Page 227 - Design and Operation of Heat Exchangers and their Networks

216 Design and operation of heat exchangers and their networks

0
With n ¼0.2 for Re sd >100, we also have
2 n 0 2 n 0
ð
ζ ¼ l bc =l bo Þ + l bc =l bi Þ
ð
s
2 0:2 2 0:2
ð
ð
¼ 0:279=0:3365Þ +0:279=0:3365Þ ¼ 1:427
The pressure drops in the crossflow section, in the window area and in
the shell-side inlet and outlet sections can then be determined with
Eq. (5.72), respectively, as follows:
ð
Δp c ¼ N b 1ð ÞΔp b,id ζ ζ ¼ 14 1Þ 1092 0:6814 0:589 ¼ 5700 Pa
b l
Δp w ¼ N b Δp w,id ζ ¼ 14 6990 0:589 ¼ 57,641 Pa
l
Δp io ¼ 2Δp b,id 1+ N rw =N rc Þζ ζ
ð
b s
¼ 2 1092 1+ 3=9Þ 0:6814 1:427 ¼ 2833 Pa
ð
The total shell-side pressure drop reads
Δp s ¼ Δp c + Δp w + Δp io ¼ 5700 + 57,641 + 2833 ¼ 66,173 Pa
(8) Optimization of the design
We can carry out the following optimization calculation
min f xðÞ ¼ N t L
x2 L, d s, l c, l bc Þ
ð
s:t:
Δp s L, d s , l c , l bc Þ Δp s,max 0
ð
Δp t L, d s , l c , l bc Þ Δp t,max 0
ð
t s,out L, d s , l c , l bc Þ t s,out,max 0
ð
Δp s C RF L, d s , l c , C RF l bc Þ Δp s,max 0
ð
Δp t C RF L, d s , l c , C RF l bc Þ Δp t,max 0
ð
t s,out C RF L, d s , l c , C RF l bc Þ t s,out,max 0
ð
to optimize the tube length L, shell inside diameter d s , baffle cut l c ,and
central baffle spacing l bc . The detailed calculation procedure using
nonlinear programming solver, genetic algorithm solver, and particle
swarm optimization can be found in the MatLab code for Example 5.1
in the appendix. For a conservative design, we take the area reserve
factor of 20% (C RF ¼1.20). The best results were obtained by the use
of the genetic algorithm solver with integer variables in millimeter as
follows: