1. Fi it Ti Th d i B d E l i l O ti i ti fFi it Ti Th d i B d E l i l O ti i ti fFinite Time Thermodynamics Based Ecological Optimization ofFinite Time Thermodynamics Based Ecological Optimization ofFinite Time Thermodynamics Based Ecological Optimization ofFinite Time Thermodynamics Based Ecological Optimization ofy gy g
I ibl Sti li d E i H t P U i G ti Al ithI ibl Sti li d E i H t P U i G ti Al ithIrreversible Stirling and Ericsson Heat Pumps Using Genetic AlgorithmIrreversible Stirling and Ericsson Heat Pumps Using Genetic AlgorithmIrreversible Stirling and Ericsson Heat Pumps Using Genetic AlgorithmIrreversible Stirling and Ericsson Heat Pumps Using Genetic Algorithm
Mishra M * Salhotra R1 Pathak A2Mishra M. , Salhotra R1., Pathak A2.
*Department of Mechanical & Industrial Engineering IIT Roorkee INDIADepartment of Mechanical & Industrial Engineering, IIT Roorkee, INDIA
1Department of Mechanical Engineering, NIT Raipur, INDIADepartment of Mechanical Engineering, NIT Raipur, INDIA
2G B P t E i i C ll P i INDIA2G.B. Pant Engineering College, Pauri, INDIAg g g , ,
ABSTRACTABSTRACT SYSTEM/ ENGINEABSTRACT SYSTEM/ ENGINE
The present work shows the ecological optimization and parametric study ofThe present work shows the ecological optimization and parametric study of
irreversible Stirling and Ericsson heat pump cycles where the external irreversibility isirreversible Stirling and Ericsson heat pump cycles where the external irreversibility is
due to finite temperature difference between working fluid and external reservoirsdue to finite temperature difference between working fluid and external reservoirs
while the internal irreversibilities are due to regenerative heat loss and other entropywhile the internal irreversibilities are due to regenerative heat loss and other entropy
i i hi h l Th l i l f i i i i d i hgenerations within the cycle. The ecological function is optimized with respect togenerations within the cycle. The ecological function is optimized with respect to
ki fl id t t (T d T ) ff ti f th t d thworking fluid temperatures (Th and Tc), effectiveness of the regenerator and theo g u d te pe atu es ( h a d c), e ect e ess o t e ege e ato a d t e
l ti Th i i f th i t hi hli ht th f G ti l ith tvolume ratio. The main aim of the paper is to highlight the use of Genetic algorithm top p g g g
optimize the cycles and to study the effect of different parametersoptimize the cycles and to study the effect of different parameters.p y y p
TT--s diagrams diagramEcological Optimization: TT--s diagrams diagramEcological Optimization:
Since in case of heat pumps the objective is to maximize the heating loadSince in case of heat pumps the objective is to maximize the heating loadSince in case of heat pumps the objective is to maximize the heating loadSince in case of heat pumps the objective is to maximize the heating load
and to minimize the entropy generation rates the objective function ofand to minimize the entropy generation rates the objective function of Generation of initial populationand to minimize the entropy generation rates, the objective function ofand to minimize the entropy generation rates, the objective function of Generation of initial population
ecological optimization is defined as:ecological optimization is defined as: Evaluation of fitness valueecological optimization is defined as:ecological optimization is defined as:
 
Evaluation of fitness value
s
 QQ Reproduction Crossover and Mutation
ers



 LH QQ
TRSTRE 
Reproduction, Crossover and Mutation
te




 LH QQ
TRSTRE i f l i
et




 0Hgen0H
TT
TRSTRE Generation of new population
me




0Hgen0H
TT
am
 ch TT Select individual having maximum fitness
ra
 ch Select individual having maximum fitness
ar
)QQ()QQ( QQ
pa
convergence satisfied ?)Q-Q()Q-Q( hLH
QQ HH
ep
yes
N = N +1
convergence satisfied ?)QQ(
=
)QQ(
=P chLH
Q
=
Q
=R
HH
H
ce
NG = NG+1
no
)++(
==P
)++(
RH
nc
no
)t+t+t(t RLHcycle )t+t+t(t RLHcycle
an
Number of generations N  N ?
)ttt(t RLHcycle )ttt(t RLHcycle
ma
no
Number of generations NG  NG,max ?
rm
no
Q
or
yes
QRH
fo
END
Q
=R=COP
HH
erf
END
==COPH
Pe
)Q-Q(P
COPH
P
Flowchart for a GeneticFlowchart for a Genetic
)Q-Q(P ch Flowchart for a GeneticFlowchart for a Genetic
QQ ch
Algorithm computation.Algorithm computation.g pg p
Effect of Th and TEffect of Th and Tc
Optimum solution by incorporating all the parametersOptimum solution by incorporating all the parameters
R T T v ε E/(C T ) T /T1000
R∆S Th Tc v εR E/(CLTL1) Th/Tc1000
800
0 999877 600 7593 599 7599 3 40258 0 796812 3 379332 1 00167
S
600
0.999877 600.7593 599.7599 3.40258 0.796812 3.379332 1.00167
TS
600
LT
400
L
CONCLUSION
400
U
CONCLUSION1
200
SU
CONCLUSION1
200
ES
8
0
RE
 Optimum solution is obtained when ROptimum solution is obtained when RS approaches to 1 i.e. reversibleS approaches to 1 i.e. reversible8
200
R
 Optimum solution is obtained when ROptimum solution is obtained when RS approaches to 1 i.e. reversibleS approaches to 1 i.e. reversible
ditiditi15
1
-200
Tc
R
condition.condition.15
S1
S4
S7
0
Tc
 The variation of ecological function with the effectiveness of regenerator and withThe variation of ecological function with the effectiveness of regenerator and with
S
S
S10
13
16
Th  The variation of ecological function with the effectiveness of regenerator and withThe variation of ecological function with the effectiveness of regenerator and with
S
S
S1
Th g gg g
volume ratio is observed which gives some local optima also but further thevolume ratio is observed which gives some local optima also but further thevolume ratio is observed which gives some local optima also, but further, thevolume ratio is observed which gives some local optima also, but further, the
optimum values can be made certain by some more number of trials in andoptimum values can be made certain by some more number of trials in andoptimum values can be made certain by some more number of trials in andoptimum values can be made certain by some more number of trials in and
d hd hEffect of effectiveness of the regenerator (ε ) around that zone.around that zone.6
Effect of effectiveness of the regenerator (εR) around that zone.around that zone.
 Th h th li it ti f GA l b l ti l ti t bTh h th li it ti f GA l b l ti l ti t b
6
 Though, as per the limitation of GA a global optimum solution cannot beThough, as per the limitation of GA a global optimum solution cannot be
5
g , p g pg , p g p
guaranteed but still for different combinations and increased number ofguaranteed but still for different combinations and increased number of
5
guaranteed, but still for different combinations and increased number ofguaranteed, but still for different combinations and increased number of
4
parameters as well as for complex objective functions finding the optimumparameters as well as for complex objective functions finding the optimum
4
L1
parameters as well as for complex objective functions, finding the optimumparameters as well as for complex objective functions, finding the optimum
3
TL
solution with GA is much easier compared to any other method especially withsolution with GA is much easier compared to any other method especially with3
LT
solution with GA is much easier compared to any other method, especially withsolution with GA is much easier compared to any other method, especially with
l l b d t h il l b d t h i2
CL
calculus based techniques.calculus based techniques.2
/C
qq
 This technique can further be more useful if the problem is of constrainedThis technique can further be more useful if the problem is of constrained1
E
 This technique can further be more useful if the problem is of constrainedThis technique can further be more useful if the problem is of constrained1 q pq p
optimisation with complex objective function and too many variablesoptimisation with complex objective function and too many variables0 optimisation with complex objective function and too many variablesoptimisation with complex objective function and too many variables0
where other techniques in general failwhere other techniques in general fail0 0 2 0 4 0 6 0 8 where other techniques in general fail.where other techniques in general fail.0 0.2 0.4 0.6 0.8
R
 Estimating the performance and finding the relative importance of differentEstimating the performance and finding the relative importance of differentR
 Estimating the performance and finding the relative importance of differentEstimating the performance and finding the relative importance of different
t th tht th thEff t f l ti ( ) parameters over the othersparameters over the othersEffect of volume ratio (v) pp
which can be used for optimum thermal design of such heat pumpswhich can be used for optimum thermal design of such heat pumps5
Effect of volume ratio (v)
which can be used for optimum thermal design of such heat pumps.which can be used for optimum thermal design of such heat pumps.
4 5
5
4.5
4
3 5
4
3.5
L1
3
TL
2.5
LT
2
2.5
C
2
E/C
1.5
E
1
0 5
1
0.5
0
0 2 4 60 2 4 6
vv