Reactor Dynamics
Code  Completion  Credits  Range  Language 

17DYR  Z,ZK  4  2+2  Czech 
 Lecturer:
 Bedřich Heřmanský (guarantor), Tomáš Bílý, Ondřej Huml
 Tutor:
 Bedřich Heřmanský (guarantor), Tomáš Bílý, Ondřej Huml
 Supervisor:
 Department of Nuclear Reactors
 Synopsis:

Kinetics of reactors, delayed neutrons, prompt neutron mean lifetime, reactor period. Dynamics of a zero reactor  the formulation of shortterm kinetic equations and parameters of delayed neutrons, simplified solutions. Transfer function of zero reactor. Coefficients of reactivity for different reactor configurations, temperature coefficients, thermal feedback, stability of reactors, linear and nonlinear kinetics. Heat transfer in reactors, reactor dynamics. Mathematical model of power reactor with thermal feedback, Simplified models of the reactor dynamics, computer models of the reactor dynamics
 Requirements:

17ZAF, 17JARE, 17TER
 Syllabus of lectures:

1st Dynamics of zero reactor (shortterm kinetics)
Hours: 6 lectures
Topics of the lectures:
Reactor Kinetics Equations
Integration of the lectures to study and interaction with other lectures, the aim of lectures. Diffusion equation. Onegroup approximation. Kinetics equations without delayed neutrons, delayed neutrons, the reactor period and the effect of delayed neutrons. Parameters of delayed neutrons. Kinetics equations with delayed neutrons (production and destruction formulation), the initial conditions.
Integral form of kinetic equations
Laplace integral transformation. Transfer functions and dynamic response basics. Derivation of kinetic equations in integral form. Roots and constants of G0 function for the six groups of delayed neutrons case. „Best“ parameters of delayed neutrons, energy spectrum correction.
Analytical solutions of kinetic equations
Response to an impulse change in reactivity (impulse response). Response to a step change in reactivity (transient response). Asymptotic period of a reactor. Special cases of a step change in reactivity. One group of delayed neutrons approximation. Response to linear changes in reactivity.
A simplified form of kinetic equations
Constant production of delayed neutrons. Prompt jump approximation: formulation of the equation in onegroup approximation, simplified response to step, harmonic and linear changes in reactivity. Numerical solutions of kinetic equations.
Transfer function of a zero reactor
Linearized model of a zero reactor. G0 function as transfer function of linearized zero reactor. Responses of linearized model to step and harmonic changes in reactivity.
Frequency response of zero reactor
Oscillatory experiments. Frequency response of linearized model of zero reactor. Bode plot. Logarithmic frequency response. Frequency response of zero reactor simplified models. Stability of zero reactor.
2nd Effect of temperature changes on the reactivity
Hours: 1 lecture
Topic of the lecture:
Dynamical systems with feedback. The stabilizing effect of the negative feedback. Reactivity temperature coefficients (RTC). Large reactor RTC. Doppler effect. Pressurized water reactors RTC (fuel RTC, coolant RTC). Effect of the boron concentration on the temperature feedback. Reactor's reactivity coefficients.
3rd Mathematical model of a power reactor
Hours: 3 lectures
Lectures:
Heat transfer in nuclear power reactors
Basic equations. Quasistationary approximation. Fuel and coolant equations in quasistationary approach (lumped parameters). Adiabatic model of the core heating. Differential approach (distributed parameters).
Mathematical model of the reactor with temperature feedback
Mathematical model and mathematical simulation of transients. Onechannel twocomponent (or threecomponent) model of the pressurized water reactor core. Classification of mathematical models according to the diffusion equations solution and thermalhydraulic processes.
Simplified models of the reactor dynamics
Nonlinear models: the NordheimFuchs model, oscillating reactor, reactor oscillation damping, model immediately jump. " Integral models: the adiabatic model, the integral model with heat losses. Linearized models with lumped parameters.
5th Transient heat transfer in the core  distributed parameters
Hours: 2 lectures
Lectures:
Analytical solutions of the transient heat transfer equation
Basic heat transfer equations, initial and boundary conditions. Solution via Laplace transformation. Formulation of heat transfers in fuel rods. First and second order approximations of the fuel rod transfer functions. Temperature delay of fuel rods. Impulse and step response.
Analytical solutions of the transient heat transfer equation of fuel channel
Basic fuel and coolant equations, initial and boundary conditions. Solution via Laplace transformation. Formulation of heat transfers in fuel channel. First and second order approximations of the fuel rod transfer functions. Temperature delay of fuel channel. Impulse and step response.
 Syllabus of tutorials:

During the seminars the problems of the above chapters are solved and the basic formulas are derived. Furthermore, numerical simulations are carried out for some transients. The seminars include measurements of fundamental dynamic processes at the VR 1 reactor.
 Study Objective:

Knowledge: Thorough knowledge of the kinetics of the reactor and the effects of temperature changes on reactor dynamics. Orientation in models of reactor dynamics. Ideas of the nuclear reactors thermal hydraulic analysis issue.
Skills: Understanding of the physical nature of processes taking place in different situations in a nuclear reactor. Application of acquired knowledge in the lectures Safety of Nuclear Power Plants.
 Study materials:

Key references:
Heřmanský B.: „Nuclear reactor dynamics“, Ministerstvo školství, Praha 1987, (In Czech)
Recommended references:
Kropš S.: „Temelin Low Power Tests“, NUSIM 2001, České Budějovice, 2001.
 Note:
 Timetable for winter semester 2019/2020:
 Timetable is not available yet
 Timetable for summer semester 2019/2020:
 Timetable is not available yet
 The course is a part of the following study plans:

 Jadarné inženýrství (compulsory course of the specialization)