:
0
Rt
C(t) = C. i( 1 - e T)+ c 0
Rt
0.T
56
Table 3.3
1. Core Model Data (from Ref.19)
1.1 Critical Boron Concentration
a. Full power, no xenon, hot, rods out........1290 ppm
b. Full power, equil. xenon, hot, rods out.... 980 ppm
1.2 Typical Neutron Flux at Full Power (n/cm2 sec)xIO1 3
fast
thermal
a. Core
center......................
b. Core outlet radius at midheigh...
c. Core top on axis.................
d. Core bottom on axis..............
5.97
3.19
3.13
1.50
1.83
1.26
1.75
1.50
2. Transient Xenon Model Data (from Ref.49)
2.1 Iodine yield fraction from fission............
0.064
2.2 Xenon yield fraction from fission.............
0.003
2.3 Iodine decay constant (10-5 sec
2.4 Xenon decay constant (10- 5 sec
1
)............
2.87
1 ).............
2.09
2.5 Xenon absorption cross-section (10-18 cm 2 )....
2.70
3. Soluble Boron Model Data (from Ref.19 and Ref.48)
3.1 Reactor primary system volume............... ..
7 6 000gal
(290
3.2 Maximum dilution rate...
3.3 Maximum boration rate.....................
3.4 Boron concentration for dilution............
)_
120 gpm
(0.5m /min)
g11
gm
3
(.04m /min)
10 ppm
3.5 Boron concentration for boration............ ..20000 ppm
57
Table 3.2 presents the equation used in the FOLLOW
code
to
calculate, for each time step, what are the bounds for the
boron concentration if either the dilution or the boration
modes were used, in order to check the capability of the
system to follow a specific load history. The numerical data
for Angra I /19/ is in Table 3.3.
3.3.3. Input Data Description for the FOLLOW Code.
The input data are divided in two levels: those defining
the plant characteristics are changed less frequently
and
are inputted through DATA statements in the MAIN program;
those defining the operation characteristics for the power
history to be followed, are read and must be provided by the
user.
The plant characteristics can be divided in data related
to the core reactivity model, which are either provided in
Table 3.3 or in Figures 3.5 to 3.8, the xenon poisoning
model, and the soluble boron system model, which are both in
Table 3.3.
The power history and operation data to be provided by
the user is organized in four card groups, which provide
informations about the operation mode to be used and the
points defining the time and power of the history to be
followed. Table 3.4 presents the organization of the input
information required by the code.
58
Table 3.4
Input Data for Code FOLLOW
Card 1
-
Format (20A4)
(TITLE(I) ,I=1, 20)
Card 2
-
Format (2110)
NPONTSMODE
NPONTS - number of points in the power
history
MODE - operation mode
MODE = 1 - part-length rods used
MODE = 2 - no part-length rods are used
Card 3
-
Format (16F5.1)
(TIME(I) ,I=1,16)
TIME - up to four cards with the selected
time values for this power history
Card 4
-
Format (16F5.1)
(POTEN(I),I=1,16)
POTEN - up to four cards with the selected
power fraction for points of this
history
Figure 3.5
(from Ref.19)
Power Defect Variation with Power Level
0
Total
Power
Defect
(pom)
500
Beginning of
Cycle
1000
End of
Cycle
1500
2000
2500
0
20
40
60
80
100
Power Level
(/)
60
Reactivit,
Full-Length Group 0
1.50
1.25
Full-Length Group D
1.00
0*751-
0.501-
Part-Length Rods
0.25
0.001
0
I
20
I
40
I
60
I
80
100
Burnup(%)
Figure 3.6
(from Ref.19)
Control Rod Worth with Burnup
61
2
Figure 3. 7
(from Ref.19)
Boron Concentration Variation with Burnup
62
-10.0
Boron
React.
Coef.
-9.5
(c)
ppm
-9.0
-8.5
-8.0
0
I
20
I
40
I
60
I
80
100
Burnup(%o)
Figure 3.8
(from Ref.19)
Boron Reactivity Coefficient with Burnup
63
Chapter IV
Fuel Element Behavior in Load-Following
4.1. Introduction.
Reactor fuel element behavior has
been extensively
studied and reported both with respect to the
failure
mechanisms ant to the remedies adopted to prevent
the
failures or to correct the problem. For example, recent
reviews of the subject /37,52,53,54/ have identified
the
evolution of the fuel elements problems, as well as the
remedies. Table 4.1 is a resume of the above references and
will be
used here as a basis for the discussion of the fuel
element behavior in load-following.
The question now to be posed is: what are the fuel
failure mechanisms which are likely to be activated by the
load-following operation of the plant? The obvious answer,
as the examination of Table 4.1 indicates, is that at least
the fuel pellet-clad mechanical and chemical interactions and
the somewhat related cladding cyclic strain fatigue problem
will have to be considered.
With respect to other failure mechanisms, besides
the
two just mentioned which are usually considered as areas of
special concern for the cyclic operation of the fuel /55/,
it is wothwhile to point out other potential difficulty. If
the fuel initial enrichment is not to be affected by a special
64
Table 4.1
LWR Fuel Element Failures and Remedies
REMEDIES:
FAILURES:
1. Early Failures
1.1 Increased design
1.1 Design related
experience and feedback
-fretting/corrosion
from reactor and
-rod bow
laboratory experiments.
-inadequate plenum volume
Improved correlations
-inadequate gap size
for fission gas release
-faulty end cap design
and fuel swelling.
1.2 Improved manufacturing
1.2 Manufacture related
procedures and quality
-pellet loading
control due feedback
-clad flaws
from reactor
and
-end cap welds
laboratory experiments.
-pellet fabrication
processing
-excessive moisture
1.3 Others
1.3.1 Intergranular attackl.3.1. Change to Zircaloy
of stainless steel clad
cladding
1.3.2 Fretting
zirconium grid
of
1.3.3 Crud deposition
2. Epidemic Failures
2.1 Internal hydriding
2.2 Densification and clad
flattening
1.3.2. change to inconel
grids
1.3.3.Better control of
coolant chemistry
2.1 -adequate fabrication
techniques
-use of hydrogen getters
2.2 -pre pressurization
of fuel rods
-incresed initial fuel
density
-thicker cladding wall
-stable fuel structure
65
Table 4.1
(continuation)
3. Current Concerns
3.1 Nodular corrosion
3.1 Improvement in water
chemistry
3.2 Fuel rod bow
3.3 Cladding fatigue
3.4 Fuel pellet and
cladding mechanical
and chemical
interaction (PCI)
3.2 Improvement in spacer
grid design
3.3 Limitation of power
cycling
3.4 -Reduced ramp rates
-modified fuel pellet
geometry
-cladding annealing
-fuel pellet and
cladding interlayers
66
fuel management procedure due the load-following operation of
the plant, the reduction of the capacity factor
65%, typical for base load operation /39/,
from say
to 40%, well
within the cyclic load range, would increase the in-core
fuel residence time from 3 years, as is practiced today in
pressurized water nuclear plants, to something like 5 years.
The effect of this extension in the in-core residence time
should be analysed with respect to the cladding
corrosion
mechanism.
To proceed this analysis, though, three areas will be
covered by the subsequent discussion on the effects of loadfollowing operation on the reactor fuel elements: the cladding
corrosion due extended in-core residence time; the cladding
strain-cycling fatigue; and the pellet-cladding mechanical
and chemical interaction.
4.2. Zircaloy Corrosion Behavior.
Only the external cladding surface corrosion aspects
will be discussed in this paragraph because internal surface
attack is somewhat related to the pellet-clad mechanical and
chemical interaction and will be covered later.
It is generally true that the corrosion resistance of
Zircaloy is adequate to assure operation of the fuel element
for a long period of time /54,56/ as long as the reactor
coolant chemistry is appropriately controlled and the fuel
67
element has no manufacture problem
components or faulty welds /56/.
with respect to faulty
Reported performance for
Zircaloy tubes that have been operating for about 4100 days
(11 years) in the Shippingport plant /58/, revealed only the
predicted behavior with a slight increase in the formation
of the oxide layer.
In order to estimate the effect of the reduction of the
plant capacity factor in the build up of the oxide film in
the external cladding surface, we can use Figure 4.1.
Considering that the fuel in-core residence time would double,
and taking 1100 days as the reference case for the
fuel
residence time, Table 4.2 presents the estimated variation
of the oxide film thickness.
and the percent variation with
respect to the total wall thickness. The maximum cladding
wastage is not considered excessive with respect to
the
allowable limits /60/.
One important aspect here is that
temperature has
a
pronounced effect on the corrosion rate of Zirealoy.
Although the core residence time will increase for the fuel
rods, the average coolant temperature is expected to
reduced by the load-following operation.
To
be
estimate the
effect of temperature reduction on cladding corrosion attack
Table 4.1 presents results for out-of-reactor experiments at
different temperatures. Those results should not be taken as
absolute values because neutron irradiation also has
a
important effect on the corrosion rate /60/, but the relative
68
PWR 3270
(excess oxygen)
BWR 29540C
PWR 33400
1000
Weight
Gain 500
A-33(
mg/dm2
Out
10 =
of
Reactor
100
10
/e/
50
'00
K--
~
/*
/
/
pre-trbns~t.
region
p.
,p,
0
~*5~0*~~
10.
100
1000
10000
Exposure Time (days)
Figure 4.1
(from Ref.56)
External Corrosion of Zircaloy Cladding
69
Table 4.2
Zircaloy Cladding Corrosion Data
From Figure 4.1:
)
Weight Gain (mg/dm2
Reference
Curve
1100 days(residence time) 2200 days
PWR 3340C00......
..
........
210 ......
350
Out-of-Reactor
125
3300 C..0 .. 0 0..
0
3100 0.........
3000 C........
*
..
0
000
00
0
*0
0 0
......
0009V0
60
......
*
0
30
......
0
0
..
230
100
50
..
Calculated Cladding Corrosion (rm) and (percent wastage):
Reference Curve
PWR 3340C
1100 days
............
2200 days
12.4 (2.17) ............
20.0(3.50)
Out-of-Reactor
330 0 C............
7.4 (1.29)
3l0 0 C............
3.5 (0.61)
300C.0......
1.8 (0.31)
0
0.0.00000
00000
0
0
0
13.6(2.38)
5.9(1.03)
2.9(0.51)
70
reduction of cladding attack with temperature is expected to
be representative of the trends for in-reactor corrosion. The
end-of-life cladding fast neutron fluence is not expected to
change under the assumptions above, although the flux levels
will be different.
Although relevant, the fuel cladding oxidation is not
considered as a limiting factor for load-following operation,
since the fuel in-core residence time is certainly one of the
variables to be defined by the
fuel management and will
probably be different if the plant is to be operated as a
base-loaded unit or in load-following.
4.3. Fatigue Analysis.
Fuel cladding strain-cycling fatigue will result
from
the pellet-cladding interaction. For the pressurized water
nuclear reactor environment, the clad tube will tend to creep
down onto
the pellet under the influence of the pressure
gradient between reactor coolant and rod internal pressure.
A typical behavior for the gap closure of a new fuel rod is
shown in Figure 4.2. After the first contact is established
at low power, the fuel pellet expansion with power
increase
imposes a strain on the cladding which constitutes the first
half of the strain cycle. When power is reduced, the formation
of a clearance between fuel and clad allows the clad
collapse down again onto the pellet after some time at
to
to
90
--
U
J
Figure 4.2 (from ref.19)
Clad and Pellet Dimension Variations with Exposure
-jJ
-J-J
71~
72
temperature and the strain cycle is complete.
The importance of this cycle on the fuel element behavior
is usually well evaluated /53,54,55/
Aas /55/
and results reported by
consider that a strain cycle of 0.6% would produce
failure after only 50 cycles. Based on low cycle
fatigue
curves for the Zirealoy/53,59/ we can consider that
the
above strain cycle value is aparently overestimeted and also
that the fatigue resistance of Zirealoy is underestimated.
Robertson /54/,
although indicating some concern that the
use of nuclear reactors in load-following could lead
to
cladding fatigue failure, indicates that strain gauges
attached to Zircaloy cladding showed that for large power
cycles, the amplitude of the strain cycle in the cladding
was only about 0.1%.
Using the design curve for irradiated Zircaloy-4 at
32000 proposed by O'Donnell and Langer /59/,
and shown in
Figure 4.3, we can prepare Table 4.3 that relates the total
strain range with the allowable number of cycles. The fatigue
design curve presented uses a safety factor of 2 on the
stresses or a factor of 20 on the number of cycles to failure
as is the practice for fatigue design curves /45/.
In order to estimate the importance of the fatigue, the
percent strain variation of the cladding internal surface was
calculated, for the fuel element to be used in Angra I /19/,
by a modified version of the LIFE-1 LWR computer code /37/.
The results are in Table 4.3 where 40% is considered as the
73
Figure 4. 3
(from Ref. 59)
Design Fatigue Curve for Irradiated Zircaloy-4
-N
-J
U
III
IA0
-4
-o
-4
It
aj
(Paw) .094
+ 33~
74
lower power limit due pre-conditioning effect, as will
be
discussed in Chapter VI.
Letts ask now what is the expected number of strain
cycles that the fuel rod has to stand for a reduced capacity
factor of 40% and no change in fuel initial enrichment as
before. Mechanical contact between cladding and fuel will be
possible only after clad creep down, as in Figure 4.2, which
will occur at about 400 equivalent full power days operation.
Supposing that the fuel residence time is again to be doubled,
the maximum number of cycles would be about 1400 if power
is changed daily and no credit is taken for the time required
for cladding creep down, discussed in Chapter VI. From Table
4.3 we see that tha allowable number of 40 to 100% strain
cycles is 2100; therefore we can operate the plant with daily
power changes equivalent to this and have acceptable fatigue
performance.
As indicated before, the fuel in-core residence time can
be changed with no apparent difficulty, as long as limitations
on the fatigue or corrosion life, or fuel management
considerations find it advisable. No ramp rate limitations
is considered here as imposed on the operation of the plant
due to either the cladding fatigue or the corrosion behavior
of the Zircaloy cladding.
75
Table 4.3
Zircaloy Cladding Fatigue Data
From Figure 4.3:
Maximum Number of Cycles
Percent Total Strain Amplitude
100000
0.19
50000
0.21
10000
0~
0.34
0.37
0.41
0~
5000
00
2000
1000
00
0.52
500
0.58
0.84
1.03
0~
100
50
10
1.66
@0
From LIFE 1-LWR(modified):
Percent Power Change
.
from 42% to 57%
from 42% to 71% ..
from 42% to 86%
from 42% to 93%
from 42% to 100%..
Percent Total
Strain Amplitude
.0
Maximum Allowable
Number of Cycles
....
0.004
infinite
....
....
0.130
0.254
infinite
.....
25000
....
....
0.326
0.406
.....
.....
15000
2100
76
4.4. Pellet -Clad Mechanical and Chemical Interaction.
It is generally recognized today that the pellet-clad
mechanical interaction plays a important role in the limitations of the allowable ramp rates for reactor power increase
/37,54,57,62,63/. Both radial and axial pellet-clad
interaction (PCI) have been extensively studied and reported
because of its impact on fuel element failures and on ramp
rate limitations. PCI will be covered here on those aspects
related to restrictions imposed on load-following operation.
The provision of a built-in gap between pellet and clad
for new fuel rods prevents PCI occurrence early in fuel life.
Results from experiments and
operation of the pressurized
water nuclear reactor has shown that this gap is taken up by
cladding creep down, fuel swelling, and fuel relocation /57/
later in the life of the fuel element as is shown in Figure
4.2.
As described before, in ease of a power increase, the
temperature rise of the fuel pellet is considerably greater
than that of the cladding. Bigger thermal expansion of the
fuel pellet results, with consequent straining of the cladding
if pellet-clad contact exists at the beginning of the ramp.
The internal environment of the fuel rod and the possible
existence of fuel cracks at pellet surface and pellet hourglassing, can produce local effects at the cladding internal
surface that will make possible the occurrence of stress
assisted corrosion of the Zircaloy clad. The iodine produced
77
from fission has been considered as a possible active element
for the internal surface attack /54,55,56,57,61,62/.
Vinde and Lunde /57/ have experimentally determined the
time to failure and the strains at failure as function
of
stress, for internally pressurized Zirealoy cladding tubes in
the presence of iodine vapors. If the cladding internal
surface stress due a defined power history is known through
a fuel behavior computer code, and a cladding failure criteria
is established, it is possible to estimate the limiting ramp
rate to avoid failure due to PCI. One important aspect to be
considered in the PCI analysis is that only up-power ramps
are potential problems
and the failure mechanism seems to be
active only when sufficient tensile stress is imposed on the
cladding internal surface, or, perhaps, when the throughthickness average tensile stress is sufficiently high /57,64/.
Let's take now the case when power is increased to a new
level and kept constant. Due the creep behavior of the
material, the cladding stresses tend to relax with time and
to accomodate a new diameter. If reactor power is now reduced,
fuel pellet temperature decreases almost instantly and a gap
is again available between pellet and clad. Any power
increase operation that is made within a reasonable time
interval and does not go beyond the power level previously
attained, will not impose any additional stress on the clad.
The clad is said to be conditioned for that specific
power
level. Now, if the low power level is kept for sufficient
78
time, the mechanisms of clad creep down, fuel swelling, and
fuel relocation, will again take up the gap, and the pelletclad mechanical contact is restablished at the lower power
level. This is a deconditioning behavior with respect to the
higher power level.
Conditioning and deconditioning of the fuel element
cladding are key points for the ramp rate analysis because,
to a large extent, they define the available gap between
pellet and clad with respect to the previous power history of
the fuel element.
The knowledge of the instantaneous gap size is fundamental for definition of the stresses imposed by the up-power
ramp on the clad. It is obvious, though, that the ramp rate
limitations for the operation of the fuel element are very
much history dependent due the dynamic behavior of the pelletclad gap size.
To define the limiting ramp rates due PCI, results of
daSilva /37/ are used. His procedure for the construction
of fuel performance maps is now described. A modified version
of the LIFE-1 LWR computer code is used with normalization of
some correlations with experimental results and the use of a
creep enhancement factor for the Zircaloy, to account for
the fuel element behavior during up-power ramps.
Decondi-
tioning of the fuel is calculated by the BUCKLE computer code
/61/,
considering the late-in-life ovality and the ovalization
creep behavior under the pressure gradient.
79
The failure criterion uses the experimental results of
Vinde and Lunde /57/. A stress concentration factor of 2 is
imposed on the results produced by the modified version of
the LIFE-1 LWR code. Conditioning of the cladding is based
on long term stress corrosion cracking (sea) tests by Busby
et al /64/ and is considered to occur at the time required
to relax 50% of the maximum stress produced by the up-power
ramp fuel pellet expansion. Figure 4.4 showns the failure
and conditioning criteria proposed to define the limiting
ramp rates.
Although PCI is not considered usually as a completely
known phenomenon /62/, the numerical results produced by the
approach proposed in /37/ seems to be compatible with
the
up-power ramp rates advised by fuel manufacturers /36/ and
are used here.
The maneuvering table /37/ reproduced here as Table 4.4,
lists the advisable ramp rates for
different fuel pre-
conditioned power levels. The rate of deconditioning and
the stress relaxation coefficient are also shown. The values
of this table will be used in Chapter VI to define the ramp
rate limits for the load-following operation of the plant
due PCI.
80
Hoop
)
Stress
(MPa
..-.
0. Vinde and. Lunde Threshold_. _.
50% Busby
Threshold
80
-
conditionin
time
60
40
20
-20
v
-40
.
0
Figure 4.4
(from Ref.37)
Failure and Conditioning Criteria
81
Table 4.4
(from Ref.37)
Maneuvering Tables (550
to
from
42
kW/m
to 600 EFPD)
41
40
39
kW/m
38
kW/m
kW/m
kW/m
kW/m
kW/m-hr
38.7
M
35.4
M
M
32.2
M
M
M
28,9
M
M
M
M
25.6
65
82
M
M
22.3
13
33
M
M
M
M
Mv
M
iv
M
M
-
19.0
6.6
13
33
*fuel element is fully conditioned for the heat
generation rate in the "from" column
M = Maximum system allowable ramp rate
Rate of Deconditioning = 0.501 kW/m-day
Stress . 50
Decay
Coefficient
.75
1.0
I
10
I
,
3
20
30
40
50
Time (hours)
82
Chapter V
Turbine Analysis
5.1. Introduction.
The hot leg of the primary side of the pressurized
water nuclear reactors, when in the hot zero power condition
operates at about 2800C, and the temperature increases
slightly when power is changed
to the hot full power level.
This value will set an upper bound for the steam generator
secondary side temperature
at
normal operation, and,
consequently, will limit the properties of the steam to be
delivered to the turbine. If compared with temperatures of
the order of 50000 now regularly found
in oil or coal
fired thermal plants, this is a moderate temperature and
will impose the use of wet steam expanding in the high
pressure turbine associated with
the pressurized water
nuclear plant. The necessity to control the secondary side
pressure and the steam generator overall heat transfer
inside reasonable limits in order to avoid
undesirable
reactivity effects in the reactor core due to primary side
cold leg temperature variations, and the fact that wet steam
is used in the high pressure turbine, will, to a
large
extent, define the load-following behavior of the turbinegenerator group of the pressurized water power plant.
To make easier the discussion of the part-load
and
83
load-following operation characteristics of the wet steam
turbines, a brief presentation of the different turbine
governing processes and the effects of moisture in the high
pressure and low pressure turbines will be made. The
full
load heat balance for the turbine of the Angra I Power Plant
/19/ was taken as the reference from which Figure 5.1, the
associated turbine expansion line, was drawn on a Mollier
diagram, assuming a total of 5% for the pressure
loss at
the stop valve and throttle valve at full power /1/.
5.2. Moisture Effects.
The water associated with the wet steam is usually
assumed to be present in the form of spherical droplets. To
evaluate the consequences of expanding this mixture of water
drops and steam in the nuclear turbine, we have to consider
the loss of stage efficiency, the erosion-corrosion problem
in the high pressure (HP) turbine, and the erosion problem
in the low pressure (LP) turbine /2,3,5/.
It was experimentally found that the efficiency
of
dry steam expansion was considerably higher than the
expansion of wet steam. An estimate of the loss of stage
efficiency due wetness can be made using the results from
Karl Baumann /2/,
which established that for each
1%
wetness present in a stage, its efficiency is likely to
decrease about 1%. More accurate results, shown on Figure
Fi gure 5.-1
Turbine Expansion Line (Angra I)
Enthalpy
Entropy
84
85
5.2, should take into account facts as the droplets to
steam velocity retio, the pressure and the geometry of the
blades /2,3,4/.
The use of wet steam in the HP portion of the light
water reactor turbines make them very special if compared
to the superheated steam turbines which have wet steam only
in the last stages of the LP turbine. In this particular,
the relative spacing between water drops in the steam at the
LP turbine can be greater by a factor of ten with respect
to
the HP turbine, at the same wetness /5/.
The higher
temperature and water drop density existing in the HP
turbine makes possible the existance of erosion-corrosion
caused by iron being
dissolved in pure water,
and
experimental results show that this reaction takes place
preferentially in the temperature range from 4 0 to
26000 /2/.
The blade erosion problem, another phenomenon, occurs
in the LP turbine and is not unique to the nuclear plants
because the water separation and steam reheater between HP
and LP turbines, makes the wet steam region of the LP
nuclear turbine very much like the fossil plant unit,
although
there is a relatively bigger unit size and mass
flow rate for the nuclear units when the same installed
capacity is considered. The most serious erosion problem
here is the damage that occurs near the tips of the last
rotor blades due the impact between the fast moving blades
86
1.00
Efficiency
Ratio
0.98
\\
Bauman Rule
0.96
High Pressure
Turbine
>
Low
Pressure
Turbine,
0*94
0.92
0.90
0
.02
.04
.06
.08
.10
Figure 5.2
(from Ref.2)
Wetness Loss for Turbines
87
and the slow moving droplets. It is generally accepted that
the maximum wetness value economically feasible is 11% /2,5/.
5.3. Turbine Governing.
When the power plant is connected to an electric grid,
the mechanical power delivered to the shaft of the turbine,
and consequently the steam consumption,
is dictated by
the grid demand on the generator. One very important aspect
to consider in the analysis of the load-following behavior
of the plant is to understand how the wet steam turbine
is usually controlled to handle different power demands.
Since the generated load depends ,mainly on the steam
flow and on the thermodynamic properties of the inlet steam,
we can identify two classes of control concepts for the
operation of the turbine /12/. In the first
case, called
constant-pressure control, the pressure before the turbine
stop valve is kept constant or changes only slightly with
power, and the mechanical power required to
match the
demand is adjusted by the actuation of a governing mechanism
which, through different positioning of a valve, changes
the flow and pressure of the steam expanding in the turbine.
Another possibility is to allow the pressure before
turbine stop valve to vary with the load, as in
the
the
sliding-pressure control, where no governing mechanism is
needed and all power changes rely on the boiler or steam
88
or steam generator reserve capacity. When a sliding-pressure
scheme is used, although no governing is required, some kind
of provisionshould be made to handle rapid load increases
because the system has generally a reduced speed of response
/12/.
Pressurized water nuclear power plant uses constantpressure control. For this case, the governing control can
be operated by a throttling valve, or by the nozzle control
process, or using a bypass scheme /1/.
Cases in which
combination of the processes above mentioned are used, can
also be found.
In the nozzle control governing process,
different
number of nozzle groups are activated, through the actuation
of independent control valves, when the turbine load
is
changed, providing a partial admission of steam proportional
to the power demand. The nozzle control
is
necessarily
restricted to the first stage of the turbine while the
nozzle areas in the other stages will remain constant. This
fact is important because it can be shown /1/
that the
absolute pressure of the steam after the first impulse stage
of a nozzle governed turbine will be directly proportional
to the rate of steam through the turbine. The same
is
true when throttle governing is used. As will be shown, this will
bring severe limatations to the operation of the wet steam
turbine.
In case of bypass governing, more than
one steam
89
admission position is provided in the turbine expansion line.
Each
valve delivers steam to a specific stage in
the
quantity and thermodynamic condition imposed by the valve
position. The valves are operated in a pre-scheduled
sequence when the demanded load does not match the power
delivered to the shaft. Since the steam flow for separate
groups of blades can now be different, depending
on
the
load and on the bypass valve positions, the pressure change
of the expansion line of the turbine with load
can be
controlled. The problem here is the sophistication
control system required to actuate properly
of the
the bypass
valves, as well as the losses associated with the throttling
of the bypass steam to meet the stage condition.
Turbine throttling is the simplest scheme of the three
because
it
requires the less elaborate control valve
actuation pattern to handle the full range of
power
variations. At each load the throttle valve is positioned
by the control system in order to operate the turbine with
constant rotational speed. The relation between
load and
steam consumption is, in general, given by the Willans line
and for the throttle governing
the Willans line is shown
to be straight /1/, indicating a linear relation between
load and staam demand. The full power steam consumption is
generally well known and for condensing turbines the no
load steam consumption is about 10% of the full load /1/.
Another characteristic of throttling is that it
can be
90
considered as a process
with
expansion work only and,
consequently, isoenthalpic /16/.
Using the above considerations about throttling
and
neglecting the effects of the last stages of the LP turbine
where the steam velocity changes appreciably with load, it
can
be shown
that
the pressure in any
row of blades,
sufficiently far away fnom the very low pressure exhaust end
is directly proportional to the steam flow /1/,
and,
consequently, to the load.
5.4. Part-Load Operation of the Wet Steam Turbine.
It is well known that big coal and oil fired power
plants can respond rapidly to load changes. Reported
specifications /12/ state that a 600 MW unit must be capable
of being brought up to full power, after an overnight
shutdown, in 20-40 minutes, and from the cold condition in
2-3 hours from burners light-up, with loading ramp rates
between 5 and 15% of full load per minute in the range from
30 to 100% full load. For these plants, the size of the HP
and IP (intermediate pressure) cylinders make it difficult
to maintain safe clearances between rotor and stator, which
involves close matching of boiler steam
with HP casing
temperatures and hot reheat steam with IP casing temperature.
The ability to raise high vacuum very quickly
in case of
startups /11/, the first stage bending stresses at part load
91
and when nozzle governing is used, the LP last
stage
vibration at part-load /7/, all are problems to
be
considered,
but the possibility to use more flexible
control schemes, as the sliding-pressure for instanee /12/,
and the relatively small steam temperature changes with
pressure due the initial superheating in the HP
and IP
turbines, regions where bigger pressure changes are expected
to occur with load, make the load-following capability of
the big superheated steam turbine generally be considered
as good /7,10,11,12/.
As mentioned before, the pressurized water nuclear
power plant operates the steam generator secondary side on
a almost constant pressure basis. Throttling is the governing
process, and is important to consider its effect
on
the
wet steam turbine, when part load operation is required.
Figure 5.3 shows the HP expansion line variation due the
throttling process, considered as an isoenthalpic
transformation. It can be noted that the temperature
variation is very significant in the wet steam region with
pressure.
For the wet steam turbine, steam temperature, pressure
and wetness all vary in a wide range with load, and their
effects should be carefully considered. Fatigue failure due
thermal stress cycling is the first concern.
It can be shown that with respect to thermal elasticity
the components of a turbine can be arranged
in ascending
92
E
N
T
H
A
L
P
Y
IIo
Figure 5.3
Throttling Effect on High Pressure Turbine
93
order of risk into pipings, casings and rotor /9/. In order
to analyse the behavior of the turbine under the temperature
and pressure variations due load-following, it will
be
sufficient, though, to investigate the response of the HP
turbine rotor, which is the most highly stressed component
/9,14/.
5.5. HP Turbine Rotor Mathematical Model.
In order to retain the most significant effects of load
following, as considered in this analysis, on the HP turbine
rotor, and still keep the problem inside reasonable
practical bounds, simplifying assumptions are
and
made, some
of which are used even in more sophisticated models /9,14,
15,16/.
It is
important to understand that the
idea
here is to estimate roughly the fatigue problem in the HP
portion of the wet-steam turbine, and to show the special
character of this problem due both the wet steam expansion
and the relatively big size of the rotor, with its
conse-
quently large thermal inertia. Only thermal and pressure
variations will be considered with load, and since the rotor
is taken as turning with constant speed, no considerations
are made about the stresses due centrifugal forces. The
form of the HP rotor, as considered here, is shown
Figure 5.4.
in
94
50 mm
180
M/S
Steam
in-
1. 50 m
Figure 5.4
(from Ref.2)
Cross Section of the High Pressure Turbine Rotor
95
The simplifying assumption for the model are:
a. Symmetry of revolution, which
is
a reasonable
consideration, because full vapor admission is used for all
loads. The model is developed considering a by-dimensional
(r,z) cross-section, axisymmetric with respect to the zdirection.
Only heat convection is modeled in the steam
metal interface, and no allowance is made for heat transfer
by irradiation, because its effect is considered negligible
/14/. For the metal temperature distribution, heat conduction
is assumed.
b. Only the body of the rotor is taken into
account
and no blades are modeled. This is a strong simplification
because important stress concentration exists at blade
roots /9/,
and the results
obtained from the model should
be taken as lower bounds for the local stress values. The
use of a stress concentration factor is discussed in Chapter
VI.
c. No creep effect is analysed because the maximum
metal temperature here is relatively small, while the creep
rates for steels are significant only for
higher
metal
temperatures /18/.
d. The steam-to-metal heat transfer coeeficient is an
96
important factor, since it will define the external metal
temperature. For superheated steam turbines, it was shown
/9/
that the heat transfer coefficient varies by a factor
of three between machine inlet and outlet, and by a factor
of eight between the beginning of startup and full load.
It is suggested also /14/ the importance of considering
two different regions for the steam-rotor heat transfer
surface, the path of steam itself through
the fixed and
moving blades, and the leakage flow along the shaft through
the labyrinth seals, which reduces the total heat flux from
steam to metal.
In wet steam flow, the heat transfer
to walls is
greatly enahnced, because the walls become wetted by liquid
droplets or water films deposited on them by impact or
condensation.
These liquid layers have a surface
temperature equal to the saturation temperature at that
pressure /2/.
It is assumed here
that the water
film
deposited over the turbine rotor is in thermal equilibrium
with the wet steam expanding in the turbine
for all loads,
and no consideration is made about the heat transfer process
existing at low loads. The leakage flow through labyrinth
seals is bounded by the pressure differential between two
adjacent stages, and again thermal equilibrium
assumed between the leaking steam and
will
be
the metal surface
water film, which reduces the impact of the labyrinth seals
on the overall steam-metal heat transfer for the
wet steam
97
turbines. The mathematical model will be built to consider
two independent heat transfer regions, that can be used by
option, if the simulation of the differences
in the rotor
surface due the existance of blades or labyrinth seals
is
desired.
e. The HP rotor is considered with its
boundaries
perpendicular to the symmetry axis as if they were perfectly
insolated on both ends.
are also taken
Holes in the rotor, if they exist,
with perfectly insolated boundaries and no
heat transfer equation is solved for their regions.
f. No consideration is made for the effect of
metal
temperature on steam, which is believed to be small /14/.
Other effects are not accounted for: supersaturation, the
Wilson points /2/ for instance, or other non-equilibrium
conditions of the steam and water phases of the wet steam.
No consideration is made for the stage increased efficiency
at part load due wetness reduction.
With all those considerations in mind,
the model
prepared to analyse the thermo-elastic behavior
of the
HP turbine rotor under load-following, will now
be
described. First, the steam and pressure dependence on
load is considered and then the
steady state and the
transient rotor temperature fields are solved using
the
98
heat conduction equation. Finally, the rotor stress field
is calculated by a thermo-elastic-plastic material model.
Detailed description of the mathematical model and
the
resulting computer codes are presented next. The computer
calculations are in two steps, the metal temperature field
calculations first, and then the associated
5.5.1.
stress field.
Steam Pressure and Temperature Dependence on Load.
The initial and final steam properties of the full
load
HP turbine operation
are considered as known data.
For the throttling process and for positions far away from
the very low pressure stages, we have:
H =H0
p =
(1)
W0
) P
(2)
0
where H is enthalpyi. p is pressure, and w is the steam
mass flow rate. Subscripted values indicate full power
conditions.
Using the linear Willans line relation for throttling,
with 10% full power steam flow at no-load,
w =[.10
+ 0.90 (
d wO
p[=0.10 + )*go ( P)
p0
(3)
(4)
99
where P is the turbine power level.
Now, using the steam tables /19/, it is possible to
find the steam temperature dependence on load,
T=
T (p,H) = T
p(p P
(5)
),H
where T5 is the steam temperature.
The temperature dependence on pressure and enthalpy,
obtained from the steam tables, should be provided as input
data to the computer code.
5.5.2. Metal External Surface Temperature.
The steam temperature dependence on load is calculated
for the HP turbine inlet point, just before the first stage
nozzle, and for the outlet point, just after the
last HP
moving blade. Between those two points a linear interpolation
is made, which associates a specific
temperature
to each
position along the steam expansion line,
T (0) -
T (z) = T (0) -
T (LJ
(6)
where L is the total length of the turbine rotor and z is
the symmetry axis.
Then, the metal external surface temperature
can be
computed as
TM(R,z) = 0
(z)
T8 (z)
i = 1,2
(7)
100
where T
is the metal temperature, R is the position of the
external metal surface point in the radial direction r,
C
and
is a multiplication factor to account for special surface
conditions on the rotor.
5.5.3. Steady-State Rotor Temperature Distribution.
The power level specified at the beginning
of
the
power history is taken as the initial steady-state condition
for the turbine. At this power level the rotor
external
surface temperature is calculated as before and imposed as
boundary condition to the Laplace form of the axisymmetric
heat conduction equation. The problem to be solved is
wi h
r-T(rz)
+
2Tm(r,z)
+
Br
br
T2(r,z)
Z2
=
0
with boundary conditions
Tr,z)
=
0
for z=0, z=L
(9)
C (z) T 5 (z)
Tm(r,z)
for r=R
T (rz)
=
0
for r=0
The finite difference formulation for the heat conduction
101
Ti+,
+ Ti, j+
2 T9
-
+
1 T- 1 2
r
h2
r
+
Ti,j+l
2 T
h2
lz
-
h
-
Ti,
+
partial differential equation is
r
+ T ij-l
=-0
Tt
= k
+ k2 Ti.1 ,
Ti+, j
+ k 3 (Ti, j+
+ T
)
or
where
k, =
r hz
2
2rhz
+
+
hr hz2
hrhz
2
+ 2rh2
(10)
2
rh2
2Z
2rh2
+
hrhz
z
+ 2rh2
r
rh 2r
3
2rhz
+
hrhz
+ 2rhr
and i is the index for the r direction, j is the index for
the z direction
From equation (10), the iterative procedure used to solve
= (1-A)
T
+ A
k T +
+ k2TP.
+ k3 (TPj+1
+ T(
(11)
)
T
+
the steady-state temperature problem, can be formulated
102
where A is a relaxation factor used to accelerate
the
convergence of the iterative procedure /24/.
5.5.4. Transient Rotor Temperature Distribution.
The time dependence of the rotor temperature field is
imposed by the variation of the metal
external surface
temperature, resulting from a specified load history given
as input data.
The equation to be solved
now is the
Poisson form of the heat conduction problem
-6Tm(r, z , t)
a1
r
+
a2Lm+
=
m(r,z,t)
Tm(r,z,t)
+r
(12)
where t is the time variable and
a2=
,
with k as the
p
thermal conductivity, CPthe specifiesheat, -and ? the density
of the metal. The problem has boundary conditions as (9) and
and known initial condition Tm(r,z,0) from the solution of
the steady-state problem.
Using the index n to represent the time variable, the
T9
=
2
a2
LTli+l,
ht
- 2 Ti.
+ Ti
,-2,j
+
-
h
r
+
T
.
associated finite difference equation can be formulated
h
r
h2
z
103
or
+
k 4T +1,j
= h
k5 T
+
T
-+ k 6 (,
+1 + Tij)
-
kc7 T
(13)
+ T
where
S2
= a
k
+
Sa 2
r
hr
kc
k5
a2
2
hr
k
a2
6 ~
k
a2
2 a2
r
2 a2
h2
+
which is the expression used to solve the transient
heat
transfer equation.
5.5.5. Rotor Stress Calculation.
The stress field is determined
a finite element formulation,
using
by the utilization of
axisymmetrie
isoparametric elements and working with an isotropie thermoelastic material model. The code ADINA /25/,
a general
purpose structural analysis finite element program, is the
model used.
104
5.6. The TURBINE Computer Code.
The mathematical model presented in the last section is
built in the computer code TURBINE, written for this thesis
study, which will now be described.
The TURBINE code is divided in two steps, the temperature
calculation and the stress calculation, which can be executed
sequentially or not, depending on the use of intermediate
storage of the data to be transfered from one step to another.
The first step reads all the input information and prepares
the nodal temperature values to be used in the finite-element
stress calculation, executed in the second step.
All
the
input information required to run the ADINA code /25/ in the
second step, is also provided as output of the first step.
The program structure and the options available
access each part of it, are presented in Figure 5.5.
to
The
flow chart of the first step, temperature calculation
ADINA input data
and
preparation, is shown in Figure 5.6, where
a short explanation of the function of each
individual
part of the program, taken as independent subroutines, is
made.
In order to run the program, the HP turbine dimensions
and cross-section profile, as well as other input information,
steam data and load history for instance, are provided.
Table 5.1 presents a detailed description of the required
105
Subroutine
read and prepare input data
BEI
t=0
<h
too small
STOP
Sub.EXPANS
Sub.TEMPME
Sub.TEMPSS
steam temperature
rotor ext.surface temp.
steady-state temperature
Sub.OUTPUT
prepare output for ADINA
next ime
step
Sub. EXPANS
Sub *TEMPME
Sub.TEMVPTR
transient temperature
Sub.OUTPUT
no
no
last time
ast hist.
YsSTO
Figure 5.6
Calculation of Rotor Temperature Field
(Fluxogram) * TURBINE Compute Code
106
COMPUTER CODE TURBINE
INPUT DATA AND
POWER HIS TORY
TURBINE THROTTL.
------
AND EXPANSION
(WILLANS LINE)
ADI NA
INP UT
DA TA
ROWR SUTFC
TEMPERATURE
PREP.
ROTOR
ANP.AN
STEPM TEMP.o
DISTRIB.
(FINITE DIFF.)
CHECK FOR LAST
----- STEP AND
POWER HISTORY
TEMPERATURE
FIELD
TAPE
ADINA
*
56
FINITE ELEMENT
STRESS FIELD CALCULATION
(AXISYMWiETRIC) (ELASTIC)
Figure 5.5
Turbine Rotor Model
ADINA
INPUT
DATA
TAPE
107
input information.
For this analysis, the input data needed by the model
is detailed in Table 5.2, where the HP turbine shown
Figure 5.4 was used as the basic design. All
in
the program
listing, as well as the input values used to plot the thermal
fatigue curves presented in Chapter .VI, is in Appendix II.
108
Table 5.1
Card 3
-
Card 2
-
Card 1
-
Input Data Cards for TURBINE
Card 4
-
Format (20A4)
(TITLE(I),I=l,20)
Format (5IlO,2FlO.5)
J1AXKMAXNDATANLOADH, ITERM, CONVOVERR
JMAX - number of points in radial direction
KMAX - number of points in axial direction
NDATA - number of points in steam property table
NLOADH - number of load histories
CONV - convergence criterium for steady state
temperature calculation
OVERR - overelaxation factor
Format (80I1)
((ID(J,K) ,J=lJMAX) ,K=lKMAX)
ID = 1 - boundary point with imposed temperature
in heat transfer region 1
ID = 2 - boundary point with imposed temperature
in heat transfer region 2
ID = 3 - isolated or symmetric boundary point
ID = 4 - interior node point
ID = 5 - as ID=1 if print is required
ID = 6 - as ID=2 if print is required
ID = 7 - as ID=3 if print is required
ID = 8 - as ID=4 if print is required
ID = 9 - point in a void region where no temperature
calculation is performed
Format (8F10.5)
RMAX, ZTOT ,PINPOUT, ALFA, CONVPl, CONVWP2, EXTPRE
maximum external radius for HP turbine rotor
maximum length for the HP turbine rotor
HP turbine inlet pressure at full load, before
first stage nozzle
POUT - HP turbine outlet pressure at full load
ALFA - time constant for metal transient temperature
CONVP1 - multiplier for heat transfer region 1
CONVP2 - multiplier for heat transfer region 2
EXTPRE - total steam pressure variation with load
RMA,
ZTOT
PIN -
-
109
Card 5
-
Format (8F10.5)
(TS(IJ),I=l,NDATA)
(PS(IJ),I=l,NDATA)
TS - steam temperature table
PS - steam pressure table
This card group should be repeated for the inlet
(J=l) and outlet enthalpy (J=2). The data should
be provided in increasing order, beginning with
the smaller pressure.
Card 6
-
For each power history the following cards should
be provided (NLOADH sets):
Format (F10.5,3I10)
TSTEP(J),NPOINT(J),NPRINT(J),ICARD(J)
TSTEP - time step for this power history
NPOINT - number of points for this power history
NPRINT - time values specified for printout
ICARD - program output option
Format (8F10.5)
(TIME(IJ) I=lNPOINT)
(FRAFP(I,J ,I=1,NPOINT)
TIME - selected time for this power history
FRAFP - fraction of full power for the selected
times
Format (8F10.5)
(TIMEPR(IJ),I=NPRINT)
TIMEPR - specified values of time for printout
110
Table 5.2
Input Data for the TURBINE Code
Steam Data (from Ref.20)
)
Inlet Enthalpy
Pressure
Temperature
(kPa)
( C
5660
4830
4140
3450
2760
2070
1790
1520
1380
1240
1100
690
350
270
260
252
241
229
214
206
198
194
189
184
174
162
Outlet Enthalpy
Pressure
Temperature
(kPa)
1380
1100
960
830
690
550
410
340
280
194
183
178
171
163
155
144
138
130
210
121
170
140
100
115
107
100
Inlet enthalpy: 2790 J/kg
Outlet enthalpy: 2580 J/kg
Material Properties (from Refs.21,22,23)
Young modulus: E = 2.07 x 105 MPa
6
Thermal expansion coefficient: o= 5.2 x 10Poisson ratio:
= 0.30
Density: ? = 4.53 kg/m3
Thermal conductivity: k = 0.17 W/cm C
High Pressure Turbine Data (from Ref.2)
RMAX = 105 cm
ZTOT = 200 cm
PIN = 5520 kPa
POUT = 1290 kPa
C
ill
Chapter VI
Ramp Rate Limitations
6.1. Introduction.
Results from the three areas
for a more
detailed analysis, will
selected in Chapter II
now be presented.
Information from the methods of Chapters III, IV and
V will
be used to form an overall picture of the load-following
behavior of a pressurized water nuclear reactor.
Fuel element ramp rate limits were shown to be strongly
history dependent. To begin this chapter, some considerations
concerning possible weekly cyclic duties for load-following
plants will be made. With the defined week load curves it is
possible, then, to judge the capability of the plant to
follow the load.
After the considerations about load-curves, numerical
results are presented for the reactivity control system, the
fuel element, and the turbine. The last paragraph will discuss
the overall behavior of the plant, when the considerations
are combined.
6.2. Weekly Load Curves for Load-Following Operation.
In
Chapter I, it was pointed out that typical ramp
rates for load-following duties are in the range of 5% per
112
minute, but nothing is said about the power ranges in which
this ramp rate is to be applied. The discussion of the dynamic
behavior of the fuel pellet-clad gap size, emphasized that
the capability of the plant to follow the load depends very
strongly on the details of the plants recent power history.
To evaluate properly the behavior of the plant we have,
therefore, to define specific load curves.
The load-curve used as the reference daily cycle /48/
for the dimensioning of the soluble boron system, considers
that power is reduced from 100% to 50% and returned
to 100%
with ramp rates smaller than 0.3% of full power per minute,
in the cycle 12-3-6-3 (that is, 12 hours at 100% power, then
3 hours to change power, then 6 hours at 50%, then 3 hours to
change). The cycle 18-6 is also considered in design
to
study rapid change capability /48/. In order to keep
the
ramp rates near the 5%/minute identified for load-following
operation, the cycle 18-0.2-5.6-0.2 will be analysed. This
cycle is displayed as cycle A in Figure 6.1. To some extent,
this cycle can be considered as a severe version of the
daily (non-Sunday) operation of the plant, which would
probably be done most days with smaller ramp rates. For this
and all the cycles here considered, it will be assumed that
the plant is operated at a lower power level during Sundays.
Another extreme load-following operation duty is to
consider that the plant is usually loaded only with the
minimum possible load. However it must still be available
113
to operate at full power within the time interval required
by the dispatcher. This would be typically the case mentioned
in Chapter I, when the plant is operating in a essentially
hydraulic system during the wet season. For this case we
can suppose that the plant assumes three diferent duties
throughout the day /42/:
-
Hot reserve period, from 5 a.m. to 5 p.m., during
which the plant should be able to go to full power within
one hour.
-
Instant reserve period, from 5 p.m. to 9 p.m., during
which the plant should be able to go to full power
in 15
minutes.
-
Cold* reserve period, from 9 p.m. to 5 a.m., during
which the plant is never asked to assume any power.
During Sundays, the plant is kept in cold reserve for
the whole day.
Considering that power is to be
changed no higher than a
5% per minute ramp rate, the minimum load to assure instant
reserve capability is 25%. For the hot reserve period we have
to consider that the plant is at least in the automatic control
range, which means no less than 15%. During the cold reserve
*The term cold implies no power production. It is not expected
that the plant is actually cooled during this time.
Figure 6.1
114
100
%Power
80
60
40
20
8.
4.
16.
12.
Load Curve A
20.
1
24.
Hours
100
%/Powe3
80.
60
-
Cold
Reserve
Instant
Reserve
Hot
Reserve
40
20.
3.
0
1
1
12.
16.
Load Curve B
2Q.
24.
20.
24.
100.
%Power
80.
60.
40
201
./
4.
8.
I
I
12.
16.
Load Curve C
115
period the plant can be kept at the hot-zero-power condition.
The load curve resulting from the above considerations
is called load curve B, and is shown in Figure 6.1.
The
actual load curve to be followed by the plant is not
necessarily cycle B, because the plant can be asked to assume
any load up to full load during the hot reserve or instant
reserve periods. Cycle B is the minimum power load-curve
that the plant should keep to assure its duty throughout the
week. A variation of cycle B, in which the hot and instant
reserve period minimum power levels are taken as 50% of full
power, called cycle C, will also be considered.
Note that, exclusive of shutdowns and returning the plant
in cold reserve on Sundays, the plant usage for the cycles
pictured are, in equivalent full power days per week, A=5.3,
B=0.7 and C=2.0.
6.3. Reactivity Control Systems Limitations.
The soluble boron reactivity control system behavior is
strongly dependent on the core burnup level, because the
total boron concentration is reduced gradually from the
beginning to the end of a fuel cycle. Both mode 1, with partlength control rods, and mode 2, without part-length control
rods, will be affected by the reduction
of
the reactor
coolant system boron concentration with burnup, but a
different behavior will be apparent, because mode 2 will
116
show a gradual loss of ramp rate capability, while mode 1
keeps the design ramp rate for most of the core life and,
when the boron concentration is relatively smallits capability
is drastically reduced for levels sometimes even smaller than
those of mode 2. This behavior is explained by the diversity
of duty of the boron dilution system in mode 1 and mode 2
operations. For large power reductions, for instance, while
mode 1 requires boron dilution to compensate for the xenon
buildup, in mode 2, depending on the ramp rate, boration can
be requested to compensate for the power defect which, in this
case, has to handled also by the boron system.
Several ramp rates have been analysed with the computer
code FOLLOW, for both operation modes and at different burnup
levels, in order to define the maximum ramp rates that
the
system is able to follow. A power history with two days of
operation was used as the reference for this ramp rate
analysis. The ramp rates are depending on the initial and
final power levels, and this dependence was analysed through
proper definition of the two-days power history.
Figure 6.2 and Table 6.1 list the results of the analysis.
The data as presented and considered here will be taken as
independent of the power history prior to the two days.
Although strickly not true, this can be considered as a good
approximation since xenon and iodine half lives are short
with respect to two days (9.2 hr and 6.7 hr, respectively).
117
Table 6.1
Reactivity Control System
Power Variations
(percent)
0
-
100
BurnupLevel
(percent)
00
20
40
60
80
100
0
-
50
00
20
40
60
80
100
50
-
100
00
20
40
60
80
100
100
-
0
00
20
40
60
80
100
100
-
50
Ramp
00
20
40
60
80
100
Rates
Node 1
Mode 2
(peroent/m"i)T
M (5%o/min)
M
M
M
M
<0.10
1*30
1.00
0076
0.53
0.24
<0.10
M
M
M
M
M
M
1.43
1.04
0.86
0.63
0.48
0.26
M
M
M
M
M
1.35
0.89
0.65
0.45
0.29
<0.10
<0010
M
M
0.52
0.35
0.15
<0.10
1.32
Mi
M
M
M1
0016
<0.10
1.00
0.71
0.49
0.24
(0.10
1039
1.22
0.65
0.41
0.26
<0.10
118
Operation Mode 1
5.0.
Ramp
Rate
(%/min
4.0
3.0
2.0
Operation Mode 2
1.0.
20
40
60
80
100
Percent Burnup
Figure 6.2
Ramp Rates for Reactivity Control Systems
( 0% to 100% full power maneuver)
119
6.4. Fuel Element Limitations.
If the behavior of only one fuel rod is analysed
with
respect to pellet-clad gap size and pellet-clad interaction,
a burnup dependence will be apparent: the first gap closure
will occur only after about 400 full power days of operation.
For reactor core operation beyond the first few cycles, we
have to consider that batches with different burnup
and
core residence time are operating. To be conservative, then,
we can impose the ramp rate limits of Table 4.4 as if the
reactor power peak were in a regionwhere first pellet-clad
contact already exists. This assumption makes the pelletclad interaction ramp rate limit burnup independent.
The first consideration now is to calculate the power
level for which the fuel rod can be taken as pre-conditioned
if the proposed load-curves are followed.
If we
apply
Table 4.4 to load-curves A, B, and C, Figure 6.3 results,
where it can be seen that the deconditioning rate is so small
relatively to the power maneuvers required to follow the
load, that the fuel rod will be conditioned for the highest
power level attained daily in the load curve, as long
as
the reactor is kept for at least three hours at this power
level. Three hours can be considered sufficient because each
time the required power level is reached, 50%
of
the
resulting stress is releived (stress relaxation factor,
from Table 4.4). With practically no deconditioning between
120
Figure 6.3
Fuel Pre-Conditioned Power for Load Curves A,Band C
............. 4
Fuel
pre-cond.
for 100%
(Load curve A)
9080-
7060.-
50-
-L---,
----...
40-
Fuel
pre-cond.
for 50%
(Load Curve C)
30Fuel
pre-cond.
for 25%
(Load Curve 1B)--
20-
10-
00-
Friday
Saturday
I
I
Monday
Sunday
I
121
one cycle and the next, after the
the
6 th
cycle of the week,
stresses existing at the first cycle would have
decayed to only 2% of the original value.
It is concluded, though, that the maneuvering table /37/
can be used directly to define the ramp rate limitations due
pellet-clad interactions as long as we take the maximum
power level attained daily for at least three hours, as the
fuel pre-conditioned power to be used in the table. We will
therefore use a preramp power
level as 100% (42 kW/m) for
curve A, 25% (10.5 kW/m) for curve B, and 50% (21 kW/m) for
curve C.
Other consideration to be made on the use of Table 4.4
is that it seems reasonable to consider that any percent
power variation between two lower levels than a specific
power maneuver of the table, can be made at least with
the
same ramp rate. This is a reasonable consideration because
the fuel temperature profile variation and the resulting
strain, will be bigger if the same percent variation is made
at higher power levels.
6.5. Turbine Limitations.
Turbine ramp rate limitations are not burnup dependent
and, although history dependent, it will be considered here
that a steady-state temperature distribution has been reached
at the beginning of each ramp rate analysis. Of course, this
122
assumption is not necessarily true for power histories with
relatively short periods of time at constant power levels,
but will be made here in order to keep inside reasonable
bounds the computer calculational time required.
Simulation of several power variations with different
ramp rates were imposed on the turbine high pressure rotor,
using the computer code TURBINE. The maximum stress
difference and the alternating stress intensity were, then,
calculated for each power maneuver, which will be dependent
on both the total power change and the ramp rate;
the
procedure used to estimate the fatigue life of the turbine
rotor, is taken from the rules for Class I components in the
ASME code /30/.
High pressure turbine rotors used in wet-steam are
reported to be made of steel alloyed with chromium,
molybdenum and vanadium /8/.
To estimate the impact of the
alternating stress intensities on the fatigue life of the
shaft, the ASME code design fatigue curve /30/ for ferrite
steels is used, and is reproduced here as Figure
6.4.
The rotor model contained in the computer code TURBINE
does not consider particularities
as, for instance, rotor
blades roots. Stress concentrations can occur at those points
which will be underestimated by the bare truncated cone used
in the model. From results of Hohn /9/,
the use of a stress
concentration factor of two seems to be appropriate
to
account for the particularities of rotor shaft not modeled.
( sto
-1 CLE S
FIG ti RE 6.4H
FA1U.cv*iV 1r- FERil/T
5T.L$(
,
. 30)
124
Table 6.2 presents, though, the resulting alternating
stress intensities for the ramp rates, where a stress
concentration factor of two have been employed. The allowable
number of cycles for each maneuver are also presented.
It is common practice to design and operate
large
turbine to withstand 10,000 cycles at least, throughout its
lifetime. Although the number seems to be small for turbines
operating in load-following and with 40 years lifetime
(14,600 total calendar days),thermal fatigue cracks propagate
slowly and are detectable during the maintenance of the
equipment. The shaft can be machined and the problem
corrected, as long as the structural behavior of the shaft
has not been affected.
The limiting ramp rates for the turbine operation are
here considered, though, as those liable to produce alternating
stress intensities compatible with a 10,000 cycles
fatigue
life.
To estimate the allowable ramp rates, Figure 6.5 can be
used, where the data from Table 6.2 is plotted, for
variations starting at the zero power level. The same procedure
could be followed for different power levels at the start of
the ramp and a general picture for the allowable ramp rates
for 10,000 cycles would be made. For our discussion here, the
data shown in Table 6.2 and Figure 6.5 will be sufficient.
Figure 6.6 presents the turbine ramp rate limitations for
load-following operation, based on the above assumptions.
125
Table 6.2
Turbine Analysis Results
Ramp Rates
0.10%/min
0.50%//min
1.00%/Min
5.00%/min
**
Power Variations
(percent)
0
0
0
0
iSalt
Number oI
Cycles
(MPa)
71,7
50
50
25
50
75
100
75
100
0
0
0
0
50
50
25
50
75
100
75
100
99.3
159.3
27,000
187.6
199.4
43.4
3,000
2,500
infinite
79.3
40,000
0
0
0
0
50
50
25
50
75
100
75
100
122.8
260.8
57.2
100.7
10, 500
2,700
1,500
1,000
105,000
21,000
0
0
0
0
50
50
25
50
75
100
75
100
138.4
7,100
220.8
1,700
950
610
75,000
11,000
79.3
80.7
80.7
28.3
37.9
194.5
233.9
275.3
313.9
70.3
117.9
Number of cycles calculated with stress concentration
factor of 2 applied to the alternating stress (Salt)
75,000
40,000
38,000
38,000
infinite
infinite
5,100
126
0.*4%/ruin
5.04/min
1.W0%/ruin
0. 3%/ruin
0.*2%/ruin
0. 5%/rir
-Q -
-
6L/min
'
100
Power
Change
M g80
70
60
50
MII
40
IIM~ilii
Nil
II
30
20
10
00
102
Cycles
Figure 6.5
Ramp Rate Influence on Cycles to Failure
(0% Initial Power)
127
Ramp
Rate
5.0.
(%/min)
4.0-
3.0'
2.0.
1.0.
0.0
I
20
I
40
60
I
I
80
100
Power Change from 0%
(/)
Figure 6.6
Turbine Ramp Rates for Power Changes from 0%
(10,000 cycles fatigue life)
128
6.6. Ramp Rate Limitations for the Plant.
From the previous paragraph, the overall picture of the
plant behavior can now
be drawn. To begin with, is important
to understand the magnitude of the ramp rate limitations just
developed and what would be the consequences if they
were
violated. For the reactivity control system, the ramp rates
shown in Table 6.1 are the maximum allowable due to physical
limitations on system
capacity. The same is not true
for
Tables 4.4 and 6.2, where the systems involved have sufficient
capacity to violate the ramp rates proposed, which are, only,
advisable limits in order to avoid or reduce the impact of
well identified problems.
The data presented and
discussed in the previous
paragraphs is replotted in Figure 6.7 to 6.9 in a form more
convenient to combine them in order to evaluate the overall
plant behavior. For those plots, the ramp rates are shown
as function of the initial power and the total power change.
Groups of points with about the same allowable ramp rate, are
joined and form a region in the plot defined by border lines.
The final power reached after the transient operation
is
defined for each point by the sloping line that passes
through the point and intersects equal initial power
power change
and
on the axes (for example, the sloping line for
Figure 6.7
100
Total
Power
9
Change 90
(percent)
129
Rea ctivity Control System Ramp Rates
(Operation Mode 2)
*ramp rates are in (/min)
-s
80
3
N
70
H
60 -R
50
40
30
20
0
N
1.e
2.0
-A
T
0
N
Beginning of Cycle
M (5.0)
10
00
I
,
I
I
40
20
60
S
0.
Y
70
60
50
N
C
-H
R
0.3
0
N
I
40
30
20
z
80% Through Q,ycle
0.
A
T
1-
I
0
N
1*5
10
00
100
Initial Power
(percent)
100
Total
Power
Change 90
(percent)
80
80
M
a
20
40
60
80
100
Initial Power
(percent)
130
Figure 6.8
Fuel Element Ramp Rates
100
Total
Power
Change
*ramp rates are in (N/min)
80
S
60 -y
40
100% Power Pre-Conditioned
(Load Curve A)
N
-C
H
R
M(5 .0
20
00
I
I
20
100
Total
Power 80
Change
(M)
60
40
40
60
80 100
Initial Power (%)
0.5*
1.3
S
N
C
50% Power Pre-Conditioned
(Load Curve C)
H
M
20
00
20
40
60
80 100
Initial Power (M)
100
Total
Power 80
Change
M%
0010
0.25
S
0.50
1.30
60 -Y
40
20
00
N
C
H
R
- 'U
25% Power Pre-Conditioned
(Load Curve B)
40
60
80 100
Initial Power (%)
131
Figure 6.9
Turbine Ramp Rates
*ramp rates are in (%/min)
100
Total
Power
90
Change
(percent)
80
S
y
70
0.3
C
60
-H
R
50
40
N
I
z
A
30
20
M (5%/min)
T
I
0
N
10
00
I
20
40
60
80
100
Initial Power
(percent)
132
for 100% final power is provided on all
plots). For all
the
plots, turbine synchronization precludes operation of the
plant, for the purpose of this thesis, at power levels
smaller than 15% of full power.
Of course, only the general trends of the plant behavior
are intended to be covered here. The conditions selected to
be plotted in those graphs, are considered as representative
of the difficulties to load-follow with the pressurized water
nuclear reactors, as perceived here. So, only mode 2 operation,
with no use of the part-length control rods, is considered
in the plots, where two representative burnups are shown.
For the fuel pellet-clad interaction ramp rates,
the data
selected is representative for the analysis of cycles A, B,
and C.
Some general comments about the behavior of the
ramp
rate limitations of each specific area, are well worth
considering:
-
Figure 6.7 for the reactivity control system in mode 2,
shows well the difficulty resulting from the limitations on
the part-length control rods use. Only a relatively small
region is left to operate at the desirable ramp rate of 5%/min
which is further reduced with core depletion. By 80% of the
core life, some power maneuvers can take as long as 8 hours
to be executed.
133
-
Figure 6.8 for the fuel element, shows the impact of
a convenient fuel preconditioning level
on the ramp rate
capability of the plant due pellet-clad interactions. When
the pre-conditioned power level decreases from 100%
25%, the ramp rate capability is also reduced from
to
the
desired 5%/min ramp rate to 0.1%/min, which would impose
15 hours to attain full load from 15% of full power and
destroy the concept of hot reserve as idealized
in cycle B.
- The shape of the curves presented in Figure 6.9 for
the turbine operation, is probably the least restrictive of
all, because only relatively big power maneuvers are limited
to smaller than desirable ramp rates. It seems
that
sufficient room is left for load-following, as long
as
very demanding cycles, like load-curve B, are avoided.
Let's now combine the limitations imposed by fuel
element, reactivity control system, and turbine, using the
corresponding plots 6.8, 6.7 and 6.9. The resulting
Figures 6.10 to 6.12 show the overall ramp rate limitations
to be applied for the plant operation to follow that specific
power history and at the burnup level analysed. From the
plots it is apparent the influence of each one of the three
mechanisms involved here in the discussion of the ramp rate
limitations.
The ramp rate limitations for each power history can
134
Figure 6.10
Plant Ramp Rate for 100% Power Pre-Cond.
*ramp rates are in (%/min)
100
Total
Power
Change
M
go
80
S
70 -
0.
N
C
60 - H
0.3
Load Curve A
R
N
40
1
.
50
0.
A
80% Through Cycle
1.0
30 - T
I
N
10
M (5.0)
20
60
40
o
100
Initial Power (/)
100
Total
Power
Change
(%o)
90
80
S
70 - Y
60
N
C
O.3
H
R
.4
50 - 0
N
40 - I
.0
Load Curve A
.5
A
2.0
Beginning of Cycle
30 - T
I
20 - 0
N
10
00
20
40
60
80
100
135
Figure 6.11
Plant Ramp Rates for 25% Power Pre-Cond.
*ramp rates are in (%o/min)
100
Total
Power
Change
90
(fo)
Load Curve B
80
S
Y
70 -N
C
60
-H
R
0.
0
50
0
.
0
N
I
e5
40 -z
080% Through Cycle
A
1.0
30 -T
I
1.5
0
N
20
10
M (5.0)
00
I
i I
60
40
20
100
80
Initial Power (%)
100
Total
Power 90
Change
M
80
_
Load Curve B
S
Y
70 -N
C
60
50
40
30
20
0.
0.
R
0
-N
I
z
A
T
00
*0
Beginning of Cycle
0.
I
0
N
3*
M
00
-
10
20
40
60
80
100
Initial Power (M)
136
Figure 6.12
Plant Ramp Rates for 50% Power Pre-Cond.
*ramp rates are in (%/min)
100
Total
Power
Change
MI
90
80
S
70
N
C
60 - H
R
50 - 0
N
40
02Y
0.3
Load Curve C
0
0.
z
80% Through Cycle
A
30-
T
20-
0
N
1.
10 -
M (5.0)
1*
00
20
40
60
80
100
Initial Power (%)
100
Total
Power
Change
(%o)
90
80S
70605040 3020-
N
0.3
3
CN0
H
R
0
N
Load Curve C
0
100
z
A
T
I
Beginning of Cycle
N
10001
20
40
60
80
100
Initial Power (M)
137
now be studied. A load curve will involve different
power
variations, each one with a specific position in the plot
and a ramp rate limitation. A representative point, which
can be defined as the one with smaller ramp rates for
instance, should be selected. The locus of representative
points for load-curves A, B, and C are plotted in the
convenient graph and will be used to support the conclusions
of this work, presented in Chapter VII.
138
Chapter VII
Conclusions and Recomendations
7.1. Conclusions.
The major conclusion of this study can be stated
by
reviewing our approach and the data and the discussion
presented in the last chapter:
- we adopted representative pressurized water reactor
plant characteristics;
- we defined a set of desirable load-following
operating cycles that would fit with at least one utility's
power demands;
- we considered a set of restrictions (from regulatory,
equipment capacity, and mechanical integrity considerations);
-
we performed a set of simplified (but plausible)
calculations;
-
and
we found that the plant so defined cannot operate in
the desired manner without violating one or more restrictions.
Cycles A, B, and C, intended to be followed with ramp
rates of 55/min, are in general not able to support
variations at levels even one order of magnitude smaller.
Although fuel element behavior has been pointed out as a
major restriction for load-following, load curve A did not
present any limitation due to fuel behavior. Other consider-
139
ations prevented curve A from being followed with reasonable
ramp rates except at the beginning of core life.
It seems clear, though, that even in case of a convenient
fuel pre-conditioning,
or more idealistically, if the fuel
element restrictions were removed, which would allow the
operation of the fuel rods with high ramp rates,
other
restrictions should be analysed. If a power history possible
to be handled efficiently by the turbine is selected, and no
fuel lement restriction is considered, which is the case for
Figure 6.10, still something must be done with respect to the
core reactivity control system.
If pressurized water nuclear reactors are to be used in
load-following at all, it will be necessary, first, to
increase its safe ramp rate capability to levels compatible
with the cyclic operation scheme demand.
Some
plant
modifications will probably be required, and even a specific
load-following system design is also to be thought as a
reasonable approach, since, as discussed before, both baseload and load-following impose particular requirements on
plant behavior.
7.2. Considerations About Plant Load-Following Capability.
By comparing the three areas of difficulty considered
here, it seems reasonable to identify the reactivity control
limitations as the most restrictive item. Without improvement
140
here, we cannot begin even a moderate effort on load-following
with pressurized water nuclear reactors. If the present
knowledge of the fuel element behavior proves to be correct,
the pellet-clad interaction and the turbine limitations can be
lived with, in case of a power cycle not too demanding. It
is important to remember, however, that the reactivity control
model used here is very simple and no analysis is made of
the possibility to use the moderator temperature feedback
as an additional control mechanism.
Based on the data presented here, it seems reasonable to
suggest that the increase of the capacity of the boron dilution
system is desirable. This is a logical way to
increase the
reactivity control capability without deviating from the
constant axial offset control. In this particular, safety
related aspects should be considered, because increasing the
dilution system capability for end-of-life operation,
result in excessive core reactivity insertion
can
from boron
dilution at the beginning of life.
The high pressure turbine limitation should be handled
if load curves as the cycle B
are to be
followed.
The
discussion on the control schemes for turbines, presented
in Chapter V, showed the temperature variations imposed on
the rotor, due either to throttling of the steam ot to partial
admission, to be a major effect. If by-pass
governing were
used, the rotor temperature variatione could be reduced by
choosing an appropriate distribution of the by-pass flows and
141
intake positions along the turbine expansion line.
Fuel pellet-clad interaction research must be continued
in order to improve the knowledge and reduce the uncertainties
on fuel behavior. Based on present understanding of the
pellet-clad mechanical and chemical interaction phenomenon,
ramp rates were suggested that are expected to avoid ramp
failure difficulties. New results may (or may not) show that
excess conservatism have been introduced in the analysis.
However, modifications of fuel element design in order to
improve its ramp rate capability can be justified even in case
of a loss of efficiency or plant power rating, if the economical
incentives for load-following justify them. The change of
the cladding or the use of surface coating either on the
pellets or on the cladding internal surface, can then be
looked as possible paths.
Of course, there is a price to pay for a specific loadfollowing design. The benefits accrued from the optimization
of the system due load-following operation of the pressurized
water nuclear power plants, should be sufficient to pay for
specific modifications of the plant, to make it a real loadfollowing unit.
7.3. Recommendations for Continuing and Supplementing this Work.
-
Improve in the core reactivity control model, which
uses a zero-dimension calculation. A one-dimensional model
142
would be much more appropriate to calculate control rod
positions and critical boron concentration, than the present
approach of curve interpolation of typical data.
-
The reactivity effect of the reactor coolant
temperature variations can be used to reduce the actuation
of the soluble boron system and should be analysed.
-
The liquid and gaseous waste disposal system behavior
should be analysed in order to verify the impact
of the
additional tritium generation and of transient operation.
-
The possibility of by-pass governing for wet-steam
turbine can be investigated.
-
It should be analysed with greater detail the
operation of the plant in the hot-zero-power condition
and the difficulties of going to a greater number of
synchronization operation for the turbine-generator group
-
The possibility and consequences of an increase in the
boron dilution system capability can be investigated.
- The experimental verification of the ramp rates
considered here for the fuel elements should be made.
143
APPENDIX
1
Listing of Computer Code
FOLLOW
C
C
C
C
FOLLOW
*
**********************************
*********************************
C
C
C
C
,
DIMENSION POTEN(50),TIME (501 ,RRSYST(143) ,FREIN (100) ,rT IT LE (2 0)
DATA SIGAXE,FLUXFP,YIELDXYIELDYDECAYYDECAYX/2.7E -18,1.08E 17,
10.00 3,0.064,0. 10 33, 0. 0752/
DATA FREIN/.001, .002,.003,.004,.005,.006,.007,.008, .009,.010,.011,6
A.012,.013,.0 14,.015,.0 16,.017,.018,.019, .020,.021,. 022,. 023 ,.024
B.025, .026, .027,.028,.029,.030,.0 32,.0 34,.036,.038,. 040,. 042,.0440,
C.046,.048,.050,.052,.054,.056,.058,.060,.062,.064,.
066,. 068,.070,
D.073,.076,.079,.082,.085,.090,.095,.100,.105,.110,r. 118,. 126,.134,
E.142,.150,.160,.170,.180,.190,.200,.213,.226,.239,.
252,. 265,. 287,
F.309,.331,.353,.375,.415, .455,.495,.535,.575,.622,. 669,. 716, .763,
G.810,.832,.854,.876,.898,.920,.936,.952,.968,.984,1 .00/
DATA VOLUMECONDILFLOWDICONBORFLOWBO/76000.,10., 7200. ,22000.,
1660./
1000 WRITE(6,1001)
1001 FORMAT(1H1)
TEP=0.
TEMP1=0.
ISAI=0o
IPRINT=O
TPRINT=3.
READ (5, 1009, END=17) (TITL,(I) ,I=1,20)
READ (5,1 ,END=17) NPONTSMODE
1 FORIMAT(8110)
READ(5,2) BURNUP
P EA D (5,2) (TIME (I) ,I=1, NPONTS)
READ (5,2) (POTEN(I),I=1,NONTS)
2 FORMAT(16F5.1)
IS ',I1,/////,46X, 'POWER
HISTORY
)
WRITE (6,1010) (TITLE (I) ,I=1,20)
WRITE(6, 1002) MODENPONTS
OMAT(/////,50X,'OPERATION MODE
10002
1HAli1 , v12, POI NTS r,/,53Xv (T IMErPOW. FF) I
Hj
. . ......
.. ....
...........
................................
DO
1004 I=1,NPONTS,4
WRITE(6,1003)
TTME(I),POTEN(I),TIME(I+1),POTEN(I+1),TIME(1+2),
1POTEN (1+2) ,TIMEII+3) ,POTEN(I+3)
1003 FORMAT(30X,4('(',F6.2,',,F4.2,')'))
1004 CONTINUE
WRITE (6,1005) BURNUP
1005 FORMAT(/////,46X,'CORE BURNUP FRACTION IS
',F4.2,/////)
CALL QUEIMA(BURNUPRPOWEO,ALF3OR,RRODDRRODCRRODPL,
1CBOROE, RXENOOR3DBRRSYSTFReIN)
RPODDO=RRODD
RRODCO=RRODC
RRODBO=RRODB
RRPLO=RRODPL
WRITE (6,1006)CBOROERPOWEOALFBOR
1006 FORMAT(30X,'CRITICAL BORON CONCENTRATION',1OX,'COLD-TO-HOT REACTIV
1ITY',/,30X, ' (EQ.XENON - HOT FULL POWER)',15X,'(POWER D!FECT)v,/,
239X, F6.1,'
PPM',25XF6.1,'
3TY COEFFICIENT IS',F5.1,'
PCM',/////,34X,'SOLUBLE BORON REACTIVI
PCM/PPN',/////)
WRITE(6,1007)RRODB,RRODC, RR3DDRRODPL
1007 FORMAT(38X,'TOTAL REACTIVITY (PCH) - CONTROL ROD GROUPS',/,32X,
1'B - tF6.1,5X,'C
- ',F6.1,5X,'D - ',6.1,5X,'PL - IF6.1)
VRITE(6,1001)
C=SIGAXB*FLUXFP
A=C*YIELDY
B=C*YIELDX
FRAFP=POTEN(1)
YODO=FRAFP*A/DECAYY
XENON=FRAFP* (A+B) / (FRAFP*C+DECAYX)
XENONO= (A+B)/(C+DECAYX)
RX3NON=RXENOO*XENON/XENONO
RPOW 8R=FRAFP*RPO WEO
PCHANX=PXENOO-RXENON
RCHA P=RPOWEO-RPOWE R+RCHANX
WRITS(6,1008)
1008 FO1hAT(///,29X,'POSTIO-CONT0L RODS',6X,'REACTIVITY OF CONTROL R
101)3',9X,'CONCENTRATION OF BORN',/12X,'TIME',4X,'POWER',9X,' (INSER
.
......
. . ......
.
.
..........
..........................
2TION) ',21X,'(PCM)
,29X,' (PPM)',/12X,'(HR)I,3X,'FRACTION',4X,'B',4X
3,'C',4X,'D',4X,'PL',7X,'B',6X,'C',6X,'D',6X,'PL',3X,'TOTAL',3X,'CR
4ITICAL MAX.DIL. MAX.BOR.',/)
1009 FORMAT(20A4)
1010 FORMAT(///,30X,20A4)
CALL OPERA(MODtFRAFPTEMPRPOWER,RXENONISAI,
1CBOROECBOROTPPODD,PRODCPRODPLXENONYODORCHANPALFBOR,
2RRODDORRODCORRODBORRPLORCHANXRRSYSTFREIN,
3TEMP1,YOLUMECONDILFLOWDI,CONBORFLOWBO)
DO 16 I=2,NPONTS
IF(POTEN(I)-POTEN(I-1))3,6,3
3 DELT=0.05
DPOTEN= (POTZN (I) -POTEN (I-1)) *DELT/(TIME(I) -TIME(I-1))
IF(DPOTEN) 4,6,5
4 ITEST=O
GO TO 7
5 ITEST=1
GO TO 7
A
DELT=1.05
DPOT?=0.
ITFST=2
7 TFMiPO=TEM?
TE M P=T3MP+D 1T
FRAF?=FRAFP+DPOTEN
IF (IT EST-1) 8,10,11
8 IF(FRAFP-POTEN (I))9,9,11
9 FR AFP=POTEN (I)
DELT=TIME (I) -TEMPO
TEMP=TIN (I)
IPRINT=1
GO TO 12
10 IF(FPAFP-POTE N(1))11,9,9
11 IF(TFMP-TIMF(I)) 12,9,9
12 CALL jKUTTA (FPArP,XENON,YODO,A,3,C, DzrAYY, DECAYXDELT)
I(TTMP-TPRI NT- .95) 13,14,14
13 IF(CIPRINT) l7,7,14
14 CONTINUE
RXENON=RX RNOO*XENON/XENONO
RPOWER='PAFP*RPOWEO
FCHANX=RXENOO -tRXENON
R CH ANP=RPOWEO-RPONER+RCHA NX
CALL OPERA(MODEFPAFP,TEMPRPOERRXEON,ISAI,
1CBOROE,CROROTPRODDPRODC, PRODPLXENONYODORCHANP,ALFBOR,
2RJRODDO, RRODCO, RRODBORRPLORCHANX, RRSYSTFREIN,
3TEIP1,VOLU ME,CONDILFLOWDICONBOBFLOWBO)
IF(ISAI.EQ.1) GO TO 1000
TPRINT=TEMP
IF(IPRINT) 17,7,16
16 IPRINIT=O
GO TO 1000
17 STOP
END
SUBPOUTINE RKUTTA(FRAFPXENONYODOABiCDECAYY,DECAYXDELT)
AA= A*FR AFP
BB=B*FRAFP
CC =C* FR A FP +DECAY X
AK11=AA-DECAYY*YODO
A K12=BB+DECAYY*YODO-CC*XENON
AK21=AA-DECAYY* (YODO+AK11/2.)
AK22=BB+DECAYY*(YODO+AK11/2.)-CC* (XENON+AK12/2.)
AK31= AA-DECAYY* (YODO+AK21/2.)
AK32=BB+DECAYY*(YODO+AK21/2.)-CC*(XENON+AK22/2.)
AK4 1= AA-DECAYY* (YODO+AK3 1)
A K42=BB+DECAYY*(YODO+AK31)-CC*(XENON+AK32)
YODO=Y1 DO+ (AK11+2. * AK21+2.*A K31+ A K41) *DE LT/6.
XENON=XENON+ (AK 12+2. *AK22+2. *AK 32+AK 42) * DELT/6.
PETURN
END
SUBROUTINE QUEIMA(BURNUPRPOcEOALFBORRRODD,R RODC,RRODPL,
1CBOROE, RXENOO,RRODBRRSYST,FREIN)
DIMENSION wREIN(100), RRSYST(143)
CXENOO=310.
IF(BURNUP.GT.O.15)
GO TO
1000
ALFBOR=8.96-BUPNUP*1.60
GO TO 1002
1000 IF(BURNUP.GT.0.38) GO TO 100 1
ALFBOR=8.72
GO TO
1002
1001 ALFBOR=8.72+(BHRNUP-0.38)*1.06
1002 CONTINUE
RXENOO=CXENOS*ALFBOR
RPOWEO=140 0 .+BURNUP*700.
CBOROE=980.*(1.-BURNUP) + 10.
RRODD= 1010.
PRODC=1500.
R RODB=900.
PRODPL=250.
DO 5 I=10,143
co
=.- ......
.
............
m
w
w
IF(I.GT.40) GO TO 1
RRSYST (I) =RRODD*FRPIN (I) +R RODPL* (FREIN (1+50) -F REIN (1+25))
GO TO 5
1 IF(I.GT.43) GO TO 2
RRSYST(I)=RRODD*FR-I- (I) +RRODPL* (FREIN(90) -FREIN (65))
GO TO 5
2 IF(I.GT.86) GO TO 3
+
PRSYST (1)=RRODD*FREIN(I) +RRODPL* (FR EIN (90) -FREIN (65) )
+
1 RRODC*FREIN (1-43)
GO TO 5
3 IF(I.GT.100) GO TO 4
RRSYST (I)=RRODD*FREIN (I) +RRODPL* (FREIN (90) -FREIN (65) )
+
1RRODC*FREIN(I-43) +RRODB*FREIN (1-86)
GO TO 5
4 RRSYST (I) =RRODD+RRODPL* (FREIN (90) -FREIN (65))
1 RRODC*FREIN (1-43) +R RODB*FREIN (1-86)
5 CONTINUE
RETURN
END
OPER A (MODE, FRAFPTEMPRPOVER, RXENONISAI,
SUBROUTINE
1CBOROECBOROT,PRODDPRODC,PRODPL,KENONYODORCHANP,ALFBOR,
2RRODDO, RBODCORRODBORRPLORCHANX, RRSYST, FREIN,
3TEMP1, VOLTJE, CONDIL,.?LOWDICONBORFLOWBO)
DIMENSION FREIN(100),RRSYST(143)
IF(MODE-1) 12,2,1
1 PRODD=0.6-FRAFP*0.5
T=100. *PRODD
RRODD=FREIN (I) *RRODDO
RRODPL=O.
RRODC=0.
PPO DB= 0.
PROD PL=O.
PRO DC= 0.
PRODB=0.
RRODT=RRODD
P qORON=PCHANP-1R00T
...... .......
......
.. .......
CBOROT=CBOROP+ RBORON/ALF BOR
GO TO 9
2 CBOR0T=CBOREk+RCUANX/ALFBOR
RRODT=RCHANP-RCHANX
DO 3 I=10,143
IF(RRSYST(I)-RRODT)3,4,4
3 CONTINUE
4 IF(I.GT.40) GO TO 5
PRODD=FLOAT(I)/100.
PRODPL=FLOAT (1+50) /100.
PRODC='.
PROD3=0.
RRODD=FREIN(I)*RRODDO
PRODPL=(*FRElIN(1+50) -FREIN (1+25)) *RRPLO
RRODC=0.
PROD8=0.
GO TO 9
5 I?(I.GT.43)
GO TO 6
PRODD=FLOAT(I)/100.
PRODPL=0.9
PRODC=0.
PRODB=O.
RRODD=FREIN (I) *RRODDO
PRODPL=(FREIN(90)-FREIN(65)) *RPPLO
RRODC=0.
RRODB=O.
GO TO 9
6 IF(I.GT.86) GO TO 7
PRODD=FLOAT(I) /100.
PRODPL=O.9
PRODC=FLOAT(I-43)/100.
PRODB=0.
RRODD=FREIN(I)*RRODDO
RRODPL= (FREIN (90) -FREIN (65)) *?PPL)
RRODC=FRel N (I -43) *RPODCO
PRODB=o.
H
0
'Ji
GO TO 9
7 IF(I.GT.100) GO TO 8
PRODD=FLOAT (1) /100.
PRODPL=0.9
PRODC=FLOAT (1-43)/100.
PRODB=FLOAT (1-86)/100.
RRODD=FRPIN (I) *RRODDO
RRODPL= (FREIN (90) -FREIN(65)) *RRPLO
RRODC=FREIN (I-43) *RRODCO
PROD B=FREIN (1-86)*RRODBO
GO TO 9
8 PRODD=1.0
PRODPL=0.9
PRODC=FLOAT (1-43) /100.
PRODB3=FLOAT (I-86) /100.
RRODD=RRODDO
PRODPL= (FREIN (93) -FREIN (65)) *RRPLO
RRODC=FREIN(I-43)*RRODCO
PODB=FRE1N (1-86) *RRODBO
9 CONTINUE
PRO DT=RRODB+RRODC+RRO DD+RRODPL
IF(TEMP-0.001) 10,10,11
10 CBORO1=CBOROT
11 CONTINUE
DITEM=TEMP-TEMP1
AUX=EXP (-PLOWBO*DITE 1/VOLUME)
CBOMAX=CONBOR* (1.-AUX)
+CBORO 1*A UX
AUX=1EXP (-FLO WDI*DITTEM/VOLtTME)
CB014IN=CONDIL* (1. -AUX) +CBOR0 1*AHX
WRI TE (6, 13) TEIP, FRAFP, PRODB, PRODC,PRODD, PRODPL, RRODB3, RRODC, RRODD,
1RRODL ,RODT, CBOROT, CBOMIN,C BOM!AX
GO TO 14
IF(C9OROT.LT.CBOMIN.OR.CBCROT.GT.CBOMAX)
T iMP 1=T EMP
CL30%1=CBOROT
12 CONTINUE
13 FORMAT(10XF6.2,3XF5.2,5X,4(FS.2),2X,5(F7.1),4XF6.1
,3X,F6.1 ,3X,
HJ
'I
..........
mw
lw
w
1F6. 1,/)
RE TU RN
14 WRITE(6,15)
15 FORMAT (/////,10X,'TH2 REQUIRED OPERATION IS NOT POSSIBLE DUE INSUF
1FICTIENT CAPACITY
ISAI=1
RETURN
END
IN THE SOLUBLE
BORON SYSTEM')
I-
..........
.. ..........
....
. ....
I'll,
................
...........
- 'w- ..
.........
...
............
..
153
APPENDIX
2
Listing of Computer Code TURBINE
--
-l
.
- ....... ................
.....
.....
:.:""
-
..............
III = I. JI
il LSd7=1 H
(31r
14 QV 0 7N*L=)iVI 63 0(
a. /a/ v riv =vs
al/o= (W' ED
a/v= Mc z
a/(Oa+v) =(r) t
D** l+i+V* *id
ZI*ZH*H=R
an* (L'0 =11
ZkI/L01~ z= Zf
L /XVWV= aN
(WnloDN
*6R 'ItNK 'alS4 'allll
'XVWa'~ln0d*NdSdS
till
1Vla'XVW1)'XYW"daI)
091 M3'NIddK Bd
WII
*Ati0JZ
'ily
N49ig~
L
9s atumadi
(08) ;)* (08) ti
S(ozz)wva~ls.L
oe)
(08)
09
(ORl) to " (0 0
09) ddaI* (OZZo1)
-(0 L) I 0drN'( *00Sd'('* 0)SJ'(OU
GI
advo l
R40ispiawi(
3HG
3
AUX=HR*HR*HZ*HZ/2./NLFA/(HR*HR+HZ*HZ)
GO TO 4
IF(HT.LT.AUX)
WRITE(6,3) AUJX,IJK
3 FORMAT(IOX,'TIME STEP HAS TO BF SMALLER THAN ',F7.4,'
1ENCY IN LOAD HISTORY ',I3)
GO TO 9
4 TIME1=TIME(1,IJK)
FOR CONVERG
FPAFP1=FRAFP (1,IJK)
IXPANS(FRAFP1,PINPOUTTSPS,NDATA,NZKMAXTSTEAM)
CALL
CONVP1,CONVP2,TBOUNDIBOUND,
TEMPME(TSTEAM,ID,
CALL
1KMAX,JMAX)
CALL TEMPSS(TSTEAMTBOUNDIBOUNDC1,C2,C3,ID,JMAXKMAX,
1ITrRMITERCONVTT1)
IHIST 1
OUTPUT(IDPRJMAXKMAXIHISTTFRAFP1,TIMElICARD,1,
CALL
1HPhZ,ITER,TITLENPRINTIJKNLOADHNSTP,NNEWN9,NCOLUM)
NPHIST=NPOINT (IJK)
NPPIN1=NPRINT(IJK)
IPRINT=1
LT.HT) IPINT=2
IF(TIMEPR(1,IJK)
DO 8 IHIST=2,NPHIST
DFRAP=(FRAFP(IHIST,IJK) -FRAFP(IHIST-1,IJK)
1TIME(IHIST-1,IJK))
)/(TIME(IHISTIJK)-
5 HT=HT1
TIME1=TIME1+HT
IIFLAG=0
I FLAG=0
IF(TIME1.GE.TIME(IHIST,IJK)) IFLAG=1
IIFLAG=1
IF(TIME1.GF,.TIMEPR(IPRINT,IJK))
GO TO 7
GO TO 6
Vn
.
............
....
...
..
...........
......
.
.....
.......
.
6
IF(IIFLAG.EQ.0.AND.IFLAG.EQ.0)
IF(IIFLAG.EQ.O.AND.IFLAG.F.Q.1)
HT=TIMEPR(IPRINTIJK) -TIME1+HT
TIMNl1=TIMEPR(IPRINT,IJK)
IPRINT=IPRINT+1
IF(IFLAG.EQ.0) GO TO 7
HT=TIIE(IHISTIJK)-TIME1+HT
TIM E1=TIM,(IHISTIJK)
7 FRAPP1=FRAFP1+DFRAFP*HT
EXPANS (FRAFP1,PINPOUT,TSPSNDATANZKMAXTSTEAM)
CALL
TEMPME(TSTEAM,IDCONV?1,CONVP2,TBOUND,IBOUND,
CALL
1KMAX,JMAX)
CALL
TEMPTR(TBOUNDIBOUNDC4,C5,A,C,HTIDJMAXKMAX,T,T1)
IF(IFLAG.EQ.O.AND.IIFLAG.EQ.0)
IF(TIMSI.LT.O.) TIME1=0.
GO TO 5
OT PUT(IDPRvJMAXKMAX,IHISTTFPAFP1,TIME1,ICARD,2,
CALL
1HRHZITER,TITLENPRINTIJK,NLOADH,NSTENNEW,N9,NCOLUM)
IF(IFLAG.EQ.1) GO TO 8
GO TO 5
8 CONTINUE
9 CONTINUE
GO TO 1
IF(NTCASE.EQ.1)
STOP
END
BEGIN(ID,IDPR,JMAX,KMAX,NDATA,TS,PSPIN,POUTRMAX,
SUBEOUTINE
1ZTOTALFA,CONVP1,CONVP2,NLOADHNPOINTTSTEPTIMEFRAFPITERM,
2CONVTI MvPRNPRINTICARDIBOUND,TITLENSTENNEWN9,NCOLUM)
CCMMON/OVER/OVERR
DIMENSION ID(80,220),IDPP(80,220) ,TS(30,2) ,PS(30,2),NPOINT(10),
1TSTEP(10),TIME(10,10),FFAFP(10O,10),TIM EPR (20,1O),NPRINT(10),
21CARD(10) ,TITLE(20) ,NCOLUM(220)
(TITLE(1) ,=1,20)
PEAD(5,1,END=42)
1 FORMAT(20A4)
1EAD(5,2)JMA!,KMAXNDATANLDADH,ITERMCONVOVERR
2 FORMAT(5I10,2F10.5)
IBOUND=O
N9=0
DO 16 K=1,KMAX
READ(5,40) (ID(JK),J1,JJMAX)
DO 16 J=1,JJMAX
ID123=ID(J,K)
GO TO
(3,5,7,10,11,12,13,14,15) ,ID123
3 IDPR(J,K)=2
4 ID(JiK)=1
IBOUND=IBOUND+1
GO TO 16
5 IDPP (J,K)=2
6 ID(J,K)=2
IBOUND=IBOUND+1
GO TO 16
7 IDPR(JK)=2
8 IF(K.EQ.1.OR.ID(J,(K-1).GT.6)
IF(J.NE.l.AND.ID(J-1,K).EQ.7
IF(ID(JK).NE.4) ID(J,K)=3
GO TO 16
9 IF(K.FQ.1.OR.ID(JK-1).EO.8)
IF(ID(JK).NE.5) TD(JK)=6
GO TO 16
10 IDPP(JK)=2
ID(J ,K)=7
GO TO 9
ID (JK)=4
1 D(J , K) =5!
H
.
: ....................
....
.........
GO T0
16
11 IDPR(JK)=1
GO TO 4
12 IDPR (JK)=1
GO TO 6
13 IDPI (JK)=1
GO TO 9
14 IDPR(JK)=1
ID(J,K)=7
GO TO 16
15 IDPR(J,K)=2
ID(JK)=8
16 CONTINUE
17
READ(5,17)RMAXZTOTPINPOUTALFACONVP1,CONVP2
FORMAT(8F10.5)
DO 18 J=1,2
READ(5, 17) (TS (IJ)
,I=1,NDATA)
READ(5,17) (PS(IJ),I=,NDATA)
18 CONTINUE
DO 20 J=1,NLOADH
READ(5,19)TSTEP(J),NPOINT(J)
,NPRINT(J),ICARD(J)
19 ?ORMAT(F10.5,3I10)
NPT=NPOINT (J)
NPR=NPRINT (J)
READ(5,17) (TIME(I,J),I=1,NPT)
READ(5,17) (FRAFP(IJ),I=1,NPT)
READ(5,17) (TIMEPR(IJ) ,I=1,NPR)
20 (ONTINUE
WRITE(6,21) (TITLE(I) ,I=1,20)
21 FORMAT(1H1,////20X,20A4)
WRITE (6,22) JMAXKMAXNDATAvLOADHITEPM ,CONV,OVERR
22 FORMAT(//,30X,'NODES IN RADIAL DIRECTION ',I4,
1/30X,'NODES IN AXIAL DIRECTION ',14,
2/30X,'NUMBER OF POINTS IN STEAM TABLES ',14,
3/30X,'NNMBER OF LOAD HISTORIES',I4,
4/30X,'iMAXIMUM ITE37TION FOR STEADY STATE TEMPERATUR7
',I4,
-
- - .
.1.1 1 .1 - -
- I
I
. , -
-
1
.1
.." I . 11:,-
-
I -
-
.
"I'll
....
...
......
.....
- .1.. .
. ... .......
-
C0
5/30X,'CONVERGENCE
CRITERION
FOR STEADY
STATE TEMPERATURE',
F6.3,
6/30X,'OVER-RELAXATION FACTOR FOR SYEADY STATE TEMPERATURE',F6.3)
23
WRITE (6,23)
FORMAT(/////,20X,'NODE NUMB7RING SPECIFICATION',
1/25X,'ID= I OR 2
2/25X,'ID= 3 TO 6
BOUNDARY NODE WITH SPECIFIED TEMPERATURE',
BOUNDARY NODE WITH ZERO HEAT FLUXI',
-
3/25X,'ID=
7
INTERIOR NODE',
4/25X,'ID=
8
EXTERNAL NODE (NOT CONSIDERED)',/)
DO 24 K=lKMAX
24 WRITE(6,39) (ID(JK),J=1,JTMAX)
WRITE(6,25)PIN,POUTRMAX,ZTOT,ALFA,CONVP1,CONVP2
25 FORMAT(/////,40X
'PIN
',F8.1,/40X,'POUT
',F8.1,
1/40X,'RMAX ',F8.1,/40X,'ZTOT
',F8.1,
2/40X,'ALFA vF8.1,/40X,'CONVPl',F7.1,/40X,'CONVP2',F7.1)
WRITE(6,26)
FORMAT(/////,30X,'STEAM DATA
(TEMPERArJ REPRESSURE) 't
1//15X,'INLET CONDITIONS')
J=1
27 DO 29 I=1,NDATA,5
WRITE(6,28) TS(IJ),PS(IJ),TS(I+1,J),PS(I+1,J),TS(I+2,J),
26
1PS(I+2,J),TS(I+3,J),PS(I+3,J),TS(I+4,J)
28 FORMAT(10I
,PS(I+4,J)
,5('(',F6.1,','F6.1,')',3X))
29 CONTINUE
IF(J.EQ.2) GO TO 31
WRITE(6,30)
30 FORMAT(//15X, 'OUTLET
CONDITIONS')
J=2
GO TO 27
31 J=1
32
WRITE(6,33)JTSTEP(J),ICARD(J)
33 FOPMAT(/////10X,'POWER
WRITE (6,34) NPOINT (J)
34
FOPMAT(//,IGX,I3,'
NPT=NPOINT(J)
NPR=NPRINT(J)
DO 35 I=1,NPT,5
HISTORY' ,13,'
POINTS SPECIFIED
HT
-
',F6.4,'
(TIME,FPAFP) '/)
ICARD',I2)
,
35 WRITE (6,36) TIM-E(IJ),jFRAFP(IJ),vTIME (I+1,rJ),rFRAFP (I+1,vJ)
1TIME(I+2,J) ,FRAFP(I+2,J) , TIME(I++3,J),FRAFP(I+3,J),TIME(I+4,J),
2FRAFP (I+4,J)
36 FORMAT(10X,5('(',F6.2,',',F6.2,')I,3X))
WRITE(6,37)NPR
37 FORMAT(//1OX,13,' TIME VALUES SPECIFIED FOR PPINTOUT')
WRITE (6,38) (TIMEPR(IJ) ,I=I,NPR)
38 FORMAT(/1OX,10(F8.3,2X))
39 FORMAT(30X,90I1)
40 FORMAT(8011)
J=J+1
IF(J.LE.NLOADH) GO TO 32
IA0=0
NSTE=0
DO 41 I=1,NLOADi
NPRIN1=NPRINT (I)
NPHI ST= NPOINT (I)
IF(TIMEPR(NPRIN1,I).LT.TI ME(NPHIST,I)) IA0=1
IF(IA0.EQ.1) NPRINT(I)=NPRINT(I)+1
IF (IA6.EQ. 1) TIMEPR (NPRIN1+1,I) =TrME(NPHISTI)
IF(ICARD(L).NE.0) NSTE=NSTE+NPRINT(I)
41 IAO=0
RETURN
42 END FILE 56
REWIND 56
REWIND 57
EXIT
....
....
..
..
..
.....
...
..
. ...........
.
...
.....
.....
........
.
CALL
END
w
SUBROUTINE OUTPUT (IDPRJMAXKMAXIHISTTFRAFP1,TIME1,ICARDNNN#
1HR,HZ ,ITERTITLENPRINT, IJKfNLOADHNSTENNEW, N9,NCOLUM)
30 0 0
DIMENSION IDPR(80,220),T(80,220),RCOOR(1000),ZCOOPR(1000),T2(
1NPRINT(10) ,TITLE(20) ,ICARD(10),NCOLUM (220)
),
REAL*8 TEMPDBT2DOUB(3000)
DATA TEMPDBT2DOUB/0.,3000*70./
GO TO 5
IF(IJK.NE.1.OR.NNN.NE.1)
1 WRITE(6,2)
2 FORMAT(1H1,/////,1OX,'NODE NUMBERING
1RE PRINTOUT',//)
T EM PO= 1.
ICAR 1=ICAP D (IJK)
AND COORDINATES FOR TEMPERATU
NUMNR=O
NNEW=O
K1=0
DO 3 K=1, KMAX
IF(IDPR(1,K).-FQ.2)
GO TO
3
GO TO
3
K1=Ki+i
NCOLUM (K)=0
DO 3 J=1,JMAX
IF(IDPR(JK).EQ.2)
IF(K.EQ.1)
NUMNR=NUMNR+1
NCOLUM(K)=NCOLUM(K1)
+1
NNEV=NNEW+1
PCOOR (NNEW) =HR* (J-1)
ZCOOR (NNEW) =H Z* (K-1)
3 CONTINUE
(IIRCOOR(II) ,ZCOOR(II),1=1, NNEW)
WRITE(6,4)
4 FORMAT(4(5XI4,'
(',F7.3,' ,',F7.3,')
)I,/)
WRITE (6 ,9) ITEF
NUMNP=NNEW
IF(ICAR1.EQ.0) GO TO 5
WRITE(56)TEMPDB, (T2DOUB(II) ,II=1, NNEW)
IF(ICAR1.EQ.1) GO TO 5
CALL ADINA(TITLE, NUMNPNUMNNSTPRCOOR,ZCOORICAR1,YKNCOLU
IJK,TIME1,RAFP1
5 WRITE(6,6)
M)
H
0\
H
6 FORMAT (////,1OX,'LOAD HISTORY ',I3,10X,'TIME=',F7.3,*
1F5.2)
IF(ICARI.NE.0) WRITE(6,10)TEMPO
NNEW=0
DO 7 K=1,KMAX
Do 7 J=1,JMAX
IF(IDPR(JK).EQ.2) GO TO 7
FRAFP=',
NNEW=NNEW+1
T2(NNEV) =T(JK)
7 CONTINUE
8 FQRMAT(6(5X,I4,' (',F6.1,')'),/)
9 FORMAT(//30X,'NUMBER OF ITERPATIONS PERFORMED FOR STEI ADY STATE TEMP
1FRATURE...,13,////)
10 FORMAT(10X,'FOR ADINA THIS TIME IS EQUIVALENT TO...' ,F5.1)
WRITE (6,8)
(I,T2
(II) ,II=1,NNEW)
TEMPDB=TEMPO
DO 11 I=1,NNEW
11 T2DUB(I)=T2(I)
IF(ICAR1.NE.0) WRITE(56) TEMPDB, (T2DOUB (11) ,II=1,NNEW)
IF (ICAR1.NX.0) TEMPO=TEM PO+1
RETURN
END
N)
...
....
......
..... ...........
SUBROUTINE
IK1,NCOLUM)
ADINA(TITLENUMNPNUMNRNSTERCOORZCOORICARD,
DIMENSION TITLE(20),ISREFB(3,1),IEQITB(3,1),IPFIB(3,1),RCOOR (1000)
1,ZCOOR (1000),ID(6),NPAR(20),PROP(25),NCOLUM(220)
DATA IDOFNEGLMODEXIDATWR,IRINTITP96,JNPORTIMASSIDAMP,
1J1MASSNIDAMPN,IEIGIOPE,NSPEFBNEQITBNPPIB,NPB,NLOAD,ICONN,
2IPSrMTYP/100111,0,1,1,0,1,0,0,0,0,0,0,0,1,1,1,0,0,0,1,1,1/
DATA INPORTNPUTSV/0,0/
DATA NPAR/2,0,1,0,0,,t4,0,U,2,0, 0,0,0,3,1,0,0,0,0/
DATA ISREFB/3*1/,IEQITB/3*1/,IPRIP/3*1/,ID/1,O,0,1,1,1/
DATA DTTSTARTOPVARIOPVAR2,DENN/1.,0.,0.,0.,,1./
DATA PROP/100.,200.,300.,400.,500.,850.,6*30000000.,
16*0. 30,6*0. 0000094, 70./
IJJ=0
NST1=NSTE
ISREFB (2,1)=NST1
IEQITB (2,1) =NST1
IPRIB (2,1) =NST1
NPAR2=0
DO 99 IJJ=1,K1
IP(IJJ.EQ.K1) GO TO 99
NPAR2=NPAR2+NCOLUM (IJJ)-1
99 CONTINUE
NEGNL=NPAR2/20
IF(20*NEGNL.LT.NPAR2)
ISAI=7
IF(ICARD.GT.3.OR.ICARD.LT.-3)
ISAI=57
100 IF(ISAI.MQ.6)
101
NEGNL=NEGNL+1
IF(ICARD.EQ.2) ISAI=6
IF(ICARD.EQ.3.OR.ICARD.EQ.-3)
WRITE(6,101)
FORMAT(1H1,////,30X,'ADINA INPUT DATA',//)
WRITE (ISAI, 1) (TITLE (I) ,=1,1 8)
WRITE(ISAI,2)NUMNPIDOFNEGLNEGNLMODEXNSTIDTTSTARTIDATWR,
1IRINTITP96,INPORTJNPORT
WRITE (ISAI,3)IMASSIDAMP,IMASSN,IDANIPN
WRITE (I5AI,3) IEIG
WRITE (ISAI,4) iOPE,oPVAR1,oPVAR2
"o-
. ..
..
..
. .
..
........
.............
.......
WRITE (ISAI,5) -NSREFBNEQITB
WRITE (ISAI,3) NPRIBNPB
WRITE (ISAI,3) NPUTSV
WRITE (ISAI,3)ISREFB (1,1) ,ISREFB (2,1) ,ISREFB (3,1)
WRITE(ISAI,3)IEQITB(1,1),IFQITB(2,1) ,IEQITB (3, 1)
WRITE (ISAI,3) IPRIB (1 ,1) ,IPPIB (2,1) ,IPRIB (3, 1)
DO 7 I=1,NUMNP
WRITE(ISAI,6)I, (ID(J),J=1,6),RCOOR (I),ZCOOR (I)
1
2
3
4
5
6
7
FORMAT(18A4)
FORMAT(I5,16,I14, 315,2E10.3,515)
FORMAT(415)
FORMAT(110,2E10.3)
FORMAT (315,E10.3)
FORMAT(lXI4,6I5,l0X, 2E10.3)
CONTINUE
8 FORMAT(2014)
9 FORMAT(15,E1O.3)
10 FORMAT (8E10. 3)
11 FORMAT (15,5K, 215)
WRITE (ISAI,3) NLOAD
WRITE(ISAI,3) ICON
J=0
IA=0
NTOC=0
DO 14 II1=1,NEGNL
II=0
IF(II1*20.LE.NPAR2)
IF(II1*20.GT.NPAR2)
NPAR (2)=20
NPAR(2)=NPAR2-(IIl-1)*20
WRITE (ISAI ,8) (NPAR (I) ,I=1,20)
WRITE (ISAI ,9) NDENN
WRITE (ISAI,10) (PROP (I) ,I=1,25)
12 J=J+1
IF(J.GE.K1) GO TO 14
NCOLUJ=NCOLUM (J) -1
NTOC=NTOC+NCOLUl (J)
13 1A=IA+1
Hs
mw
I1=II+1
NOD1=NTOC+I A+1
NOD2=NOD1-1
NOD3=NOD2-NCOLUN (J)
NOD4=NOD3+1
WRITE(ISAI, 11) IIIPS,MTYP
WRITE (ISAI,3) NOD1,NOD2,NOD3, NOD4
IF(IA.LT.NCOLUJ.AND.II.LT.NPAR(2))
IF(IA.EQ.NCOLUJ) IA=0
IF(II.LT.NPAR(2)) GO TO 12
14 CONTINUE
GO TO
13
L.,JJ=TJ+ 1
1F(ICARD.LE.-3) ISAI=6
IF (ICARD.EQ.-4.AND.IJJ.EQ.2)
IF(ICARD.LE.-3.AND.IJJ.LT.2)
IF(ICARD.EQ.-4.AND.IJJ.EQ.2)
R ETUR N
END
ISAI= 7
GO TO 100
GO TC 100
lellilillilli................
amelsm
asemenemileme
.
0%
EXPANS (FR AFP1,PINPOUTTSPSNDATA,NZ, K MiAXTSTEAM)
SUBROUTINE
DIMENSION TS (30,2) ,PS(30, 2), TSTEAM (220) ,PRES (2) ,TEM (2)
PRES (1) =(0.1+0.9*FRAFP1) *PIN
PR ES (2) =(0. 1+0.9*FRA FP1) *POUT
Do 3 3=1,2
DO 1 1 =1,NDATA
IF(PS(IJ) .GT.PRFS(J)) GO TO 2
1 CONTINUE
2 TEM(J)=(TS(IJ)-TS(I-1,J) )*(PRES(J)-PS(I-1,J))/(PS
1PS(I-1,J))+TS(I-1,J)
3 CONTINUE
DTEM= (T EM (2) -T EM (1) )/N Z
(IJ)-
TSTEAM (1) =TEM (1)
DO 4 I=1,NZ
4 TSTEAM (I+1)=TSTEAM (I) +DTEM
RETURN
END
GI
SUBROUTINE
1KNAX,JMAX)
TEMPME(TSTEAM,ID,CONVP1,CONVP2, TBOUNDIBOUND,
DIMENSION TSTEAM (220) ,ID (80,220) ,TB3OUND (1000)
II=0
DO 2 K=1,KMAX
DO 2 J=1,JMAX
IF(ID(JK) .GT.2) GO TO 2
II=1I+1
IBOU ND=II
IF(ID(JK).EQ.2) GO TO 1
TBOUND (II) =CONVP I*TSTEAM (K)
GO TO 2
1 TBOUND(IT) =CONVP2*TSTEAM(K)
2 CONTINUE
RETUR N
END
.. .............
TEMPSS(TSTEAM,TBOUND,IBOUND,C1
SUBROUTINE
1ITERMITER,CONV, T,TI)
,C2,C3,IDJMAXKMAX,
COMMON/OVER/OVERP
DIMENSION TSTEAM(220),TBOND(100),CI(8C),C2(8),C3(80),ID(
8
0,
2 2
0)
1 ,T(80,220) ,T1 (80,220)
ITER=O
II=0
DO 2 K =1,KMAX
DO 2 J=1,JMAX
IF(ID(J,K).LT.3) GO TO
T (JK)=TSTEAM (K)
Ti (J,K) =TSTEAI (K)
GO TO 2
1
1 11=II+1
Ti (J,K)=TBOUND (II)
T (J,K) =TSTEAM (K)
2 CONTINUE
IF(II.NE.IBOUND) WRITE(6,3)IIIBOUND
3 FORMAT(//,10X,'ERROR IN BOUNDARY TEMPERATURES
IBOrIND=',I4)
1'
4 ICONV=1
ITER=ITER+1
-
II=',I4,
DO 11 K=1,KMAX
DO 11 J=2,JMAX
ID123=ID(JK)
GO TO
(11,11,5,6,7,8,9,11),1D123
5 T(J,K)=(C1(J)+C2(J))*T1(J+1,K)+C3(J)*(T1(J,K+1)+T(JK-1))
GO TO 10
6 T(J,K)=(C1(J)+C2(J))*T1(J-1,K)+C3(J)*(Tl(J,K+1)+T1(JK-1))
GO TO 10
)
7 T(JK)=C1(J)*T1(J+1,K)+C2(J)*T1(J-1,K)+2.*C3(J)*T(J,K+1)
GO TO 10
9 T(JK)=C1(J)*T1(J+1,K)+C2(J)*T1(j-1,K)+2.*C3(J)*T1(J,K-1)
GO TO 10
9 T(J,K)=C (J)*T1 J+1,K)+C2(J)*T1(u-1,K)+C3(J)*(T1(JK+1)+T1(JK-1))
10 TEST=ABS (T (JK) -T(J,K)
H
co
-
-
-
.1.
1
-
-
.-, , -
-
- I-
--
n.-
--
- -- I
--
I I
I
-
I - - - -
- ---
--
-
I- - -
---
,
---
I-
. .
.
.......
..
H
ON 51
dflLN0a
t7
f)(Wal o=ANOJGN*O*AOI s )aI
1
SUBROUTINE TEMPTR (TBOUND,IBOUNDC4,CS,A,C, HTID,JMAX,KMAXi,T,T1)
DIMBNSION TBOUND (1000) ,C4 (80),C5 (80) ,ID(80,220),T(80,220),TI (80,
1220)
I I=0
DO 1 K=1,KMAX
DO 1 J=1,JMAX
IF(ID(JK).GE.3) GO TO 1
1i=II+1
T (J,, K) =TBOUND (II)
1 T1 (JK)=T(JK)
DO 8 K=1,KMAX
DO 7 J=2,JMAX
ID123=ID(JK)
GO TO
(7,7,2,3,4,5,6,7),1D123
2 T(JK)=HT*((C4(J)+A)*T1(J+1,K)+C* (T1(J,K+1)+T1(J,K-1))
1-C5 (J) *T1 (JK))+Tl (JK)
GO TO'7
3
T(J,K)=HT*((C4 (J)+A)*T1(J-1,K)+C*(T1
(JK+1)+T1(J,K-1))
1-C5(J) *T 1 (JK) )+T1 (JK)
GO TO 7
4 T(J,K)=HT*(C4(J)*T1(J+1,K)+A*T1(J-1,K)+2.*C*T1(J,K+1)
1-C5 (J) *TI (JK)) +T 1(JK)
GO TO 7
5 T(J,K)=HT*(C4 (J)*T1(J+1,K)+A*T1(J-1,K)+2.*C*TI(JK-1)
1-C5(J)*T1(J,K))+T1(JK)
GO TO 7
6 T(JK)=HT*(C4(J)*TI(J+1,K)+A*T1(J-1,K)+C*(T1(JK+1)*T1(JK-1))
1-C5 (3) *T1 (JK)) +TI (JK)
7 CONTINUE
8 T(1,K)=T(2,K)
RETURN
EliD
0j
.............. -
..
-
-4
--. I--
-
Z
- ,.1
171
APPENDIX
III
Angra I Nuclear Power Plant
Data
(from Ref.19)
Thermal and Hydraulic Design Parameters
Reactor Core Heat Output
1876 MWt
2.
Heat Generated in Fuel
97.4%
3.
System Pressure, Nominal
15.5MPa
4.
System Pressure, Minimum Steady State
15. 3MPa
5.
Total Thermal Flow Rate for Coolant (x106
32. 2kg/hr
6.
Coolant Average Velocity along Fuel Rods
490.cm/sec
7.
Nominal Coolant Inlet Temperature
287. 50C
8.
Average Coolant Temperature Rise in Vessel
37. C
9.
Average Coolant Temperature Rise in Core
38.5 0
10.
Average Coolant Temperature in Core
307.0 C
)
1.
11. Average Coolant Temperature in Vessel
305.0C
12.
17.6kW/m
Average Thermal Output
13. Maximum Thermal Output for Normal Operation
42.0kW/m
172
Core Mechanical Design Parameters
1.
Number of Fuel Assemblies
121
2.
U0 2 Rods per Assembly
235
3.
Rod Pitch
1.23cm
4.
Fuel Rod Out side Diameter
0.95cm
5.
Diametral Gap
165 m
6.
Clad Thickness
570 m
7.
Clad Material
8.
Fuel Pellet Material
9.
Density of Fuel Pellet
Zircaloy-4
U0 2 Sintered
95% of Theoretical
10. Diameter of Fuel Pellet
0.82cm
11. Fuel Pellet Length
1.35cm
12.
Control Assembly Absorber
13. Control Assembly Clad Material
14. Clad Thickness for Control Assembly
15. Number of Control Assemblies
16. Number of Absorber Rods Per Cluster
Ag-In-Cd
Type 304 SS-Cold Worked
445 m
33full/4part
20
Additional Plant Data Has Been Provided Throughout the Text
173
List of References
1)
W. J. Kearton, "Steam Turbine Theory and Practice",
Isaac Pitman and Son, London,1958.
2)
M. J. Moore and C. H. Sieverding, "Two-Phase Steam
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Corporation, Washington, 1976.
3)
I. I. Kirilov and R. M. Yablonik,
"Fundamentals of
the Theory of Turbines Operating on Wet Steam", NASA
TT F-611, Washington, November 1970.
4)
R. C. Spencer and E. H. Miller, "Performance of Large
Nuclear Turbines", Combustion
5)
,
pp.24-30, August 1973.
F. R. Harris, "Problems Posed by the Wet Steam Turbines
in Nuclear Power Plants", Journal of Science and
Technology, Vol.36 -
6)
Number 3, 1969.
J. M. Mitchell, "Trends in the Design of Highly Rated
Steam Turbines", the Institution of Mechanical Engineer,
Steam Plant Group, Proceedings Vol.183 - Part 30, London
1969
174
7)
N. 0. Parsons, "The Contribution of Service Experience
to the Development of Modern Large Steam Turbines" the
Inst. of Mech. Eng.,
Steam Plant Group, 064/71, London
1971.
8)
G. Riollet, M. Widmer and J. Tessier, "Les Turbines
a
Vepeur de Grande Puissance Associees aux Reacteur
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9)
A. Hohn, "Steam Turbines on Startup", Combustion,
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10)
G. Wronski, A. Davies and B. D. Burrows, "Behavior of
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11)
J. T. Moore, "Engineering Planning and Designing of
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K. Buchwald et al., "Design Behavior and Operational
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175
13)
J. S. Sohre, "Steam T!arbine Blade Failures, Causes
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C. J. Benjamin et al.,"Bi-Dimensional Calculation and
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R. U. McCrae, A. Montagne and M. Douglass, "Experience
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16)
Part 81, London, 1965.
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18)
W. E. Cooper, "Notes on Design of Elevated Temperature
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176
19)
Furnas Centrais Eletricas S/A,
"Final Safety Analysis
Report - Angra I Nuclear Power Plant", Rio de Janeiro,
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20)
J. H. Keenan and F. G. Keyes, "Steam Tables", John
Wiley and Sons, New York, 1969.
21)
N. P. Suh and A. P. L. Turner, "Elements of the Mechanical
Behavior of Solids", McGraw Hill Co., New York, 1975.
22)
S. H. Crandall et al., "An Introduction to the Mechanics
of Solids", McGraw Hill Co., New York, 1972.
23)
1A. M. El-Wakil, "Nuclear Heat Transport", International
Textbook Co., Scranton, 1971.
24)
M. Clark and K. F. Hansen, "Numerical Methods of Reactor
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25)
K. J. Bathe, "ADINA - A Finite Element Program for Aut.
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26)
P. J. Nicholson, "LWR Instrumentation and Control", Class
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177
27)
D. D. Lanning, "Power Reactors", Class Notes of M.I.T.
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28)
J. F. Tichit, "Important Structural Considerations in
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29)
P. C. Riccardella and T. R. Mager, "Fatigue Crack
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260-279, 1972.
30)
ASME, "Boilers and Pressure Vessels Code", Section III,
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31)
H.N. Paduano, G. E. Liebler and J. M. Pugsley, "Effects
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32)
E. F. Duhn, D. D. Malinowski and i. D. Fletcher, "Three
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P. J. Wasling et al., "Correlation of PWR Steam Generator
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178
Westinghouse Nuclear Energy Systems, "Topical Report
-
34)
Reactor Coolant Pump Integrity in Loca", WCAP-8163,
September 1973.
35)
Westinghouse Nuclear Energy Systems, "Pipe Breaks
for
LOCA Analysis of the Westinghouse Primary Coolant Loop",
WCAP-8172, July 1973.
36)
Verbal communication from the Engineering Department of
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37)
Othon L. P. da Silva, "Fuel Element Performance Maps for
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38)
F. M. Swengel, "Quick Star and Cyclic Capacity For the
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39)
Commonwealth Edison Staff, "Appraisal of Nuclear Power
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40)
R. E. Balzhiser,
"R and D Status Report: Fossil Fuel and
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1977
41)
Furnas Centrais Eletricas S/A, personal communication.
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43)
R. Schuster,
"Directions in Peaking", Power Engineering,
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44)
J. S. Spencer, "Physical Justification of the Term:State
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45)
J. E. Meyer, "Structural Mechanics in Nuclear Power
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46)
K. Hornyik, "Tritium Generation in the Coolant-Moderator
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47)
P. J. Sipush et al., "Load-Following Demonstration
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T. Morita et al., "Topical Report - Power Distribution
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A. F. Henry, "Nuclear Reactor Analysis", MIT Press,
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180
50)
A. E. Green and A. J. Bourne, "Reliability Technology",
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D. D. Ebert et al., "Maneuvering Experience at Calvert
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52)
N. Eickelpasch, R. Seepolt and U. Wolff, "Implication
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53)
Y. Y. Liu, "A Probabilistic Approach in Nuclear Reactor
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54)
J. A. L. Robertson, "Nuclear Fuel Failures, Their Causes
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55)
S. Aas, "The Effects of Load-Following Operation on Fuel
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1975.
56)
R. Manzel and H. Stehle, "KWU in*Reactor Experience with
LWR Fuel", Proc. European Nuclear Conference, Vol.3
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181
57)
K.Vinde and L. Lunde, "Fuel Element Failures Caused by
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58)
E. Hillner,"Corrosion and Hydriding Performance of Zircaloy
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Pressurized Water Reactor", ASTM-STP 551, Zirconium
in Nuclear Applications, pp.449-462, 1974.
59)
W. J. O'Donnell and B. F. Langer, "Fatigue Design Basis
for Zircaloy Components", Nuclear Science and Engineering
20, pp.1-12, 1964.
60)
A. L. Bement, "Nuclear Fuels", Class Notes of MIT Course
22.72, Spring 1976.
61)
P. J. Pankaskie, "BUCKLE, An AnAlytical Computer Code for
Calculating Creep Buckling of an Initially Oval Tube",
Battelle Pacific Northwest Lab., May 1974.
62)
J. T. A. Roberts et al.,
"
On the Pellet-Cladding
Interaction Phenomenon", Nuclear Technology, Vol.35,
mid-August 1977.
63)
S. Aas, K. D. Olshansen and K. Vindem, "Fuel Failures Caused
by Overpower Ramps", Nuclear Fuel Performance Conf.,London,
1973.
182
64)
C. C. Busby, R. P. Tucker and J. E. McCanby,
"Halogen
Stress Corrosion Cracking os Zircaloy-4 Tubing", Journal
of Nuclear Materials 55, pp. 6 4- 8 2, 1975.