EVOL Winter school November 2013EVOL Winter School First day: Reactor physics, neutronics and thermal-hydraulics of Molten Salt Reactor Organizer: Sandra Dulla Politecnico di Torino (POLITO) Dipartimento Energia Torino, Italy

November 2013 EVOL Winter School 2 Structure of the first day The objective of this first day is to convey a “complete” set of information concerning the neutronics/thermal-hydraulic behavior of a molten salt reactor Specific focus is on the TMSR, based on a Thorium fuel cycle, accordingly to the objectives of the EVOL project The audience is supposedly coming from very different backgrounds…

November 2013 EVOL Winter School 3 Lectures and lecturers

November 2013 EVOL Winter School 4 Neutronics of MSR - basics This first lecture should serve as an introduction to the peculiarities of MSR for what concerns neutronics/thermalhydraulics Various aspects will be introduced, that will be treated in more detail in the following lectures This is supposed to be the easy part of the day

November 2013 EVOL Winter School 5 Basic concepts for Gen-IV systems 6 reactor concepts have been chosen in the perspective of offering significant advances in: –Sustainability  minimal generation of nuclear waste –Safety and reliability  enhanced nuclear safety –Economics  reduced capital cost –Proliferation resistance  further reduction of the risk of weapons materials proliferation –Physical protection

November 2013 EVOL Winter School 6 Gen-IV reactors The Molten Salt Reactor (MSR) –fission power from a molten salt fuel –fast or epithermal-spectrum –integrated fuel cycle

November 2013 EVOL Winter School 7 MSR in a nutshell The multiplying medium is in a fluid phase, flowing through the reactor core the fissile salt acts both as nuclear fuel and system coolant The presence of a velocity field in the multiplying medium affects its neutronic behavior  can be considered as a “stronger” neutronic / thermalhydraulic coupling with respect to other reactor concepts

November 2013 EVOL Winter School 8 MSR in a nutshell

November 2013 EVOL Winter School 9 MSR in a nutshell Neutronics / thermalhydraulics Fuel cycle

Multiphysics of MSR Neutronic behavior is affected by the thermalhydraulics of the molten salt –«Standard» feedback phenomena as in any reactor concept (Doppler, thermal expansion, …) Effects associated to the motion of the fluid –Dragging of the delayed neutron precursors –Consequences on the steady-state and transient behavior November 2013 EVOL Winter School 10 I will discuss these effects, to introduce the relevance of the studies that will be described in the following lectures …

Neutronics in MSR What happens when neutrons are propagating in a medium in motion ? –Collisions (localized phenomena) with the atoms of the medium –Free flights between collisions –Neutrons are not «affected» by the fact that the medium is moving (are not dragged in any way) –We may take into account the motion through the cross sections Σ(x)  Σ(x 0 -ut) … not really the case … November 2013 EVOL Winter School 11

Neutronics of MSR Consequence ? The neutron balance equation is unchanged w.r.t. standard reactor concepts Instead, the fission products that are precursors of delayed neutrons are dragged by the fluid medium, so the balance equation for them needs to be modified November 2013 EVOL Winter School 12

Neutronics of MSR Continuity equations for precursors with a velocity field The velocity u represents the macroscopic velocity field in the medium The mathematical nature of the problem is changed (boundary conditions required) November 2013 EVOL Winter School 13

Neutronics of MSR Full model Additional coupling to the TH model –Temperature-dependence of cross sections (as usual) –Explicit presence of velocity field u in the neutronic model (also in zero-power mode !! See the MSRE benchmark) November 2013 EVOL Winter School 14

Possible reactor configurations November 2013 EVOL Winter School 15 MSRE-like reactor Presence of a bank of pipes (with potential moderator in- between pipes  thermal neutron spectrum) TMSR reactor Homogeneous configuration of the core (no moderation, fast spectrum, better for transmutation) How different is the fuel flow in these two configurations ? A lot …

The effects of fuel motion in sinthesis November 2013 EVOL Winter School 16 The precursors are dragged within the reactor core  delayed emissions happen in different positions with respect to prompt fissions Part of the precursors exit from the core and decay in the primary circuit  loss of delayed neutrons The undecayed fraction of precursors re-enter the core and may produce their delayed neutrons within the active region

The effects of fuel motion The consequence on the neutronics associated to the fuel motion will be described for complicate reactor design in the following lectures I would rather propose some simple approaches to the problem, to give you the flavour of the effects that you will be seeing in real-life applications November 2013 EVOL Winter School 17

Effects of fuel motion – steady state Dependence of the multiplication eigenvalue k on the velocity field and delayed neutron characteristics Spatial redistribution of the delayed neutron precursors density and reduction of their importance November 2013 EVOL Winter School 18

November 2013 EVOL Winter School 19 Effects of fuel motion Solution to the simplest problem ever (1D diffusion, slab geometry, analytical approach) to see how the physics works Recirculation time in the external circuit

November 2013 EVOL Winter School 20 Results (1) u=0 mfp/s τ c  ∞ τ ℓ  ∞ k eff = ∆ρ=0 β eff =650 pcm

November 2013 EVOL Winter School 21 Results (2) u=0.1 mfp/s τ c =500s τ ℓ =1000s k eff = ∆ρ=-2pcm β eff =647 pcm u new definition … i will say a few words in a moment

November 2013 EVOL Winter School 22 Results (3) u=1 mfp/s τ c =50s τ ℓ =100s k eff = ∆ρ=-132pcm β eff =518 pcm u

November 2013 EVOL Winter School 23 Results (4) u=2 mfp/s τ c =25s τ ℓ =50s k eff = ∆ρ=-265pcm β eff =386 pcm u

November 2013 EVOL Winter School 24 Results (5) u=5 mfp/s τ c =10s τ ℓ =20s k eff = ∆ρ=-415pcm β eff =236 pcm u

November 2013 EVOL Winter School 25 Results (6) u=10 mfp/s τ c =5s τ ℓ =10s k eff = ∆ρ=-459pcm β eff =194 pcm u

Effect of fuel motion – steady state Summary –Fluid-dynamics affects the criticality state of the reactor –The distribution of precursors is distorted (depending on decay constants) –The flux is usually almost unperturbed (due to small value of the delayed neutron fraction β) –The presence of recirculation spots is to be avoided with even more attention … this aspect is to be addressed in CFD calculations November 2013 EVOL Winter School 26

Effect of fuel motion - dynamics The analysis of the transient behavior of MSR is –Important to identify the peculiarities of the physics of MSR w.r.t. solid fuel systems –Important to assess the role of coupled neutronics /thermalhydraulics –Fundamental to prove the stability and safety of the concept –Just one example on how the physics if MSR affects the time-dependent behavior … November 2013 EVOL Winter School 27

The role of delayed neutrons Neutron kinetics can be characterized by the value of the delayed neutron fraction β –Dependent on the fuel adopted –In the range 300 – 700 pcm –A larger value of β implies a less prompt response  safer and easier control November 2013 EVOL Winter School 28

The role of delayed neutrons The dynamic role of the delayed neutrons depends also on the energy spectrum of the system –Delayed neutrons have a softer spectrum –In a thermal system this implies a larger role in fission production –The opposite may occur when dealing with a fast system –To evaluate this role  beta effective November 2013 EVOL Winter School 29

Beta effective The quantity beta effetive allows to quantify the effective role of delayed neutrons in dynamics Evaluated as integral of the delayed production weighted on the neutron importance (deterministic approach) Evaluated as difference in multiplication constant when delayed fissions are neglected (Monte Carlo approach) November 2013 EVOL Winter School 30

Beta effective Both definitions (equivalent at the first order) evaluate the different role of delayed neutrons in kinetics, associated to their softer spectrum –β eff > β phys for thermal systems –β eff < β phys for fast systems These are the kind of results you may get when running ERANOS, MCNP, SERPENT … November 2013 EVOL Winter School 31

Beta effective in MSR In MSR, the role of the delayed neutrons is affected also by the fuel motion –In principle, the role will be reduced (due to production in the primary circuit and displacement in the reactor core) –To evaluate the amount of this reduction, a different calculation approach need to be adopted November 2013 EVOL Winter School 32

Beta effective in MSR How to evaluate the β eff in MSR, some examples of approaches adopted –Reduce it by a fraction equal to the fraction of precursors still decaying in the core (both in deterministic and stochastic approaches) –Use a different definition of the weighted integral (using the precursor importance instead of the flux) –All of these definitions produce a smaller value of β eff November 2013 EVOL Winter School 33

Example of results (from EVOL WP2) November 2013 EVOL Winter School 34

Why interested in β eff ? All the integral parameters (effective delayed neutron fractions, effective lifetime, …) have a role in the dynamic simulation of the system in point-like models The analysis of these parameters can allow to identify some potential issues in the dynamic behavior November 2013 EVOL Winter School 35

Relevance to MSR β eff characterize the dynamic behavior It would be advisable to have a «large» β eff MSR are interesting in the perspective of transmutation and breeding  use of nuclear fuels with lower β phys values November 2013 EVOL Winter School 36 Importance of safety studies involving transient scenarios

Summary On the basis of the discussion we just had we can say that –MSR require accurate coupled NE/TH anaysis to understand their peculiar behavior LECTURES IN THE MORNING AND BEGINNING OF AFTERNOON –The definition of the composition of the fuel and its evolution play a significant role in this perspective LECTURE IN THE AFTERNOON November 2013 EVOL Winter School 37

November 2013 EVOL Winter School 38