NPRE 402 Nuclear Power Engineering Fall 2017

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1 NPRE 40 Nuclear Power Engineering Fall 017 Number Date Assigned Due Date Description 1 8/8 9/6 8/30 9/6 3 9/1 9/8 Once built and operational, nuclear power plants become cash cows for their operators. Consider a 1,000 MWe nuclear power plant costing about $5,000 per installed kwe of capacity. Calculate: 1. The capital cost of the plant in billions of dollars.. If it operates for 60 years at a capacity factor of 90 percent, the amount of electrical energy in kw.hr it would produce per year. 3. Sold to electrical consumers at 5 cents / kw.hr, the generated income stream in $ million /year. 4. The total income stream in $ billion over 60 years of operation. Calculate the speed in meters per second of neutrons possessing the following energies: i. Fast neutron from fission at MeV, ii. Intermediate energy neutron at 10 kev, iii. Thermal energy neutrons at 0.05 ev. Hint: Use the expression for the kinetic energy as E= ½ mv for the neutron. Data mine the Chart of the Nuclides for the following information on elements used in nuclear applications: 1. Naturally occurring isotopes and their natural abundances.. Atomic masses of isotopes in atomic mass units (amu). For the following elements: a) Uranium (U). b) Thorium (Th). c) Carbon (C). d) Hydrogen (H). e) Lead (Pb). f) Beryllium (Be). g) Lithium (Li). h) Sodium (Na). i) Boron (B). j) Cadmium (Cd). k) Fluorine (F) Apply conservation of charge and of nucleons to balance the following fissile breeding reactions: 1.

2 4 9/6 9/13 n U U U e e 0 1 n U e. 1 n 3 Th Th Th e e 0 1 n Th e 3. 1 n 38 1 U n d 1e Balance the following nuclear reactions: 1. 1D + 1T 3 0n 1 + (DT fusion reaction). 1D + 1D 1H 1 + (Proton branch of the DD fusion reaction) 3. 1D + 1D 0n 1 + (Neutron branch of the DD fusion reaction) 4. 1D + He 3 He 4 + (Aneutronic or neutronless DHe 3 reaction) n 3Li + (tritium breeding reaction) n Li n + (tritium breeding reaction) T T n + (neutron multiplier reaction) n + B He + (neutron absorption reaction) Identify the following technical specifications of the Chicago Pile number 1 (CP-1) reactor. 1. Thermal power in Watts(thermal), Wth.. Fuel material 3. Moderator material 4. Control rods material 5. Safety (Scram) material If a single fission reaction produces about 00 MeV of energy, use Avogadro s law to calculate the number of grams of the fissile elements: 1. U 35. Pu U Np 37 that would release 1 kt of TNT equivalent of energy. Assume that all the energy release is available, except for the energy carried away by the antineutrinos, as well as the delayed fission products beta particles and gamma rays, which is not fully recoverable.

3 Hint: Use Avogadro s law to estimate the number of nuclei in a given weight of the fissile material: g[ gm] N nuclei A A M[ amu] nuclei mole 4 [ ] v, v [ ] Balance and complete the following nuclear fusion and tritium breeding reactions that may occur in thermonuclear devices: 3 1 D T 17.6MeV Li + 0n (thermal) Li + 0n (fast) He + 0 n MeV 0n 1 + 9U n I n 1 + 9U n Xe He (.05 MeV)+ (.73 MeV) MeV 5 9/8 9/15 6 9/11 9/18 Fill out the following table describing the partition of energy release in a single fission reaction; Distribution of Fission Energy Kinetic energy of fission fragments Prompt gamma rays energy Kinetic energy of fission neutrons Beta particles from fission products Delayed gamma rays from fission products Antineutrinos from fission products Energy release per fission event Neutron- gamma reactions with device fragments Unavailable antineutrinos energy Unavailable fission products beta particles Unavailable fission products gamma rays Energy available in a fission event Energy [MeV] The yield from the Hiroshima device was 1.5 kt of TNT equivalent, and the yield from the Nagasaki device was kt of TNT. Assuming that one critical mass of lead-reflected U 35 Oralloy at about 30 kgs, and one critical mass of Pu 39 at about 10 kgs were used to generate these yields, compare the energy release efficiencies of the two devices as the fraction or percentage of the fissile material converted into energy in the case of the gun barrel versus the implosion processes. mass fissioned Hint: Define efficiency as initial critical mass Balance the catalyzed DD reaction that could be used in a second generation fusion reactor: 1 D D H 4.03 MeV D D n 3.7 MeV 1 D T n 17.6 MeV 3 1 D He H 18.3 MeV D MeV

4 7 9/13 9/0 8 9/15 9/ 9 9/18 9/5 For space propulsion using a magnetic nozzle, the following neutronless or aneutronic fusion reaction would be used: 3 1D He Balance then calculate the Q values or energy releases in MeV from the following nuclear reactions: 1. 1 D + 1 T 3 0 n 1 + (DT fusion reaction). 1 D + 1 D 1 H 1 + (Proton branch of the DD fusion reaction) 3. 1 D + 1 D 0 n 1 + (Neutron branch of the DD fusion reaction) 4. 1 D + He 3 He 4 + (Aneutronic or neutronless DHe 3 reaction) n Li + (tritium breeding reaction) n Li n + (tritium breeding reaction) T T n + (neutron multiplier reaction) n + B He + (neutron absorption reaction) n U n I Y 96 (fission reaction) n U n Xe Sr 97 (fission reaction) n U 35 0 n Ba Kr 97 (fission reaction) Apply conservation of momentum and energy to estimate the energy release partitioning in the following binary nuclear reactions: 1. 1 D + 1 T 3 0 n 1 + (DT fusion reaction). 1 D + 1 D 1 H 1 + (Proton branch of the DD fusion reaction) 3. 1 D + 1 D 0 n 1 + (Neutron branch of the DD fusion reaction) 4. 1 D + He 3 He 4 + (Aneutronic or neutronless DHe 3 reaction). In a possibly future matter/antimatter reactor, use the mass to energy equivalence relationship to calculate the energy release in ergs, Joules and MeV from the complete annihilation of: a. An electron/positron pair. b. An antiproton/proton pair. Consider the following masses: m electron = m positron = x 10-8 gram m proton = m antiproton = x 10-4 gram. Calculate the Q values of the following non-binary nuclear reactions: C B (Positron decay reaction) 6 5 1e e 8Ni * 1T 1e He Pu He 9U Cu (Orbital electron capture reaction) (Negative beta decay reaction) (Alpha particle decay reaction) Combine the two equations: E mc [ ergs] c E h h to deduce the equation: m R where: h R c erg.sec cm 48 3

5 10 9/0 9/7 Calculate the activity of 1 gm of the radium isotope Ra 6 in Becquerels and Curies. Discuss the relationship to the Ci unit of activity. 11 9/ 9/9 1 9/5 10/ 1. Accessing the chart of the nuclides generate the decay chain of U 38 and identify its end stable decay product.. Radon as a daughter in the decay chain of uranium is gaseous at room temperature. It is an inert or noble gas that does not interact chemically in the body. However it decays into Pb 10 which attaches itself to vegetation such as tobacco leaves as a solid and subsequently decays into Po 10 which emits an energetic alpha particle with 5.3 MeV of energy. The inhalation of these two isotopes in the particulate matter of cigarettes smoke delivers to the average smoker a radiation dose equivalent or effective dose of 8 rems (radiation equivalent man) per year to the basal cells of the bronchial tissue. The cancer dose is the total radiation dose that if spread through a population would cause one additional cancer death and is considered to be approximately,000 rems. Calculate the ensuing radiological risk in units of cancer deaths per year in a population of one million smokers. A radioisotope power generator uses the isotope 84 Polonium 10. If its specific thermal power is 141[Watts(th)/gm], its half-life is 0.38 year, and the thermal to electrical conversion efficiency is 40 percent, determine: 1. The weight of the isotope needed to produce 30 Watts(e) of electrical power.. The electric power after 0.76 year of operation. 3. The electric power after 1.5 years of operation. 13 9/7 10/4 14 9/9 10/4 The isotope 38 Strontium 90 is a pure beta emitter without gamma rays emissions. This makes it particularly suitable for radio isotopic power generation. Its half-life is 9 years and its beta disintegration energy is MeV. 1. Calculate its specific activity in Becquerels per gram and Curies per gram.. Calculate its specific power generation in Watts/gm. 3. For a 100 Watts of thermal power in a radioisotope power generator, how many grams of 38 Sr 90 are needed 4. After 9 years of operation, what would its activity and its power become 5. After 58 years of operation, what would its activity and its power become Use: 1 Curie=3.7x10 10 Bq, 1 [MeV/sec]=1.60x10-13 Watts, A v =0.6x10 4 [nuclei/mole]. The isotope 81 Thallium 04 has a half-life of 3.78 years. It decays through beta decay to 8 Pb 04 with a branching ratio of 97.1 percent with decay energy of MeV. It also decays through electron capture to 80 Hg 04 with a branching ratio of.9 percent with decay energy of MeV. a. Calculate its total specific activity in [Becquerels / gm]. b. Calculate its total specific activity in [Curies/gm]. c. Calculate the specific thermal power generation in [Watts(th) / gm]. d. For a 100 Watts of thermal power in a Radioisotope Heating Unit (RHU) power generator for a Mars mission, how many grams of 81 Thallium 04 would be needed e. The Cassini space probe to Saturn needs an electrical supply of 1 kilowatt(e) of power. If it were powered by a Radioisotope Thermoelectric Generator (RTG) operating at a conversion efficiency of 9 percent, what would be the needed amount of 81 Thallium 04 Write down the units and the abbreviations of the following radiological quantities: Radiological Quantity Conventional System Unit SI System Unit Activity Absorbed dose

6 15 10/ 10/4 The naturally occurring isotope K 40 is widely spread in the environment. In fact, the average concentration of potassium in the crustal rocks is 7 [g/kg] and in the oceans is 380 [mg/liter]. K 40 occurs in plants and animals, has a half-life of 1.3 billion years and an abundance of percent. Potassium's concentration in humans is 1.7 [g/kg]. In urine, potassium s concentration is 1.5 [gm/liter]. 1) Calculate the specific activity of K 40 in Becquerels per gram and in Curies/gm of K 40. ) Calculate the specific activity of K 40 in Becquerels per gram and in Curies per gm of overall potassium. 3) Calculate the activity of K 40 in Becquerels and in Curies in the human body for an average weight of 70 kgs. 4) Calculate the specific activity of K 40 in urine in [Bq/liter] /6 10/13 List the laws and corollaries for energy conversion and extraction from the environment. List three energy flow systems from which energy can be extracted /9 10/ /11 10/18 Construct a table comparing the Engineered Safety Features for the following designs: 1. PWR. BWR Assuming that heat rejection occurs at an ambient temperature of 0 degrees Celsius, for the average heat addition temperatures T a given below, compare the ideal Carnot Cycle thermal efficiencies of the following reactor concepts: 1. PWR, 168 o C.. BWR, 164 o C. 3. CANDU, 141 o C. 4. HTGR, 05 o C. 5. LMFBR, 15 o C. Expand the acronyms used for the reactor concepts /13 10/0 0 10/16 10/3 1 10/18 10/5 A Stirling cycle engine using a radioactive isotope for space power applications operates at a hot end temperature of 650 o C and rejects heat through a radiator to the vacuum of space with a cold end temperature at 10 o C. Calculate its ideal Stirling cycle efficiency. A Boiling Water Reactor (BWR) produces saturated steam at 1,000 psia. The steam passes through a turbine and is exhausted at 1 psia. The steam is condensed to a subcooling of 3 o F and then pumped back to the reactor pressure. Compute the following parameters: a. Net work done per pound of fluid. b. Heat rejected per pound of fluid. c. Heat added by the reactor per pound of fluid. d. The turbine heat rate defined as: [(Heat rejected +Net turbine work)/net turbine work] in units of [BTU/(kW.hr)] e. Overall Thermal efficiency. You may use the following data: From the ASME Steam Tables, saturated steam at 1,000 psia has an enthalpy of h = 1,19.9 [BTU/lbm]. At 1 psia pressure the fluid enthalpy from an isentropic expansion is 776 [BTU/lbm]. The isentropic pumping work is.96 [BTU/lbm]. The enthalpy of the liquid at 1 psia subcooled to 3 o F is [BTU/lbm]. 1 [kw.hr] = 3,41 [BTU] For heat rejection at 0 degrees Celsius, compare the Carnot cycle efficiencies for an HTGR operating in the following modes: a) Process heat, b) Electrical power generation, c) Hydrogen production.

7 10/0 10/7 3 10/3 10/ /5 11/1 5 10/7 11/3 6 10/30 11/3 7 11/1 11/3 8 11/6 11/13 Compare the voltages generated by a single fuel cell element when it is operated at: a. 0 o C, b. 100 o C. Use: S 163. J / K, H 85,800 J, F (Farady s constant) = 96,487 [Coulombs] or [Joules/Volt]. What is the implication in terms of fuel cell operation High Temperature Electrolysis (HTE) has a high efficiency: electrolysis Calculate the efficiency of a hydrogen production system:. hydrogen electrolysis electrical for the cases of: 1. A nuclear system using the Steam Cycle,. A nuclear system using the Brayton Gas Turbine Cycle. Discuss the implications of your results. Write a one page summary about one of the Generation IV nuclear power plants designs under consideration, e. g. The Molten Salt Breeder Reactor. Include a diagram and specify your source such as the Idaho National Laboratory web site ( Identify the level of enrichment in U 35 of: 1. Natural uranium,. Enrichment level of Depleted Uranium, DU, 3. Level of enrichment for LWRs. An executive at an electrical utility company needs to order natural uranium fuel from a mine. The utility operates a single Heavy Water Reactor (HWR) 1,000 MWe power plant of the CANDU type using natural uranium, and operating at an overall thermal efficiency of 1/3. What is the yearly amount of: a. U 35 burned up by the reactor b. U 35 consumed by the reactor c. Natural uranium fuel that the executive has to contract with the mine per year as feed to his nuclear unit An executive at an electrical utility company needs to order uranium fuel from a mine. This utility operates a single 1,000 MWe PWR power plant operating at an overall thermal efficiency of 1/3. The fuel needs to be enriched to the 4 w/o in U 35 average level. Consider that the enrichment plant generates tailings at the 0. w/o in U 35 level. Calculate is the yearly amount of natural uranium that the executive has to contract with the mine as feed to his nuclear unit. List the methods used for the isotopic tailoring and enrichment of the heavy isotopes. Compare the ratio in the separation radii (R 1 / R ) in the electromagnetic separation method (Calutron) for the separation of the ions of the isotopes and molecules: a) U 35 and U 38, b) Li 6 and Li 7. Compare the Coulomb energy repulsion in MeV in a fusion plasma between the nuclei of: 1. Deuterium. Lithium 3. Carbon Complete the main fusion chain reactions in main-sequence stars of large mass as the Carbon- Nitrogen chain consisting of a collective of six reactions:

9 11/8 11/15 30 11/10 11/17 1H 1 + 6 C 1 + + 1.95 MeV + 1 e 0 + e + 1.50 MeV 1H 1 + 6 C 13 + + 7.54 MeV 1H 1 + 8O 15 + + 7.35 MeV 8O 15 + 1 e 0 + e + 1.73 MeV 1H 1 + + He 4 + 4.

8 9 11/8 11/ /10 11/17 1H C MeV + 1 e 0 + e MeV 1H C MeV 1H 1 + 8O MeV 8O e 0 + e MeV 1H He MeV e 0 + e MeV 1. The following nuclear reactions would occur in the blanket surrounding the plasma to breed the tritium needed for a first generation DT fusion reactor: n Li T n Li n T n Li Li The catalyzed DD reaction would occur in a second generation fusion reactor: 1 D D H 4.03 MeV D D n 3.7 MeV 1 D T n 17.6 MeV 3 1 D He H 18.3 MeV D MeV 3. For space propulsion using a magnetic nozzle, the following neutronless fusion reaction would be used: 3 1D He 3 Calculate the attainable density of metallic uranium with a density of 18.9 [ gm / cm ] included in hybrid fusion-fission inertial confinement pellet if it is imploded by a laser driver in cylindrical and spheric geometry to: a) One half its initial radius b) One tenth its initial radius. Define the Lawson Criterion. What is the type of fusion device shown in the diagram. Identify on the diagram the following components: 1. Transformer core,. Toroidal field magnet coils, 3. Toroidal magnetic field, 4. Poloidal plasma current, 5. Poloidal magnetic field, 6. Resultant magnetic field /13 11/7 Identify the types of fusion devices shown in the diagrams

11/15 11/7 33 11/17 11/7 34 11/7 1/4 35 11/9 1/6 36 1/1 1/8 In the Oppenheimer-Phillips deuteron wave polarization and

83 Bi 10 10 83 84 Po Po Pb 10 06 84 8 Complete the following nuclear reactions that would have occurred at the Oklo natural

n + + 1 0 9 9 + e + + 0 * 9 93-1 + e + + 0 * 93 94-1 + He 4 94 9 n + + He + e + +3 1 4 0 * 0 9 9-1 List the domains of

Prove that the divergence of the gradient leads to the Laplacian operator in the leakage term of the neutron diffusion

9 11/15 11/ /17 11/ /7 1/ /9 1/6 36 1/1 1/8 In the Oppenheimer-Phillips deuteron wave polarization and disintegration process encountered in Low Energy Nuclear Reactions (LENRs), the following reactions occur: D Bi Bi Bi Po Po Pb Complete the following nuclear reactions that would have occurred at the Oklo natural nuclear reactors sites. n e * e * He n + + He + e * List the domains of application of Transport Theory. Prove that the divergence of the gradient leads to the Laplacian operator in the leakage term of the neutron diffusion equation:.( D) D Enunciate and write the statement of Fick s law of neutron diffusion. What does the unit of the barn equal to in square centimeters and square meters Access the Chart of the Nuclides for,00 m/sec or thermal neutrons, and determine the total microscopic cross sections for the following isotopes: 1. U 35. Pu 39 Estimate their:

10 1. Number densities,. Total macroscopic cross-sections, 3. Total mean free paths. Calculate the total cross sections and the mean free paths of thermal neutrons in the following moderators: 1. H O. D O 37 1/4 1/ /6 1/13 In a neutron flux of 10 8 [n/(cm.sec)], what is the neutron absorption rate in 1 cm 3 of a material with a macroscopic absorption cross section of 0.1 cm -1 Through direct substitution prove that the different general forms given for the solution of the Simple Harmonic Oscillator in its forms: a) x( t) x( t), b) x( t) x( t) do indeed satisfy the underlying differential equations. Calculate the fluxes and the currents in the following situations: 1. At the center of a line of length with two sources of strength S at each end.. A square of side length at the center and at the midpoint of one side, where neutron sources of strengths S [neutrons/second] are placed at each one of the vertices. Carry on the calculations: a. In a vacuum, b. In a diffusing medium with a diffusion coefficient D and a diffusion length L. Note: Fick s law applies only in the case of a diffusing medium. 39 1/8 1/ /8 1/13 1U9316Assignments Policy Assignments will be turned in at the beginning of the class period, one week from the day they are assigned. The first five minutes of the class period will be devoted for turning in, and returning graded assignments. Late assignments will be assigned only a partial grade. Please try to submit them on time since once the assignments are graded and returned to the class, late assignments cannot be accepted any more. If you are having difficulties with an assignment, you are encouraged to seek help from the teaching assistants (TAs) during their office hours. Questions may be ed to the TA's, but face-to-face interaction is more beneficial. Although you are encouraged to consult with each other if you are having difficulties, you are kindly expected to submit work that shows your individual effort. Please do not submit a copy of another person's work as your own. Copies of other people's assignments are not conducive to learning, and are unacceptable. For further information, please read the detailed assignments guidelines.

NPRE 402 Nuclear Power Engineering Summer 2018

NPRE 402 Nuclear Power Engineering Summer 2018 Number Date Assigned Due Date Description 1 6/11 6/18 2 6/13 6/20 1. Define the Quad unit of energy in terms of BTUs and Joules. Use the 2017 Sankey diagram