1. NUC E 470: FINAL
PROJECT REPORT
Team Members: Nicholas Manuk and Troy Todd
Report Submitted: December 14, 2015
2. 1
Abstract:
The following report indicates the methods we chose in creating a four loop PWR. The final
product we were to create is a steady reactor that can return to steady state after a transient is
implemented. The model we created would reach a theoretical steady state, by this we mean it
would show steady state in our chosen plots but not in our output text file. We push through
this difficult in the attempt to make a transient work that would increase our power %5. This
did not work and we have thus omitted most graphs and tables dealing with this.
3. 2
Table of Contents:
Abstract.........................................................................................................................................1
Table of Contents ..........................................................................................................................2
List of Figures ................................................................................................................................3
List of Tables .................................................................................................................................4
Introduction...................................................................................................................................5
Model Development......................................................................................................................6
Steam Generator ........................................................................................................................6
Reactor Vessel/Cores and Pressurizer........................................................................................10
Pump...........................................................................................................................................16
Turbine........................................................................................................................................17
Results of Systems.........................................................................................................................19
Steam Generator ........................................................................................................................19
Reactor Vessel/Cores and Pressurizer........................................................................................23
Pump...........................................................................................................................................26
Turbine........................................................................................................................................29
Plant at Steady State.....................................................................................................................30
Plant Transient..............................................................................................................................38
Conclusions ...................................................................................................................................39
Appendix........................................................................................................................................40
4. 3
Figures:
Figure 1 – Model of Steam Generator implemented in TRACE....................................................7
Figure 2 – Representation of the PWR Reactor Vessel and all of its inner components [Source:
Nuc E 470 Course Textbook] .........................................................................................................11
Figure 3- Representation of the cross section of the reactor vessel. [Source: Nuc E Course
Textbook].......................................................................................................................................12
Figure 4– Inputs to Reactor Vessel Height ...................................................................................12
Figure 5- Input Data on the Reactor Radial Rings ........................................................................12
Figure 6 – The TRACE model of the completed Reactor Vessel and Pressurizer..........................15
Figure 7 – Model of Pump Test systemin TRACE.........................................................................17
Figure 8 – Control Block diagram for the Turbine Work...............................................................19
Figure 9 – Graph of Hot Leg and Cold Leg temperature................................................................20
Figure 10 – Graph of mass flow rate in both Hot Leg and Cold Leg .............................................21
Figure 11 – Graph of Mass Flow Rate into and out of Steam Generator......................................22
Figure 12 – Graph of Liquid Levels in Downcomer and Boiler......................................................23
Figure 13 – Exit Mass Flow Rate for Hot Leg – Reactor Vessel ....................................................24
Figure 14–Cold Leg Exit Temperature – Reactor Vessel...............................................................24
Figure 15 –Reactor Power – Reactor Vessel.................................................................................25
Figure 2 – Hot Leg Exit Temperature – Reactor Vessel ................................................................26
Figure 3 – Pressurizer Pressure Difference – Reactor Vessel.......................................................26
Figure 18- Pressurizer Water Level - Reactor Vessel....................................................................27
Figure 19- Mass Flow Rate from Hot Leg through Coolant Pump and into Cold Leg ...................28
Figure 20- Pressure Levels from RCP into Cold Leg ......................................................................29
Figure 21 – Turbine Power ............................................................................................................30
Figure 22 – Steady State Final Reactor Model ..............................................................................31
Figure 4- Hot Leg Exit Mass Flow Rate - Steady State...................................................................32
5. 4
Figure 24- Hot Leg Exit Temperature - Steady State.....................................................................33
Figure 25- Hot Leg Exit Pressure - Steady State............................................................................34
Figure 5 - Pump Pressures - Steady State .....................................................................................35
Figure 6 - Steam Mass Flow out of SGs - Steady State..................................................................36
Figure 78 - Steam Temperature - Steady State.............................................................................37
Figure 89- Water Levels in Boiler - Steady State...........................................................................38
Figure 30 - Cold Leg Exit Temp. - Steady State..............................................................................39
Tables:
Table 1 – List of Values implemented in Steam Generator seen in Figure 1................................12
Table 2 –Vessel and Core data......................................................................................................14
Table 3 – Pressurizer, Pump, Surge Line, and Cold, Hot, and Crossover Leg data. ......................16
Table 4 – Table of Data implemented into coolant pump test section........................................17
6. 5
Introduction:
The nuclear power plant is one of the most incredible marvels of modern science that
there exists today. Nuclear power affects lives around the United States and all around the
world. Serving as one of the main power sources for homes and businesses, nuclear energy is
something to marvel. That being said, the control of a nuclear power plant is where all of this
magic begins. The proper control of a nuclear power plant, specifically a Pressurized Water
Reactor (PWR), includes not allowing coolant to boil, creating a proper mass flow over large
stretches of piping, and maintaining single or two phase flow as necessary. It is beneficial from
the standpoint of safety, economics, and efficiency standpoint that a nuclear reactor operates
well on all cylinders. This includes the steam generator, turbine, reactor vessel, and coolant
pump to name a few. The PWR utilizes highly pressurized and very heated water as a means of
heating up cooler water, converting it into steam, and having that steam spin a turbine to
produce massive amounts of electricity, while the hot water maintains its position in a loop
through the entire reactor.
In this experiment the program known as the Symbolic Nuclear Analysis Package (SNAP)
was used to model these steps, and investigate the differences in pressure, temperature, and
mass flow through several portions of the nuclear reactor facility, and most importantly,
evaluate its safety vs. expected results. The goal is to build individual reactor pieces (Steam
Generator, Reactor Vessel, Coolant pumps) and evaluate them individually to earn a better
appreciation and understanding of how they work, and ultimately put them all together to see
how one’s input affects another’s output and vice versa. This PWR will be modeled and the
results will be analyzed through the APT Plot application. An analysis on these plots will be
conducted, and a transient will be enacted during a simulation to further investigate how the
reactor behaves under new conditions. The experiment will conclude with a discussion of what
was learned and suggestions for future work.
7. 6
Model Development:
Model Development of Steam Generator:
The steamgenerator we modeled is based off a given model from the stgenSS3.inp model
presented throughout this course. The model we used is a simpler representation of a real
steam generator. Steam generators that are implemented in power plants have many more
items of interest that need to be considered such as heat transfer. This model needed several
adjustments to the geometry to match what we planned on creating in our model. The table
below lists the information used to create the steam generator. Also present is a copy of a
single steamgenerator created in TRACE, only one is listed due to the other 3 being exact
replicas of this model. To create the steam generator we would implement many calculations
were needed to get exact values of our geometry. As seen in the table below the given values
were useful in finding our values. Due to the number of calculations we needed to do only the
most significant ones will be discussed in detail in this section. The remaining calculations can
be found in the appendix on the appropriate headline for the steam generator.
An important value in this system and that it is critical in implementation is the Steam
Generator Tube Inner Flow Area. This value is calculated by the equation:
𝐴 𝑇𝑢𝑏𝑒
𝐼
=
𝜋
4
(𝐷 𝑇𝑢𝑏𝑒
𝐼
)2
This value is critical due to the change it has on the flow rate through the steam generator and
thus impacting the flow through the hot and cold leg of our pipes. An example of an issue is if
the calculated is too high then the flow rate will decrease and the reactor coolant pump will
have to increase in speed to match the required flow (if this exceeds the rated speed then the
pump could fail). Along with this calculation 2 other values decide this flow rate. They are listed
below, in order the Plenum Inlet and Outlet Hydraulic Diameter.
𝐴 𝑃𝐿
𝐼
=
𝜋
4
∗ 𝐷 𝐻𝐿
𝐼 2
𝐴 𝑃𝐿
𝐼
=
𝜋
4
∗ 𝐷 𝐻𝐿
𝐼 2
These values are the inlet to the tube flow area. These values should be smaller than the overall
tube hydraulic diameter, this increase the flow area into the pipes and thus out of the pipe
allow for the steam generator to run the turbine.
On the copy of the TRACE model of the steamgenerator below, some important aspects can be
identified, such as the above calculations as well as each section of the steam generator (i.e.
feedwater nozzle, downcomer, etc.).
8. 7
Figure 9 – Model of Steam Generator implemented in TRACE
1. Steam Generator Tube Bundle
2. Steam Generator
3. Transition Cone
4. Feedwater Nozzle
5. Steam Generator Downcomer
6. Steam Generator Exit/Turbine Input
7. Feedwater Input
Primary Side Given As-Built Units
Tube Outer Diameter 0.01905 0.01905 m G
1. 6.
5.
4.
3.
2.
7.
9. 8
Tube Wall Thickness 0.001092 0.001092 m G
Tube Inner Diameter 0.016866 0.016866 m C
Average Tube Length 16 16 m G
Number of Tubes 4674 4674 G
Tube Inner Flow Area 2.23E-04 2.2E-4 m^2 C
Tube Pattern Square Square G
Tube Pitch 0.027 0.027 m G
Tube Inside (Dh) 0.016866 0.016866 m C
Hot Leg ID 0.75 0.75 m G
Cold Leg ID 0.7 0.7 m G
Plenum Inlet Flow Area Hot Leg 0.4418 0.4418 m^2 C
Plenum Inlet Flow Area Cold Leg 0.3848 0.3848 m^2 C
Tube Sheet Flow Area 2.88 2.88 m^2 C
Tube Sheet Thickness 0.6 0.6 m G
Plenum Height 1.6 1.6 m G
Plenum Volume Average Flow Area 0.6603889 0.6603889 m^2 C
Total Plenum Volume 9.323 1.32 m^3 C
Plenum Inlet Hydraulic Diameter 0.75 0.75 m C
Plenum Outlet Hydraulic Diameter 0.7 0.7 m C
P.S. Inlet Temperature 610 550 K G
P.S. Outlet Temperature 560 550 K C
P.S. Pressure 15513203 1.55137E7 Pa G
SG P.S. Flow Rate 4600 4600 K g/s G
Tube Bundle Outer Radius 1.57 1.57 m C
Tube Bundle Inner Radius 0.081 0.081 m C
Average Tube Bundle Radius 0.8255 0.8255 m C
Length of Average Tube Bundle Bend 2.59 2.59 m C
Height of Tube Bundle 6.97 6.97 m C
Height of Tube Bundle Straight Portion 5.406 5.406 m C
Tube Bundle Material
Inconel
600 m G
Secondary Side
Boiler Region Hydraulic Diameter 6 0.0937 m C
Downcomer Annulus Width 0.06 0.06 m G
Downcomer Flow Area 0.90477 0.9077 m^2 C
Downcomer Hydraulic Diameter 0.18 0.18 m C
Equivalent Tube Bundle Diameter 1.44 1.44 m C
Feedwater Temperature 503.15 503.15 K G
Height of Bottom Boiler Transition 0.1 0.1 m G
Height of Secondary Side 14.4 14.4 m C
Height of Transition Cone 0.8945 0.8945 m C
10. 9
Lower Boiler Flow Area 5.771 5.771 m^2 G
Lower Shell ID 3.29 3.29 m G
SG Total Height 16.8 16.8 m G
Steam Flow Rate per Loop 644 460 kg/s G
Steam Line Diameter 0.84 0.84 m G
Steam Pressure 7708338 1.5E6 Pa G
Transition Cone Hydraulic Diameter 0.1 0.1 m G
Transition Cone Volume Average Flow
Area 8.264 8.264 m^2 C
Tube Bundle Flow Area 6.522 6.522 m^2 C
Tube Heat Transfer Area (Outside
Tube) 0.955 0.955 m^2 C
Tube Lane Area 0.50382 0.50382 m^2 C
Tube Lane Width 0.162 0.162 m C
Upper Dome Height 0.5 0.5 m G
Upper Dome Volume 0.261799 0.261799 m^3 G
Upper Dome Volume Average Flow
Area 0.5235 0.5235 m^2 G
Upper Shell Fluid Volume 50.14 50.14 m^3 C
Upper Shell Height 6.6 6.6 m G
Upper Shell Hydraulic Diameter 6 6 m G
Upper Shell ID 4.6 4.6 m G
Upper Shell Voume Average Flow Area 16.6 16.6 m^2 C
Volume of Transition Cone 7.392 7.392 m^3 C
Wrapper Wall Inner Diameter 3.11 3.11 m C
Wrapper Wall Thickness 0.03 0.03 m G
Table 1 – List of Values implemented in Steam Generator seen in Figure 1
11. 10
Model Development of the Reactor Vessel/Core and Pressurizer
The following model development and parameter selection was composed surrounding the
given data of the R2/D3 PWR. This was one of the more difficult components to compose,
given the nature of its design. There includes in this component a core barrel and a reactor
vessel surrounding it, with a small downcomer area between them. The sample file
reactorCore.inp was used as a starting point in developing this model. To model the heat which
is present through each portion of the reactor, heat structures were aligned as fuel rods, and on
the sides of the core barrel and reactor vessel. In addition, cold and hot leg pipes which are
connected to the left and right sides of the vessel, respectively mimic the flow immediately
coming in and out of the reactor vessel. The inlet and outlet water flow in and out of the cold
and hot leg pipes have temperature and pressure specifications set by Breaks and Fills that
attempt to portray conditions seen in the steamgenerator model. A pressurizer was connected
to one of the four hot legs to maintain high pressure, such that the water flowing out of the
reactor vessel does not boil while under such high temperatures.
re.
12. 11
Figure 2 – Representation of the PWR Reactor Vessel and all of its inner components, which were used to model the
experimental design. [Source: Nuc E 470 Course Textbook]
The reactor vessel modeling on TRACE allows for height changes to 7 different regions
vertically. Using the above figure as a guide, those 7 regions were selected as follows: 1 – (the
bottom most region) was selected to be the height of the lower plenum, which is everything
underneath the core barrel in the figure. 2 is the thickness of the lower support plate. 3, 4, and
5 are collectively the height of the fuel assembly. 6 is the height of the upper guide structure,
and 7 is the height of the upper dome, which is above the upper support plate. These results
are shown as inputs to the TRACE model in the figures below. Radially, There are two regions,
the first being the core barrel, and the second being the downcomer, which has a boundary
condition set by the vessel wall. This shape was based off of the following figure. The azimuthal
sections of the core was assumed to be 90 degrees, which is a clear assumption because for
each fuel rod to be utilized evenly, the 4 sections must be equal in shape.
Figure 3- Representation of the cross section of the reactor vessel. [Source: Nuc E Course Textbook]
13. 12
Figure 4– Inputs to Reactor Vessel Height
Figure 5- Input Data on the Reactor Radial Rings
The following Table will assess the parameters that were used as inputs to create the Reactor
Vessel.
Parameter As built Unit
Active Fuel Length 4 m
Centerline Height of Cold Leg 7.884 m
Centerline Height of Hot Leg 7.884 m
Core Barrel ID 3.5752 m
Core Barrel OD 3.88 m
Core Barrel Thickness 0.1524 m
Core Flow Area 10.02 m^2
14. 13
Core Fluid Volume 27.060617 m^3
Core Hydraulic Diameter 3.574 m
Core Thermal Power 3.50E+03 MW_t
Downcomer Flow Area 0.90477 m^2
Downcomer Height 8.8 m
Downcomer Hydraulic Diameter 0.18 m
Downcomer Width 0.28 m
Efficiency 32 %
Equivalent Diameter of Core 2.861 m
Flow Area of Upper Head 13.93471094 m^2
Flow Rate Per Hot Leg 4600 Kg/s
Fuel Assembly Array 17 x 17 N/A
Fuel Pellet Diameter 0.008001 m
Fuel Rod Cladding Thickness 0.0005588 m
Fuel Rod Diameter 0.0094996 m
Fuel Rod Gas Gap Thickness 0.0001905 m
Fuel Rod Lattice Square N/A
Fuel Rod Pitch 0.0126 m
Height of Lower Plenum 2.22 m
Height of Upper Dome 2.2 m
Height of Upper Head 4.1 m
Height of Upper Support Plate (bottom) 10.75 m
Holes in LCSP 80 m
Holes in UCSP 80 m
Inlet Temperature 587 K
LCSP Flow Area 5.834310912 m^2
LCSP Fluid Volume 3.109687716 m^3
LCSP Hole Diameter 0.3048 m
LCSP Thickness 0.533 m
Loss coeff. For LCSP 0.1388878173 N/A
Loss coeff. For UCSP 0.01034427299 N/A
Net Electrical Power 6.71E+02 MW_e
Number of Fuel Assemblies 193 N/A
Number of Fuel Rods per Ass. 264 N/A
Outlet Temperature 605 K
Primary Side Pressure 15713203 Pa
Reactor Vessel Height 13.253 M
Reflector Thickness 0.4324 M
Thickness of Upper Support Plate 0.34 M
Total Assembly Height 4.21 M
Total Core Area 2.9559 m^2
15. 14
UCSP Flow Area 5.834310912 m^2
UCSP Fluid Volume 2.522756038 m^3
UCSP Hole Diameter 0.3048 m
UCSP Thickness 0.051 m
Vessel ID 4.44 m
Vessel OD 4.952 m
Vessel Wall Thickness 0.256 m
Volume of Lower Plenum 5.470524 m^3
Volume of Upper Dome 15.1976 m^3
Volume of Upper Head 52.7834 m^3
Table 2 –Vessel and Core data
The parameters that are in boldface font represent the values that were calculated using the
rest of the parameters (given) and knowledge of PWR geometry. The values that were
calculated were calculated using the equations listed in the appendix.
Figure 6 – The TRACE model of the completed Reactor Vessel and Pressurizer
Many changes were made in the development of the core model, for instance, the inlet speeds
and energy of the core needed to have slight adjustments following many attempts to achieve
steady state. In several of the attempts to run the reactor, the fuel elements became too hot
and therefore power needed to be reduced and pressure needed to be raised, although that
will be discussed more in the subsystemresults section.
The following are the initial conditions for the Pressurizer and the details that went into
developing it. The purpose of the pressurizer is to maintain a high pressure and therefore
16. 15
keeping the coolant in the liquid phase. This high pressure is maintained by water flowing into
the pressurizer, which is set to be 50% full upon initial conditions, and compressing the gas that
compresses with the rising water level.
Parameter As-Built Values Units
Cold Leg ID 0.7 m
Hot Leg ID 0.75 m
Crossover Leg ID 0.7 m
Length of Cold Leg 7 m
Length of Hot Leg 8.438 m
Length of Crossover Leg 14.6125 m
Pressurizer ID 2.8 m
Pressurizer Heater Power 1386000 W
Surge Line Length 10 m
Surge Line ID 0.3556 m
Pressurizer Volume 75 m^3
Pressurizer Height 12.18 m
Reactor Coolant Pump Flow Area 0.38465 m^2
Reactor Coolant Pump Hydraulic Diameter 0.7 m
Table 3 – Pressurizer, Pump, Surge Line, and Cold, Hot, and Crossover Leg data.
The length of the cold leg was specified to be cold leg diameter multiplied by 10. The hot leg
length was calculated similarly, but this included a 45 degree angle, which can be seen in the
above figure. Pressurizer height was determined by dividing the volume by the given flow area
(derived from inner diameter), assuming that the pressurizer is shaped roughly like a cylinder.
17. 16
Model Development of Pump:
The pump model was pulled from a table of data (listed below) given to us by the instructor.
We decided to use pump 3 on our model as it passed our test systemand produced a steady
state graph at a lower pump speed. The pump was used to drive the coolant flow from the hot
leg to the cold leg. This is important to the mode as it helps achieve steady state between our
hot leg and cold leg mass flow rates. After implementing the standard data we connected 4
pumps to our systems. The pump was placed between our hot leg and cold leg with a crossover
leg consisting of X 90 degree angles and X 45 degree angles. After these pumps were in place, a
copy of the pump and each of the pipes were placed between a break and fill to test our
system. We set the break and fill to a constant mass flow rate, and set the initial conditions to
replicate our steamgenerator model. This test systemcan be seen below in figure X. The
parameters we used are listed in table X.
Figure 7 – Model of Pump Test system in TRACE
Parameter Given Values As-Built Values Units Source
Crossover Leg ID 0.7 0.7 m G
Length of Cold
Leg
7 7 m C
Length of Hot
Leg
8.438 8.438 m C
Coolant Pump
Flow area
0.38465 0.38465 m^2 C
Coolant Pump
Hydraulic
Diameter
0.7 0.7 m C
RCP MOI 3460 N/A kg-m^2 G
RCP Hr 843 N/A m^2/s^2 G
RCP Tr 42850 N/A N-m G
RCP Q’’’ 5.58 N/A m^3/s G
RCP ρr 1000 N/A kg/m^3 G
RCP ωr 124.4 N/A rad/s G
Table 4 – Table of Data implemented into coolant pump test section
18. 17
Turbine Model Development
The turbine that was requested in this particular model only required output results.
Therefore, the best and simplest way to go in modeling turbine behavior is to use a set of signal
and control blocks.
To model the work done by the turbine, the simple thermodynamic property can be used which
states that the work done in a system can be calculated by subtracting term 1: the summation
of mass flow out of a systemmultiplied by the enthalpy of the steamin question from term 2:
the same summation of mass flow and enthalpy flowing into a system.
This equation can be modeled by the mathematical expression
𝑊 = ∑ 𝑚̇ ℎ
𝑖𝑛
− ∑ 𝑚̇ ℎ
𝑜𝑢𝑡
̇
To solve for these parameters control blocks were set up to pull information from the steam
flowing out of the steamgenerator boiler on the top edge, right as it leaves into the break.
Also, the mass flow rate in and out of the turbine were assumed to be equal, because the
efficiency term of 0.32 will take care of any frictional loss effects during calculation.
The only variable that is not immediately available is hout. This can be found by using the
expression:
ℎ 𝑜𝑢𝑡 = ℎ𝑖𝑛 − 𝜂(ℎ𝑖𝑛 − ℎ 𝑜𝑢𝑡,𝑠 )
Using the SNAP steam tables, based on the inlet temperature and pressure, hin was determined
to be 1.56E6. Using the outlet entropy (3.5 Kj/kg –K), and atmospheric pressure as inlet
conditions, the hout,s was found to be 1.19E6. Now, using 0.32 as the efficiency variable, we
find that hout = 1.072 E6 J/kg.
This was utilized in the following block diagram to solve for turbine work.
19. 18
Figure 8 – Control Block diagram for the Turbine Work.
20. 19
Results:
Steam Generator Results:
Before implementing the steamgenerator into our overall reactor model we created a test
system that plugged in the flow rate and temperature expected from our reactor by
implementing fills, this can be seen above in figure X. To test the steamgenerator we looked at
the temperature, mass flow rates, and liquid levels in the system. The first thing we analyzed
was our Temperature change. Before we looked at the APTplot of our temperature we
hypothesized that it should remain steady through the steam generator tube bundles due to
the initial conditions set forth by our fill (pressure being constant across and the heat structure
being set to the same temperature as our inlet water). As seen in the plot below we were
correct in our assumptions.
Figure 9 – Graph of Hot Leg and Cold Leg temperature.
21. 20
The next item we viewed to see if our steam generator was operating in steady state was the
mass flow rates of our tube bundles and our inlet by the feedwater nozzle and the exit mass
flow rate of the steamgenerator break. These are illustrated in the below graphs
Figure 10 – Graph of mass flow rate in both Hot Leg and Cold Leg
22. 21
Figure 11 – Graph of Mass Flow Rate into and out of Steam Generator
As see above the mass flow rate in and out of our tube bundles are identical, however they are
reflected across the x axis due to the orientation of our pipes (the pipes are reflected across a
neutral axis to provide the symmetry that exists in real life steamgenerators). After reviewing
those values we reviewed the inlet and outlet rate of our steam generator and noticed that the
outlet rate oscillates right around the inlet rate and determined that the issue could be
resolved when the pressure was decreased in our system. We decreased the pressure from
4.85 MPa to 1.5MPa. This produced the state above and showed us that the steamgenerator
was nearly perfect at steady state by itself (more adjustments to our model would be done in
our overall model as to save us time and insure an accurate result)
The last piece of interest for us to view if the model is at steady state was the liquid levels of
the Downcomer and Boiler. Towards the end of the time we ran the calculation for the value
should level out as the boiler consistently produced steam and the downcomer should steadily
pump out water. This graph demonstrates the capabilities of our model.
23. 22
Figure 12 – Graph of Liquid Levels in Downcomer and Boiler
From this graph we can see that the model has indeed reached a steady state that is agreeable
from a nuclear power plant view.
24. 23
Reactor Vessel and Pressurizer Subsystem Results.
Figure 13 – Exit Mass Flow Rate for Hot Leg – Reactor Vessel
The above figure demonstrates the mass flow out of the hot leg. It is unsurprising that it settles
around 4600 kg/s, because that is the speed at which the inlet flows were set.
Figure 14–Cold Leg Exit Temperature – Reactor Vessel
25. 24
The above figure demonstrates how the cold leg temperature remained constant throughout
the experiment, because this is the temperature the feedwater is set to.
Figure 15 –Reactor Power – Reactor Vessel
The reactor power remained constant, seeing as how the power setting was set to “[5]
Constant Power”. It is worth mentioning, however, that the power could only be ran at a low
value. The fuel pins would melt at a higher power, likely due to the inadequate coolant running
throughout the system. This power, however was ample in explaining the trends that are seen
typically in a reactor vessel.
26. 25
Figure 10 – Hot Leg Exit Temperature – Reactor Vessel
The above figure shows the hot leg exit temperature. Each leg converges to a temperature
near 587, which is the inlet temperature. The water is shown to increase briefly in
temperature, due to the water running through the much warmer reactor vessel.
Figure 11 – Pressurizer Pressure Difference – Reactor Vessel
27. 26
The above figure addresses the difference in pressure seen in the pressurizer. This is expected,
because the pressurizer has components of water and gas, and it would be unusual if the gas
had a lower or equal pressure to the liquid, since it is the condensed vapor that creates the high
pressure throughout the reactor.
Figure 18- Pressurizer Water Level - Reactor Vessel
The pressurizer water level remains fairly constant throughout the 400 second test. This is very
good for the reactor system, because it indicates that there is not much of a deviation from the
pressurizer setpoint.
Pump Results:
Inside our test systemwe adjusted the speed rate of our pump to create the systemat steady
state. With the rated head being at 124.4 we decided to start with a speed of 100 rad/sec. This
produced a flow that was about 600 kg/s below what the expected mass flow was designed to
be. We then set forth testing various speeds before finally setting the speed value at 110 kg/s.
This produced the coolant flow at the desired. The graphs below show that our model achieved
a steady state flow between our hot leg into our cold leg pipes. We then graphed the pressure
differences between our inlet and outlet of our pump and the exit pressure of our pipe to see if
there was any pressure difference.
28. 27
Figure 19- Mass Flow Rate from Hot Leg through Coolant Pump and into Cold Leg
29. 28
Figure 20- Pressure Levels From RCP into Cold Leg
As these graphs show, the pump system reaches a steady state at the desired mass flow rate
with the pump speed set at 110 kg/s. The inlet pressure decreases in the pump but as it leaves
the pump it reaches the same pressure as our cold leg exit pressure. The next step is to
implement this subsystem 4 times into the overall reactor model. With more connections and
point of loss for flow and pressure the flow rate may need to be increased to find the issue.
30. 29
Turbine Results
Figure 21 - Turbine Power
The turbine work seen here is a result of the control block diagram that was derived and
explained earlier in this report. It considered the inlet and outlet enthalpies and mass flow
rates that were measured at the top of each steam generator. This is the major connection to
the turbine that was never physically modeled through TRACE. This figure implies that the
Turbine produces around 5.2 gigawatts, which is incredibly unlikely, seeing as how the reactor
has a total power of 3.5 gigawatts. That being said, the issue here could have been the lack of
efficiency that went into the calculation. If the turbine is 32% efficient, the turbine can only
produce a maximum of 1.632 gigawatts, which is much more reasonable in this type of
engineering situation.
31. 30
Steady State Plant
Figure 22 – Steady State Final Reactor Model
Above is the connection of all of the components previously mentioned in detail. It connects
the steam generators, tube bundles, hot legs, cold legs, crossover legs, pumps, reactor vessel
and pressurizer all in one connected system. The goal here was to reach steady state, a
situation where variables that are measured over a long period of time no longer have very
much deviation from a flat, linear pattern, void of much change. The greatest challenge here
was to have all of the components work in harmony after they worked individually. Many of
the parameters needed to be changed, such as core power and inlet pressure. The following
figures will display how after changing several of the initial conditions, steady state was
approached.
32. 31
Figure 12- Hot Leg Exit Mass Flow Rate - Steady State
The above figure is similar to that seen in the reactor vessel model. The flow rate settles
around 4600 kg/s which is the initial mass flow rate that was mimicked in the individual reactor
model. This indicates that the water is flowing through the reactor and through the steam
generator at an ideal and constant rate
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.
Figure 24- Hot Leg Exit Temperature - Steady State
This figure shows how the hot leg exit temperatures settled around the values of 563 K and 558
K. This fluctuation is small enough that it is generally negligible when it comes to heat transfer
properties or phase change. The difference in temperature could be due to heat structure
placement within the reactor vessel/core, or the steam generator.
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Figure 25- Hot Leg Exit Pressure - Steady State
The hot leg exit pressure was constant for each part of the hot leg. It is slightly lower than the
input pressure of 1.56 E 07, however the difference is fairly negligible. The difference is
perhaps due to some small inefficiencies in the pressurizer with initial conditions.
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Figure 13 - Pump Pressures - Steady State
The change in pressure in the in the pumps is indicative of the effectiveness of the pump. The
pressure drop of around 0.3 MPa is slightly smaller than expected, but the fact that it is
constant implies that slight changes in pump speed would not ruin the pressure drops found
throughout the reactor.
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Figure 14 - Steam Mass Flow out of SGs - Steady State
The mass flows out of the steam generators are all generally following the same trend. The
value of mass flow fluctuates between 450 kg/s and 500 kg/s, which is not much unlike the inlet
coolant speed of 460 kg/s. This indicates that the steamgenerator will not be filling up with
water, which is good. There is a constant flow of mass in and out at all times.
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Figure 158 - Steam Temperature - Steady State
The steamoutlet temperature fluctuates over time to a range of 495 K and 510 K. This
fluctuation is similar to the fluctuation in steam mass flow out of the SG, and therefore the
fluctuation in kinetic energy makes sense with a fluctuation in temperature.
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Figure 169- Water Levels in Boiler - Steady State
As mentioned previously, the mass flow rates in and out of the steam generator are fairly
consistent with each other, leading to little to no fluctuation in boiler level. The average level
seen is around 1.6 meters.
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Figure 30 - Cold Leg Exit Temp. - Steady State
The above figure demonstrates a small fluctuation in cold leg temperature, that is very similar
in shape and degree of fluctuation of the hot leg exit temperature.
Steady state values were not completely perfect in each of the figures presented, however the
model behaved well and converged on to small ranges of values. The initial conditions can be
altered slightly to create a more steady state, however in the interest of time, this degree of
steady state seemed acceptable. Steady state was generally achieved around 1200 seconds.
The systemtended to operate at a more steady state at lower initial powers, however
experienced failures at lower powers as well.
Plant Transient:
With the limited time we had and the issues we ran into we were unable to complete the
transient part of this assignment. After reaching what we believed to be steady state we
attempted to initiate a restart case and graphically adjust the model to implement a 5%
increase in power. After many attempts this proved to be fruitless. We dug further and looking
into our trcout.txt file (the standard trouble shooting file we have used for this entire project)
we noticed that the system would not converge to steady state. With time short we decided to
attempt to initiate the transient in an informal way. This method would be to introduce a
control switch that would be fed the real time of our problem and after it reached a time set by
40. 39
us the increase to power would be added into the system. This attempt to introduce the
controller proved to be a more troublesome experience than we thought. After many fatal
error messages we decided to abandon the implementation of the transient. While this ignores
a part of the model that would be critical to a real world application, we believe that with more
time and knowledge of this systemcould solve this issue with minor effort.
While we did not put the transient in we still wanted to have a basic understanding of what
would occur. From previous courses we knew that when the power was jumped up the mass
flow rate, temperatures and pressures would spike and then approach a new steady state
(except for the mass flow rate as this is a set value). Without a working model that can show us
the exact spikes this is the best analysis we can offer on this Transient case.
Conclusions:
After performing the analysis of each subsystemand reviewing each parameter and the overall
base model, we determined that our model reached a steady state case within our chosen time
frame (1200 seconds). While the system SNAP did not tell us that our model was at steady state
review of our flow rates, temperatures, and pressures shows us that steady state is obviously
only a few steps away, but due to time we were unable to have the complete systemrunning.
This led to our transient being omitted from our working model for the reasons list above. This
model is useful in showing us how difficult it can be to work with an unfamiliar systemand the
challenges that will be found as we work through each systemand how we can make it the
most efficient we can make it.
