The course covers the fundamental aspects of dynamics and control of the main components of a nuclear plant.

In particular, the basic elements of linear system theory will be provided to allow the students to have a solid basis for dealing with the subsequent topics, namely, neutron kinetics, thermal-hydraulics, and, dynamics and control. Particular attention will be given to the coupling of neutronics and thermo-hydraulics to study the problems of stability and to understand the neutronic behaviour of a nuclear reactor: (a) during short transients resulting from normal reactor operation or accidental conditions, and, (b) in the medium term as results of the reactor operation.

At the end, fundamentals of detailed multiphysics treatment of nuclear systems will be provided.

During the course, a number of exercises will be performed and explained in the class and home works will be assigned to raise the student's awareness of the main engineering aspects and of the use of software to solve reactor dynamics and control problems.

This course will also examine the outcomes of research projects and international scientific activities in the area of reactor dynamics.

At the end of the course, visits at Research Centers (LENA Lab, SIET Lab) are foreseen.

The students will know and comprehend:

• the mathematical and physical approaches required to analyse dynamics of nuclear reactor and for investigating the stability of nuclear systems; the governing equations describing reactor kinetics and the coupling equations between neutronics and thermal-hydraulics in a lumped system; the models of the main components of a nuclear reactor and the basics of nuclear reactor control.

The students will be able to:

• describe the time-dependent behaviour of a nuclear reactor and solve the point kinetics equations for various reactivity insertions; formulate a model for the simulation of dynamics of core and primary components, and, couple the nuclear steam supply system behaviour to reactivity feedback mechanisms;
• formulate, analyse and solve problems relevant to reactor dynamics, stability and control and perform stability analyses of nuclear reactors and nuclear power plants;
• Exhibit fluent use of scientific terminology in technical and engineering communications.

Mathematical Fundamentals and Systems Theory. Laplace transforms, transfer functions, state space approach, feedback, transient analysis, stability.

Point Kinetics Equations. Derivation and limitations of the Point Reactor Kinetics Equations. Solution with one effective delayed group and six delayed groups. The In-hour Equation. The Inverse Method. Solutions of the Point Reactor Kinetics Equations with different reactivity insertions. Approximate solutions: constant delayed neutron production rate approximation, Prompt Jump approximation. Linearized Point Reactor Kinetics Equations and related transfer functions.

Reactivity Feedback and Reactor Dynamics. Mathematical and physical description of neutronic feedback. Models of feedbacks: temperature and power coefficients of reactivity. The transfer function of a reactor with feedback. Linear stability analysis. Nonlinear point reactor kinetics. Experimental determination of reactor kinetic parameters and reactivity. Static and dynamic techniques for reactivity determination.

Reactivity control. General considerations involved in reactivity control related to different nuclear reactors. Movable control rods. Control rod worth. Control rod effects on core power distributions. Burnable poisons. Chemical shim. Excess reactivity and shutdown margin. Temperature defect and power defect.

Modelling and behaviour of nuclear power plants components. Thermodynamics of Energy Conversion Systems. Steady flow: first and second law applications. Response of a PWR pressurizer to load changes. A equilibrium single-region formulation. Analysis of final equilibrium pressure conditions. General analysis of transient pressurizer behaviour. Non-equilibrium, two-region formulation (vapor-only, liquid-only regions). Linear and non-linear approaches. Dynamics of steam generators for nuclear reactors: Drum Type - Once Through – U-tube Boiler.

Introduction to multi-physics. An Introduction to multi-physics simulation. Multi-physics modelling of nuclear reactor systems. Introduction to OpenFOAM software as a multi-physics solver.

Home works. During the course, three home works based on the coursework will be assigned. The course also includes the use of calculation tools such as Matlab and Simulink.

A basic knowledge of nuclear engineering (Suggested Course - Introduction to Nuclear Engineering or equivalent), reactor physics (Suggested Course - Fission Reactor Physics or equivalent), and, Calculus is required. The students are expected to be familiar with fundamentals of thermodynamics (Suggested Course - Applied Thermodynamics and Heat Transfer or equivalent).

The evaluation consists of a written test and an oral examination.

Written test aims at verifying the ability of the students to solve problems of kinetics, dynamics and stability applied to nuclear reactors, and, in general, to verify that the expected learning outcomes have been achieved.

The oral test aims at corroborating the knowledge of the course topics, with particular attention on the ability to describe and model the following: core neutronics, thermal-hydraulics of different nuclear reactor component, stability/instability problems with a numerical estimation.

Lastly, there will be a question about one of the assigned home works to test the ability to discuss and communicate in a professional manner the analyses and results of the proposed homework.