Page 344 - Fluid mechanics, heat transfer, and mass transfer

THERMAL DESIGN OF SHELL AND TUBE HEAT EXCHANGERS 325

& J l : Correction factor for baffle leakage effects includ- of tubes in the bundle. The effective tube pitch,

ing tube-to-baffle and shell-to-baffle leakage (A- and L tp, eff , which is equal to L tp for 30 and 90 tube

E-streams). layouts while for 45 staggered layouts,
➢ The pressure differences between neighboring
baffle compartments force a fraction of the flow L tp; eff ¼ 0:707L tp : ð10:71Þ
through the baffle-to-tube hole gaps in the baffle
➢ A typical value of J l is in the range of 0.7–0.9.
(A-stream) and through the annular space between
J l < 0.6 should be avoided. The maximum value of
the shell and the baffle edge (E-stream).
J l is 1.0.
➢ These streams reduce the part of the flow that
passes over the tube bundle as cross flow (B- ➢ For refrigeration chillers and water-cooled con-
stream), reducing both the heat transfer coefficient densers, a value of 0.85–0.9 is achievable because
and pressure drop. of their tighter constructional tolerances and smal-
ler clearances than TEMA standards.
➢ E-stream is very detrimental to thermal design as it
is not effective for heat transfer. & J b : Correction factor for bundle bypassing effects due
to the clearance between the tube and the inner wall
➢ If the baffles are put too close together, then the
of the shell (C-stream) and the bypass lane created by
fraction of the flow in the leakage streams
any pass partition lanes.
increases compared with the cross flow.
➢ (F-stream) in the flow direction. F-stream is not
- J l is a function of the ratio of total leakage area
always present and can be eliminated completely
per baffle to the cross-flow area between adja-
by placing dummy tubes in the pass partition lanes.
cent baffles, the ratio of the shell-to-baffle leak-
C-stream can be reduced by a tighter fit of the tube
age area to the tube-to-baffle leakage area, and is
bundle into the shell and also by placing sealing
estimated from
strips (in pairs) around the bundle perimeter, up to
J l ¼ 0:44ð1 r s Þþ½1 0:44ð1 r s ފexp½ 2:2 r lm Š: a maximum of one pair of strips for every two tube
rows passed by the flow between the baffle cuts.
ð10:64Þ
The sealing strips can increase the value of J b .
3=2
r s ¼ S sb =ðS sb þ S tb Þ: ð10:65Þ J b ¼ exp½ C bh F sbp f1 ð2r ss Þ gŠ: ð10:72Þ
C bh is an empirical factor with a value of 1.35 for
r lm ¼ðS sb þ S tb Þ=S m : ð10:66Þ
laminar flow (100 N Re ), 1.25 for transition and
turbulent flows (N Re > 100).
- The shell-to-baffle leakage area, S sb , the tube-to-
baffle hole leakage area, S tb , for N tt (1 F w ) tube F sbp ¼ S b =S m ; ð10:73Þ
holes, and the cross-flow area at the bundle
centerline S m are determined by the following where S m is as given earlier and
equations:
S b ¼ L bc ½D s D 0tl Šþ L pl Š: ð10:74Þ
S sb ¼ 0:00436D s L sb ð360 u ds Þ; ð10:67Þ

where L sb is the diametrical shell-to-baffle clear- L pl is the width of bypass lane between tubes, L pl is
ance and the baffle cut angle u ds in degrees is 0, for situations without a pass partition lane or
such a lane normal to the flow direction. L pl is 1/2
1
u ds ¼ 2 cos ½1 2ðB c =100ފ: ð10:68Þ the actual dimension of the lane, for a pass par-
tition lane parallel to the flow direction. It can be
assumed to be equal to D t , tube diameter.
2
2
S tb ¼½p=4fðD t þ L tb Þ D gN tt ð1 F w ފ:
t
r ss ¼ N ss =N tcc ; ð10:75Þ
ð10:69Þ
where r ss is the number of sealing strips and N ss is
the number of pairs, if any, passed by the flow to
S m ¼ L bc ½L bb þðD ctl =L tp; eff ÞðL tp D t ފ:
the number of tube rows crossed between baffle
ð10:70Þ tips in one baffle section N tcc .
L bc is the central baffle spacing, L bb is the bypass
N tcc ¼ðD s =L pp Þ½1 2ðB c =100ފ: ð10:76Þ
channel diametrical gap, N tt is the total number