51
1 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

Vivanco Dunning Toptan FinalProject NucE470

Embed Size (px)

Citation preview

Page 1: Vivanco Dunning Toptan FinalProject NucE470

1

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

Page 2: Vivanco Dunning Toptan FinalProject NucE470

Dunning, Toptan, Vivanco NucE 470 Final Project 2013

2

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.

Page 3: Vivanco Dunning Toptan FinalProject NucE470

Dunning, Toptan, Vivanco NucE 470 Final Project 2013

3

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

Page 4: Vivanco Dunning Toptan FinalProject NucE470

Dunning, Toptan, Vivanco NucE 470 Final Project 2013

4

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

Page 5: Vivanco Dunning Toptan FinalProject NucE470

Dunning, Toptan, Vivanco NucE 470 Final Project 2013

5

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

Page 6: Vivanco Dunning Toptan FinalProject NucE470

Dunning, Toptan, Vivanco NucE 470 Final Project 2013

6

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

Page 7: Vivanco Dunning Toptan FinalProject NucE470

Dunning, Toptan, Vivanco NucE 470 Final Project 2013

7

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

Page 8: Vivanco Dunning Toptan FinalProject NucE470

Dunning, Toptan, Vivanco NucE 470 Final Project 2013

8

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

Page 9: Vivanco Dunning Toptan FinalProject NucE470

Dunning, Toptan, Vivanco NucE 470 Final Project 2013

9

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.

Page 10: Vivanco Dunning Toptan FinalProject NucE470

Dunning, Toptan, Vivanco NucE 470 Final Project 2013

10

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

Page 11: Vivanco Dunning Toptan FinalProject NucE470

Dunning, Toptan, Vivanco NucE 470 Final Project 2013

11

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.

Page 12: Vivanco Dunning Toptan FinalProject NucE470

Dunning, Toptan, Vivanco NucE 470 Final Project 2013

12

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:

Page 13: Vivanco Dunning Toptan FinalProject NucE470

Dunning, Toptan, Vivanco NucE 470 Final Project 2013

13

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:

Page 14: Vivanco Dunning Toptan FinalProject NucE470

Dunning, Toptan, Vivanco NucE 470 Final Project 2013

14

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.

Page 15: Vivanco Dunning Toptan FinalProject NucE470

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

Page 16: Vivanco Dunning Toptan FinalProject NucE470

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

Page 17: Vivanco Dunning Toptan FinalProject NucE470

17

Figure 2.4. Input data section for geometry and connections of Reactor Vessel

Page 18: Vivanco Dunning Toptan FinalProject NucE470

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

Page 19: Vivanco Dunning Toptan FinalProject NucE470

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

Page 20: Vivanco Dunning Toptan FinalProject NucE470

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: (

)

Page 21: Vivanco Dunning Toptan FinalProject NucE470

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

Page 22: Vivanco Dunning Toptan FinalProject NucE470

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.

Page 23: Vivanco Dunning Toptan FinalProject NucE470

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.

Page 24: Vivanco Dunning Toptan FinalProject NucE470

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

Page 25: Vivanco Dunning Toptan FinalProject NucE470

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

Page 26: Vivanco Dunning Toptan FinalProject NucE470

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.

Page 27: Vivanco Dunning Toptan FinalProject NucE470

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.

Page 28: Vivanco Dunning Toptan FinalProject NucE470

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.

Page 29: Vivanco Dunning Toptan FinalProject NucE470

29

Figure 6.3: Hot leg mass flow rate

Figure 6.4: Temperature difference between hot and cold legs

Page 30: Vivanco Dunning Toptan FinalProject NucE470

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

Page 31: Vivanco Dunning Toptan FinalProject NucE470

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

Page 32: Vivanco Dunning Toptan FinalProject NucE470

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.

Page 33: Vivanco Dunning Toptan FinalProject NucE470

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

Page 34: Vivanco Dunning Toptan FinalProject NucE470

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

Page 35: Vivanco Dunning Toptan FinalProject NucE470

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

Page 36: Vivanco Dunning Toptan FinalProject NucE470

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%.

Page 37: Vivanco Dunning Toptan FinalProject NucE470

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

Page 38: Vivanco Dunning Toptan FinalProject NucE470

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

Page 39: Vivanco Dunning Toptan FinalProject NucE470

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

Page 40: Vivanco Dunning Toptan FinalProject NucE470

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)

Page 41: Vivanco Dunning Toptan FinalProject NucE470

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)

Page 42: Vivanco Dunning Toptan FinalProject NucE470

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

Page 43: Vivanco Dunning Toptan FinalProject NucE470

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.

Page 44: Vivanco Dunning Toptan FinalProject NucE470

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.

Page 45: Vivanco Dunning Toptan FinalProject NucE470

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.

Page 46: Vivanco Dunning Toptan FinalProject NucE470

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

Page 47: Vivanco Dunning Toptan FinalProject NucE470

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.

Page 48: Vivanco Dunning Toptan FinalProject NucE470

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

Page 49: Vivanco Dunning Toptan FinalProject NucE470

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

Page 50: Vivanco Dunning Toptan FinalProject NucE470

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].

( )

(

) (

)

(

) (

)

(

) ( )

( )

( )

Page 51: Vivanco Dunning Toptan FinalProject NucE470

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; }