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Nuclear Engineering: Mathematical Modeling and Simulation [Minkštas viršelis]

(Professor and Dean Graduate Studies, Air University, Islamabad, Pakistan)
  • Formatas: Paperback / softback, 548 pages, aukštis x plotis: 276x216 mm, weight: 1520 g, 220 illustrations (70 in full color); Illustrations
  • Išleidimo metai: 22-Mar-2022
  • Leidėjas: Academic Press Inc
  • ISBN-10: 0323906184
  • ISBN-13: 9780323906180
Kitos knygos pagal šią temą:
Nuclear Engineering: Mathematical Modeling and SimulationDidesnis paveikslėlis
  • Formatas: Paperback / softback, 548 pages, aukštis x plotis: 276x216 mm, weight: 1520 g, 220 illustrations (70 in full color); Illustrations
  • Išleidimo metai: 22-Mar-2022
  • Leidėjas: Academic Press Inc
  • ISBN-10: 0323906184
  • ISBN-13: 9780323906180
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9780323906180.html
Raktažodžiai:

Nuclear Engineering Mathematical Modeling and Simulation presents the mathematical modeling of neutron diffusion and transport. Aimed at students and early career engineers, this highly practical and visual resource guides the reader through computer simulations using the Monte Carlo Method which can be applied to a variety of applications, including power generation, criticality assemblies, nuclear detection systems, and nuclear medicine to name a few. The book covers optimization in both the traditional deterministic framework of variational methods and the stochastic framework of Monte Carlo methods.

Specific sections cover the fundamentals of nuclear physics, computer codes used for neutron and photon radiation transport simulations, applications of analyses and simulations, optimization techniques for both fixed-source and multiplying systems, and various simulations in the medical area where radioisotopes are used in cancer treatment.

  • Provides a highly visual and practical reference that includes mathematical modeling, formulations, models and methods throughout
  • Includes all current major computer codes, such as ANISN, MCNP and MATLAB for user coding and analysis
  • Guides the reader through simulations for the design optimization of both present-day and future nuclear systems
About the author xiii
Foreword xv
1 The atom and nuclear radiation
1(1)
1.1 The atom
1(5)
1.1.1 Nuclear stability
5(1)
1.1.2 Binding energy
6(1)
1.2 Radioactive decay
6(2)
1.2.1 Alpha decay
8(1)
1.2.2 Beta decay
9(1)
1.2.3 Gamma decay
10(1)
1.2.4 Radioactive nuclides in nuclear technologies
11(1)
1.3 Interaction of radiation with matter
12(12)
1.3.1 Interaction of alpha rays with matter
12(4)
1.3.2 Interaction of beta radiation with matter
16(3)
1.3.3 Interaction of gamma radiation with matter
19(5)
1.4 Sources and effects of radiation
24(6)
1.4.1 Radiation dose
26(1)
1.4.2 Absorbed dose
26(1)
1.4.3 Equivalent dose
27(1)
1.4.4 Effective dose
28(1)
1.4.5 Radiation safety limits
28(1)
1.4.6 Radiation detection
29(1)
1.5 Atomic densities of elements and mixtures
30(4)
1.6 Mathematical modeling and simulation
34(10)
1.6.1 Alpha particle transport simulation
35(1)
1.6.2 Interaction of electrons with matter
35(5)
1.6.3 Interaction of gamma radiation with matter
40(1)
1.6.4 Radiation dose from Calfornium-252 gamma source in water
41(3)
Capabilities developed
44(1)
Nomenclature
44(2)
Problems
46(1)
References
47(4)
2 Interactions of neutrons with matter
51(52)
2.1 Kinetic theory
51(2)
2.2 Types of neutron interactions
53(5)
2.2.1 Neutron scattering in the lab and center of mass systems
55(3)
2.3 The microscopic cross-section
58(5)
2.4 The macroscopic cross-section
63(1)
2.5 Flux measurement
64(2)
2.6 Reaction rates
66(1)
2.7 Neutron slowing down, diffusion and thermalization
67(7)
2.8 Resonance cross-section
74(6)
2.9 Nuclear fission
80(8)
2.9.1 The fission process
80(1)
2.9.2 Critical energy
81(3)
2.9.3 Fission yield
84(1)
2.9.4 Number of neutrons emitted in fission
84(1)
2.9.5 Fissile and fertile materials
85(1)
2.9.6 The fission spectrum
86(2)
2.10 Criticality
88(10)
2.10.1 Diffusion theory
90(1)
2.10.2 Transport theory
91(1)
2.10.3 Monte Carlo simulation
92(6)
Problems
98(1)
Nomenclature
98(2)
References
100(3)
3 Nuclear reactors and systems
103(46)
3.1 Status of nuclear power
103(4)
3.1.1 Generations of nuclear power
103(3)
3.1.2 Reactors shut down
106(1)
3.1.3 The future of the nuclear power industry
106(1)
3.2 Nuclear reactor systems
107(9)
3.2.1 Pressurized water reactor
108(2)
3.2.2 Boiling water reactor
110(2)
3.2.3 Pressurized heavy water reactor
112(1)
3.2.4 Gas cooled reactor
113(1)
3.2.5 Fast breeder reactor
114(2)
3.3 Marine propulsion reactors
116(4)
3.3.1 Introduction
116(1)
3.3.2 US nuclear submarine program
116(1)
3.3.3 Former Soviet/Russian nuclear submarine program
117(1)
3.3.4 Submarine programs: UK, France, China, India and Pakistan
117(1)
3.3.5 Modern-day submarines
117(1)
3.3.6 Technical features
118(2)
3.3.7 HEU/LEU submarine reactors
120(1)
3.4 Plutonium production reactors
120(1)
3.5 Small modular reactors
121(7)
3.5.1 Design features of SMRs
121(4)
3.5.2 Very small modular reactor
125(1)
3.5.3 Generation-IV reactors
125(2)
3.5.4 Radiation source term
127(1)
3.6 Nuclear fusion
128(4)
3.6.1 The fusion reaction
128(1)
3.6.2 Magnetic confinement fusion
129(1)
3.6.3 Inertial confinement fusion
130(2)
3.7 Space propulsion
132(6)
3.7.1 Conventional rocket designs
132(1)
3.7.2 Space exploration
132(2)
3.7.3 Nuclear rocket designs for deep space exploration
134(4)
3.8 Nuclear power systems in space
138(3)
3.8.1 Radioisotope thermal generators
138(1)
3.8.2 Small nuclear auxiliary power systems
138(3)
3.9 Conclusions
141(1)
Problems
141(1)
Nomenclature
142(2)
References
144(1)
Annex: The physics of nuclear fusion
145(4)
4 Mathematical foundations
149(62)
4.1 Ordinary differential equations
150(6)
4.1.1 The Poisson equation: steady-state heat conduction in 1-D
153(2)
4.1.2 Coupled first-order ODEs: the point kinetics equations
155(1)
4.2 Partial differential equations
156(9)
4.2.1 Equations of fluid dynamics
156(1)
4.2.2 The 1-D time-dependent heat conduction
157(1)
4.2.3 Laplace equation: 2-D steady-state heat conduction
158(1)
4.2.4 Heat conduction in 2-D and 3-D
159(5)
4.2.5 Flux formulation
164(1)
4.3 Integral equations
165(5)
4.3.1 An important integral equation for neutron transport
169(1)
4.3.2 Integral equations in neutron transport
169(1)
4.4 Integro-differential equations
170(4)
4.5 Numerical methods
174(11)
4.5.1 The Finite Difference Method
174(4)
4.5.2 The Finite Element Method
178(7)
4.6 Approximate methods
185(1)
4.6.1 The Ritz method
185(1)
4.6.2 The Rayleigh--Ritz variational method
186(1)
4.6.3 The weighted residual method
186(1)
4.7 The adjoint function
186(1)
4.8 Random processes, probability, and statistics
187(14)
4.8.1 Random processes
188(1)
4.8.2 Markovian processes
188(1)
4.8.3 Population and sample
188(1)
4.8.4 Random variables, PDF, and CDF
189(6)
4.8.5 Random numbers
195(1)
4.8.6 Sampling from PDFs
196(3)
4.8.7 Kullback--Leibler divergence for uniform random numbers
199(1)
4.8.8 The law of large numbers
199(1)
4.8.9 The central limit theorem
200(1)
4.9 Evaluation of integrals
201(5)
4.9.1 The Monte Carlo method for numerical integration
203(3)
Problems
206(1)
Nomenclature
207(1)
References
208(3)
5 The neutron diffusion equation
211(48)
5.1 The conservation equation
211(2)
5.2 The one-group diffusion equation
213(8)
5.2.1 Nonmultiplying systems
213(2)
5.2.2 Multiplying systems
215(4)
5.2.3 One-group criticality
219(2)
5.3 The two-group diffusion equation
221(13)
5.3.1 Nonmultiplying systems
221(6)
5.3.2 Multiplying systems
227(3)
5.3.3 Two-group criticality
230(4)
5.4 The multigroup diffusion equation
234(4)
5.4.1 Numerical solution of the multigroup diffusion equations
235(3)
5.5 Effect of fuel concentration on critical mass
238(10)
5.5.1 Goertzel's theorem
239(1)
5.5.2 Nonuniform fuel distribution: a slab model
239(5)
5.5.3 Nonuniform fuel distribution: a spherical model
244(3)
5.5.4 Critical core with flat thermal flux loading
247(1)
5.6 The two-group adjoint diffusion equations
248(3)
5.7 Core neutronics with diffusion equations
251(5)
Problems
256(1)
Nomenclature
257(1)
References
258(1)
6 The neutron transport equation
259(46)
6.1 Structure of the neutron transport equation
260(8)
6.1.1 An integro-differential form of the neutron transport equation
260(5)
6.1.2 The two-group transport equation
265(1)
6.1.3 The integral form of the transport equation
266(2)
6.1.4 Multigroup form of the integral transport equation
268(1)
6.2 Exact solutions of the transport equation
268(17)
6.2.1 The classic albedo problem
270(1)
6.2.2 Infinite medium with a plane isotropic source
270(4)
6.2.3 Finite sphere with a point isotropic source
274(11)
6.3 Numerical methods for solving the transport equation
285(13)
6.3.1 The discrete ordinates method
285(2)
6.3.2 The Spherical harmonics method
287(6)
6.3.3 The DPN method
293(2)
6.3.4 The BN method
295(1)
6.3.5 The finite element method
296(1)
6.3.6 The nodal method with transport theory
296(1)
6.3.7 Hybrid methods
297(1)
6.3.8 Criticality estimates
297(1)
6.4 Transport theory for reactor calculations
298(4)
6.4.1 Collision probability method
299(1)
6.4.2 Method of characteristics
299(3)
Problems
302(1)
Nomenclature
302(1)
References
303(2)
7 The Monte Carlo method
305(32)
7.1 Stochastic simulation
305(3)
7.1.1 Markov processes
305(1)
7.1.2 Events in a random walk
305(1)
7.1.3 The physics of interactions
306(1)
7.1.4 Nuclear interaction data
306(1)
7.1.5 How do we know an answer is good?
306(2)
7.2 Simulation of a random walk
308(8)
7.2.1 Monte Carlo simulation
308(1)
7.2.2 Estimators and tallies
309(3)
7.2.3 Sampling a source
312(1)
7.2.4 Sampling the "distance to collision"
313(1)
7.2.5 Determining the type of event
313(1)
7.2.6 Determining the nuclide of interaction
314(1)
7.2.7 Processing a scattering event
314(1)
7.2.8 Processing a fission event
314(1)
7.2.9 Processing a capture event
315(1)
7.2.10 Processing an escape-from-system event
315(1)
7.2.11 Mean and variance
315(1)
7.2.12 Batch, history, random walk and events
316(1)
7.3 Modeling the geometry
316(12)
7.3.1 Geometries for illustration of Monte Carlo simulation
320(8)
7.4 Demonstration
328(4)
7.5 Variance reduction methods
332(1)
7.6 Estimating perturbations with Monte Carlo simulation
333(1)
7.7 Conclusions
333(1)
Problems
334(1)
Nomenclature
334(1)
References
335(2)
8 Computer codes
337(12)
8.1 Neutron and radiation transport codes
338(2)
8.1.1 ANISN
338(1)
8.1.2 DOT
338(1)
8.1.3 TORT
338(1)
8.1.4 PARTISN
339(1)
8.1.5 MCNP
339(1)
8.1.6 TART
339(1)
8.1.7 MORSE
339(1)
8.1.8 KENO
340(1)
8.1.9 Other Monte Carlo codes
340(1)
8.2 Time-dependent reactor kinetics codes
340(1)
8.3 Thermal hydraulics codes
340(1)
8.4 Radiological protection codes
341(1)
8.5 Performance and safety analyses
341(1)
8.6 Nuclear data
341(3)
8.6.1 MCNP
344(1)
8.7 Conclusion
344(1)
Problems
344(1)
Nomenclature
345(1)
References
345(4)
9 Optimization and variational methods
349(30)
9.1 Introduction
349(1)
9.2 Deterministic optimization
350(11)
9.2.1 Deterministic optimization without constraints
350(1)
9.2.2 Deterministic optimization with algebraic constraints
351(1)
9.2.3 Optimal solution with a system of first-order ordinary differential equation constraints
352(3)
9.2.4 Optimal solution with a system of first-order ordinary differential equation constraints
355(5)
9.2.5 Optimal discrete control (Pontryagin maximum principle)
360(1)
9.3 Controller design and optimization
361(4)
9.4 Dynamic programming
365(2)
9.5 Stochastic optimization
367(6)
9.5.1 Genetic algorithms
367(5)
9.5.2 Particle swarm optimization
372(1)
9.6 Applications of optimization in reactors
373(2)
9.6.1 Multi-objective core optimization
373(1)
9.6.2 Pressurized water reactor core pattern optimization
374(1)
9.6.3 Controller proportional integral derivative
374(1)
9.6.4 Radiation shielding
374(1)
9.6.5 Some other applications of optimization
375(1)
Problems
375(1)
Nomenclature
375(1)
References
376(3)
10 Monte Carlo simulation in nuclear systems
379(38)
10.1 Introduction
379(2)
10.2 Bare critical assemblies
381(7)
10.2.1 Godiva
381(5)
10.2.2 Jezebel
386(2)
10.3 Criticality safety
388(1)
10.3.1 Storage of interacting units
388(1)
10.3.2 Storage of uranium hexafluoride cylinders
388(1)
10.4 Radiation moderation and shielding
389(1)
10.4.1 Radiation moderation for a neutron generator
389(1)
10.4.2 Radiation shielding
390(1)
10.5 Nuclear fission applications
390(11)
10.5.1 Unit lattice cell and fuel assembly of the AP1000 reactor
390(4)
10.5.2 The Toshiba 4S reactor
394(6)
10.5.3 Micronuclear reactor
400(1)
10.6 Nuclear fusion applications
401(4)
Problems
405(1)
Nomenclature
405(1)
References
406(2)
Annex A MCNP listing for Godiva (Section 10.2.1)
408(2)
Annex B MCNP input listing (Jezebel, Section 10.2.2)
410(2)
Annex C MCNP input listing (BKIOShld, Section 10.5.1)
412(1)
Annex D MCNP input listing (BK10AP10, Section 10.5.1)
413(4)
11 Comparisons: Monte Carlo, diffusion, and transport
417(32)
11.1 Introduction
417(1)
11.2 Criticality in a bare sphere
417(4)
11.2.1 One-group diffusion theory criticality
417(1)
11.2.2 Two-group diffusion theory criticality
418(1)
11.2.3 One-speed transport theory criticality
419(2)
11.3 The classic albedo calculation
421(2)
11.4 Flux in a slab
423(5)
11.4.1 Diffusion theory
423(1)
11.4.2 Transport theory
424(1)
11.4.3 Monte Carlo simulation
425(1)
11.4.4 Comparison
425(3)
11.5 Flux in a finite sphere with a point isotropic source
428(5)
11.5.1 Diffusion theory
428(2)
11.5.2 Transport theory exact solution
430(1)
11.5.3 Monte Carlo simulation
431(2)
Problems
433(1)
Nomenclature
433(1)
References
434(1)
Annex A MATLAB Program AlbedoSlabDiffTh.m (Section 11.3)
435(3)
Annex B MCNP Input File BK11Albd (Section 11.2)
438(2)
Annex C MATLAB Program CH11 ExactSolSlabJan03.m (Section 11.4.4)
440(9)
12 Exercises in Monte Carlo simulation
449(40)
12.1 Sampling from a distribution function
449(4)
12.1.1 Sampling from a normal distribution
450(1)
12.1.2 Sampling from a Watt fission spectrum
451(2)
12.2 Estimating the neutron flux in a non-multiplying sphere
453(9)
12.2.1 The simulation process
453(3)
12.2.2 MATLAB program for point source in a finite non-multiplying sphere
456(4)
12.2.3 Results
460(2)
12.3 Reflected assemblies
462(2)
12.4 Reactor core modeling
464(9)
12.4.1 Input file
464(1)
12.4.2 Surrounding cells
465(1)
12.4.3 Source description
466(1)
12.4.4 Plotting the geometry
467(3)
12.4.5 Tally cards
470(1)
12.4.6 Reaction rates
470(1)
12.4.7 Plotting tallies
471(2)
12.5 Radiation safety and shielding
473(1)
12.6 Perturbation calculations
474(2)
12.7 MCNP geometry plotting in core neutronics
476(4)
Problems
480(2)
Conclusions
482(1)
Nomenclature
482(1)
References
483(1)
Annex A MATLAB Program CH12_NormalSampling.m
484(2)
Annex B MATLAB Program CH12_Watt Sampling.m
486(3)
13 Optimization in nuclear systems
489(20)
13.1 Introduction
489(1)
13.2 Reactor core design optimization
489(4)
13.3 Fusion neutronics design optimization
493(1)
13.4 Radiation shielding design optimization
494(1)
13.5 Fuel loading pattern optimization
495(6)
13.5.1 Optimal distribution: Pontryagin's maximum principle
498(3)
13.6 Radiation detection or optimization
501(2)
13.7 Controller design optimization
503(1)
Problems
504(1)
Nomenclature
505(1)
References
506(3)
14 Monte Carlo simulation in medical physics
509(12)
14.1 Introduction
509(3)
14.1.1 The production of radio-isotopes
510(1)
14.1.2 Alpha radiation therapy
511(1)
14.2 Brachytherapy
512(5)
14.2.1 Monte Carlo simulation in brachytherapy
512(2)
14.2.2 Monte Carlo simulation to calculate energy deposition and dose distribution for brachytherapy
514(3)
Nomenclature
517(1)
References
517(4)
Index 521
Zafar ullah Koreshi [ B.Sc. (Hons) Nuclear Engineering, Queen Mary College, University of London (UK); M.S, Nuclear Engineering, University of Wisconsin, Madison (USA), Ph.D Nuclear Engineering, University of Cambridge] is Professor at Air University, having contributed as Dean Faculty of Engineering and currently is Dean Graduate Studies at Air University. His experience has been in the Pakistan Atomic Energy Commission, Dr. A Q Khan Research Laboratories, National University of Sciences and Technology, and at Air University, Islamabad. He has published in Annals of Nuclear Energy, Progress in Nuclear Energy, Nuclear Technology and Radiation Protection, ASME Journal of Nuclear Engineering and Radiation Sciences and at several other leading international journals. Dr. Koreshi has been Track Chair at the International Conference on Nuclear Engineering held in the USA, China and Japan and has presented his research at the American Nuclear Society Annual Meetings. He is Member American Society of Mechanical Engineers (ASME), Professional Engineer Pakistan Engineering Council and Life Member Pakistan Nuclear Society. He has also received commendations for being Reviewer of prestigious journals. Prof. Zafar Koreshi is an Associate Editor of the ASME Journal of Nuclear Engineering and Radiation Science.