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[Discipline]: Mathematics Documents

Documents below are listed chronologically. Use the links on the left or below to filter documents by keyword. Use the links above to jump to a specific year on this page.

Number of files: 53

    1969-01-02---------Jump to [Top]
  1. The Effect of Bypass Characteristics on Parallel Channel Flow Instabilities, by M.B. Carver, AECL, 1969-01-02. Doc type: Paper.
    Summary: This article is definitive because nobody could figure out why all the instability codes gave stability thresholds well below the measured threshold power in the experiments done at Canadian Westinghouse. The paper determines analytically that this is because the small bypass stabilized the experimental system as it could not maintain a constant pressure drop, which all the codes assumed at step 1.
    Keywords: [Concept] - [SI] 03000 Engineering Science and Technology 33100 Main Heat Transport System [Discipline] Mathematics Mechanical Engineering [Topic] Basic Equations Collections Conceptual Modelling Process Systems Thermalhydraulics [Phase] Design Analysis Safety Analysis [Audience] Engineer Grad
    - Proceedings of the Institution of Mechanical Engineers, Volume 184, 1969 BYPASS PIME_CONF_1969_184_083_02.pdf (703 kb)
    2. 1975-07-01---------Jump to [Top]
  2. FORSIM a FORTRAN Oriented Simulation Package for the Automated Solution of Partial and Ordinary partial Differential Equation SYSTEMS, by M.B. Carver, AECL, 1975-07-01. Doc type: Report.
    Summary: FORSIM was Mike's vehicle for all the work he did in PDEs/ODEs including stiff equation solvers, reactor kinetics and mass action chemical kinetics, sparse matrix approximation to the Jacobian, integration over discontinuities, and parameter identification. In about a dozen PPV papers. FORSIM started as just an ODE simulator to replace MIMIC for the AECL Sheridan Park engineers.
    Keywords: [Concept] - [SI] 03000 Engineering Science and Technology 30000 Reactor, Steam Generators and Auxiliaries 32000 Moderator System 33000 Primary Heat Transport System 36000 Steam Generator Steam and Water Systems [Discipline] Mathematics Mechanical Engineering [Topic] Basic Equations Collections Modelling Process Systems Thermalhydraulics [Phase] Design Analysis Safety Analysis [Audience] Engineer Grad
    - AECL 4608, November 1973 FORSIM_AECL4608.pdf (538 kb)
    3. 1978-01-01---------Jump to [Top]
  3. Efficient Integration over Discontinuities in Ordinary Differential Equation Simulation, by M.B. Carver, AECL, 1978-01-01. Doc type: Paper.
    Summary: Efficient integration algorithms for ordinary differential equations take integration steps that are as large as the error control criteria permit. Events or discontinuities in equation definition are often implicitly defined to occur when a variable reaches a critical value, for example a fuel rod surface reaching saturation temperature, and this requires the integrator to basically restart the calculation precisely at the point of change. Instead integrators will "hunt" for the discontinuity wasting a lot of computer time, and will eventually "step over" the discontinuity using integration points either side of the event. This paper shows that if the discontinuity is defined and monitored as an additional part of the equation set, such a restart can be optimized, thus ensuring that the event will be defined as an integration restart point.
    Keywords: [Concept] - [SI] 03000 Engineering Science and Technology 33100 Main Heat Transport System 36000 Steam Generator Steam and Water Systems [Discipline] Mathematics#Mechanical Engineering [Topic] Modelling Process Systems Thermalhydraulics [Phase] Design Analysis Safety Analysis [Audience] Engineer Grad
    - Mathematics and Computers in Simulation, XX, 1978 efficient-integration-over-discontinuities-in-ordinary-differential-equation.pdf (467 kb)
    4. 1978-08-01---------Jump to [Top]
  4. The method of lines and the advective equation, by M.B. Carver and H.W. Hinds, AECL, 1978-08-01. Doc type: Paper.
    Summary: This article showed that the common approach of first order differencing, used in almost all thermalhydraulic computer programs, would not properly solve the simplest hyperbolic PDE on the market. Despite the errata, it is Carver's most cited publication and laid the foundations for many higher order analyses by others, and Carver's pseudo-characteristic method of lines (PCMOL) solution of the thermalhydraulic conservation equations.
    Keywords: [Concept] - [SI] 03000 Engineering Science and Technology 33100 Main Heat Transport System 36000 Steam Generator Steam and Water Systems [Discipline] Mathematics#Mechanical Engineering [Topic] Basic Equations Modelling Process Systems Thermalhydraulics [Phase] Concept Design Analysis Safety Analysis [Audience] Engineer Grad
    - Simulation, August,1978. Also published as AECL 6155 AdvectiveEqn.pdf (804 kb)
    5. 1980-01-01---------Jump to [Top]
  5. Pseudo-characteristic method of lines solution of first-order hyperbolic equation systems, by M.B. Carver, AECL, 1980-01-01. Doc type: Paper.
    Summary: This paper introduced a new concept, pseudo-characteristics, which allows the directionality dictated by the method of characteristics to be applied on a fixed grid basis. This is the method that N.P. Kolev Nuclear Institute of Bulgaria and M. B. Carver used to apply to the EVUT form of the thermalhydraulic conservation equations at the OECD/CSNI conference on two phase flow, Pasedena, 1981. In this MACS paper, discretization of the PDEs is discussed, using higher order upwind biased derivatives of each of the Lagrange polynomials and the Hermite polynomials. Results are shown for incompressible flow in a hydraulic jump and for compressible flow in the EVET thermalhydraulic conservation equations.
    Keywords: [Concept] - [SI] 03000 Engineering Science and Technology 33100 Main Heat Transport System 36000 Steam Generator Steam and Water Systems [Discipline] Mathematics#Mechanical Engineering [Topic] Modelling Process Systems Thermalhydraulics [Phase] Design Analysis Safety Analysis [Audience] Engineer Grad
    - Mathematics and Computers in Simulation, 22, 1980 pseudo-characteristic-method-of-lines-solution-of-first-order-hyperbolic-equation.pdf (455 kb)
    6. 1980-04-01---------Jump to [Top]
  6. Mathematics, Course 221, OPG, 1980-04-01. Doc type: Course.
    Summary: This course proves an introduction to two topics: equipment reliability evaluation, and calculus.
    Keywords: [Concept] Mathematics [SI] - [Discipline] Mathematics [Topic] Basic Equations Conceptual [Phase] Concept Operation [Audience] Engineer Manager
    - Full Course 20043000.pdf (3593 kb)
    - 221.00-1 Index and Objectives, 20043001.pdf (124 kb)
    - 221.00-2 Indroduction, 20043002.pdf (132 kb)
    - 421.10-4 Standard Notation, 20043003.pdf (122 kb)
    - 421.20-1 Algebra Fundamentals, 20043004.pdf (239 kb)
    - 421.40-1 Graphs, 20043005.pdf (153 kb)
    - 421.40-2 Graphing Functions, 20043006.pdf (80 kb)
    - 321.10-3 Logarithms and Exponentials, 20043007.pdf (210 kb)
    - 321.10-4 Use of Logarithmic Scaled Graph Paper, 20043008.pdf (347 kb)
    - 221.10-1 Basic Reliability Concepts, 20043009.pdf (154 kb)
    - 221.20-1 The Straight Line, 20043010.pdf (166 kb)
    - 221.20-2 The Derivative, 20043011.pdf (259 kb)
    - 221.20-3 Simple Applications of Derivatives, 20043012.pdf (127 kb)
    - 221.20-4 Differentiating Exponential Functions, 20043013.pdf (193 kb)
    - 221.20-5 The Derivative in Science and Technology, 20043014.pdf (213 kb)
    - 221.30-1 The Integral, 20043015.pdf (194 kb)
    - 221.30-2 Application of the Integral as an Infinite Sum, 20043016.pdf (371 kb)
    - 221.40-1 Appendix 1 : Review Exercises, 20043017.pdf (202 kb)
    - 221.40-2 Appendix 2 : Questions Bearing Directly on Course 221 Content from Recent AECB Nuclear General Examinations, 20043018.pdf (75 kb)
    - 221.40-3 Appendix 3 : Solving Quadratic Equations, 20043019.pdf (84 kb)
    - 221.40-4 Answers to Assignments and Review Exercises, 20043020.pdf (268 kb)
    7. 1981-04-01---------Jump to [Top]
  7. Thermal-Hydraulics in Recirculating Steam Generators: Thirst Code User's Manual, by M.B. Carver, AECL, 1981-04-01. Doc type: Report.
    Summary: THIRST is for modeling ThermalHydraulics In Recirculating Steam generators. This manual gives complete details of the mathematical derivation and numerical solution of the 3D, 2Phase thermalhydraulic equilibrium conservation equations inside a reactor boiler and also explains the many constitutive correlations required. Finally the manual fully defines the immense amount of input detail required to model the primary side heat transfer and the secondary side water boiling and recirculating in the complex tube-in-shell geometry of a prototypical CANDU steam generator.
    Keywords: [Concept] - [SI] 03000 Engineering Science and Technology 36000 Steam Generator Steam and Water Systems [Discipline] Mathematics#Mechanical Engineering [Topic] Fluid Mechanics Heat Transfer Modelling Process Systems Thermalhydraulics [Phase] Design Analysis Safety Analysis [Audience] Engineer Grad
    - AECL 7254, April 1981 THIRSTusersR43667.pdf (2290 kb)
    8. 1981-07-01---------Jump to [Top]
  8. Mathematics, Nuclear Training Course 121, OPG, 1981-07-01. Doc type: Course.
    Summary: Probability and reliability concepts applied to station operation.
    Keywords: [Concept] Mathematics [SI] - [Discipline] Mathematics [Topic] Basic Equations Conceptual [Phase] Concept [Audience] Engineer Manager
    - Cover page, Table of contents, Objectives 20040101.pdf (167 kb)
    - Introduction, 20040102.pdf (194 kb)
    - Probability, 20040103.pdf (610 kb)
    - Safety Systems Analysis, 20040104.pdf (404 kb)
    - Safety Systems Analysis - Solutions to Sample Problems, 20040105.pdf (455 kb)
    - The Binomial Distribution and Power System Reliability, 20040106.pdf (302 kb)
    - The Normal Distribution and Applications, 20040107.pdf (193 kb)
    - Basic Reliability Concepts, 20040108.pdf (638 kb)
    - Operation in the Wearout Mode, 20040109.pdf (237 kb)
    - Some Modern Reliability Topics, 20040110.pdf (634 kb)
    - Appendix 1: Confidence Limits, 20040111.pdf (219 kb)
    - Appendix 2: Solutions to Assignments, 20040112.pdf (636 kb)
    9. 1982-01-01---------Jump to [Top]
  9. A Method of Limiting Intermediate Volume Fraction in Iterative Two-Fluid Computations, by M.B. Carver, AECL, 1982-01-01. Doc type: Paper.
    Summary: This is seminal and the core contribution in Carver's thesis. The ICE guys, Harlow & Amsden and the IPSA guys, Spalding & Patankar had not got it quite right for air/water conditions where the water totally dominates the pressure field calculation when it is based on mass flux balance, as this is dominated by the water component and neglects continuity of the air. Herein, a volumetric balance fixes that and the calculation also converges better with the constraint mentioned in the title.
    Keywords: [Concept] - [SI] 03000 Engineering Science and Technology 33100 Main Heat Transport System 36000 Steam Generator Steam and Water Systems [Discipline] Mathematics#Mechanical Engineering [Topic] Modelling Process Systems Thermalhydraulics [Phase] Design Analysis Safety Analysis [Audience] Engineer Grad
    - Journal of Mechanical Engineering Science, Vol. 24, No. 2, 1982 limiting_volume_fraction_JMES_JOUR_1982.pdf (374 kb)
    10. 1984-12-01---------Jump to [Top]
  10. Two Dimensional Modelling of the Homogenizing Effects of Flow Obstructions in Two Fluid Flow, by M.B. Carver and M. E. Salcudean, AECL, 1984-12-01. Doc type: Paper.
    Summary: It is well known that obstructions in two fluid flow have the effect of homogenizing the two fluid mixture, resulting not only in a more uniform phase distribution, but also in a significant reduction of the ratio of fluid velocities. This paper describes a 2D, 2Fluid computer program written by the first author to do proof of principal studies of 2fluid redistribution around bends and past obstacles. The details necessary for modelling air/water flows in these geometries have been introduced here before extending the work to 3D. The paper shows that these phase redistribution effects can be modelled using the two fluid computer program, and compares results to those obtained in a recent experiment on flow past obstructions.
    Keywords: [Concept] - [SI] 03000 Engineering Science and Technology 33100 Main Heat Transport System [Discipline] Mathematics#Mechanical Engineering [Topic] Modelling Thermalhydraulics [Phase] Design Analysis Safety Analysis [Audience] Engineer Grad
    - Mathematics and Computers in Simulation 26(6):pp 475–484, December 1984 two-dimensional-modelling-of-the-homogenizing-effects-of-flow-obstructions.pdf (1202 kb)
    11. 1987-04-01---------Jump to [Top]
  11. Development and Application of a Three-Dimensional Two-Fluid Numerical Algorithm for Simulation of Phase Redistribution by Bends and Obstructions, by M.B. Carver, AECL, 1987-04-01. Doc type: Other.
    Summary: Mike completed his Ph.D in parallel to his full time position at AECL as branch head of Applied Mathematics at CRNL. Upon completion he was appointed adjunct professor at McMaster and was co-supervisor of two degrees.
    Keywords: [Concept] - [SI] 03000 Engineering Science and Technology 33100 Main Heat Transport System [Discipline] Mathematics#Mechanical Engineering [Topic] Process Systems Thermalhydraulics [Phase] Design Analysis Safety Analysis [Audience] Engineer Grad
    - Ph.D Thesis, Department of Mechanical Engineering, University of Ottawa, April 1987 ThesisNL56352.pdf (4350 kb)
    12. 1990-01-01---------Jump to [Top]
  12. Reliability for Management and Professional Staff , Course PI 21, Nuclear Training Centre, OPG, 1990-01-01. Doc type: Course.
    Summary: A six part introductory reliability course for management and professional staff.
    Keywords: [Concept] Mathematics [SI] - [Discipline] Mathematics [Topic] Basic Equations Conceptual [Phase] Concept Operation [Audience] Engineer Manager
    - Full Course 20043300.pdf (1585 kb)
    - Course Table of Contents, 20043301.pdf (219 kb)
    - PI 21.00 Intro to the Course, 20043302.pdf (104 kb)
    - PI 21.01 An Introduction to Reliability, 20043303.pdf (166 kb)
    - PI 21.02 Reliability Concepts, 20043304.pdf (384 kb)
    - PI 21.03 Process Systems, 20043305.pdf (185 kb)
    - PI 21.04 Availability of Safety Systems, 20043306.pdf (250 kb)
    - PI 21.05 Modern Reliability Techniques, 20043307.pdf (208 kb)
    - PI 21.06 Reporting and Administration, 20043308.pdf (111 kb)
    13. 1995-08-01---------Jump to [Top]
  13. Numerical Solution of the Thermalhydraulic Conservation Equations from Fundamental Concepts to Multidimensional Analysis, by M.B. Carver, , 1995-08-01. Doc type: Report.
    Summary: This material was presented as part of a short course in Two-Phase Flow and Heat Transfer at McMaster University and is documented in report form for further reference. The discussion briefly establishes some requisite concepts of differential equation theory, and applies these to describe methods for numerical solution of the thennalhydraulic conservation equations in their various forms. The intent is to cover the general methodology without obscuring the principles with details. As a short overview of computational thermalhydraulics, the material provides an introductory foundation, so that those working on the application of thennalhydraulic codes can begin to understand the many intricacies involved without having to locate and read the references given. Those intending to work in code development will need to read and understand all the references.
    Keywords: [Concept] - [SI] 03000 Engineering Science and Technology 33100 Main Heat Transport System 36000 Steam Generator Steam and Water Systems [Discipline] Mathematics#Mechanical Engineering [Topic] Basic Equations Collections Conceptual Modelling Process Systems Thermalhydraulics [Phase] Design Analysis Safety Analysis [Audience] Grad
    - AECL-11387, ARD-TD-550, Revision 1 (2017) to the original (1995) Carver AECL-11387[3628]-WithAddendum.pdf (6457 kb)
    14. 1997-04-01---------Jump to [Top]
  14. Software Quality Assurance: Practical Procedures to Meet CSA Standards, by M.B. Carver, CNSC, 1997-04-01. Doc type: Report.
    Summary: In the Canadian nuclear industry at the time, only the ASSERT code team and the NUCIRC team used definitive SQA (Software Quality Assurance), which identifies exactly what version of the computer code is being used for a given application, and every component used to build that version. A drive to apply such standards to all computer programs started in the 1990s, and Mike co-authored the 1995 AECL Reactor Development SQA manual. Upon his retirement, representatives of the then AECB (now CNSC) asked him to write a SQA guide for the industry that would bring all computer codes teams in line with CSA standards ( N286.7 & Q936).This report is CNSC-info-0669, 1997. To date the ASSERT-PV development team has followed these standards, the CATHENA team has not. Source attribution: Archived in the public domain at http://www.nuclearsafety.gc.ca/eng/about/past/timeline-dev/resources/documents/infohistorical/info-0669.pdf .
    Keywords: [Concept] - [SI] 03000 Engineering Science and Technology 30000 Reactor, Steam Generators and Auxiliaries 33100 Main Heat Transport System 36000 Steam Generator Steam and Water Systems [Discipline] Mathematics#Mechanical Engineering [Topic] Modelling Thermalhydraulics [Phase] Design Analysis Safety Analysis [Audience] Engineer Grad
    - Atomic Energy Control Board, Report INFO-0699, April 1997, http://www.nuclearsafety.gc.ca info-0669.pdf (3262 kb)
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