CONSERVATION EQ UATIONS

Lumped-paramete r form ulation

 M cv  m ˙

 t i

(m ass)

→ i

 ( M V ) cv   ˙ →  →

( m V ) i 

i j

 E  

F j (m om entum)

V 2  

c v  Q ˙  W ˙    m ˙  h   gz   (energy )

 t i   2   i

 S cv  Q ˙  ˙

 t    T 

  ( m ˙ s ) i  S gen (entropy)

j   j i

1 D formulation

     G

(m ass)

 t  z

 G 

 G 2 

 P  p

 t  

 z  

   z

 w w   g cos  (m om entum)

A

  h   G  h  q " p h    P  G (  P   w p w )  (energy )

 t  z A   t   z A 

D iffer e ntia l ( 3 D ) form ulation

     (  →  0 ( m a s s )

V )

 t →

 → → → →

 [ V  V   V ]   P    2 V   g

 t

(m om entum, for incom p ressib l e fluid)

 c [  T  →   T ]    →  q     T DP   (energy )

p  t V q " Dt

Sy m bols:		Subscripts:
A	Flow Area	cv	Control Volume
c	Specific He at	gen	Generation
E	Internal Energy	h	heated
F	Force	P	Pressure
g	Gravitational Accel eration	r	Radial
G	Mass Flux	w	Wall or Wetted
h	Enthalpy
m ˙	Mass Flow R a te	Greek Sy m bols
M	Mass		Therm . Expansion Coeff.
p	Peri m e t e r		Dissipation function
P Q ˙	Pressure Rate of Heat Transfer	 	Viscosity Density
S, s	Entropy		Shear Stress
t	Ti m e
T	Te m p erature
V	Velocity

W ˙ Rate of Energy Transfer as Work

z Elevation

REACTOR THERMAL PERFORMANCE P ARAME T E R S

Paramete r	Name	Typical values PWR BWR		Units
q ˙ q ′ q  q ′″ Q ˙	Power of fuel rod Linear heat generation rate (or linea r po w e r) Heat flux Volum e tric heat generation rate Core power	67 18 600 350 *	77 20 530 240 *	kW (BTU/hr) kW / m (BTU/hr-ft) kW / m 2 (B TU /hr-ft 2 ) MW /m 3 (B TU /hr-ft 3 ) MW

* It varies m u ch from plant to plant

For a fuel rod operating at st eady-state conditions, the parame ters are related as follows:

q ˙  q  L  q  2  R co

L  q    R 2 L  Q ˙ / N

W h ere R f is the f u el pellet rad i us, R co is the fuel rod outer radius, L is the f u el rod a c tiv e (hea ted) length and N is the total num ber of fuel rods in the core.

M IT OpenCourseWare http://ocw.mit.edu

22.06 Engineering of Nuclear Systems

Fall 20 10

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