heat transfer rates either using optimization techniques or improving system design by introducing roughness elements. In case of solar air heater, the working ...
Thermal Performance Optimization of Smooth Flat Plate Solar Air Heater (SFPSAH) using Simulated Annealing: Evaluation and Comparisons Siddhartha, Sant Ram Chauhan, Varun and Naveen Sharma Abstract-- Nowadays, the interest of researcher growing in the field of optimization of solar systems in order to improve the thermal performance by reducing friction losses and increasing heat
transfer
rates
either
using
optimization
techniques
or
improving system design by introducing roughness elements. In case of solar air heater, the working fluid is air which reduces the probability of corrosion and also decreases the weight of collector and correspondingly reduces the cost. The thermal performance of solar air heater is low which can be increased by rising heat transfer rates which can be obtained by using high flow rates. In
this
work,
simulated
annealing
algorithm
has
been
implemented to optimize the thermal performance of flat plate solar air heater and predict the optimized set of design and operating parameters. The concept of simulated annealing based on the physical annealing process in statistical mechanics which governs first law of thermodynamics. The algorithm for the optimization is developed as well as simulation is carried out based upon the code developed in MATLAB. The design and operating parameters which affect the thermal performance are wind velocity, irradiance; tilt angle, mass flow rate, ambient temperature, emissivity of plate and number of glass cover plates. In this work the optimized set of these parameters are obtained and the optimized thermal performance is evaluated. The
results
obtained
show
that
the
maximum
thermal
performance is 72.48 % for three number of glass plate at an 2 irradiance of 600 W/m •
Solar collectors (air/ water) are used for the optimal and efficient utilization of solar energy in solar thermal systems and have a wide range of applications in all fields of living like residential, agricultural and industrial fields for various purposes like: seasoning of timber, green house heating, curing and drying of industrial products and concrete building components [1]. Solar air heaters have disadvantages of relatively low heat storage capability and have problems allied to freezing, boiling, corrosion and salt deposits, inspite of having simple design and easy operation. Simulated annealing (SA) is a generic probabilistic metaheuristic used in evolutionary computation to fmd approximate solutions to the global optimization problem in a large search domain. The inspiration came from annealing in metallurgy, a technique involving heating which causes the atoms to displace from their initial positions and wander randomly through higher energy states and after slow cooling gives them more chances of finding configurations having refmed grain structure as shown in Fig. 1. It belongs to the class of stochastic methods which uses mutation and effective and efficient in performing global search and shrivels the vast domain into smaller ones.
The final results obtained from this technique are compared with other optimization techniques like PSO, GA and found to be satisfactory.
These
results
are
also
compared
with
the
experimental results.
Index Terms- Thermal performance, Optimization, Solar air
heater, Simulated Annealing.
Hwt
u=>
I. INTRODUCTION
I
N the present scenario, the nation's development and progress in living standard are estimated by per capita energy consumption due to which fast depletion of conventional sources, hence for continuous and reliable supply of energy alternate energy resources that are renewable has been searched and energy conversion systems based on these technologies are discovered and installed that can provide a sustainable future. Solar energy is one of the most promising amongst such resources and has the potential to supplies and fulfills all the present and future energy needs on a lifelong basis.
Initial structure of the
Final structure of the material
Fig.l. The analogy of SA.
Due to promlsmg prospective and wide range of applications of these methods researchers are now using these methods for evaluation, estimation, prediction and Copyright Notice: 978-1-4673-6008-11111$31.00 ©2012 IEEE
2
optimization of various solar energy systems. Fung et. al. [2] proposed an optimization algorithm based upon SA technique for the hybrid energy system. The developed algorithm estimated the optimal generator setting and battery charging/discharging schedules having an objective of maximize the performance of the battery and minimize running cost of the generator. Ekren and Ekren [3] used SA algorithm for optimization of a PV/wind hybrid energy conversion system with battery storage. The objective of this study is the minimization of total cost of the system and random simulation is carried out by using probabilistic distribution for hybrid system on a stand-alone hybrid system using the historical mean solar radiation and wind speed data for the period of 2001-2003 recorded at meteorological station. The result obtained from this study has been compared with response surface methodology (RSM) results [4-5] and an improvement of 10.13% is achieved. Hui [6] developed an algorithm based upon adaptive simulation annealing genetic algorithm (ASAGA) and predict the design parameters for maximum fuel economy in case of hydraulic hybrid vehicle (HHV). The results drew from this study shows that the key components size and position of optimal parameters of HHV, increases the thermal performance and minimizing the final consumption and following features like: low algorithm complexity, potential to obtain global optimal, required very less model treatment and not much affected by discontinuities in system model and has disadvantage of low computation efficiency as compared to successive quadratic programming and the convergence of the SA is not as fast as genetic algorithm [7] of SA has also concluded. Faber et al. [8] applied SA for the dynamic optimization of energy and chemical engineering processes for various case studies such as: batch reactor optimization and simplified combined-cycle power plant with penalty and no penalty terms are performed. The result shows that initial annealing temperature is very vital and it is problem specific parameter in SA. In present work, a tread to exploit the potential of SA in order to optimize the thermal performance of a SFPSAH with estimating the desired optimal sets of design and operating parameters like wind velocity, tilt angle, emissivity of plate and ambient temperature which are decisive for ultimately finding the best thermal performance. II. SIMULATED ANNEALING (SA) Simulated Annealing (SA) was proposed by Kirkpatrick, Gelatt and Vecchi in 1983 and by Cerny in 1985 [9]. This method was basically an adaptation of Metropolis-Hastings algorithm invented by Rosenbluth [10]. It was derivative free and global search stochastic strategy that can work in very high-dimensional searches in given computational domain. This process can be observed as a single individual evolutionary algorithm in which crossovers are disabled and only mutations are used and based upon the annealing process and successfully implemented to discrete, continuous and complicated combinatorial problems. SA finds applications in various power system processes like network reconfiguration,
unit commitment, transmISSIOn expansion planning, maintenance scheduling, etc. SA has the ability to deal with arbitrary cost and systems functions, inability to refine optimal solution and has able to escape easily from local minima and quickly reach in the vicinity of an optimal solution. The repeated annealing process is one of the major limitations of SA optimization technique. For certain problems, simulated annealing may be more effective than exhaustive enumeration - provided that the goal is merely to find an acceptably good solution in a fixed amount of time, rather than the best possible solution. III. PROBLEM FORMULATION The thermal performance of a SFPSAH can be predicted on the basis of detailed consideration of heat transfer processes and correlations for heat transfer coefficient, heat removal factor etc. The problem formulated in following manner. Objective function: TJ lh
Maximize
=
Fo
[
(m ) - V 0
( � )] To
Ti
(I)
Biondi et al. [11] proposed an expression for efficiency of solar air heaters. The top loss coefficient (Ut) is determined using relation (2) given by Klein's [12], heat removal factor at outlet (Fo) and temperature rise (To-Tj) are computed by the equations (3) and (5) respectively. U,
�
[(C
/ T,)[(T, -
�
nf
)/(N
+
+
:. r
+
_GCp[ -- (-UOF'/GCP�J)
Fo -
I-e
Vo
[
where F·= O.024Re08pr04
(To - T, ) =
[
Ac
{( ) j ra
-
(3)
�/ O.024Re08pr04 � +uo ]
U0
(Tp
-
T
a
) /m C p
}]
(4)
(5 )
Constraints of the problem: Number of glass cover plate (N) is varied in steps of 1 from 1 to 3. Solar radiation intensity (I) is varied in steps of 200 from 600 to 1200 W/m2. Re is varied in steps of 2000 from 2000 to 20000. 1 :s V :s 3, here V is the wind velocity in m/s; 280 :S Ta :S 310, here Ta is the ambient temperature;
oo:sp :S 70°, here P is the tilt angle; 0.85 :S cp:S 0.95, here emissivity of glass plate (cp); The transmittance - absorptance product ('ra) is 0.85; Emissivity of glass plate (Cg) is 0.88; Skeleton of an optimizing Algorithm based on SA: • Randomly picks feasible solutions in the search space. Copyright Notice: 978-1-4673-6008-11111$31.00 ©2012 IEEE
3 • Improving on a solution by always accepting better cost neighbors. • Allowing for a stochastically guided acceptance of worse-cost neighbors. • Gradually decreasing the probability of accepting worse-cost neighbors.
IV. SA ALGORITHM FOR THE PROBLEM Each step of the SA algorithm replaces the current solution by a random nearby solution, chosen with a probability that depends both on the difference between the corresponding function values and also on a global parameter T, that is gradually decreased during the process. As T is large, the current solution changes almost randomly, but increasingly downhill as T tends to zero. SA algorithm used to estimate the maximum thermal performance and the optimized set of values of systems operating and designed parameters. A.
B.
TABLE I EXPERIMENTAL RESULTS COMJ'ARED WITH RESULTS OBTAINED BY GA AND PRESENT STUDY AT MOST CLOSEST OPERATING VALUES (N=I, V=I, 1=1000 W/M2 Experimental GA obtained Present study S. No values Values [14] values [13] I. 17.70 16.5% 27.48% 2. 30.02 40.11% 26% 38.18 3. 48.12% 37.8% 57.66% 49.31 4. 50.0%
Ql
fij
_71
>
g�
�1.5
�
.
i
;
o
1000
2000
3000
c
200
�
100
00
4000
Iteration
0
4 Number of ;eliables (4)
Current Temperature
Set the values for Ae, Eg, Cp, wt, ht, ta Set the value for N, I, Re Initial solution Xl in X (Search domain) Initialize best function value Fbest corresponding solution Xbesl Initialize tp Initialize K= 1
?§Ql � :J
f" -
)
-
10
"-
E 2
�:J
c
of
F and the
Calculation while K < Kmax and F (x) < Fbesl ih Generate xne g bonr at random in the search space domain h i g bou ne If F (x j = F(x), then counter =counter + 1 IfF (xneighbouf) < F(x), then x =xneighbouf ih If F (x'te g bour) < Fbes\ then Fbesl = F (xneighbour) and Xbesl = i h g bour ne x If F (xneighboj > F(x) Then generate R =a ramdom number [0,1], ll. =Fneighbouf Fbest
a= 1/(1
�
Best point
Best Function Value: -71.5106
-70.5
Initialization
_
C.
clearly enlightened in Table 1.
ih
If a> R, then x = xne g bouf (Change of state) K=K+ 1 Update tp until (tp (K+1) -tp (K)) < 0.0001
Terminate Return Fbest and Xbesl V. RESULTS AND DISCUSSIONS
In this work, the optimization of thermal performance of SFPSAH for different set of optimized values of design and operating parameters has been carried out by developing algorithm for simulated annealing with and without threshold acceptance criterion and the trend shown in Fig. 2. The results obtain from SA has been compared with most closest values of experimental data and found to be great proximity in terms of thermal performance as compared to GA results, it is
5
() 4 Number of ;eliables (4)
A.
Fig. 2. Trend of best function value, best operating point and current temperature at last iteration.
Effect of Reynolds Number on Thermal Performance
The effect of Reynolds number (Re) on the thermal performance for different values of solar radiation intensity and number of glass cover plates is presented in Tables 2 to 4. As it is seen from the Tables 2 to 4, that the thermal performance increases as the Reynolds number increases for fixed value of glass cover plate. The turbulence effect in the flow directly affects the heat transfer rate. As Reynolds number increases turbulence in the flow increases which causes higher heat transfer rate and therefore higher thermal performance. TABLE 2 VARIATION OF THERMAL PERFORMANCE WITH RE AT DIFFERENT SOLAR RADIATION INTENSITY FOR N=I Thermal Performance (%) Re 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
I = 600 W/m2 19.5737 31.9158 40.3917 46.2107 50.9748 54.8929 57.6921 60.3319 62.3207 64.0582
1=800 W/m2 18.7072 30.836 39.2944 45.5684 50.2908 54.1293 57.1511 59.6272 61.4528 63.3172
1=1000 W/m' 17.6966 30.0172 38.1824 44.6621 49.3149 53.4182 56.5065 59.0541 61.1254 62.9629
1=1200 W/m2 17.4604 29.0595 37.6487 43.9187 48.8642 52.7259 55.7717 58.3572 60.3263 62.3454
Copyright Notice: 978-1-4673-6008-11111$31.00 ©2012 IEEE
4 TABLE 3 YARIATION OF THERMAL PERFORMANCE WITH RE AT DIFFERENT SOLAR RADIATION INTENSITY FOR N=2 Thennal Perfonnance (%) Re
1=600 W/m2 25.6859 39.8566 48.6497 54.6175 58.9721 62.1944 64.709 66.7539 68.3109 69.7965
2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
1=800 W/m2 24.5662 38.3891 47.5704 53.7162 58.1612 61.3731 64.1098 66.1263 67.8595 69.3062
1=1000 W/m2 23.5642 37.5379 46.5347 52.6971 57.3815 60.7765 63.3947 65.6112 67.4154 68.8388
1=1200 W/m2 22.6143 36.5246 45.6225 51.9252 56.4899 60.0281 62.9441 65.1525 67.0587 68.5195
C. Effect of Number of Glass Plates on Thermal Performance From the Fig. 4 it is clear that with increase in number of glass plates the thermal performance of a SFPSAH has been enhanced. Fig. 4 shows that the maximum value of thermal performance is observed for three glass cover plates at solar radiation intensity of 600 W1m2 and minimum for single glass cover plate at solar radiation intensity of 1200 W/m2• As the number of glass cover plate increases the cost, obscurity and intricacy of the system. The maximum value of thennal 2 perfonnance is estimated to be 72.48% for 600 W1m solar radiation intensity and three number of glass plates. 70
TABLE 4 YARIATION OF THERMAL PERFORMANCE WITH RE AT DIFFERENT SOLAR RADIATION INTENSITY FOR N=3 1=600 W/m2 19.5737 31.9158 40.3917 46.2107 50.9748 54.8929 57.6921 60.3319 62.3207 64.0582
2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
1=800 W/m2 18.7072 30.836 39.2944 45.5684 50.2908 54.1293 57.1511 59.6272 61.4528 63.3172
1=1000 W/m2 17.6966 30.0172 38.1824 44.6621 49.3149 53.4182 56.5065 59.0541 61.1254 62.9629
1=1200 W/m2 17.4604 29.0595 37.6487 43.9187 48.8642 52.7259 55.7717 58.3572 60.3263 62.3454
B.
In this section, the effect of solar radiation intensity on the thennal perfonnance of SFPSAH is analyzed with respect to designloperating parameters. Fig. 3 shows the effect of solar radiation intensity on thennal performance for single glass cover plate. The trend is similar for the two and three number of glass cover plate. As can be seen from the Fig. 3, when the solar radiation intensity increases, the thennal perfonnance decreases because of increase in top loss coefficient.
60
;R o
....,������1
Q) 50 u C III E
.gQ)
§ 0..
m
40
EQ)
.c f-
30
20
2000
4000
6000
6000
10000
Re
12000
14000
16000
16000
20000
VI. CONCLUSIONS The optlllllzation of thermal performance was conducted using simulated annealing. The conclusion drawn from the present study: 1. In general, as the Reynolds number is increased, the thermal performance increases for all the cases considered. 2. The result shows that the thermal performance increases with number of glass cover plates and tilt angle. 3. From the comparison, it is clear that the optimal thennal performances obtained from SA are closer to experimental as compared to GA. 4. The maximum thennal performance obtained at V=1 mis, �=70°, 1=600 W/m2, Ep=0.85 and Re=20000. VII. REFERENCES [ I]
40
0..
m
[2]
E
Q) 30 .c f-
[3]
20
2000
50
.gQ)
Fig. 4. The effect of number of glass plates on thennal perfonnance (I = 600 W/m\
Effect of Solar Radiation Intensity on Thermal Performance
--- 1=600 W/m',--- I = 800 W/m', -.t.---- 1 = 1000 W/m',---T-I = 1200 W/m'
60
�c
Thermal Perfonnance (%) Re
---N = 1,-e-N =2,-.t.----N = 3
4000
6000
8000
10000
Re
12000
14000
16000
18000
20000
Fig. 3. The effect of solar radiation intensity on thennal perfonnance (N = I).
[4]
Yarun, R.P. Saini, S.K. Singal, A review on roughness geometry used in solar air heaters, Solar Energy, 81 (2007) 1340-1350. Fung C.c., Ho S.c.Y. and Nayar c.y., "Optimisation of a hybrid energy system using simulated annealing technique", 10th Conference on Computer, Communication, Control and Power Engineering, 5 (1993) 235-238. O. Ekren, B.Y. Ekren, Size optimization of a PY/wind hybrid energy conversion system with battery storage using simulated annealing. Applied Energy, 87 (20 I0) 592-598. O. Ekren, B.Y. Ekren, Size optimization of a PY/wind hybrid energy conversion system with battery storage using response surface methodology. Applied Energy, 85(11) (2008) 1086-101.
Copyright Notice: 978-1-4673-6008-11111$31.00 ©2012 IEEE
5 [5]
[6]
[7]
[8]
[9]
O. Ekren, B.Y. Ekren, Break-even analysis and size optimization of a PYIwind hybrid energy conversion system with battery storage - a case study. Applied Energy, 86(7-8) (2009) 1043-54. S. Hui, Multi-objective optimization for hydraulic hybrid vehicle based on adaptive simulated annealing genetic algorithm, Engineering Applications of Artificial Intelligence, 23 (2010) 27-33. K. Mitchell, M. Nagrial, J. Rizk, Simulation and optimization of renewable energy systems, Electrical Power and Energy Systems, 27 (2005) 177-188. R. Faber, T. Jockenhovel, G. Tsatsaronis, Dynamic optimization with simulated annealing, Computers and Chemical Engineering, 29 (2005) 273-290. S.A. Kalogirou, Optimization of solar systems using artificial neural networks and genetic algorithms, Applied Energy, 77 (2004) 383-405.
[10] S.A. Kalogirou, Prediction oftlat-plate collector performance parameters using artificial neural networks, Solar Energy, 80 (2006) 248-259. [11] P. Biondi, L. Cicala, G. Farina, Performance analysis of solar air heaters of conventional design, Solar Energy, 41 (1988) 101-107. [12] S.A. Klien, Calculation of tlat plate loss coefficients, Solar Energy, 17 (1975) 79. [13] Yarun, Siddhartha, Thermal performance optimization of a tlat plate solar air heater using genetic algorithm, Applied Energy, 87 (2010) 1793-1799. [14] Yarun. Study of thermohydraulic performance of solar air heaters provided with artificially roughened duct. M. Tech. Thesis. AHEC IIT Roorkee June 2004.
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