JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN
MECHANICAL ENGINEERING
THERMO-HYDRAULIC PERFORMANCE
OPTIMIZATION OF PLAIN AND LOUVERED FINROUND TUBE AIR COOLED HEAT EXCHANGERS
USING GENETIC ALGORITHM DURING WET
SURFACE CONDITIONS
1
RAJUL GARG, 2 SHASHI K.JAIN, 3 SATYASHREE GHODKE
1
M-Tech student, Department of Mechanical Engineering, Technocrats Institute of
Technology, Bhopal.
2 Associate Professor, Department of Mechanical Engineering, Technocrats Institute of
Technology, Bhopal
3 Associate Professor, Department of Mechanical Engineering, Technocrats Institute of
Technology, Bhopal
garg.rajul2010@gmail.com,shashi_jain72@yahoo.com,ghodke.satyashree@yahoo.com
ABSTRACT: The use of Air Cooled Heat Exchangers (ACHE) is of great interest due to the possibility of
generating power at a lower cost than using water particularly in the areas or the conditions of low ambient
temperatures. Here we develop a performance optimization methodology as a step towards estimating the
thermo- hydraulic potential of using air as a heat extraction fluid on plain- fin and louvered fin round- tubes of
the heat exchanger. This performance optimization methodology applied here is based upon the standard
correlations developed by different authors time to time. In this study two cases: Plain-Fin-round-tube air
cooled heat exchanger and Louvered-fin-round-tube heat exchanger has been taken and their performance is
optimized based upon certain design and operating parameters. The optimized result is then compared with
each other and validated against the conventional optimization techniques.
Key Words : Air Cooled Heat Exchanger, Genetic Algorithm, Matlab, Optimization, Thermal Hydraulic
Analysis, Plain- Fin- Round – Tube, Louvered-Fin-Round-Tube Heat Exchanger.
1. INTRODUCTION
The Air-cooled heat exchanger, also known as dry
cooler, air-cooler or fin-fan cooler is a device which
rejects heat from a fluid or gas directly to ambient air.
When cooling both fluids and gases, there are two
sources readily available, with a relatively low cost,
to transfer heat to…..air and water. The obvious
advantage of an air cooler is that it does not require
or require very less amount of water as a cooling
medium, which means that equipment require
cooling, need not to be near a cooling water reservoir.
In contrast to the shell and tube heat exchangers, the
problems associated with treatment and disposal of
water have become more tedious with government
regulations and environmental concerns. The aircooled heat exchanger provides a means of
transferring the heat from the fluid or gas into
ambient air, without environmental concerns, or
without great ongoing cost.
The applications for air cooled heat exchangers cover
a wide range of industries and products, however
generally they are used to cool gases and liquids
when the outlet temperature required is greater than
the surrounding ambient air temperature. The
applications include Engine cooling, Condensing of
gases and steam, Oil and gas refineries, Compressor
stations for gas pipelines, Subsurface gas storage
facilities, Bakeries to preheat ovens and provide
steam for other equipment.
This study is based upon the Engineering Data Book
on Air Cooled Heat Exchangers written by Anthony
M. Jacobi (2010), who compiles the different thermal
hydraulic performance correlations of air cooled heat
exchangers.
Using the basic framework of GA, a technique for
multi-constraint minimization has been developed in
the present work. The technique has been applied to
obtain the design and variables of Air Cooled heat
exchanger (ACHE) for the optimum values of
designated parameters.
In this exercise, the minimization of thermal
hydraulic parameters has been targeted for specified
heat duty constraints under different combinations of
space and flow restrictions. Finally a comparison
between the optimum designs attained under different
design constraints and conditions have been made.
ISSN 0975 – 668X| NOV 10 TO OCT 11 | VOLUME – 01, ISSUE - 02
Page 80
JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN
MECHANICAL ENGINEERING
The effect of GA parameters on the optimal solution
has been seen. Further the effect of different
constraints on the solution has been discussed. The
methodology used is not new, but the system like Air
Cooled heat exchanger, it has been applied and the
way it has been used is probably new to the
researchers working in this area.
2. THERMAL HYDRAULIC PERFORMANCE
METHODOLOGY
This study is directed towards in-tube flows, and it
provides the tools necessary to predict heat transfer
and friction factors/pressure drop for two- phase and
single- phase in-tube flows. This study is particularly
important in determining air-side heat transfer and
pressure drop conditions for heat exchanger analysis
and design optimization. However, in many systems
heat transfer to and from air is very important.
Furthermore, because the applications motivating this
study towards the use of plain-fin and louvered finround tube heat exchangers, the focus will be on
those families of heat exchangers.
Many engineers find the widespread use of the
Colburn j factor to characterize heat transfer, rather
than the Nusselt Number, a confusing aspect of airside analysis. While the usage of j is probably due to
early adoption in a seminal book (Kays and London,
1955), there is a theoretical basis for its use. For a
steady, laminar, zero- pressure- gradient boundary
layer, it can be shown through scale analysis that,
except at very low Prandtl numbers, Nu = C1Re½
Pr1/3, where C1 is an order- unity constant. For a
steady, turbulent internal flow it is known that the
heat transfer can be reasonably presented by Nu =
C2Re4/5 Pr1/3, where C2 is a constant. Motivated by
boundary layer theory for laminar flows and our
knowledge of turbulent flows, we form the Colburn j
factor,
j = Nu / Re Pr 1/3
and anticipated heat transfer correlations will take a
power- law from,
j = A. Re –B
where B is likely to range from 0.2 to 0.5, depending
upon the nature of the flow.
In some cases the heat transfer calculations are
coupled to or constrained by pressure- drop
calculations. In order to calculate the flow rates,
pressure drop, or fan power (pumping power); the
friction factor must be known. By analogy to heat
transfer, we might expect the friction factor will
follow a power- law.
f = C. Re –D
The Air- conditioning and Refrigeration Technology
Institute (ARTI) sponsored research in the early
2000’s to review and advance the state of the art in
air- side heat transfer. Much of what is reported in the
following section is derived from that work (Jacobi et
al., 2001-2005).
2.1 PERFORMANCE OF PLAIN-FIN, ROUND
TUBE AIR COOLED HEAT EXCHANGERS
When the heat exchanger is operated under wet
conditions, the retained condensate on the air-side
surface changes the surface geometry and the air flow
pattern and can increase surface heat transfer
resistance. In an experimental study of condensate
drainage characteristics, perhaps the first in which
retained mass of condensate was measured along
with thermal- hydraulic performance, Korte and
Jacobi (2001) showed that the mass of retained
condensate decreases as air velocity increases, and
condensate can degrade heat transfer by occupying
surface area and blocking airflow. Due to decreased
retention at high velocity both j and f under wet
conditions differ from those of dry conditions by less
at higher Reynolds number for the plain fin and tube
heat exchanger.
On the basis of experimental data Wang et. al.
(1997a) reported fin spacing to be unimportant to
both f and j under wet conditions. To the contrary,
Korte and Jacobi (2001) reported sensible heat
transfer and pressure drop dependent on fin spacing
and contact angle. For these heat exchangers with
relatively large fin spacing, Korte and Jacobi did not
find the sensible j to decrease under wet conditions,
as reported by others for heat exchangers with a small
fine pitch. They found that f was higher under wet
conditions than for dry conditions with a small fine
spacing, but wet and dry- surface f factors differed
by less than the experimental uncertainty for large fin
spacing.
Regarding wet surface conditions most heat
exchanger performance studies consider only fully
wet surfaces, but a partially wet condition can occur
in application. For partially wet conditions, it is
necessary to consider the dry and wet surface fin area
separately for proper fin efficiency calculation; a
method for accomplishing this is discussed by Park
and Jacobi (2010).
2.2 PERFORMANCE OF LOUVERED-FIN,
ROUND
TUBE
AIR
COOLED
HEAT
EXCHANGER
Fin spacing has a small effect on j and f (Chang et al.
1995); Wang et al. (1998) reported that j decreases
as fin spacing decreases for ReDc < 1000 and j is
independent of fin pitch for ReDc >1000. The effect of
fin spacing on f factor was found to be small
compared to the case of plain- fin heat exchanger.
Reflecting this dependence of j on Reynolds number,
Wang et al. (1999a) provided two separate j factor
correlations, each applicable in a particular Reynolds
number range.
Air- side friction decreases for a smaller tube
diameter as reported by Wang et al. (1998). They
reported that heat transfer decreases for a large tube
diameter at low Reynolds number, because the
ineffective downstream region is greater for a larger
tube.
Wang and Chang (1998) suggested that the heat
transfer enhancement due to louvers become
ISSN 0975 – 668X| NOV 10 TO OCT 11 | VOLUME – 01, ISSUE - 02
Page 81
JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN
MECHANICAL ENGINEERING
negligible under wet conditions for a frontal area
velocity lower than 0.7m/s, implying the decrease in
sensible heat transfer coefficient due to condensation
is greater for interrupted fins than for plain fins.
Based on their experimental data, they concluded that
a hydrophilic coating decreases pressure drop but
does not affect sensible heat transfer (Liu and Jacobi,
2009). Since the condensation mode (filmwise or
dropwise) is a crucial parameter that depends upon
the surface contact angles, generalized conclusions
about the effect of relative humidity on heat
exchanger performance should be made with a
careful consideration of surface condition.
2.3 HEAT EXCHANGER CORRELATION FOR
A ROUND- TUBE HEAT EXCHANGER WITH
WET SURFACE CONDITIONS
Correlation for plain-fin-round-tube heat exchangers
for wet surface conditions, as identified by Wang et
al. (1997) isi)
Colburn j factor:
j = 0.29773ReDc-0.364 ε-0.168
and,
ii)
Friction factor f (associated with flow rates
& pressure drop etc.):
f = 28.209ReDc-0.5633 N-0.1026 [Fp/Dc]-1.3405 ε-1.3343
Where, ε is effectiveness.
Correlation for Louvered-fin-round-tube heat
exchangers for wet surface conditions, as identified
by Wang et al. (1997) is i)
Colburn j factor:
j = 9.717 ReDcJ1 [Fp/ Dc] J2 [Pl/Pt] J3 ln [3-(Lp/Fp)] 0.07162
N-0.543
Where,
J1 = - 0.023634 – 1.2475 [Fp/Dc] 0.65 [Pl/Pt] 0.2 N-0.18
J2 = 0.856 e tanθ
J3 = 0.25 ln (ReDc)
ii)
Friction factor f (associated with flow rates
& pressure drop etc.):
f = 2.814 ReDcF1 [Fp / Dc] F2 [Pl / Dc] F3 [(Pl / Pt)
+0.091] F4 [Lp / Fp] 1.958 N 0.04674
Where,
F1 = 1.223 – 2.857 [Fp / Dc] 0.71 [Pl / Pt] -0.05
F2 = 0.8079 ln (ReDc)
F3 = 0.8935 ln (ReDc)
F4 = -0.999 ln [2Γ/µf]
Γ = m/WN: condensate flow rate per unit width per
tube row
µf = dynamic viscosity of water
3. CONSTRAINED MINIMIZATION
If there are number of constraint conditions and the
objective function needs to be minimized, the
problem is modified as under:
Minimise f(X),
X= [x1,.............,xk]
Where, gj(X) =0, j = 1,.................., m
and xi, min ≤ xi ≤ xj, max ; i = 1,...............,k
The problem can be recast into unconstrained
maximization problem and the solution may be
obtained as outlined earlier. The first step is to
convert the constrained optimization:
m
Minimise f(X) + ∑ Ø (gi(X));
i=1
problem into an unconstrained one by adding a
penalty function term. Subjected to
xi, min ≤ xi ≤ xj, max ; i = 1,...............,k
Where Ø is the penalty function defined as, F (g(X))
= R (g(X)) 2
R is the penalty parameter having an arbitrary large
value.
The second step is to convert the minimization
problem to a maximization one. This is done
redefining the objective function such that the
optimum point remains unchanged.
The conversion used in the present work is as follows
Maximize F(X),
Where,
m
F (X) = 1 / {f (X) + ∑ Ø (gi(X))};
i=1
The above algorithm can be used for minimizing the
total annual cost of Air- Cooled heat exchanger.
4. THERMO-HYDRAULIC PERFORMANCE
OPTIMIZATION OF FINNED-ROUND-TUBE
AIR COOLED HEAT EXCHANGERS UNDER
WET
SURFACE
CONDITIONS
USING
GENETIC ALGORITHM
The statement of the optimization problem would be
as follows for Plain and Louvered fins:
Minimize f(x) = (Colburn factor j) Plain/ Louvered fins
and Minimize f(x) = (Friction factor f) Plain/ Louvered Fins
Subjected to the common constraints of design and
operating parameters, as per Wang et al. (1997) for
Plain fin wet surfaces and Wang et al.(2000) for
Louver fin wet surfaces.
400 ≤ ReDc ≤ 5000
0 ≤ Dc ≤ 10.23
0.12 ≤ δf ≤ 0.13,
1.2 ≤ FP ≤ 3.20
1≤N≤6
19 ≤ Pt ≤ 25.4
19 ≤ Pl ≤ 22
24.4 ≤ θ ≤ 28.2
0 ≤ Lh ≤ 1.07
2 ≤ Lp ≤ 2.35
0≤ε≤1
Experimental Uncertainties for Plain fin wet surfaces
are:
j – 92% data within 10% and f - 91% data within
10%
and Experimental Uncertainties for Louvered fin wet
surfaces are:
j – 80.5% data within 10% and f – 85.3% data within
10%
5.
RESULT AND DISCUSSIONS
Though the designer has some independence in
selecting the GA parameters, it has been observed
ISSN 0975 – 668X| NOV 10 TO OCT 11 | VOLUME – 01, ISSUE - 02
Page 82
JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN
MECHANICAL ENGINEERING
Fitness value
0
0
10
30
40
50
60
Generation
Current Best Individual
70
80
90
100
4000
3000
2000
1000
0
1
2
3
4
Number of variables (5)
5
ε
N
Fp
Dc
10.23
Figure 5.2
Table: 5.2
Re
Mean fitness
20
f
0
10
20
30
40
50
60
Generation
Current Best Individual
70
80
90
100
6000
4000
1.05
4
0.99612
6
2
It is observed that the population size 20, Double
vector population type, Crossover fraction =0.8 and
Gaussian mutation function gives the optimized value
of Colburn j function for wet surface of louvered fin
round tube heat exchanger (Refer Figure 5.3).
Best: 0.0066285 Mean: 0.0070809
2000
0.025
0
10
20
30
40
50
60
Generation
Current Best Individual
70
80
90
1
2
3
4
5
6
Number of variables (9)
7
8
9
100
6000
4000
2000
0
N
θ
Lh
j
26.16
1.07
0.006
Lp
2.00
1.23~1
Pt
25.34
19.0412 Pl
Figure 5.3
The optimum value of Colburn factor j is obtained by
optimizing the individual design and operating
parameters range for louvered – fin heat exchanger
as: Re (Reynolds Number), N (No. of tube rows), F p
(Fin spacing), Pl (Centre- to- centre tube spacing in
longitudinal air flow direction), P t (Centre- to- centre
tube spacing in traverse air flow direction) and θ
(Louver angle) with their lower [400; 1.2; 19; 19; 2;
1; 24.4;]] and upper bounds [5000; 3.2; 22; 25.4;
2.35; 6;28.2] by keeping the outer Diameter of the
tube collar Dc and Air-side hydraulic length Lh as
constant (10.23 mm & 1.07 mm respectively). The
range of optimum values obtained is as under:
Table: 5.3
Dc
Friction factor f renders its optimum value under
certain design and operating conditions as:
The optimum value of friction factor f is obtained by
optimizing the individual design and operating
parameters range of plain –fin heat exchanger as: Re
(Reynolds Number), ε (Effectiveness), N (No. of tube
rows) and Fp (Fin spacing) with their lower [400; 0;
1; 1.2] and upper bounds [5000; 1; 6; 3.2] by keeping
the outer Diameter of the tube collar Dc as constant
(10.23 mm). The range of optimum values obtained
is as under:
0.01
0.005
10.23
Figure 5.1
For the range tested (Figure 5.1), the penalty function
parameters (Initial penalty=10 and Penalty fraction
=100) does not show any effect on the optimized
function; so an arbitrary value, 100, is selected for the
solution.
The design parameters (Re, ε and N) are varied
individually, keeping other parameters fixed at that of
optimum j.
Due to restriction in heat duty, the domain of feasible
design becomes very small, but the optimum values
of Re (Reynolds Number), ε (Effectiveness) and N
(No. of tube rows) with their lower [400; 0; 1] and
upper bounds [5000; 1; 6] provide insight into
minimum j would be shown as under:
Table: 5.1
j
Re
ε
N
0.0020
4986.60
0.00328
3.62~4
Mean f itness
0.015
Fp
3
3.061
2
Number of variables (3)
0.02
Current best individual
1
Fitness value
Best f itness
0
4999.67 Re
Current best individual
10
3875.81
Fitness value
Best fitness
Mean fitness
20
3.198
Best: 0.0020773 Mean: 0.0022874
x 10
Best fitness
30
5.972~6
-3
8
Best: 1.0505 Mean: 1.0664
40
Current best individual
that the selection of proper GA parameters renders
quick convergence of the algorithm and the proper
GA parameters are problem specific (Wolfersdorf et
al., 1997; Grefenstette, 1986). Therefore, initially, an
exercise has been made following the methodology
of Wolfersdorf et al., (1997) to select the optimum
GA parameters for the present problem. It is observed
that the population size 20, Double vector population
type, Crossover fraction =0.8 and Gaussian mutation
function gives the optimized value of Colburn j
function for wet surface of plain fin round tube heat
exchanger (Refer Figure 5.1).
It is observed that the population size 20, Double
vector population type, Crossover fraction =0.8 and
Gaussian mutation function gives the optimized value
of friction factor f for wet surface of louvered fin
round tube heat exchanger (Refer Figure 5.4).
ISSN 0975 – 668X| NOV 10 TO OCT 11 | VOLUME – 01, ISSUE - 02
Page 83
JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN
MECHANICAL ENGINEERING
Best: 0.7292 Mean: 0.77947
10
Fitness value
Best fitness
Mean fitness
5
Current best individual
0
0
10
20
30
40
50
60
70
Generation
Current Best Individual
80
90
100
6000
4000
2000
0
1
2
3
4
5
6
7
8
Number of variables (11)
9
10
11
Re
Fp
Dc
Pl
Pt
Lp
N
Г
µf
m
W
f
4824.15
3.19
10.23
21.76
19.6
2.34
1.19
160.68
0.0008
0.67
65.33
0.72
Figure 5.4
The optimum value of friction factor f is obtained by
optimizing the individual design and operating
parameters range for Louvered- Fin heat exchanger
as: Re (Reynolds Number), N (No. of tube rows) and
Fp (Fin spacing), Pl (Centre- to- centre tube spacing
in longitudinal air flow direction), P t (Centre- tocentre tube spacing in traverse air flow direction), Г
(Condensate mass flow rate per unit width per unit
tube row), m (Mass of fluid), Lp (Louver spacing)
and W (Width) with their lower bounds as [400; 1.2;
19; 19; 2; 1 0 0 0] and upper bounds as [5000; 3.2;
22; 25.4; 2.35; 6; ∞; ∞; ∞ ] by keeping the outer
Diameter of the tube collar Dc as (10.23 mm) and
Dynamic viscosity of water µf as (0.798 x 10-3 Ns/m2)
as constant. The range of optimum values obtained is
as under:
Table: 5.4
It is obvious from Table 5.1(Plain fin wet surface
condition) that at high Reynolds Number (Re=
4986.60) and moderate number of tube rows as 4;
colburn factor j renders low values i.e 0.002 but from
Table 5.3 (Louver fin wet surface condition) for same
range of design and operating parameters it exhibits
Reynolds number as (Re= 4999.67), largest number
of tube rows as 6; Colburn factor j renders relatively
high values i.e. 0.006. Which concludes that for the
same design and operating parameter range Louvered
fin- round tube heat exchangers renders high rate of
heat transfer as compare to Plain fin- round tube.
On the other hand from Table 5.2 (Plain fin wet
surface condition) that at moderate Reynolds Number
(3875.81) and large number of tube rows as 6;
friction factor f renders high value as 1.05, i.e high
pressure drop condition persist at moderate Reynolds
Number and large number of tube rows. On contrary
to Plain fin case; Table 5.4 (Louver fin wet surface
condition) for same range of design and operating
parameters, exhibits high Reynolds number as
(4824.15), less number of tube rows as 1; friction
factor f renders low values as 0.72, which make it
obvious that low pressure drop condition persist at
high Reynolds Number and lesser tube rows, in case
of Louvered fin- round tube air cooled heat
exchangers during wet conditions or during
dehumidification process.
It is obvious from above study that Louvered fin –
round tube heat exchangers exhibit better
performance as compare to Plain fin in the same
conditions but the only parameter become contrary,
i.e. number of tube rows. It may be compensated by
the proper selection of tube material and then its
optimality can be studied.
6. CONCLUSION
An optimization model of Air Cooled Heat
Exchanger having a large number of design variables
of both discrete and continuous type has been
developed using a genetic algorithm. A case of Plain–
fin- round-tube and Louvered-fin-round-tube model
has been solved for optimum thermo-hydraulic
performance. The parametric study of selected input
variables and their effects on solution/ performance is
anticipated. The result can be very useful for the
designers to start with such complex thermal system.
7. REFERENCES
[1]
Anthony M. Jacobi, “Heat Transfer to Air
Cooled Heat Exchangers”; 2010, Engineering Data
Book-III; P 6-1 to 6-40, Wolverine Tube Inc., USA.
[2]
Anthony M. Jacobi, “Preliminary Design
Procedures”; 2010, Engineering Data Book-III; P
226-234, Wolverine Tube Inc., USA
[3]
“Air Cooled Heat Exchangers”, Mechanical
Engineers' handbook, 2nd ed., Edited by Myer Kutz,
P 1611- 1626; John Wiley & Sons, Inc.
[4]
Korte,
C.
and
Jacobi,
A.M.,
(2001);”Condensate Retention Effects on the
Performance of Plain-Fin-and- Tube Heat
Exchangers: Retention Data and Modeling”;
International Journal of Heat Transfer, 123:5, 926936.
8. NOMENCLATURE
[1]
ReDc: Reynolds number at outside diameter
of a tube color
[2]
ReDh: Reynolds number at air-side hydraulic
diameter
[3]
δf : Fin thickness
[4]
FP: Fin Pitch or Fin Spacing
[5]
Pt: centre- to-centre tube spacing transverse
to air flow direction
[6]
Pl: centre- to-centre tube spacing in air flow
direction
[7]
N: Number of tube rows in air flow
direction
[8]
Do: Outer Diameter
[9]
Dc: outer Diameter of the tube collar
[10]
R 1-5: Heat Transfer Resistance at different
sections of the setup
[11]
ε: Effectiveness
ISSN 0975 – 668X| NOV 10 TO OCT 11 | VOLUME – 01, ISSUE - 02
Page 84