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# Reactor Physics_ Thermal Hydraulics and Neutron Transport

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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  faf dV
reactor



faf * dV

sample



faf * 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  kT  qc   vC T

Conservation of Energy

T   C     qk  qc   p  q t

Thermal Hydraulics


Temperature Distribution in the Fuel
Tmax

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   Df v t
Diffusion Coefficient

D  1 ltr , ltr  1 tr 3 tr  t   s ,   32A
<< How is D calculated? >>

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