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The Mechanical and Nuclear Engineering Department
NUCE 470 - FALL 2013
POWER PLANT SIMULATION with TRACE
FINAL PROJECT
Prepared by: ANDREW DUNNING
AYSENUR TOPTAN
RICKY VIVANCO
Delivery date: 12 / 16 / 2013
Due date: 12 / 16 / 2013
Dunning, Toptan, Vivanco NucE 470 Final Project 2013
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ABSTRACT
The main objective of this project was to create a model that simulated a pressurized
water reactor (PWR) at steady state. In order to simulate a PWR, we used the Symbolic
Nuclear Analysis Package (SNAP) and TRACE coding software to create models of each
component of a PWR. A steam generator, reactor core and core vessel, reactor coolant pump
and pressurizer models were created and simulations were run until the steady state results
coincided with the given parameter. After we were satisfied with each component, we created
four copies of the steam generator and reactor coolant models and connected them to the
reactor core vessel to create a four loop PWR model. The components were connected in the
order of typical PWR loops and the pressurizer was connected by surge line to the hot leg of
the first loop. We then ran simulations until the compiled model approached the parameters
given in the assignment. The observed a turbine output of about 850 MW which is 27% of the
3,125 MW thermal power output simulated by our core model. After completing a 5%
increase in thermal power to 3281.25 MW, we observed an accurate temperature, pressure
and mass flow increase. With Richardson Extrapolation of the steam generator and C++
coding, we were able to achieve a .0065% error in mass flow rate at the exit nozzle.
Dunning, Toptan, Vivanco NucE 470 Final Project 2013
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TABLE OF CONTENTS
Abstract ............................................................................................................................................................ 1
Table of Contents ........................................................................................................................................ 1
List of Figures ................................................................................................................................................ 1
List of Tables .................................................................................................................................................. 1
Nomenclature ............................................................................................................................................... 1
I. Introduction ............................................................................................................................................... 1
II. Model Development ............................................................................................................................. 1
1. Steam Generator Model ............................................................................................................... 2
2. Reactor Vessel/ Core and Pressurizer Model .......................................................................... 2
3. Pump Model ..................................................................................................................................... 2
4. Turbine Model ................................................................................................................................. 2
III. Subsystem Results ................................................................................................................................ 1
5. Steam Generator Results .............................................................................................................. 2
6. Reactor Core/ Vessel Results ...................................................................................................... 2
7. Plant Base Steady State Results ................................................................................................... 2
8. Plant Transient Results .................................................................................................................. 2
IV. Steam Generator Subsystem Richardson Error Analysis ................................................. 4
V. Conclusion ................................................................................................................................................. 4
VI. References ................................................................................................................................................ 4
Appendix A: List of Enclosures ............................................................................................................ 4
Appendix B: Richardson Error Analysis ........................................................................................... 4
Dunning, Toptan, Vivanco NucE 470 Final Project 2013
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FIGURES
Figure 1.1: Steam Generator Geometry................................................................................................... 8
Figure 1.2: Nodalization used for UTube Steam Generator in TRACE ............................................ 9
Figure 1.3: Feedwater Mass Flow Controller ....................................................................................... 14
Figure 1.4: Downcomer/Boiler Region Mass Flow Controller ......................................................... 14
Figure 2.1: Cut-out of a Reactor Pressure Vessel ............................................................................... 15
Figure 2.2: Simplified Reactor Pressure Vessel Geometry ................................................................ 16
Figure 2.3: General view of the Reactor Vessel and Core Model ................................................... 16
Figure 2.4: Input data section for geometry and connections of Reactor Vessel ........................ 17
Figure 2.5: Input Data Section For Volumetric and Edge Data of Reactor Vessel....................... 18
Figure 2.6: Control System for the Temperature Difference Calculation Between Hot Leg and
Cold Leg ............................................................................................................................................ 18
Figure 4.1: Control Block Schematic for Turbine Output Power ................................................... 23
Figure 5.1: Primary side Hot and Cold Leg Temperatures .............................................................. 24
Figure 5.2: Boiler liquid level ................................................................................................................... 25
Figure 5.3: Downcomer liquid level ...................................................................................................... 25
Figure 5.4: Steam mass flow rate ........................................................................................................... 26
Figure 6.1: Reactor mass flow rate ...................................................................................................... 27
Figure 6.2: Temperature difference between hot leg and cold leg ................................................ 28
Figure 6.3: Hot leg mass flow rate ....................................................................................................... 29
Figure 6.4: Temperature difference between hot and cold legs ..................................................... 29
Figure 7.1: Pressurized Water Reactor Plant ........................................................................................... 30
Figure 7.2: Primary Mass Flow Rate ......................................................................................................... 31
Figure 7.3: Hot Leg Temperature ............................................................................................................. 31
Figure 7.4: Primary Side Pressure ............................................................................................................. 32
Figure 7.5: Pump pressure ......................................................................................................................... 32
Figure 7.6: Reactor Power ......................................................................................................................... 33
Figure 7.7: Steam Mass Flow Rate ............................................................................................................. 33
Figure 7.8: Steam Temperature ................................................................................................................. 34
Figure 7.9: Boiler Water Level .................................................................................................................. 34
Figure 7.10: Control Blocks Schematic ..................................................................................................... 35
Figure 7.11: Turbine Output Power during the steady-state ................................................................. 36
Figure 8.1: Steam Generator Feedwater and Exit Steam Mass Flow Rate (General Trend) ................. 37
Figure 8.2: Steam Generator Feedwater and Exit Steam Mass Flow Rate (closer view to transient) .. 37
Figure 8.3: Transient Primary Mass Flow Rate ....................................................................................... 38
Figure 8.4: Transient Reactor Power ........................................................................................................ 38
Figure 8.5: Cold leg temperature during the transient ............................................................................ 39
Figure 8.6: Hot leg temperature during the transient ............................................................................. 39
Dunning, Toptan, Vivanco NucE 470 Final Project 2013
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Figure 8.7: Steam Generator boiler water level during the transient (general view) ........................... 40
Figure 8.8: Steam Generator boiler water level during the transient (closer view to transient) ........ 40
Figure 8.9: Downcomer water level during the transient ....................................................................... 41
Figure 8.10: Downcomer water level during the transient (closer view to transient) ......................... 41
Figure 8.11: Primary side pressure during the transient ........................................................................ 42
Figure 8.12: Pump pressure during the transient ................................................................................... 42
Figure 8.13 Turbine outlet power during the transient .......................................................................... 43
Figure 8.14: Turbine inlet temperature during the transient .................................................................. 44
Figure 8.15: Turbine inlet pressure during the transient ........................................................................ 44
Figure 9.1: Steam exit mass flow rate for Richardson Error Analysis ................................................. 45
Tables
Table 1.1: Steam Generator Primary Side Parameters ..................................................................... 10
Table 1.2: Steam Generator Secondary Side Parameters ................................................................. 11
Table 2.1: Reactor Core and Reactor Core Vessel Parameters .................................................. 19
Table 3.1: Reactor Coolant Pump Parameters ................................................................................... 21
Table 3.2: Reactor Coolant System Parameters ................................................................................. 21
Table 8.1: Transient Power Table ........................................................................................................... 37
Table 8.2: Transient Secondary Side Steam Fill Table ........................................................................ 37
Table 9.1: Prescribed steam generator feedwater flow rate transient .......................................... 45
Dunning, Toptan, Vivanco NucE 470 Final Project 2013
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NOMENCLATURE
LCSP LOWER CORE SUPPORT PLATE
PWR PRESSURIZED WATER REACTOR
SG STEAM GENERATOR
UCSP UPPER CORE SUPPORT PLATE
RCS REACTOR COOLANT SYSTEM
SS STEADY STATE
Dunning, Toptan, Vivanco NucE 470 Final Project 2013
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I. INTRODUCTION
When studying the safety and reliability nuclear power plant operations, thermal-hydraulic coding is
an essential tool. When designing a nuclear reactor, these codes are helpful in determining precise
estimations of reactor systems parameters even while design feature are still being modified. This leads
to more efficient power production while minimizing. In addition to precision calculations, the analysis
codes can also predict accident scenarios when simulating a reactor system model. This proves helpful
since accident scenarios typically cannot be performed on any real life platform due to cost, feasibility
and safety concerns.
The pressurized water reactor (PWR) design is the most popular in the nuclear power industry.
The PWR design uses light water (H2O) under high temperatures and pressure to generate electricity.
The system is comprised of a primary and secondary loop. The primary loop, which includes the
reactor pressure vessel and core, steam generator, pressurizer and reactor coolant pump, runs heated
and cooled liquid water in closed recirculation. The PWR usually consists of 4 separate primary loops
connected to one reactor core and pressure vessel. The secondary loop recirculates of water that is
heated by the primary loop via the steam generator and then cooled when run through the connected
turbine that generates electricity. Each component of the primary and secondary loop of the PWR
design was modeled for this project.
For our models, the Symbolic Nuclear Analysis Package (SNAP) software and TRACE coding
software were used to simulate the function of PWR model. SNAP provides visuals when generating
the components of the PWR system and allows modifications of the boundary conditions for each
component. Using data given, various parameters were estimated to generate each component of the
PWR system. To being, we modeled the steam generator and reactor core and vessel separately to
minimize error in comparison to modeling them together. After our models were able to reach steady
state, they were connected and simulated together. The system parameters were then slightly adjusted
in many areas to ensure the compiled system could reach steady state as well. Finally, we studied the
effects of change in power on the other reactor systems through transient analysis of our model. The
complete development of our system is described in this report.
Key Plant Data Parameter Value
Parameter Value Steam Pressure 6825809 Pa
Core Thermal Power 3125 MW Steam Flow Rate per Loop 480 ks/s
Net Electrical Power 1000 MW Pressurizer Volume 75.0 m^3
Efficiency 32% Number of Fuel Assemblies 193
Hot Leg Temperature 598 K Fuel Lattice 17 x 17
Cold Leg Temperature 565 K Active Fuel Length 3.70 m
RCS Mass Flow per Loop 4400 kg/s Rods Per Assembly 264
Primary System Pressure 1551323 Pa Number of Control Rods 53
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II. MODEL DEVELOPMENT
1. STEAM GENERATOR MODEL
In this section, we evaluate and analyze the steam generator model created for our
PWR. The TRACE file from a previous steam generator model was used and modified
to meet our specifications given in Tables 1.1 and 1.2. The steam generator is modeled
to be a U-Tube type steam generator, whose basic geometries can be seen in figure 1.1.
The steam generator is comprised of two loops, a primary side and secondary side. The
primary side of the steam generator comes from the Hot leg of the reactor coolant
system that runs the highly pressurized heated water from the reactor pressure vessel
through the steam generator. The primary coolant enters the steam generator through
the bottom plenum which separates into thousands of small U-tubes. The water then
travels up and down the steam generator into the exit plenum. The water runs up and
down only once, hence the pipes being named U-tubes. While the water runs through
the U-tubes, the secondary side provides water at a lower temperature and pressure through the downcomer of the steam generator, whose outlet is at the bottom of the
structure. The water fills the steam generator to steady water level and is heated by
the U-tubes it is surrounding. The heated water in the U-tubes heat the secondary
water until a steady flow of steam is forced to the top of the steam generator and
through a nozzle that connects to the turbine generator. In summary, the hot primary
side liquid transfers heat to the secondary side to produce steam that moves the
turbine.
Figure 1.1. Steam Generator Geometry
Dunning, Toptan, Vivanco NucE 470 Final Project 2013
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Figure 1.2 Nodalization used for UTube Steam Generator in TRACE
A simplified volumetric nodel scheme was used to model the structures of the steam generator. The
way the structures were divided can be seen in the figure above. The figure also shows the cells of each
structure. The cells were used to make sure that the correct values of flow area and flow rate are
running when the simulation is tested. Some structures, such as the U-tubes, are not modeled exactly.
So, calculations had to be made to assign parameters that averaged the bundle of U-tubes. Other
calculations were also performed to model each structure and assign the parameters needed for TRACE
to simulate the model as accurately as possible. These parameters were calculated from given
parameters for the primary and secondary side. Tables 1.1 and 1.2 give a summary of the overall
parameters of the primary and secondary side of the steam generator.
Dunning, Toptan, Vivanco NucE 470 Final Project 2013
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Table 1.1. Steam Generator Primary Side Parameters
Parameter SI Units British Units
Tube outer diameter 0.0222 m 0.874in
Tube wall thickness 0.00105 m 0.0413in
Height of tube bundle 9 m 30ft
Hot leg inner diameter 0.7 m 3ft
Cold leg inner diameter 0.7 m 3ft
Number of SG tubes 5000 5000
Hot leg plenum inlet flow area * 0.3848451 m2 596.511sqin
Plenum exit flow area * 1.58654356 m2 17.1 ft2
Volume average flow area of the plenum * 4.75963068 m2 4.14 ft2
Total plenum volume a 4.75963068 m3 4.14 ft2
Primary side inlet temperature 598 K 617 deg F
Primary side outlet temperature 565 K 617 deg F
Primary side pressure 1551323 Pa 225psi
SG primary side flow rate 4400 kg / s 301.5 slug/s
U-tube inner diameter * 0.0201 m 0.791 in
Average tube length * 17.4 m 57.08
Hydraulic diameter of primary side * 0.0201 m 0.791 in
Wetted perimeter of boiler primary side * 315.7300617 m 1035 ft
SG tube inner flow area * 1.58654356 m2 17.1 ft2
SG tube inner surface area * 5493.703073 m2 59133 ft2
Total tube volume * 33.67557988 m3 362.5285 ft2
* Calculated parameters
a Since the precise shape of the plenum is unknown, the volume has been calculated by multiplying the
area by a height of one meter
Dunning, Toptan, Vivanco NucE 470 Final Project 2013
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Table 1.2. Steam Generator Secondary Side Parameters
Parameter SI Units British Units
SG overall height 20 m 65.6ft
Feedwater inler diameter 0.364 m 14.3in
Downcomer height 10.0177 m 32.8ft
Lower shell outer diameter 3.5 m 11.5ft
Lower shell thickness 0.0668 m 2.19ft
Upper shell outer diameter 4.5 m 14.8 ft
Upper shell thickness 0.0889 m 3.5 in
Feedwater temperature 503.15 K 445.73 deg F
Secondary side pressure 6825809 Pa 990 psi
SG secondary side flow rate 480 kg/s 32.9 slug/s
Lower shell inner diameter * 3.3664 m 11.04ft
Upper shell inner diameter * 4.3222 m 14.18ft
Boiler outer diameter * 1.214207708 m 3.98ft
Boiler inner diameter * 1.154207708 m 3.79ft
Hydraulic diameter of boiler region * 0.034024861 m 1.34in
Hydraulic diameter of downcomer * 2.152182292 m 7.06ft
Wetted perimeter of secondary side * 701.0596196 m2 7546.0
Hydraulic diameter of feedwater * 0.4554 m 1.49ft
Wetted perimeter of downcomer area * 14.39040352 m 47.21ft
SG tube outer surface area * 6067.672051 m2 65304.6 ft2
SG tube total flow area * 1.58654356 m2 17.07 ft2
Flow area of boiler region * 5.963364 m2 64.12 ft2
Area of boiler region * 1.157912793 m2 12.46 ft2
Downcomer flow area * 7.742728887 m2 83.3 ft2
Lower shell area * 8.90064168 m2 95.8 ft2
Boiler wall thickness * 0.03 m 1.18in
Boiler flow area - 5.963364 m2 64.18 ft2
Boiler flow area + 1.046303846 m2 11.26 ft2
Feedwater flow area * 0.104062115 m2 1.12 ft2
U-tube pitch a 0.02442 m 0.96in
* Calculated parameters
- excluding tubes
+ including tubes
a chosen parameter for the pitch of a U-tube unit cell
The following are the equations used to determine the unknown par1ameters of the steam
generator. Tables 1.1 and 1.2 show which parameters were given and which needed to be
calculated based of the given parameters. For the following calculations, the square lattice is
assumed and calculations are done being based on that assumption.
Dunning, Toptan, Vivanco NucE 470 Final Project 2013
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Primary Side Calculations:
Inner U-tube diameter for the Steam Generator is determined by subtracting the twice the
shell thickness from the outer shell diameter.
( )
Flow area of the inlet plenum:
Total flow area of inner Utubes:
Flow area of the exit plenum:
Volume averaged flow area of the plenum:
Inlet plenum volume: ( )
Wetted perimeter of primary side:
Hydraulic diameter of Primary side:
Steam Generator Tuber Inner surface area:
Steam Generator Tube area:
Dunning, Toptan, Vivanco NucE 470 Final Project 2013
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Secondary Side Calculations:
Lower inner shell diameter: ( )
Upper shell diameter: ( )
Boiler inner diameter: √( )
Boiler outer diameter: ( )
Total surface area of outer Utubes:
Area of the boiler region:
Downcomer flow area:
(
)
Lower shell Area:
(
)
Flow area of boiler region: (
)
Area of inner boiler region:
Feedwater flow area:
Secondary side wetted perimeter:
Downcomer wetted perimeter: ( )
Hydraulic diameter of boiler region:
Hydraulic diameter of downcomer:
Dunning, Toptan, Vivanco NucE 470 Final Project 2013
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Description of the feedwater flow controller:
Figure 1.3 Feedwater Mass Flow Controller
Mix mass flow from the steam generator feedwater is subtracted from the steam generator boiler.
Change in the mass flow rate will be determined according to the difference between the two.
Figure 1.4 Downcomer/Boiler Mass Flow Controller
Mass flow from the steam generator downcomer is divided by the absolute value of mass flow from the
steam generator boiler. This ratio will give us how mass flow changes in the regions of downcomer and
boiler.
15
2. REACTOR VESSEL / CORE AND PRESSURIZER MODEL
In this section, we evaluate and analyze the reactor core and reactor core vessel of our
PWR system. The TRACE file we started with was a given model which we modified to meet
our specifications given in Tables 2.1. The model and the changes we made to it, were designed
to simulate a general reactor core and reactor vessel used in a typical, four loop PWR. To
being the path through the vessel, pressurized water at high temperature in single phase is
driven into the reactor vessel through four inlet nozzles. The flow path is set toward the
bottom of the vessel through the downcomer region. The flow is then driven upward through
the lower core support plate, core, and upper core support plate. This core region is where
the water is heated by the thermal power of the fuel rods. Then the flow exits the reactor
vessel through four exit nozzles that are each connected a separate steam generator. The
primary goal of the reactor pressure vessel and reactor core is to heat the primary loop water
while keeping it in liquid state through pressurization.
Figure 2.1: Cut-Out of a Reactor Pressure Vessel
16
Figure Error! No text of specified style in document.2: Simplified Reactor Pressure
Vessel Geometry
A simplified volumetric nodel scheme was used to model the structures of the reactor core
and pressure vessel. The way the structures were divided can be seen in figure 2.3-2.5. The
figures also show the cells and different view of the structure. The cells were used to make
sure that the correct values of flow area and flow rate are simulated when the simulation is
running. Some structures, such the core region, are not modeled exactly. So, calculations had
to be made to assign parameters that averaged the flow areas of different regions. Other
calculations were also performed to model each region of the core and vessel and assign the
parameters needed for TRACE to simulate the model as accurately as possible. These
parameters were calculated from given parameters for the primary and secondary side. Table
2.1 gives a summary of the overall parameters of reactor core and reactor core vessel.
Figure 2.3 : General view of the Reactor Vessel and Core Model
17
Figure 2.4. Input data section for geometry and connections of Reactor Vessel
18
Figure 2.5. Input Data Section For Volumetric and Edge Data of Reactor Vessel
Figure 2.6. Control System for the Temperature Difference Calculation Between Hot Leg
and Cold Leg
19
Table 2.1. Reactor Core and Reactor Core Vessel Parameters
Parameter SI Units British Units
Vessel outer diameter 4.75 m 15.5ft
Vessel wall thickness 0.256 m 10.07in
Downcomer width 0.3 m 11.8in
Core barrel thickness 0.1524 m 6in
Reflector thickness 0.321 m 1.05ft
Fuel rod diameter 0.009499 m 0.373in
Fuel rod cladding thickness 0.000559 m 0.022in
Fuel rod gas gap thickness 0.000191 m 0.00751
Control rod diameter 0.009677 m 0.381in
Holes in LCSP 80 80
LCSP hole diameter 0.3048 m 12in
Holes in UCSP 80 80
UCSP hole diameter 0.3048 m 12in
Active fuel length 3.70 m 12.13
Inlet temperature 565 K 557.33deg F
Outlet temperature 598 K 616.73 deg F
Primary side pressure 1551320 Pa 225psi
Flow rate per hot leg 4400 kg / s 30.15 slug/s
Fuel rods per assembly 264 264
Number of fuel Assemblies 193 193
Surface area, control rods * 1.61132978 m2 17.3 ft2
Fuel pellet diameter * 0.008001 m 0.315in
Core area diameter * 3.20926974 m 10.5ft
Area of core region * 8.09 m2 87.1 ft2
Vessel inner diameter * 4.238 m 13.9ft
Diameter of core barrel * 3.3332 m 10.9ft
Area of Core Barrel * 8.72594814 m2 93.9 ft2
Flow area of Core Barrel * 8.72594814 m2 93.9 ft2
Barrel wetted perimeter * 10.4715566 m 34.3ft
Hydraulic diameter of core barrel * 3.3332 m 10.9ft
Hydraulic diameter of core * 0.01175642 m 0.463ft
Hydraulic diameter of downcomer * 0.31142712 m 12.2
Downcomer wetted perimeter * 24.7431837 m 81.0 ft.
Core wetted perimeter * 1522.21637 m 4994.09ft
Flow area of LCSP * 5.83727015 m2 62.8 ft2
Flow area of Core * 4.47396 m2 48.1 ft2
Flow area of Downcomer * 1.92642461 m2 20.7 ft2
Number of Control Rods 53 53
Pitch a 0.01260 m 0.04134ft
* Calculated parameters
a typical PWR fuel rod pitch
20
Calculations:
Fuel Pellet Diameter: ( )
Core Area Diameter: ( )
Area of Core Region:
Vessel Inner Diameter:
Core Barrel Diameter:
Core Barrel Diameter:
Core Barrel Area:
Core Barrel Flow Area:
Core Barrel Wetted Perimeter:
Core Barrel Hydraulic Diameter:
Core Hydraulic Diameter:
Downcomer Hydraulic Diameter:
Downcomer Wetted Perimeter:
( )
Core Wetted Perimeter:
Support Plate Flow Area :
Core Flow Area:
Downcomer Flow Area:
(
( ) )
Upper & Lower Core Support Plate Loss Coefficient: (
)
21
3. PUMP MODEL
For the pump models, we decided to use the given parameters for pump number 2 from
the built in model within SNAP. The model used built in Westinghouse pump curves.
We connected the four pump models to the cold legs of our loops and adjusted the
flow rate until we were able to reach steady state. The final pump parameters can be
seen in table 3.1 and 3.2.
Table 3.1. Reactor Coolant Pump Parameters
Parameter Pump 2
Parameter
Reactor Coolant Pump MOI 3455.0 kg-m2
Reactor Coolant Pump Hr 911.0 m2/s2
Reactor Coolant Pump Tr 35933.0 N-m
Reactor Coolant Pump Q''' 6.0 m3/s
Reactor Coolant Pump ρr 754.0 kg/m3
Reactor Coolant Pump ωr 124.5 rad/s
Reactor Coolant Pump Flow
Area 0.45673 m2
Reactor Coolant Pump Dh 0.762 m
In The pressurizer model we assumed a 60% water volume ratio and were given that
the total volume of the pressurizer was 75 m3. After choosing an inner diameter of 3 m,
we calculated the rest of the dimensions and parameters. The final parameters of the
pressurizer can be seen in table 3.2
Table 3.2. Reactor Coolant System Parameters
Parameter SI Units British Units Cold Leg ID 0.762 m 2.5ft
Hot Leg ID 0.762 m 2.5ft
Crossover Leg ID 0.762 m 2.5ft
Length of Cold Leg 7.620 m 2.5ft
Length of Hot Leg 7.620 m 2.5ft
Length of Crossover Leg 15.240 m 50ft
Pressurizer ID 3.000 m 9.842ft
Pressurizer Heater Power 1.860 MW ft-lbf/s
Pw Pressurizer 9.425 m 1341.0 hp
Pressurizer Flow Area 2.356 m2 25.4 ft2
Dh Pressurizer 1.000 m 3.28ft
Surge Line Length 10.000 m 32.8
Surge Line ID 0.356 m 1.17ft
Pressurizer Volume 75.000 m3 2648.6 ft3
Pressurizer Height 10.610 m 34.8
Reactor Coolant Pump FA 0.457 m2 4.91 ft2
Reactor Coolant Pump Dh 0.762 m 2.5ft
22
Calculations for the RCS parameters
Lengths of hot leg and cold are considered to be 10 times the inner diameter of the hot
and cold lengths respectively. For the length of the crossover leg, the length is calculated
based on the 20 times the inner diameter of the crossover leg.
Wetted perimeter of the pressurizer is determined by the following relation
To calculate the pressurizer flow area, relation of
has been used.
For the calculation of the hydraulic diameter of pressurizer, 4 times flow area of the
pressurizer is divided by the wetted perimeter of pressurizer which have been
calculated soon. In order to calculate the pressurizer height, volume of the pressurizer
is divided by pressurizer flow area.
Flow area of the reactor coolant pump is obtained via
. Finally, the hydraulic
diameter of the reactor coolant pump is assumed to be same with cold leg inner
diameter to be consistent.
23
4. Turbine Model
In the project, the turbine was not required as a different model in the med file.
Therefore, the turbine output work was evaluated via the control blocks. The control
block scheme for the turbine output power is illustrated in Figure **. The control blocks
are constructed to perform an energy balance across the turbine to estimate produced
turbine work. To calculate the output work, the following relation was used
∑
∑
Figure 4.1 Control Blocks Schematic for the Turbine Output Power Estimation with the
assumption of 0.90 isentropic efficiency and the ideal plant parameters.
24
This relation bases on the total energy produced by turbine from the inlet and
outlet streams through the turbine. Four streams were considered entering the turbine
since the reactor was a four-sensor Pressurized Water Reactor. Signal blocks were used
to obtain the steam exit slow rates and steam enthalpies from the exits of steam
generators to calculate the total inlet energy for the turbine. To calculate the exit
energy, exit enthalpy was assumed as a constant and exit flow rate which was same with
the inlet mass flow rate with corresponding to conservation of mass. The exit enthalpy
was calculated with the assumption of 0.90 isentropic efficiency at atmospheric pressure
conditions as
( )
The values used during calculations were obtained from the reference [****]. 2.33x
J/kg was accepted as a constant during the calculation of the produced turbine work.
III. SUBSYSTEM RESULTS
5. STEAM GENERATOR RESULTS
Figure 5.1 Primary side hot and cold leg temperatures
25
Figure 5.1 above shows the Primary side hot and cold leg temperatures of the
standalone Steam Generator results of the pre-finalized steam generator model. This
figure shows the temperature difference across the primary side before the boiler fills.
The boiler can be seen to fill steadily in figure 5.2 below. As stated this was the pre-
finalized model and was corrected in the base steady state model by adjusting the steam
mass flow rate of the secondary side.
Figure 5.2: Boiler liquid level
Figure 5.3: Downcomer liquid level
26
Figure 5.2 and Figure 5.3 simply show that the water levels and were the primary source
in determining the accuracy of the model. As stated above, the model continued to fill
causing a fatal error until the secondary steam mass flow rate was adjusted prior to the
model implementation into the Base Steady State model.
Figure 5.4: Steam mass flow rate
In Figure 5.4, it can be seen that the Steam mass flow rate of the secondary side reaches
a steady state of 320 kg/s. This value is lower than the final value that can be seen from
the Base Steady state model in the sections to follow.
27
6. REACTOR CORE / VESSEL RESULTS
Figure 6.1: Reactor mass flow rate
In Figure 6.1 shows the Reactor Core mass flow to be 4400 kg/s. Figure 6.2 shows the
temperature difference across the core before the time step was adjusted.
28
Figure 6.2: Temperature difference between hot leg and cold leg
Time-step is changed to 1.0e-05 for minimum and 0.1 for maximum. This change
enhances the convergence of the steady-state solution.
29
Figure 6.3: Hot leg mass flow rate
Figure 6.4: Temperature difference between hot and cold legs
30
Figure 6.3 and Figure 6.4 show the core mass flow rate and temperature difference of
the pre-finalized core model. The heat structures to model the vessel and boiler wall
are to be inserted, the results of which can be seen in the base steady state model
section to follow.
7. PLANT BASE STEADY STATE RESULTS
After developing and correcting the major components of each separate Subsystem,
that is the Steam Generator and the Reactor Core Models, were combined to form a
four loop compound PWR model that can be seen in figure 7.1 below. This model
included the addition of the hot leg, cold leg, and cross-over piping, as well as a
pressurizer system on loop one.
Figure 7.1: Pressurized Water Reactor Plant
31
This primary loop model was run to steady state in approximately one thousands
seconds. The Steady state primary mass flow rate, seen in figure 7.2, can be seen to be
slightly smaller than the 4400 kg/s that was expected. The hot and cold leg temperature
difference can be seen only around 30 K in figure 7.3.
Figure 7.2: Primary Mass Flow Rate
Figure 7.3: Hot Leg Temperature
32
Figure 7.4: Primary Side Pressure
Figure 7.5: Pump pressure
The pressure of the system is seen as expected in figure 7.4, but the pump pressure run
with some discrepancy in figure 7.5.
33
Figure 7.6: Reactor Power
The Reactor power seen above in Figure 7.6 is constant as expected for the steady state
model, this graph simply serves as a steady state basis. Figure 7.7 below shows the
Steady State secondary side Steam Mass flow rate of the steam generator. The flow
rate is below the goal of 480kg/s but must be maintained at this level in order not to fill
the boiler.
Figure 7.7: Steam Mass Flow Rate
34
Figure 7.8: Steam Temperature
The steam temperature of the secondary side is shown to reach steady state, and is in
an acceptable range as seen in Figure 7.8 above. It can be seen to approach a lower
temperature prior to the time at which the boiler water level achieves a steady state
value which is seen below in figure 7.9.
Figure 7.9: Boiler Water Level
35
The control block Schematic in figure 7.10 above simply illustrates that the boiler water level is
a signal variable parameter.
Figure 7.10: Control Blocks Schematic
for the Boiler Water Level Estimation
36
Figure 7.11: Turbine Output Power during the steady-state
Figure 7.11 shows the calculated turbine output power at steady-state conditions. The
steady-state value of the turbine power is about 850 MW which corresponds to an
approximate value for the plant efficiency 27%. Under all the assumptions, the resulting
plant efficiency is quite close to the given plant efficiency 32 %. The relative error is
calculated as15%.
37
8. PLANT TRANSIENT RESULTS
Upon developing a compound four loop base steady model, and seeing it runs to a
reasonable Steady state solution, the model was run using a five percent power
transient modeled with the table lookup Power option under the power component in
the restart case. The secondary side flow rate was also set to a transient state to
compensate for the increase in temperature from the resulting power step. The power
transient was a five percent increase and can be shown below in table 8.1 and the
Secondary side flow rate transient can be seen in table 8.2 next to it. This can also be
seen graphically in figure 8.1 and 8.2 below which show the Steam Generator feed water
and exit steam mass flow rate on both a macro and microscopic level.
Figure 8.1 Steam Generator Feedwater and Figure 8.2 Steam Generator Feedwater and
Exit Steam Mass Flow Rate (General Trend) Exit Steam Mass Flow Rate (closer view to
transient)
Table 8.1 Transient Power Table Table 8.1 Transient Secondary Side Fill Table
38
Figure 8.3: Transient Primary Mass Flow Rate
The Figure 8.3 above, shows the Primary Mas Flow rate evaluated at the hot leg which is
for an unknown reason affected by the power transient but stays mainly consistent with
the steady state model. And Figure 8.4 below shows the transient jump in reactor
power.
Figure 8.4: Transient Reactor Power
39
Figure 8.5: Cold leg temperature during the transient
Above in Figure 8.5 is the microscopic and microscopic cold leg temperature near the transient
which suffer only just over a one degree change during the transient. While Figure 8.6 below
shows the micro and macroscopic Hot leg temperature just after the transient.
Figure 8.6: Hot leg temperature during the transient
40
Figure 8.7: Steam Generator boiler water level during the transient (general view)
Next, we will look at the Steam generator boiler water level. We can see the macro in figure
8.7 above and the micro in figure 8.8 below. There is a small drop in water level of about three
centimeters, which is intuitive because as the temperature increases with power, more water
boils off. Even though this is counteracted by the increase in secondary side steam mass flow, a
differential of three centimeters was deemed acceptable.
Figure 8.8: Steam Generator boiler water level during the transient (closer view to transient)
41
Figure 8.9: Downcomer water level during the transient
We also recorded the Down comer water level on a macro, figure 8.9 above, and micro, figure
8.10 below. The downcomer water level increase is caused by the increase in Steam mass flow.
Figure 8.10: Downcomer water level during the transient (closer view to transient)
42
Figure 8.11: Primary side pressure during the transient
Finally we model the system pump pressure which encounters a minor jump after the transient
seen in figure 8.11 above. And the system pump pressure in figure 8.12 below which has the
same differential between pumps that we saw in the base steady state calculation.
Figure 8.12: Pump pressure during the transient
43
Figure 8.13 Turbine outlet power during the transient
As shown in the Figure 8.13, the turbine outlet power reaches the value of 870 MW
which is same with the value at steady-state conditions as one can expect to obtain. It is
already known that the applied transient is before 500 seconds and the system
compensates that value. At the beginning of the solution, the decrement in the
secondary mass flow rate leads to decrease in the produced power through the turbine.
44
Figure 8.14: Turbine inlet temperature during the transient
Namely, Figure 8.14 shows the decrement in the secondary mass flow rate is causing the
turbine inlet temperature decrease.
Figure 8.15. Turbine inlet pressure during the transient
It is clear to observe that there is no obvious change in the turbine inlet pressure as
one can expect.
45
IV. STEAM GENERATOR SUBSYTEM RICHARDSON ERROR
ANALYSIS
Richardson extrapolation is a sequence acceleration method which is used to
improve the rate of convergence of a sequence in numerical analysis. The
Richardson extrapolation error analysis was performed using the isolated steam
generator model in which feedwater flow transient is generated as in the following
Table *. The feedwater flow transient is applied three cases which have different
steam generator meshes. Steam exit mass flow rate change with time is shown at
Figure *.
Table 9.1: Prescribed steam generator feedwater flow rate transient
t [s] Feedwater
Flow Rate
[kg/s]
0 350
200 350
201 330
300 330
301 350
400 350
Figure 9.1: Steam exit mass flow rate versus time with the initiation of the feedwater
flow rate transient.
46
The mass flow rates for the Richardson Error Analysis were evaluated at the 25 seconds
for each cases. The point was chosen in order to estimate the error changes since it
was required to obtain the steam mass flow rate error at a point which it undergone
the largest change. A code which had been written in C++ language was included at
Appendix II to evaluate the error analysis by utilizing the Richardson extrapolation error
analysis. The calculated error was assigned to finest mesh. Under the desired
considerations, a time of 205 seconds was chosen to obtain the steam exit mass flow
rates for each case. The obtained steam exit mass flow rates were 352.4356 kg/s,
354.3546 kg/s and 354.6854 kg/s respectively for the cases base, x2 and x4 meshes. The
mesh sensivity studies were performed in accordance with the number of cells being
doubled with the refinement ratio progressively. The spatial order of accuracy is
calculated via the written code as
(
) ( )=-2.536324
The spatial error being associated with the finest mesh was evaluated as
( )
=±2.318701 kg/s
47
V. CONCLUSIONS
The major components of a PWR were developed separately to model a typical PWR
design. The parameters of each system component was calculated and adjusted based on
simulation results until steady state could be achieved at a desired value. We were able to
achieve steady state when the components were put together. Our outputs also came
relatively close to our desired plant data as shown in our results section. After achieving
steady state, a transient was initiated by imposing a 5% increase in reactor power. The
changes in the reactor systems, such as temperature, pressure and mass flow rate, were as
expected. As a result of the core power increase, the output power of the turbine increase
proportionally as well. The model perfectly capable of modeling the transient and the
marginal power increase did not fatally perturb the reactor system or components.
Achieving symmetry between each primary loop and determining the proper mass flow
rate within them took the most effort. Overall, our model and simulation were created
successfully and supported us in gaining further insight into the capabilities of SNAP and
TRACE.
48
VI. REFERENCES
[1] NUCE470 final report Group F. Sample report for the final project.
[2] Numerical Methods for Ordinary Differential Equations, 2nd edition
by J.C. Butcher
[3] Duderstadt, J. J., & Hamilton, L. J. (1942). Nuclear Reactor Analysis. Ann Arbor,
Michigan: John Wiley & Sons.
[4] Lamarsh J. R., & Baratta, A. J. (2001). Introduction to Nuclear Engineering. Upper
Saddle River NJ: Prentice Hall.
[5] Buongiorno, J. (Fall 2010). PWR Description. 22.06: Engineering of Nuclear
Systems. MIT, Cambridge, MA. Retrieved (Fall 2013) from
http://ocw.mit.edu/courses/nuclear-engineering/22-06-engineering-of-
nuclear-systems-fall-2010/lectures-and-readings/MIT22_06F10_lec06a.pdf
49
APPENDIX A: LIST OF ENCLOSURES
File Name Description
FinalProject.med Annotated SNAP Model Editor File for the plant
RichardsonExtrap_Model.med SNAP Model Editor File Richardson Extrapolation
FinalSteadyState_Input.inp Plant steady state run input file
FinalSteadyState_output.out Plant steady state run output file
Restart_Input.inp Plant transient run input file
Restart_Output.out Plant transient run output file
RichardsonExtrap_C++Code.cpp C++ code for the Richardson Error Analysis
50
APPENDIX B: Richardson Error Analysis
Richardson extrapolation consists of calculating a result in a manner that depends on a small
parameter, and for which the error in the calculation varies systematically as the parameter
varies. By using a sequence of values of the parameter, much of the effect of the errors can be
eliminated so that improved accuracy results [2].
( )
(
) (
)
(
) (
)
…
(
) ( )
( )
( )
…
51
Written C++ code for the Richardson Error Analysis
// RICHARDSON EXTRAPOLATION #include <iostream> #include <stdio.h> #include <math.h> #include <errno.h> #define _CRT_SECURE_NO_DEPRECATE #define PI 3.142857 using namespace std; FILE *pout; errno_t err = fopen_s(&pout, "richardson.txt", "w+"); int main(void) { // Open for write if (err != NULL) { printf("\nThe files were not opened...\n", err); } else { printf("\nThe files were opened...\n"); long double r_value = 0.0; long double func[3] = { 0, 0, 0 }; long double error[3] = {0, 0, 0}; long double p[3] = {0, 0, 0}; printf("enter the values of the functions respectevily. f1, f2 .. fn\n"); for (int i = 0; i < 3; i++) { printf("f(%d) : \t",i); cin >> func[i]; } printf("enter the value of r \n"); cin >> r_value; for (int i = 2; i < 3; i++) { p[i] = (func[i] - func[i - 1]) / (func[i-1] - func[i - 2]); p[i] = log(p[i]) / log(r_value); error[i] = func[i - 1] - func[i - 2]; error[i] /= pow(r_value, p[i]) - 1; fprintf(pout, "%llf \t %llf \n", p[i], error[i]); } } fclose(pout); return 0; }