Exchanger Sizing Notes

1. Kern’s Description of Shell Side Flow in
SHELL-AND-TUBE HEAT EXCHANGER
P M V Subbarao
Professor
Mechanical Engineering Department
I I T Delhi
Another Peculiar Averaging
Method.….

2. Shell-Side Reynolds Number
Reynolds number for the shell-side is based on the
equivalent diameter and the velocity based on a
reference flow:
s
e
s
s
s
D
A
m




Re
s
e
s
s
e
s
s
s
D
G
D
U





Re

3. Shell Side Fluid Flow

4. Classification of Shell Side Flow

5. Thermodynamic Similarity of Counter & Cross Flow
Heat Transfer

6. Fluid dynamic Similarity of Counter & Cross Flow
Heat Transfer ?!?!?!

7. Tube Layout & Flow Structure
A Real Use of Wetted Perimeter !

8. Tube Layout
• Tube layout is characterized by the included angle between
tubes.
• Two standard types of tube layouts are the square and the
equilateral triangle.
• Triangular pitch (30o layout) is better for heat transfer and
surface area per unit length (greatest tube density.)
• Square pitch (45 & 90 layouts) is needed for mechanical
cleaning.
• Note that the 30°,45° and 60° are staggered, and 90° is in
line.
• For the identical tube pitch and flow rates, the tube layouts
in decreasing order of shell-side heat transfer coefficient
and pressure drop are: 30°,45°,60°, 90°.
• The 90° layout will have the lowest heat transfer
coefficient and the lowest pressure drop.

9. • The square pitch (90° or 45°) is used when jet or
mechanical cleaning is necessary on the shell side.
• In that case, a minimum cleaning lane of ¼ in. (6.35 mm)
is provided.
• The square pitch is generally not used in the fixed header
sheet design because cleaning is not feasible.
• The triangular pitch provides a more compact
arrangement, usually resulting in smaller shell, and the
strongest header sheet for a specified shell-side flow area.
• It is preferred when the operating pressure difference
between the two fluids is large.

10. Tube Pitch
• The selection of tube pitch is a compromise between a
• Close pitch (small values of PT/do) for increased shell-side
heat transfer and surface compactness, and an
• Open pitch (large values of PT/ do) for decreased shell-side
plugging and ease in shell-side cleaning.
• Tube pitch Pt is chosen so that the pitch ratio is 1.25 < PT/do <
1.5.
• When the tubes are to close to each other (PT/do less than
1.25), the header plate (tube sheet) becomes to weak for
proper rolling of the tubes and cause leaky joints.
• Tube layout and tube locations are standardized for industrial
heat exchangers.
• However, these are general rules of thumb and can be
“violated” for custom heat exchanger designs.

11. Identification of (Pseudo) Velocity Scale

12. Shell Side Pseudo Flow Area
The number of tubes at the centerline of the shell is
calculated by
T
s
tc
P
D
N 
B
C
P
D
B
C
N
A
T
s
tc
s .
.
. 

where is Asthe bundle cross flow area, Dsis the inner diameter of
the shell, C is the clearance between adjacent tubes, and B is the
baffle spacing
o
T d
P
C 


13. Pseudo Shell side Mass Velocity
s
s
s
A
m
G


The shell-side mass velocity is found with
  B
d
P
P
D
A o
T
T
s
s 




14. Selection of Shell Diameter

15. Shell Diameter
The number of tubes is calculated by taking the shell circle and
dividing it by the projected area of the tube layout. That is
where Apro-tube is the projected area of the tube layout expressed
as area corresponding to one tube, Ds is the shell inside
diameter, and
CTP is the tube count calculation constant that accounts for the
incomplete coverage of the shell diameter by the tubes, due to
necessary clearances between the shell and the outer tube
circle and tube omissions due to tube pass lanes for multitude
pass design.
2
4
S
tube
pro
t
shell D
CTP
A
N
A





16. Projected area of Tube Layout
2
T
tube
pro P
A 

2
T
tube
pro P
CL
A 


Where PT is the tube pitch and CL is the tube layout constant.

17. Coverage of Shell Area

18. The CTP values for different tube passes are given
below:

19. Pseudo Shell side Mass Velocity
s
s
s
A
m
G


The shell-side mass velocity is found with
B
C
P
D
B
C
N
A
T
s
tc
s .
.
. 

o
T d
P
C 

CTP
CLP
N
D T
t
S
2
2
4



20. Shell side Equivalent (Hydraulic) Diameter
• Equivalent diameter employed by Kern for correlating
shell side heat transfer/flow is not a true equivalent
diameter.
• The direction of shell side flow is partly along the tube
length and partly at right angles to tube length or heat
exchanger axis.
• The flow area at right angles is harmonically varying.
• This cannot be distinguished based on tube layout.
• Kern’s experimental study showed that flow area along the
axis showed excellent correlation wrt
• Tube layout, tube pitch etc….

21. Equivalent Counter Flow : Hydraulic or Equivalent
Diameter
• The equivalent diameter is calculated along (instead of
across) the long axes of the shell and therefore is taken
as four times the net flow area as layout on the tube
sheet (for any pitch layout) divided by the wetted
perimeter.
r
erperimete
heattransf
De
area
flow
-
Free
Net
4


22. Free Flow Area for Square Layout:
2
2
2
2
4
4
4
1
4 O
T
O
T
flow d
P
d
P
A




















Free Flow Area for Triangular Layout:















 2
0
0
4
360
60
3 O
triangle
flow d
A
A

















 2
0
0
4
360
60
3
2
1
O
flow d
height
base
A

 
2
2
2
0
0
0
8
4
3
4
360
60
3
60
2
1
O
O
T
T
flow d
P
d
Tan
P
P
A T






















23. Perimeter for square Layout: O
O
e d
d
P 









4
4
Perimeter for triangular Layout:
2
360
60
3 0
0
O
O
e
d
d
P

 









Equivalent diameter for square layout:
O
O
T
e
flow
square
e
d
d
P
P
A
D












2
2
4
4
4
Equivalent diameter for Triangular layout:
2
8
4
3
4
4
2
2
O
O
e
flow
triangular
e
d
d
P
P
A
D
T















