Page 72 - Design and Operation of Heat Exchangers and their Networks

Basic thermal design theory for heat exchangers 59

1
τ o ¼ μ du ¼ f o ρu 2 (2.143)
dr 2 m
r¼r o
1
τ i r i + τ o r o 2
τ ¼ ¼ f ρu m (2.144)
r i + r o 2
Eq. (2.141) yields the following Fanning friction factors:
2
r 1 2
i
ð
16 1 r i Þ r
i
2lnr i
f i Re ¼ (2.145)
2
r 1
2 i
r i 1+ r
i
lnr i
2
r 1
2 i
ð
16 1 r i Þ r
o
2lnr i
f o Re ¼ (2.146)
2
r 1
2 i
r o 1+ r
i
lnr i
2
16 1 r i Þ
ð
f Re ¼ 2 (2.147)
r 1
2 i
1+ r
i
lnr i
where the Reynolds number is defined with the hydraulic diameter d h :
Re ¼ u m d h =μ ¼ u m d o d i Þ=μ (2.148)
ð
2.2.1.5 Frictional pressure drop in two-phase flow
The frictional pressure drop in two-phase flow is much more complicated
than that in single-phase flow. The two-phase pressure drop is linked to the
momentum exchange between the liquid phase and vapor (or gas) phase and
can be characterized by the two-phase flow pattern. For example, for flow
boiling in a horizontal tube, the flow pattern changes from single-phase liq-
uid flow to bubbly flow, stratified flow, wavy flow, slug flow, annular flow,
mist flow, and finally single-phase vapor flow. For upward flow boiling in a
vertical tube, the flow pattern can be bubbly flow, slug flow, churn flow,
wispy-annular flow, annular flow, and mist flow. More detailed descriptions
about the flow patterns and flow pattern maps can be found in the book of
Collier and Thome (1994).
We can use the method of Lockhart and Martinelli (1949) for approx-
imate prediction of the frictional pressure drop for fully developed, incom-
pressible horizontal gas/liquid flow. The two-phase frictional pressure drop
is evaluated by the single-phase frictional pressure drop multiplied with a
2
two-phase multiplier ϕ :