JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN
MECHANICAL ENGINEERING
THERMO-HYDRAULIC PERFORMANCE OPTIMIZATION OF PLAIN AND LOUVERED FIN- ROUND TUBE AIR COOLED HEAT EXCHANGERS USING GENETIC ALGORITHM DURING WET SURFACE CONDITIONS
1 RAJUL GARG, 2 SHASHI K.JAIN, 3 SATYASHREE GHODKE
1M-Tech student, Department of Mechanical Engineering, Technocrats Institute of Technology, Bhopal.
2Associate Professor, Department of Mechanical Engineering, Technocrats Institute of Technology, Bhopal
3 Associate Professor, Department of Mechanical Engineering, Technocrats Institute of Technology, Bhopal
,,
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.
ISSN 0975 –668X| NOV 10 TO OCT 11 | VOLUME – 01, ISSUE - 02Page 1
JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN
MECHANICAL ENGINEERING
Key Words : Air Cooled Heat Exchanger, Genetic Algorithm, Matlab, Optimization, Thermal Hydraulic Analysis, Plain- Fin- Round – Tube, Louvered-Fin-Round-Tube Heat Exchanger.
ISSN 0975 –668X| NOV 10 TO OCT 11 | VOLUME – 01, ISSUE - 02Page 1
JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN
MECHANICAL ENGINEERING
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 air-cooled 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.
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 fin- round 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 air- side 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 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) is-
i)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%
- RESULT AND DISCUSSIONS
Though the designer has some independence in selecting the GA parameters, it has been observed 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).
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
Re / ε / N / j4986.60 / 0.00328 / 3.62~4 / 0.0020
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:
Figure 5.2
Table: 5.2
Re / ε / N / Fp / Dc / f3875.81 / 0.99612 / 5.972~6 / 3.198 / 10.23 / 1.05
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).
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), Fp (Fin spacing), Pl (Centre- to- centre tube spacing in longitudinal air flow direction), Pt (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
Re / Fp / Dc / Pl / Pt / Lp / N / θ / Lh / j4999.67 / 3.061 / 10.23 / 19.0412 / 25.34 / 2.00 / 1.23~1 / 26.16 / 1.07 / 0.006
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).
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), Pt (Centre- to- centre 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:
Re / Fp / Dc / Pl / Pt / Lp / N / Г / µf / m / W / f4824.15 / 3.19 / 10.23 / 21.76 / 19.6 / 2.34 / 1.19 / 160.68 / 0.0008 / 0.67 / 65.33 / 0.72
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.