1st Edition

Dynamic Simulation of Sodium Cooled Fast Reactors

By G Vaidyanathan Copyright 2023
    272 Pages 113 B/W Illustrations
    by CRC Press

    This book provides the basis of simulating a nuclear plant, in understanding the knowledge of how such simulations help in assuring the safety of the plants, thereby protecting the public from accidents. It provides the reader with an in-depth knowledge about modeling the thermal and flow processes in a fast reactor and gives an idea about the different numerical solution methods. The text highlights the application of the simulation to typical sodium-cooled fast reactor.

    The book

    • Discusses mathematical modeling of the heat transfer process in a fast reactor cooled by sodium.

    • Compares different numerical techniques and brings out the best one for the solution of the models.

    • Provides a methodology of validation based on experiments.

    • Examines modeling and simulation aspects necessary for the safe design of a fast reactor.

    • Emphasizes plant dynamics aspects, which is important for relating the interaction between the components in the heat transport systems.

    • Discusses the application of the models to the design of a sodium-cooled fast reactor

    It will serve as an ideal reference text for senior undergraduate, graduate students, and academic researchers in the fields of nuclear engineering, mechanical engineering, and power cycle engineering.




    Chapter 1   Introduction
    1.1 General
    1.2 Basics of Breeding
    1.3 Uranium Utilization
    1.4 Components of Fast Reactors
    1.5 Overview of Fast Reactor Programs
    1.6 Need for Dynamic Simulation
    1.7 Design Basis
    1.8 Plant Protection System
    1.9 Sensors and Response Time
    1.10 Scope of Dynamic Studies
    1.11 Modelling Development


    Chapter 2   Description of Fast Reactors
    2.1 Introduction
    2.2 Fast Breeder Test Reactor (FBTR)
     2.2.1. Reactor Core
    2.2.2 Reactor Assembly 
    2.2.3. Sodium Systems
    2.2.4 Decay Heat Removal
    2.2.5 Generating Plant
    2.2.6 Instrumentation and Control
    2.2.7 Safety
    2.3 Prototype Fast Breeder Reactor
    2.3.1 Reactor Core
    2.3.2 Reactor Assembly
    2.3.3 Main Heat Transport System
    2.3.4 Steam Water System
    2.3.5 Instrumentation and control
    2.3.6 Safety
    2.4 Neutronic Characteristics of FNRs
    2.5 Thermal-Hydraulic Characteristics of FNR


    Chapter 3 Reactor Heat Transfer
    3.1 Introduction
    3.2 Reactor Core
     3.2.1 Core Description
     3.2.2 Fuel Pin
     3.2.3 Subassembly
    3.3 Coolant Selection
    3.4 Control Material Selection
    3.5 Structural Material Selection
    3.6 Heat Generation
    3.7 Reactivity Feedback
     3.7.1 Doppler Effect
     3.7.2 Sodium Density and Void Effects
            3.7.3 Fuel Axial Expansion Effect
            3.7.4 Structural Expansion
            3.7.5 Bowing
    3.8 Decay Heat
    3.9 Solution Methods
     3.9.1 Prompt Jump Approximation
     3.9.2 Runge Kutta Method
     3.9.3 Kaganove Method
     3.9.4 Comparison of different Methods
     3.9.5 Solution   Methodology
    3.10 Heat Transfer in Primary System
     3.10.1 Core Thermal Model
     3.10.2 Fuel Restructuring 
            3.10.3 Gap Conductance
     3.10.4 Fuel Thermal Model
     3.10.5 Solution Technique
    3.11 Determination of Peak Temperatures: Hot Spot Analysis
    3.12 Core Thermal Model validation in FBTR and SUPER PHENIX
     3.13 Mixing of Coolant Streams in Upper Plenum
     3.13.1 Solution Technique 
    3.14 Lower Plenum/Cold Pool
    3.15 Grid Plate
    3.16 Heat Transfer Correlations for Fuel Rod Bundle


    Chapter 4 IHX Thermal Model
    4.1 Introduction
    4.2 Experience in PHENIX
    4.3 Thermal Model
    4.4 Solution Techniques
     4.4.1 Nodal Heat Balance Scheme
     4.4.2 Finite Differencing Scheme
    4.5 Choice of Numerical Scheme
     4.5.1 Nodal Heat Balance for Unbalanced Flows
     4.5.2 Modified Nodal Heat Balance Scheme (MNHB)
    4.6 Heat Transfer Correlations
    4.7 Validation


    Chapter 5 Thermal Model of Piping
    5.1 Introduction
    5.2 Thermal Model
    5.3 Solution Methods
    5.4 Comparison of Piping Models


    Chapter 6 Sodium Pump
    6.1 Introduction
    6.2 Electromagnetic Pumps
    6.3 Centrifugal Pump
     6.3.1 Pump Hydraulic Model
     6.3.2 Pump Dynamic Model
     6.3.3     Pump Thermal Model


    Chapter 7 Transient Hydraulics Simulation
    7.2Momentum Equations
    7.3Free Level Equations
    7.4Core Coolant Flow Distribution 
    7.5IHX Pressure Drop Correlations
     7.5.1       Resistance Coefficient for Cross Flow
     7.5.2.  Resistance Coefficient for Axial Flow
    7.6 Pump Characteristics
    7.7 Computational Model
    7.8 Validation Studies
    7.9 Secondary Circuit Hydraulics
     7.9.1 Secondary Hydraulics Model
     7.9.2 Natural Convection Flow in Sodium-Validation Studies


    Chapter 8   Steam Generator
    8.1 Introduction
    8.2 Heat Transfer Mechanisms
    8.3 Steam Generator Designs
        8.3.1. Conventional Fossil Fuelled Boilers Drum Type Once Through Steam Generators
        8.3.2 Sodium Heated Steam Generators
    8.4 Thermodynamic Models
    8.5 Mathematical Model
    8.6 Heat Transfer Correlations
        8.6.1 Single Phase Liquid Region
        8.6.2 Nucleate Boiling
        8.6.3 Dry-Out
        8.6.4 Post Dry-Out
        8.6.5 Superheated Region
        8.6.6 Sodium Side Heat Transfer

    8.7 Pressure Drop
    8.8 Computational Model
        8.8.1Solution of Water /Steam Side Equations
        8.8.2 Solution of Sodium, Shell, And Tube Wall Equations
    8.9 Steam Generator Model Validation


    Chapter 9   Computer Code Development
    9.1 Introduction
    9.2 Organization of DYNAM
    9.3 Axisymmetric Code STITH-2D
    9.4 Comparison of Predictions of DYANA-P And DYANA-HM


    Chapter 10   Specifying Sodium Pumps Coast-Down Time
    10.1 Introduction
    10.2 Impact of Coast Down Time in Loop Type FNR
    10.3 Impact of Coast Down Time in Pool Type FNR
    10.4 Considerations for Deciding Flow Coast Down Time
    10.5 Scram Threshold Vs Coast Down Time
         10.5.1. FHT Effect on Maximum Temperatures
         10.5.2 FHT to Avoid Scram for Short Power Failure
    10.6 Secondary pump FHT
    10.7 Primary FHT for Unprotected Loss of Flow

    Chapter 11   Plant Protection System
    11.1 Introduction
    11.2 Limiting Safety System Settings for FBTR
         11.2.1 Safety Signals and Settings
         11.2.2 Limiting Safety System Adequacy for FBTR
    11.3 Limiting Safety System Settings for PFBR
        11.3.1 Design Basis Events
        11.3.2 Core Design Safety Limits
        11.3.3 Selection of Scram Parameters
    11.4 Shutdown System
    11.5 Event Analysis


    Chapter 12   Decay Heat Removal System
     12.1 Introduction
     12.2 Natural Convection Basics
     12.3 DHR System Options in FNR
        12.3.1 DHR in Primary Sodium
        12.3.2 DHR in Secondary Sodium
        12.3.3 Steam Generator Auxiliary Cooling System
        12.3.4 DHR Through Steam-Water System
        12.3.5 Reactor Vessel Auxiliary Cooling System
     12.4 DHR in FBTR
       12.4.1 Heat Removal By Air In SG Casing
       12.4.2 Loss of Offsite and Onsite Power with SG Air Cooling
       12.4.3 Loss Of Offsite And Onsite Power Without Reactor Trip
    12.5 DHR in PFBR
       12.5.1 Thermal Model
       12.5.2 Decay Heat Exchanger (DHX) Model
       12.5.3 Hot Pool Model
       12.5.4 Air Heat Exchanger Model (AHX) Model
       12.5.5 Piping
       12.5.6 Expansion Tank
       12.5.7   Air Stack/Chimney
       12.5.8   Hydraulic Model
       12.5.9 DHDYN Validation on SADHANA Loop
    12.6 Role of Inter Wrapper Flow
    12.7 Role of Secondary thermal capacity


    Chapter 13 Modelling of Large Sodium-Water Reaction
    13.1 Introduction
    13.2 Leak Rate
      13.2.1 Water Leak Rate model
      13.2.2 Steam leak rate model
    13.3 Reaction site dynamics
      13.3.1 Spherical bubble model
      13.3.2 Columnar bubble model
      13.3.3 Solution technique
      13.3.4 Validation of Reaction site model
    13.4 Sodium Side System Transient
    13.5 Discharge Circuit System Transient
    13.6 Analysis of Pressure Transients for PFBR
    13.7 Failure of a greater number of tubes than design basis leak




    Dr G.Vaidyanathan, B.E., MBA, PhD served the Department of Atomic Energy, India over a period of 38 years until 2010. As a group director of the Fast Reactor Technology group at the Indira Gandhi Centre for Atomic Research (IGCAR), Kalpakkam, which is devoted to the development of Fast Reactors in India. He is a specialist in numerical and experimental thermal hydraulics and safety analysis. He was one of the key persons involved in the design and development of the experimental Fast Breeder Test Reactor (FBTR) and the Prototype Fast Breeder Reactor (PFBR) in India. He has contributed to the inhouse development of thermal hydraulic computer codes and during commissioning tests in FBTR the predictions of these codes were substantiated.

    After 2010 Dr Vaidyanathan has been teaching nuclear energy and alternative systems in the Indian universities. He has brought out 4 books on nuclear energy. These books have been welcomed by many professors teaching nuclear subjects in in Indian and Foreign universities. He has developed a video module comprising of 30 lectures on nuclear reactors and safety under the NPTEL program of IIT & IISc and these have been extensively used.

    Dr Vaidyanathan is a life fellow of the Institution of Engineers India, life member f the Indian nuclear society and Indian society of heat & mass transfer. He has 37 journal publications to his credit. He continues to contribute to the department as a member of the sodium safety panel (SSP) at IGCAR and the Advisory Committees for Safety review of various Projects (ACPSR) at the Atomic Energy Regulatory Board, India.