Reactor Physics, Thermal Hydraulics and Neutron Transport

1
Reactor Physics, Thermal Hydraulics and Neutron
Transport

• Associate Professor Dr.Sunchai Nilsuwankosit
• Department of Nuclear Technology
• Faculty of Engineering, Chulalongkorn University

2
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
3
Reactor Physics

• Fast and Thermal Fluxes in Reactor

fast flux
fuel
fuel
fuel
moderator
moderator
moderator
moderator
thermal flux
4
Reactor Physics

• Fast and Thermal Fluxes in Reactor

fast flux
thermal flux
core
reflector
reflector
5
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
• where W is the size of the reactor core and T is
  the thickness of the reflector.

ltlt How to calculate for d? gtgt
6
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
• 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

ltlt How to calculate for importance function? gtgt
7
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

ltlt What is the feedback coefficient due to void
fraction? gtgt
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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

• Heat Transfer
• Conduction
• Convection
• Conservation of Energy

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Thermal Hydraulics

• Temperature Distribution in the Fuel

Fuel Gap
Tmax
Fuel Clad
T0
Fuel Meat
r1
r2
r3
ltlt How to calculate for T? gtgt
10
Thermal Hydraulics

• Temperature Distribution in Coolant along the
  Channel

Flow Scheme
Single Phase (vap.)
Droplet Flow
Heat flux across the interface
Two Phase
Transition Flow
Bubbly Flow
Single Phase (liq.)
x0
T0
Tb
Direction of Flow
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Thermal Hydraulics

• Safety Parameters
• CHF Critical Heat Flux
• DNB Departure of Nucleate Boiling
• Burnout Condition where the heating surface has
  no
• contact with the liquid coolant
• Hot Spot The condition defined for the thermal
  safety of a
• reactor.

• 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.

12
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
13
Neutron Transport

• Transport Equation

14
Neutron Transport

• Transport Equation

• From Transport Equation to Diffusion Equation

Ficks law
Diffusion Coefficient
ltlt How is D calculated? gtgt