Page 178 - Design and Operation of Heat Exchangers and their Networks

166 Design and operation of heat exchangers and their networks

4.1.2.11 Critical heat flux
The critical heat flux for upward flow through vertical tubes can be evalu-
ated by (Drescher and K€ohler, 1981; Herbst, 2013)

3
F
q cr ¼ 10 F p r d F L F G (4.90)
where
¼ 10:3 17:5p r +8p 2 (4.91)
F p r r

p ffiffiffiffiffiffiffiffiffi
F d ¼ max d 0 =d,0:6 (4.92)
F G ¼ e 1:5_x ð G=G 0 Þ 0:68p r 1:2_x 0:3 (4.93)
2
with d 0 ¼0.008m and G 0 ¼1000kg/m s

1, L=d 80
F L ¼ 2a hom d=L (4.94)
e , L=d < 80
The homogenous void fraction is expressed as
ρ _x
l
a hom ¼ (4.95)
ρ _x + ρ 1 _xð Þ
l g
The validity range of Eq. (4.90) is 4mm d 40mm,
2 2
29bar p 200bar, and 500kg/m s G 5000kg/m s and the subcooling
at inlet Δt sub 75K.
ð
ð 0:68p r 0:3Þ ln G=G 0 Þ lnF G
Since F G can be rewritten as _x ¼ , the critical void
ð
1:5+ 1:2ln G=G 0 Þ
fraction can be obtained from Eq. (4.90) as

3
F
ð
ð 0:68p r 0:3Þ ln G=G 0 Þ lnq cr +ln 10 F p r d F L
_ x ¼ (4.96)
ð
1:5+1:2ln G=G 0 Þ
For horizontal tubes, dry out at the top and bottom of the tube inside
happens at different void fraction. The difference can be obtained from
16
Δ_x cr ¼ _x cr,low _x cr,up ¼ (4.97)
2
ð 2+ FrÞ
where the modified Froude number is defined by
p
_ x cr G= ρ g
ffiffiffiffiffi
Fr ¼ r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (4.98)

gd ρ ρ cosθ
l g
The critical void fractions can be written as
_ x cr,up ¼ _x cr Δ_x cr =2 (4.99)