Single Phase 22
1
A PWR has dimensions and operating conditions given below.
Core Height
144 inches
Core Mass Flux
2.62 x 10
6
lbm/hr-ft
2
Number of Fuel Rods
56,876
Rod Diameter
0.374 inches
Rod Pitch
0.496 inches
Core Inlet Loss Coefficient
1.5
Core Exit Loss Coefficient
1.5
Grid Loss Coefficient
0.5
Number of Grids
8
Pressure
2250 psia
Core Inlet Temperature
560 F
Maximum Channel Heat Flux
265,700 Btu/hr-ft
2
Extrapolation Distance
0.866 ft
You may assume an axial heat flux profile of the form
′′
=
′′
+
⎛
⎝
⎜
⎞
⎠
⎟
q
z
q
z
H
e
( )
sin
(
)
0
π
λ
Determine the acceleration, friction, forms, elevation and total pressure loss.
Compare to that which would be
obtained from a simple Bernoulli’s Equation approach where the density is approximated by the average channel
density
2
/
)
(
inlet
exit
ρ
ρ
+
and the density is evaluated at the average coolant temperature.
Assume the same
treatment holds for viscosity also.
Solution
Integrate the conservative form of the steady-state Momentum Equation over the channel length
(
)
1
1
g
A
z
vvA
P
z
P
A
g
g
c
x
x
w
w
x
c
∂
∂
ρ
∂
∂
τ
ρ
θ
= −
−
−
sin
(1)
or
1
2
2
2
2
2
g
z
G
P
z
f
D
G
g
K
z
z
G
g
g
g
c
e
c
j
j
c
j
c
∂
∂
ρ
∂
∂
ρ
δ
ρ
ρ
θ
⎛
⎝
⎜
⎞
⎠
⎟ = −
−
+
−
⎧
⎨
⎪
⎩
⎪
⎫
⎬
⎪
⎭
⎪
−
∑
(
)
sin
(2)
where we have assumed a uniform flow area and a vertical flow channel.
For convenience the momentum equation
has been written in terms of the mass flux.
1
2
2
2
1
2
1
2
2
1
2
2
1
2
1
2
g
z
G
dz
P
z
dz
f
D
G
g
dz
K
z
z
G
g
dz
g
g
dz
c
e
c
j
j
c
j
c
∂
∂
ρ
∂
∂
ρ
δ
ρ
ρ
⎛
⎝
⎜
⎞
⎠
⎟
= −
−
+
−
⎧
⎨
⎪
⎩
⎪
⎫
⎬
⎪
⎭
⎪
−
∫
∫
∫
∑
∫
∫
(
)
(3)
(
)
(
)
1
2
2
2
1
2
1
2
2
2
2
1
1
H
H
g
g
g
G
K
g
G
D
L
f
P
P
g
G
c
c
j
j
j
j
i
c
i
i
e
i
i
c
i
−
−
−
−
−
−
=
⎭
⎬
⎫
⎩
⎨
⎧
−
∑
∑
ρ
ρ
ρ
ρ
ρ
(4)
Rearranging gives for the core pressure drop

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