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Reactor Physics, Thermal Hydraulics and Neutron Transport Associate Professor Dr.Sunchai Nilsuwankosit Department of Nuclear Technology Faculty of Engineering, Chulalongkorn University Reactor Physics Neutron Fluxes in Reactor le1 extended length predicted by transport theory = 0.71 ltr le2 extended length predicted by diffusion theory = (2/3) ltr Neutron Flux by diffusion theory Neutron Flux by transport theory le1 le2 Reactor Physics Fast and Thermal Fluxes in Reactor fast flux moderator moderator fuel fuel moderator fuel moderator thermal flux Reactor Physics Fast and Thermal Fluxes in Reactor fast flux thermal flux reflector core reflector Reactor Physics Reflector Saving The size of a reactor with the reflector installed can be much smaller than that of a reactor with the same material but without the reflector. The reduction in size is called the reflector saving. For the reflector that is of the same material as the moderator, the reflector saving d of a 1-D reactor can be expressed as d W tanh T . W where W is the size of the reactor core and T is the thickness of the reflector. << How to calculate for d? >> Reactor Physics Importance As the neutron fluxes at various locations affect the criticality of the reactor and its power producing capability differently, a parameter to identify the level of effect for the neutron flux at a specific location is defined. Such parameter is called “importance function” or “adjoint flux” and is denoted as f where k f* s , 1 ks Ks is the multiplication factor for an isentropic neutron source at the given location. In general, the reactivity change at one location can be estimated with the importance as k sample * k k faf dV reactor faf * dV sample faf * dV f f f dV * reactor . << How to calculate for importance function? >> Reactor Physics Feedback Coefficient It is often found that a change in the configuration or the condition of the reactor can largely affect the criticality of the reactor. In such case, if t is the parameter presenting the configuration or the condition that is changed, the feedback coefficient can be described as f t k . t << What is the feedback coefficient due to void fraction? >> Thermal Hydraulics Power Density The amount of energy generated per unit volume per unit time due to the fission in the reactor is called “power density” and is described as p f f . Heat Transfer Conduction Convection qk kT qc vC T Conservation of Energy T C qk qc p q t Thermal Hydraulics Temperature Distribution in the Fuel Tmax Fuel Gap Fuel Clad Fuel Meat T0 r1 r2 r3 << How to calculate for T? >> Thermal Hydraulics Temperature Distribution in Coolant along the Channel Flow Scheme Single Phase (vap.) Droplet Flow Heat flux across the interface qh h T Ts Transition Flow Two Phase Bubbly Flow Single Phase (liq.) x0 T0 Tb Direction of Flow Thermal Hydraulics Safety Parameters Critical Heat Flux Departure of Nucleate Boiling Condition where the heating surface has no contact with the liquid coolant The condition defined for the thermal safety of a reactor. CHF DNB Burnout Hot Spot • Nuclear Hot Spot Safety condition due to the variation in neutron fluxes. • Engineering Hot Spot Safety condition due to the mechanics and the flow distributions. Thermal Hydraulics Hot Spot Factors Fc factor to be considered for coolant temperature rising Ff factor to be considered for temperature rising across the interface Fe factor to be considered for temperature rising over fuel element Nuclear Hot Spots Neutron Disribution Fuel Concentration Engineering Hot Spots Fuel Element Warpage Fuel Element thermal Conductivity Fuel Element Dimensions Flow Distribution Heat Transfer Coefficient Neutron Transport Transport Equation n J S L t S s f f L t J n n d J vn ˆ J vn ˆ J v n d J d f v n d ˆ J d n t J s f f t J d Neutron Transport Transport Equation n t J s f f t J d J s f f t vn d J sf f f s a f J f f af From Transport Equation to Diffusion Equation 1 f Fick’s law D 2f f f af J Df v t Diffusion Coefficient D 1 ltr , ltr 1 tr 3 tr t s , 32A << How is D calculated? >>
