Page 75 - Design and Operation of Heat Exchangers and their Networks

62 Design and operation of heat exchangers and their networks

For two-phase flow, the local fluid density can be expressed as

ρ ¼ aρ +1 að Þ ρ (2.163)
g l
in which a is the void fraction defined as the space- and time-averaged frac-
tion of the channel volume (or channel cross-sectional area) that is occupied
by the gas.
Unlike the vapor mass fraction, the void fraction cannot be evaluated by
the mass balance or energy balance. The relationship between the void frac-
tion and vapor mass fraction depends on the ratio of the gas phase velocity to
the liquid phase velocity (known as the slip ratio s):

_ x 1 aÞρ
u g ð l
s ¼ ¼ (2.164)
u l ð 1 _xÞaρ g
If the two phases are well mixed or the property differences between the
two phases are small, then we can use the homogeneous model with s¼1. It
yields
_ x=ρ g
a ¼ (2.165)
_ x=ρ +1 _xÞ=ρ l
ð
g
For annular flow, it can be evaluated by a simple relationship with the
2
two-phase multiplier ϕ l calculated from Eq. (2.151) (Hewitt and Hall-
Taylor, 1970, Eq. (5.10)):

a ¼ 1 ϕ 2 1=2 (2.166)
l
2.2.3 Acceleration pressure drop
The acceleration pressure drop arises from the momentum change of fluid
flowing from one cross section to another. For single-phase flow,

dp a ¼ Gdu ¼ Gd G=ρð Þ (2.167)
If the density ρ is constant, after integration from section 1 to section 2,
Eq. (2.167) becomes
1 2 2 ρ 2 2
Δp a,1 2 ¼ G G ¼ u u (2.168)
2ρ 2 1 2 2 1
In a straight channel, the cross-sectional area is constant; therefore, G also
keeps constant. Eq. (2.167) can be easily integrated, which yields
2
Δp a,1 2 ¼ Gu 2 u 1 Þ ¼ G 1=ρ 1=ρð 2 1 Þ (2.169)
ð