Answers to Questions for Introduction to Nuclear Reactor Physics

1

Information Classification: General

Solution Manual Answers to Questions for Introduction to Nuclear Reactor Physics

Answers to Questions in Chapters 1 to 23

Chapter 1

Questions for Chapter 1

The following questions cover the material presented in this chapter, and in some cases, previous chapters as well. They are designed to test how well the student has acquired a working knowledge of the subject matter.

• Name at least four types of nuclear particles that are produced in a reactor core. Ans: Neutrons, photons, neutrinos, electrons,

and alpha particles

• How many times higher is the coolant pressure in a PWR than it is in a BWR ? Ans: A factor of 2.15

3. What reactor has a thicker pressure vessel – a PWR or a BWR ? Ans: A PWR

• Conceptually speaking, what is the difference between a fission product and a fission fragment ? Ans: A fission fragment is a

fragment of an atomic nucleus that is produced immediately after the nucleus splits apart. It rips through the electron cloud surrounding the atom, and has no electrons attached to it. This causes it to have a very large positive charge. Over a period of time, it acquires additional electrons around it, and becomes what is known as a fission product. A fission product can also be produced after a fission fragment decays, and the most common example of this is after radioactive beta decay.

• What material is used in the construction of a gas reactor pressure vessel ? Ans: Concrete
• In what document can the standards for the construction of nuclear reactor pressure vessels be found ? Ans: In Section III of the

ASME Boiler and Pressure Vessel code

• What is the most common type of nuclear reactor in use in the world today ? Ans: The PWR
• What contributions did Thomas Edison and Nikola Tesla make to the field of nuclear power ? Ans: They helped to create many

of the components that are used in the “back ends” of nuclear power plants today, and they helped to create the modern electrical power distribution system, or power grid

• What is the second most common type of nuclear reactor in use in the world today ? Ans: The BWR
• Approximately how many commercial nuclear power plants are in operation in the world today ? Ans: About 500

11. How many coolant loops does a CANDU reactor have ? Ans: Two

• Who invented the modern steam turbine which is found in nuclear power plants today ? Ans: Charles Parsons
• What coolant is used in the primary loop of a CANDU reactor, and what coolant is used in the secondary loop ? Ans: Heavy

water is used in the primary loop and light water is used in the secondary loop

• What component is the shaft of a steam turbine connected to in a nuclear power plant ? Ans: The electrical generator
• What is the frequency of the alternating current produced by the electrical generators in a modern nuclear power plant, and how

many phases does this current have ? Ans: 60 cycles per second and three phases – at least in the United States

• What are the two basic types of steam generators that are used in nuclear power plants today ? Ans: Once through (or straight)

steam generators and U-Tube steam generators

• Name at least one type of reactor that does not require a steam generator. Ans: BWR
• What reactor has a thicker pressure vessel – a BWR or a LMFBR ? Ans: A BWR
• What are the inlet and outlet temperatures from the steam generators in the primary loop of a PWR ? Ans: The inlet temperature

is about 325 C (liquid water), and the outlet temperature is about 275 C (liquid water)

• At what temperature does the steam leaving the secondary loop of these steam generators become completely saturated ? Ans:

At about 275 C

• In a water steam mixture, what is the definition of the quality x ? Ans: The fraction of the mass of the water steam mixture that

consists of steam alone

• What term is used to describe the sub loops within the primary loop of a PWR ? Ans: The hot legs or the cold legs
• Some steam generators are also designed to produce superheated steam. What does the term ”superheated steam” refer to, and

why is superheated steam preferable to saturated steam ? Ans: Superheated steam has a higher energy content or specific enthalpy than saturated steam. Because of this, it is drier, and it allows more energy to be extracted from the steam before it starts to condense in the power turbines.

• Why does the electric power that you receive from a nuclear power plant come in the form of alternating current rather than

direct current ? Ans: Because alternating current has lower transmission line losses

• Who did George Westinghouse originally buy the patents from that led to the rise of the Westinghouse Electric Corporation,

which is now the largest supplier of nuclear power plants in the world today ? Ans: Nikola Tesla (Introduction to Nuclear Reactor Physics, 1e Robert Masterson) 1 / 4

2

Information Classification: General

• What are the inlet and outlet temperatures from the steam generators in the secondary loop of a PWR ? Ans: The inlet

temperature is about 220C (for liquid water) and the outlet temperature is about 275 C (for saturated steam). Note: These numbers can change slightly depending upon the design of a specific plant

• In a water steam mixture, how is the void fraction  defined ? Ans: The fraction of the volume of the water steam mixture that

consists of steam alone

• Name two men who are primarily responsible for the electrical generating systems that all nuclear power plants use today. Ans:

Nikola Tesla and Thomas Edison

• What contribution did JP Morgan make to the field of nuclear power, and who was his chief rival ? Ans: He financed the

development of the electrical power industry in the United States and was the primary mentor and financier of Thomas Edison.His chief rival was John D. Rockefeller, who happened to be the richest man who ever lived.

• After the rise of John D. Rockefeller and JP Morgan, who were the two scientists who were primarily responsible for inventing

the “front ends” (i.e., the reactor cores) that most modern nuclear power plants use today? Ans: Enrico Fermi and Robert Oppenheimer

• What is the fundamental difference between a coal-fired power plant and a nuclear power plant ? Do you think coal powered

power plants produce higher energy steam or lower energy steam than nuclear power plants do ? Ans: The primary difference is in the way that the energy is produced. Nuclear power plants use nuclear fission to produce heat and coal powered power plants burn fossil fuels to produce heat. Because coal fired power plants operate at a higher average temperature, they produce higher energy steam than nuclear power plants do

• What famous thermal cycle do most of the nuclear reactors in the world use today ? Ans: The Rankine cycle
• What reactor of the following four reactor types has the highest core power density, and what reactor has the lowest: PWRs,

BWRs, CANDU reactors, and LMFBRs ? Ans: The LMFBR has the highest core power density and the CANDU reactor has the lowest.

34. What type of fuel does a commercial PWR use? Ans: Enriched uranium dioxide

• What reactor uses heavy water and natural uranium fuel ? Ans: The Canadian CANDU reactor
• What reactor has three separate coolant loops, and why does it have this many loops ? Ans: The LMFBR; It has three coolant

loops because the sodium in the primary loop becomes radioactive, and so an intermediate loop is necessary before the liquid sodium reaches the steam generators

• In the nuclear power business, what does the term NSSS refer to ? Ans: The Nuclear Steam Supply System
• Who is the primary manufacturer of BWRs in the world ? Ans: The General Electric Company

39. What is the thermal efficiency of a typical PWR? Ans: About 34 %

• Approximately what percentage of the electric power in the United States is generated by nuclear power ? Ans: About 20%
• What is the shape of the control rods in a PWR, and what is the shape of the control rods in a BWR ? Ans: The control rods in a

PWR are cylindrical in shape and the control rods in a BWR are cruciform in shape

• What reactor has a higher thermal efficiency – a PWR, a BWR, or a LMFBR ? Ans: The LMFBR
• In the nuclear power business, what is the word SCRAM an abbreviation for ? Ans: A safety control rod axe man
• Suppose that one gram of uranium is completely converted into energy in a nuclear power plant. Assuming that the plant

thermal cycle is 33% efficient, now many kilowatt hours of electricity does this produce ? Ans: Earlier in the chapter, we learned that 1 Kilowatt hour requires a nuclear power plant to produce approximately 1.08 x 10 7 joules of thermal power. We also learned in Chapter 7 that one gram of uranium releases approximately 8.64 x 10 10 joules of thermal energy. Thus burning one gram of uranium produces approximately 8000 kilowatt hours of electricity

• At the average cost of electricity in the world today, approximately how many dollars of electricity does this one gram of burned

uranium produce ? Ans: If we assume that the average cost of electricity in the world today is about 12 cents per kilowatt hour, then 8000 kilowatt hours (which is equivalent to burning one gram of uranium) will cost about $ 960 USD

• Assume that one kilogram of uranium ore costs $ 100, and that it contains 0.711 % U-235. Assuming that all of the U-235 is

ultimately recoverable, how many kilograms of natural uranium does it take to produce 1 gram of U-235 ? Ans: 1.4 kilograms

• Using the information presented in problems 44, 45, and 46, estimate the fuel cost per kilowatt hour for a typical nuclear power

plant in the world today (excluding enrichment and fabrication costs) Ans: The fuel cost is approximately $140/8000 kilowatt hours = 1.75 cents per kilowatt hour.

• What percentage of the commercial nuclear reactors in the world today are PWRs ? Ans: About 2/3 (67%)
• Where is the fuel “bred” in a fast breeder reactor ? Ans: In the blanket
• What industrial country has the highest percentage of its electrical power generated by nuclear power plants? Ans: France,

where nuclear power generates about 80% of the total electric demand

• What is the average thermal efficiency of a Canadian CANDU reactor? Ans: Between 29 % and 30 %
• Write a mathematical expression for the definition of the power density PD for a nuclear reactor core. Ans: PD = Q / V CORE =

PTHERMAL / V CORE

• What is the average burnup of a fast reactor fuel assembly ? Ans: About 100,000 MWD/metric ton
• Who was the richest man who ever lived ? Ans: John D. Rockefeller, who had a net worth of approximately 2/3 of a Trillion

dollars

• What has a higher average burnup – a fast reactor fuel assembly or a thermal reactor fuel assembly ? Ans: A fast reactor fuel

assembly has a much higher average burnup (by a factor of about two)

• Nuclear power plants are a major competitor to coal fired power plants in the world today. Is the energy content of the cooling

water in the core of a nuclear reactor higher or lower than that in the boilers of a modern coal-fired power plant ? Ans: The 2 / 4

3

Information Classification: General

energy content is actually higher (per kilogram) in a coal fired power plant because the steam boilers can operate at a much higher temperature (They do not have to worry about the fuel rods melting).

• What is the typical outlet temperature of the water from a commercial PWR core, and what is the typical outlet temperature

from the steam from one of its steam generators ? Ans: The typical outlet temperature of the water from the core is about 325 C and the outlet temperature of the steam from the steam generators is about 275 C

• If you were put in charge of building a nuclear power plant today, what type of nuclear power plant would you build and why?

Ans: The instructor should take a position on this subject and defend it to the class

• What is the minimum diameter and the maximum diameter of the fuel pellets that are used in most commercial nuclear reactors

? Ans: Between 0.7 cm and 1.5 cm (7 mm and 15 mm)

• What is the single most important factor, except for the material composition, that determines the size of a nuclear fuel pellet ? Ans:

the rate at which heat can be removed from the fuel pellet

• Name three common materials that can be used for the cladding in a PWR or a BWR. Ans: Stainless steel, zirconium, and an alloy

of zirconium known as Zircaloy

• How thick is the cladding that is used in a typical PWR fuel assembly ? Ans: About two thirds of a millimeter (~0.60 mm)
• What is the primary ceramic material that nuclear fuel pellets are made from today ? Ans: Uranium dioxide or UO2
• What is the concentration of U-235 in a fresh PWR fuel pellet ? Ans: Between 4.0% and 5.0 %
• How thick is the fuel to cladding gap in a commercial thermal water reactor fuel rod ? Ans: About a tenth of a millimeter (~0.10

mm)

• What is the name of the gas that is normally added to reactor fuel rods to increase their thermal conductivity and to improve the heat

transfer coefficient across the fuel/cladding gap ? Ans: Helium (H2)

• What does the “pitch” of a reactor lattice refer to ? Ans: The center to center spacing between adjacent fuel rods
• How many fuel rods are there in a modern fuel PWR assembly ? Ans: Not including the spaces used for instrumentation channels

and the control rods, between 225 and 289 fuel rods

• How many fuel rods can be found in a modern BWR fuel assembly ? Ans: Not including the spaces used for instrumentation

channels and water holes, between 64 and 100

• What fraction of the fuel assemblies in a typical PWR core contain control rods ? Ans: About 1 in four (1/4)
• If you shut down a nuclear reactor to be refueled, and the fuel rods are still giving off a lot of radioactive decay heat, what is the one

thing you do NOT want to do while the reactor is cooling down ? Ans: Shut off the reactor coolant pumps

• How many fuel assemblies can be found in the core of a large commercial BWR ? Ans: A large commercial BWR core contains

about 800 fuel assemblies

• Name two common geometries that are used for reactor fuel assemblies. Ans: Square and hexagonal (triangular).
• What is the purpose of the steel shroud or “can” that surrounds a BWR or LMFBR fuel assembly ? Ans: To prevent voids from

propagating into other fuel assemblies in the event the coolant boils

• How many fuel assemblies are there in large PWR core? Ans: A large PWR core contains about 200 fuel assemblies
• What fuel assembly geometry has the highest theoretical power output ? Ans: A hexagonal fuel assembly
• What is the purpose of introducing burnable poisons into a reactor fuel assembly ? Ans: To reduce the radial and axial power peaks.

Burnable poisons may also be used to reduce the number of control rods that are used.

• Name three common burnable poisons. Ans: Gadolinium, hafnium, and various isotopes of boron
• What does the term uranium enrichment refer to? Ans: Increasing the concentration of U-235 in natural uranium from 0.7% to

much higher values between 2% and 99%

• What are the control rods in a modern reactor fuel assembly usually made from ? Ans: Boron or Cadmium
• From which direction are the control rods normally inserted into a fuel assembly in a PWR ?, Ans: from Above
• From which direction are the fuel rods normally inserted into a fuel assembly in a BWR ? Ans: From below
• Using the numbers presented earlier in the chapter, how much thermal power does a typical PWR fuel assembly generate ?

Approximately 15 MW of thermal power

• For the same volumetric power output, which type of fuel assembly has a smaller pitch – a square fuel assembly or a hexagonal one

? Ans: A hexagonal one

85. What is the shape of an American BWR control rod ? Ans: cruciform

• Using the numbers presented earlier in the chapter, how much thermal power does a typical BWR fuel assembly generate ? Ans:

About 3 MW of thermal power

• In which type of reactor do the fuel assemblies have the highest volumetric heat generation rate ? Ans: In a LMFBR
• What is the electrical power output of a commercial PWR with 200 fuel assemblies ? Ans: About 1000 MWE
• How thick is the cladding that covers the fuel rods in a BWR ? Ans: About three quarters of a millimeter (~0.75 mm)
• What percentage of the overall length of a PWR fuel rod contains fissionable material (i.e, UO2 or PuO2) ? Ans: About 2/3 of the

overall length

• How long is a typical PWR fuel assembly ? Ans: About 4 meters or 12 feet long
• What alloy of zirconium is used to surround the fuel rods in a BWR ? Ans: Zircaloy II
• What percentage of the overall length of a PWR fuel rod does NOT contain fissionable material, and what is this additional region

called ? Ans: About one third of the length of a reactor fuel rod does not contain any fissionable material, and this region of the fuel rod is called the fission gas plenum.

• What alloy of zirconium is used to surround the fuel rods in a PWR core ? Ans: Zircaloy IV 3 / 4

4

Information Classification: General

• Approximately what percentage of the fuel rods in a commercial PWR are allowed to fail under normal operating conditions ? Ans:

Approximately one thousandth of 1 percent (0.0010 %) of the fuel rods

96. What is the shape of a normal PWR fuel rod ? Ans: Cylindrical

• In what units is the burnup of the fuel usually measured ? Ans: The average burnup of the fuel is usually measured in MWD/ton or

by the percentage of initial heavy metal atoms (IHMA) that are burned.

• What is another term for the heavy water that is used as the moderator in a Canadian CANDU reactor? Ans: Deuterium
• Fill in the following sentence with the appropriate word or phrase: As a design rule for a LWR, the fuel to cladding gap should be

_______ of the thickness of the cladding. Ans: One thrid

• What percentage of the core of a PWR consists of fuel or fuel rods (by volume) ? Ans: Approximately 25 % or 1/4 of the volume of

the core

• Does a LMFBR fuel assembly have a higher average burnup or a lower average burnup than a water reactor fuel assembly ? Can

you explain the reason why this happens to be the case ? Ans: A LMFBR has a higher average burnup. This is because the enrichment of the fuel is higher, and so higher burnups are possible before the fuel has to be replaced

• Now consider three separate types of commercial power reactors – a PWR, a BWR, and a CANDU reactor. Which one of these

reactors has the lowest average power density and which one has the highest? What factors do you think determine the power density in each case ? The CANDU reactor has the lowest average power density and the PWR has the highest. This is because the CANDU reactor has the lowest average enrichment, and the PWR has the highest.

• There are two types of commercial pressurized water reactors – the Westinghouse PWR and the CANDU PWR. What are the

moderating materials that are used to produce thermal neutrons in each of these designs ? Ans: The Westinghouse PWR uses ordinary light water (H2O) as the moderating material, and the CANDU reactor uses heavy water or Deuterium (D2O)

• What is the average concentration of U-235 in a CANDU reactor fuel rod ? Ans: 0.710 %
• Approximately how many fuel rods are there in a large 1000 MWE PWR ? Ans: Between 40,000 and 50,000
• What type of material is normally used to surround the fuel rods in a LMFBR ? Ans: Stainless steel cladding
• How is the power level in a Boiling Water Reactor increased or decreased by the reactor operator without having to move any of the

control rods ? Ans: By increasing or decreasing the flow rate through the core

• If the power to the reactor control system in a PWR is suddenly interrupted, a PWR can still be shutdown safely. Exactly how does

a PWR effect a safe shutdown in this case ? Ans: The power to the electromagnets holding the control rod in place is cut off, and this causes the control rods to fall back into the core under the influence of gravity alone

• Name three common materials that can be used for reactor control rods and two common materials that can be used for burnable

poisons. Ans: Common materials that are used for reactor control rods include boron, silver, indium, cadmium, and hafnium, and common materials that are used for burnable poisons include gadolinium and hafnium

• What is the US NRC’s definition of a control rod ? Ans: “A rod, plate, or tube containing a material such as

hafnium, boron, etc., used to control the power of a nuclear reactor. By absorbing neutrons, a control rod prevents the neutrons from causing further fissions”

• What is the advantage of using a burnable poison in a reactor fuel assembly ? Ans: Burnable poisons are used to help to reduce the

size of the radial and axial power peaks in the fuel assembly

• When discussing the Canadian PHWR, what does the term CANDU stand for ? Ans: CANada Deuterium Uranium reactor
• In addition to uranium-235, what other fissile material can be commonly found in the fuel rods of a fast reactor ? Ans: Plutonium-

239

• What isotope of Boron absorbs the most neutrons in a reactor control rod ? Ans: Boron-10
• How long can military reactors (used in nuclear warships and submarines) be operated before they need to be refueled ? Ans:

Normally every 40 to 50 years

• Where are the spent fuel assemblies that are removed from a reactor core initially stored ? Ans: In a spent fuel pool
• If a 17x17 PWR fuel assembly contains control rods, approximately how many control rods does the fuel assembly contain ? Ans:

About 24

• What is the standard outage period for a commercial water reactor when it is time for the reactor to be refueled ? Ans: The standard

outage period has been about 1 month since the 1990s.

• Name at least one type of western reactor that can be refueled while the reactor is still operating. Ans: The CANDU pressurized

heavy water reactor, although some gas reactors can also be refueled without shutting them down

• Approximately what percentage of the core of a thermal water reactor consists of the structure and the coolant ? Ans:

Approximately 25% of the core consists of structural materials, and 50 % of the core consists of moderator or coolant

• In what direction are the fuel assemblies positioned in the core of a CANDU reactor ? Ans: Horizontally
• Complete the following sentence: In a High Temperature Gas Reactor, the fuel consists primarily of small ________. Ans:

microspheres

• What is the ratio of the thickness of the cladding in a General Electric BWR to the thickness of the cladding in a Westinghouse

PWR ? Ans: About a factor of 1.25

• Why is the fuel to cladding gap about the same in a PWR as it is in a BWR ? Ans: Because the thermal expansion of the uranium

dioxide fuel is about the same, and because the burnup of the fuel is comparable as well.

• Complete the following sentence: The reactor accident at Fukushima, Japan was an example of a Loss of ________ event. Ans:

Circulation

• Name two places where a spent fuel pool can be found at a reactor site. Ans: In the containment building or in the auxiliary building
• / 4