Page 74 - Design and Operation of Heat Exchangers and their Networks

Basic thermal design theory for heat exchangers 61

with

64=Re, Re < Re cr
f D,s ¼ 0:25 (2.155)
0:3164=Re ,Re > Re cr

0:45
Re cr ¼ 2300 1 + 8:6 r=r c Þ (2.156)
ð
For two-phase frictional pressure drop, Colombo et al. (2015) proposed a
correlation,inwhichcorrectiveparametersareincludedintothetwo-phasemul-
tiplierofLockhartandMartinellitoaccountfortheeffectofthecentrifugalforce:
2
2
ϕ ¼ 0:13ϕ De 0:15 ð ρ =ρ Þ 0:37 (2.157)
l l,s l m l
where
h i 1
ρ ¼ _x=ρ +1 _xÞ=ρ (2.158)
ð
m g l
2
ϕ l,s is the two-phase multiplier for straight tube, calculated from
Eq. (2.151) with C¼20 for turbulent flow of both liquid and vapor phases
and the Lockhart-Martinelli parameter X as
! 0:1
ρ
0:9
0:5
1 _x g μ l
X ¼ (2.159)
_ x ρ μ
l g
2.2.2 Static pressure drop
The static pressure drop (hydrostatic pressure) is the difference in pressure at
two points within a fluid column, due to the weight of the fluid:

Δp g ¼ ρ gΔH (2.160)
m
in which g is acceleration due to gravity, H the elevation, and ρ m the mean
density of the fluid column.
In a pipe flow, the static pressure drop can be expressed as.

dp g ¼ ρ gsinθdz (2.161)
where θ denotes the angle of inclination of the tube. For upward flow, θ>0;
therefore, the static pressure drop is positive. For downward flow, the static
pressure drop is negative. ρ is the local fluid density.
The total static pressure drop can be calculated by integration of the local
pressure drop gradient over the whole pipe length:
Z
L
Δp g ¼ g ρsinθdz (2.162)
0