Page 212 - Design and Operation of Heat Exchangers and their Networks

Optimal design of heat exchangers 201

where d h,s is the shell-side hydraulic diameter:
2 2
4 s πd o
Square pitch : d hs ¼ (5.36)
p
ffiffiffi πd o 2 2
4 3=4 s πd =2
o
Triangular pitch : d hs ¼ (5.37)
πd o =2
The shell-side Reynolds number Re s is defined as
_ md hs
Re s ¼ (5.38)
A sc μ

5.2.2.2 Bell-Delaware method
In the shell side, the segmental plate baffles make the flow pattern very com-
plex. The main flow stream in the shell side is the crossflow flowing succes-
sively over the tube bundle sections formed by two adjacent baffles (denoted
as stream B by Tinker (1951)). However, there are significant portions of
bypassing and leakage streams flowing through necessary constructional
clearances, such as tube-to-baffle hole leakage stream through the annular
clearance between the tubes and baffle holes of a baffle (stream A),
bundle-to-shell bypass stream through the annular spaces between the tube
bundle and shell (stream C), shell-to-baffle leakage stream through the clear-
ance between the edge of a baffle and the shell (stream E), and tube-pass par-
tition bypass stream through open passages formed by tube layout partitions
(stream F).
In the Bell-Delaware method, the shell-side heat transfer coefficient α s is
based on the heat transfer coefficient for ideal crossflow, α id , modified with a
set of correction factors (see Shah and Sekulic, 2003, Eq. (9.50)):

α s ¼ α id J c J l J b J s J r (5.39)
The heat transfer coefficient for ideal crossflow can be calculated with the
correlation of Martin (2002). For the inline tube bundles,
0:1
α id d o 1=3 Re tb +1
½
Nu id ¼ ¼ 0:404 1:18HgPr 4s t =π d o Þ=s l Š
ð
λ Re tb + 1000
(5.40)
For the staggered tube bundles with s l d o ,
1=3
Nu id ¼ 0:404 0:92HgPr 4s t =π d o Þ=s d Š (5.41)
½
ð