Reactor Dynamics

Garant předmětu:

Lecturer:

Tutor:

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 short-term 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 (short-term 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. One-group 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 one-group 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. One-channel two-component (or three-component) model of the pressurized water reactor core. Classification of mathematical models according to the diffusion equations solution and thermal-hydraulic processes.

Simplified models of the reactor dynamics

Nonlinear models: the Nordheim-Fuchs 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:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: