1. TRANSIENT EVALUATION OF A GEN-IV LFR DEMONSTRATION PLANT THROUGH A LUMPED-PARAMETER ANALYSIS OF COUPLED KINETICS AND THERMALHYDRAULICS ANALYSIS OF COUPLED KINETICS AND THERMALHYDRAULICS Sara Bortot, Antonio Cammi LEADER PROGRESS MEETING, W.P. 4 TASK 4.4 Preliminary definition of the Control Architecture CIRTEN - POLITECNICO DI MILANO November 18 th, 2010, Bologna

2. OUTLINE  Context and goals  Reactor configuration  Analysis approach  Mathematical model  Simulation results  Conclusions  WORK PROPOSAL – TASK 4.4

3. CONTEXT and GOALS ►Lead-cooled Fast Reactor (LFR) selected by the Generation IV international Forum (GIF) as one of the candidates for the next generation of nuclear power plants ►significant technological innovations need of a demonstrator reactor (DEMO)  study of plant global performances  refining/finalizing the system configuration REACTOR DYNAMICS  design of an appropriate control system

4. REACTOR CONFIGURATION ParameterValueUnit Thermal Power300MWth Average Coolant Outlet T480°C Coolant Inlet T400°C Average Coolant Velocity3.0m s -1 Clad Max T600°C Clad Out Diameter6.00mm Clad Thickness0.34mm Pellet Outer Diameter5.14mm ParameterValueUnit Pellet Hole Diameter1.71mm Fuel Column Height650mm Fuel Rod Pitch8.53mm Number of Pins/FA744- SS box beam inner width45.65mm SS box beam outer width48.65mm Number of Inner/Outer FAs10/14- Pu Enrichment Inner/ Outer29.3/32.2vol.% CORE LAYOUT

5. ANALYSIS APPROACH (1) H Ψ C i CORE T f T c T l T in δρ(t) δψ(t) δT in (t) δT f (t) δT c (t) δT l (t) δq(t) δT out (t) δT in (t) δH(t) δT f (t) δT c (t) δT l (t) δρ(t) δH(t) Kinetics Thermal-hydraulics Reactivity Input T out

6. ANALYSIS APPROACH (2) MAIN ASSUMPTIONS - NEUTRONICS -neutron time fluctuations independent of spatial variations -spectrum independent of neutron level -core lumped source of neutrons with prompt heat power -neutron population and neutron flux related by constants of proportionality POINT-KINETICS APPROXIMATION

7. ANALYSIS APPROACH (3) MAIN ASSUMPTIONS – THERMAL-HYDRAULICS -average channel representation -single-node heat-exchange model -3 distinct temperature regionsfuel cladding coolant -energy balance over the fuel pin surrounded by coolant -reactor powerinput retrieved from reactor kinetics LUMPED-PARAMETER APPROACH

8. MATHEMATICAL MODEL (1) NEUTRON KINETICS EQUATIONS - - ASSUMPTION t ≤ 0 steady state - - perturbation around steady state solution - - linearization SMALL-PERTURBATION APPROACH with: - - ψ = n(t)/n 0 = q(t)/q 0 - - η i = C i (t)/C i0

9. MATHEMATICAL MODEL (2) THERMAL-HYDRAULICS EQUATIONS ASSUMPTIONS: - - constant properties - - axial conduction neglected - - T l = (T in + T out )/2 SMALL-PERTURBATION APPROACH Time constants: -  -  f = M f C f /k fc -  -  c1 = M c C c /k fc -  -  c2 = M c C c /h cl -  -  l = M l /Γ

10. MATHEMATICAL MODEL (3) REACTIVITY EQUATIONS - - α D = Doppler coefficient - - α L = coolant density coefficient - - α Z = axial expansion coefficient - - α R = radial expansion coefficient - (Linked option) - α H = CR-related coefficient - - Function of fuel average temperature cladding average temperature coolant average temperature coolant inlet temperature externally introduced reactivity (ideal control rod)

11. REACTIVITY COEFFICIENTS CALCULATION DOPPLER LEAD DENSITY RADIAL EXPANSION AXIAL EXPANSION MATHEMATICAL MODEL (4)

12. SIMULATIONS (1) SOLUTION TECHNIQUE – MIMO (Multiple Input Multiple Output) SYSTEM modelling equations state-space representation: state vector: output vector: input vector:

13. SIMULATIONS (2) ERANOS-2.1, JEFF-3.1 data library calculations

14. RESULTS (1) LEAD INLET TEMPERATURE PERTURBATION (+10 K) Reactivity Lead average temperature Power Fuel average temperature Clad average temperature Core outlet temperature

15. RESULTS (2) CONTROL ROD EXTRACTION (+50 pcm) Reactivity Power Fuel average temperature Lead average temperature Clad average temperature Core outlet temperature

16. RESULTS (3) REACTOR CORE OPEN-LOOP STABILITY Study of the system representative TRANSFER FUNCTION qualitative insights into the response characteristics of the system STABILITY all the system poles with negative real parts

17. CONCLUSIONS ►preliminary evaluation of DEMO core dynamics ►coupling of NEUTRONICS and THERMAL-HYDRAULICS ►prediction of DEMO reactions to 10°C increase of lead inlet T 50 pcm insertion by ideal CR ►stable system ►significant impact of reactivity insertion on reactor power (steady state: + 32/25 % nominal value at BoC/EoC) and fuel temperature (+ 276/220 K at BoC/EoC) ►model with satisfactory capability of predicting the system response to both perturbations (small errors figured) ►generally slight impact of assuming the fuel linked to the cladding or the radial expansion driven by the coolant average temperature ►useful tool allowing a relatively quick, qualitative analysis of fundamental dynamics and stability aspects

18. WORK PROPOSAL ►Primary loop modeling ►Secondary loop modeling ►Coupling between primary and secondary loops ►Sensitivity analysis ►Control and measured variables definition ►Control strategy assessment (SISO loops and Multi-variable control, e.g. MPC) TASK 4.4 Preliminary definition of the Control Architecture