Page 73 - Design and Operation of Heat Exchangers and their Networks

60 Design and operation of heat exchangers and their networks

dp f 2 dp f 2 dp f
¼ ϕ ¼ ϕ (2.149)
dz l dz g dz
tp l g
where the two frictional pressure drops are calculated for each of the two
phases as if it flows alone in single-phase flow. By defining the Lockhart-
Martinelli parameter X as the ratio of these pressure drops,
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

dp f dp f
X ¼ = (2.150)
dz dz
l g
the two-phase multiplier can be correlated as (Collier and Thome, 1994)
2
ϕ ¼ 1+ C=X +1=X 2 (2.151)
l
2
ϕ ¼ 1+ CX + X 2 (2.152)
g
where C has the following values:
Liquid Gas C
tt
turbulent turbulent ðÞ 20
vt
viscous turbulent ðÞ 12
tv
turbulent viscous ðÞ 19
viscous viscous ðÞ 5
vv
Whether the liquid pressure drop or gas pressure drop is used in
Eq. (2.149) depends on the values of corresponding two-phase multiplier:
8
2
> ϕ 2 dp f , ϕ ϕ 2
> l l g
<
dp f dz
¼ l (2.153)
dz > 2 dp f 2 2
tp > ϕ , ϕ > ϕ
: g l g
dz
g
2.2.1.6 Frictional pressure drop in curved tubes
A correlation for frictional pressure drop in curved tubes was proposed by
Schmidt (1967) as
8
0:97 0:312
ð
ð
1+0:14 r=r c Þ Re 1 0:644 r=r c Þ , ð 100 < Re < Re cr Þ
<
4
4
f D,c =f D,s ¼ 1+2:88 10 r=r c Þ 0:62 =Re, ð Re cr < Re < 2:2 10 Þ
ð
: 0:53 0:25 4 5
1+0:0823 1 + r=r c Þ r=r c Þ Re ,2 10 < Re < 1:5 10
ð
ð
(2.154)