Multi-objective Optimization of Condensation Heat Transfer inside Horizontal Tube using Particle Swarm Optimization Technique

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1 Mult-objectve Optmzaton of Condensaton Heat Transfer nsde Horzontal Tube usng Partcle Swarm Optmzaton Technque Ravndra Kumar a *, P. Kumar b a* Research Scholar, Department of Mechancal Engneerng, Natonal Insttute of Technology, Jharkhand, Inda kumarravndramahto@gmal.com b Assocate Professor, Department of Mechancal Engneerng, Natonal Insttute of Technology, Jharkhand, Inda pkshmdme@gmal.com Abstract--In ths paper, heat transfer coeffcent and frctonal pressure drop durng condensaton of refrgerant nsde a smooth tube are formulated as a mult - optmzaton problem and solved usng partcle swarm optmzaton (PSO) algorthm. The objectve of ths work s to predct the optmum values of refrgerant mass flux and vapor qualty for whch there s a maxmum condensaton heat transfer and mnmum flow frctonal pressure gradent nsde tube. The PSO algorthm was run for mass flux and vapor qualty range from 100 kg/m 2 -s to 250 kg/m 2 -s and 0.1 to 0.8 respectvely. The optmum refrgerant mass flux and vapor qualty predcted by partcle swarm optmzaton algorthm are kg/m 2 -s and 0.79 respectvely. Keyword- Condensaton, Frctonal pressure gradent, Heat transfer coeffcent, Partcle swarm optmzaton I. INTRODUCTION Over the years, a number of expermental works have been done on condensaton heat transfer and pressure drop for dfferent refrgerants and tube geometres. The effect of desgn and operatng parameters on heat transfer coeffcent and pressure has been nvestgated by researchers. Heat transfer coeffcent and pressure drop were determned usng several emprcal correlatons. A lttle attenton has been gven on the optmzaton of heat transfer and pressure drop durng the condensaton of the refrgerant nsde plan tube. The heat transfer coeffcent and pressure drop depend on many factors such as mass flux, vapour qualty and propertes of refrgerant, tube s geometry and orentaton. The heat transfer coeffcent and pressure drop are found to ncrease wth the ncreasng mass flux and vapor qualty of refrgerant. The condensaton heat transfer nsde tube s accomplshed by pump work. The pump work s found to ncrease wth pressure drop along the tube durng condensaton. The desgn and operatng parameters are requred to be optmzed to acheve maxmum heat transfer and mnmum pressure drop. Exstng lterature reveals that many researchers have used dfferent optmzaton methods for the desgn optmzaton of heat exchangers. Artfcal neural network (ANN) and genetc algorthm (GA) used to develop the emprcal correlatons for heat transfer characterstcs durng the downward flow of R-134a nsde smooth and corrugated tubes [1, 2]. Heat transfer rate and pressure drop n shell and tube heat exchanger was optmzed usng genetc algorthm [3]. Genetc and partcle swarm optmzaton (PSO) algorthms were employed for thermo economc optmzaton of shell and tube condenser [4]. Teachng-learnng based optmzaton (TLBO) technque was used to optmze the cost, weght, effectve of plate fn heat exchanger [5]. Effectveness and cost optmzaton of the plate fn exchanger was performed usng modfed teachng-learnng based optmzaton technque [6]. Heat transfer coeffcent optmzaton durng condensaton of refrgerant nsde smooth horzontal tube was done through TLBO [7]. The objectve of the present paper s to predct the optmum value of refrgerant mass flux and vapor qualty for whch there s maxmum heat transfer coeffcent and mnmum pressure drop durng the condensaton of R- 245fa nsde the plan horzontal tube usng partcle swarm optmzaton method. DOI: /jet/2017/v91/ Vol 9 No 2 Apr-May

2 II. PARTICLE SWARM OPTIMIZATION TECHNIUQE (PSO) Partcle swarm optmzaton (PSO) s a populaton based evolutonary optmzaton method proposed by Kennedy [8]. Fgure 1 shows the flow chart of PSO. In partcle swarm optmzaton algorthm the populaton s randomly ntalzed and moves n randomly selected drectons through the search space and keeps record of the best prevous poston of tself and ts neghbors as well. The populaton updates after each generaton based on the best locaton acheved by a partcle, Pbest, and other best locaton acheved by any other partcle among the populaton, gbest, so far. In partcle swarm optmzaton the populaton s updated after each generaton by changng the velocty and poston of each partcle towards Pbest and gbest. The velocty and poston are updated accordng to equatons 1 and 2. t+1 t t t t t v = w v +c 1rand 1[gbest -x ]+c 2rand 2[gbest -x ](1) t+1 t t+1 x = x +v (2) Where, = populaton ndex t = generaton t x = poston of th partcle. t v = velocty of th partcle. t Pbest = best prevous poston of partcle. t gbest = the best partcle among all partcles n a swarm. rand 1, rand 2 are two dfferent random numbers n the range [0 1] Local and global search s balanced by nerta weght w. The hgh nerta weghts permt travellng the large desgn space whle small nerta weghts permt travellng only nearby regon of the desgn space by partcles. The value of nerta weghts s consdered n the range [ ]. The optmum value of nerta weghts mproves the performance of the algorthm. The acceleraton coeffcents c 1 and c 2 are recognzed as cogntve and socal parameters. The cogntve and socal parameters pull each partcle towards Pbest and gbest respectvely. Small value of constants allows partcles to travel far away from the target regons before beng pulled back, whle hgh value of constants results n sudden movement towards the target regon [9]. Bergh F and Engelbrecht [10] have reported effect of c 1, c 2, and w, on varous standard functons. In the present paper, partcle swarm optmzaton algorthm was run consderng the followng parameters: Number of partcles = 50 Number f teraton = 100 Cogntve parameter (c 1 ) = 2 Socal parameter (c 2 ) = 2 Inerta weghts range [ ] III. PROBLEM FORMULATION FOR MULTI OBJECTIVE OPTIMIZATION For optmum performance of the condenser, the heat transfer coeffcent and pressure drop along the flow are requred to be optmzed. Mult-objectve optmzaton of maxmzaton and mnmzaton functons together can be done consderng a sngle objectve functon, as represented by Eq. 3. ω f 1(z) (1-ω) f 2(z) maxf(z) = - (3) * * f1 f2 Where, combned objectve functon f (z) s a functon of two functons f 1 () z and f 2 () z to bemaxmzed and * f 1 * f2 are the maxmum and mnmum values of () 1 f z and f () 2 mnmzed respectvely., sngle objectve problem separately. Here ω s the weght assgned to objectve functons. z when solved, as a DOI: /jet/2017/v91/ Vol 9 No 2 Apr-May

3 Fg. 1. Flow chart of partcle swarm optmzaton algorthm. IV. EXPERIMENTAL SYSTEM The partcle swarm optmzaton algorthm results were valdated wth expermental data obtaned from the expermental system shown n Fgure 2. The expermental system s a concentrc double ppe heat exchanger havng two test sectons of length one meter each. The nner and outer dameters of nner tube are 9.4 mm, mmand that of the outer tube are 43 mm, 50 mm. The experments were carred out accordng to the parameters shown n Table 1. A multchannel data acquston system was ncorporated wth expermental system for data recordng. R-245fa vapor and coolng water were flown n counter drecton through the nner and outer tubes nsde the test sectons. The refrgerant vapor comng from the test secton 2 flows through the post condenser where the entre amount of refrgerant vapour converted nto lqud. Ths entre lqud refrgerant flows through the evaporator, made of stanless steel tube havng nsde dameter, outsde dameter and length 16 mm, 17.5 mm and 3.6 m respectvely. A step-down transformer ncorporated wth evaporator controls the vapor qualty of refrgerant. A coroles mass flow meter was connected to control the refrgerant mass flow rate. Four T-type thermocouples were fxed at each sx axal locatons to quantty the accurate temperature of outer wall of the nner tube. The refrgerant pressure at the nlet and outlet of each test secton was measured by pressure gauge. The pressure dfference across the test secton was measured usng a pressure transducer. Condenser pressure was taken as the average refrgerant pressure of both test sectons. Refrgerant propertes were taken accordng to average condenser pressure. DOI: /jet/2017/v91/ Vol 9 No 2 Apr-May

4 24 DT1 DT2 PT1 PT2 PT3 P1 8 PT4 P2 DG1 DG V2 19 V V9 6 7 V10 P4 P S V8 V5 V4 9 V V7 V Fg. 2. Schematc dagram of expermental system. 1 Test-secton 9 Post-condenser 17 Voltmeter 25 Data acquston system 2 Outer tube 10 Corols mass flow meter 18 Power analyzerp Pressure gauge 3 Flanged jont 11 By-pass valve 19 Cable DG dfferental pressure 4 Vsual secton 12 Pump 20 Transformer DT pressure -transducer 5 Thermocouple 13 Frequency controller 21 Varac 6 Thermople 14 HP cut-out 22 Flter 7 Turbne flow- meter 15 Electrcal solator 23 Chargng valve 8 24 V DC power supply 16 Evaporator 24 Purge valve Table 1. Operatng parameters Parameters Value Refrgerant mass flux (kg/m 2 s) Heat flux (kw/m 2 ) Condensng pressure (kpa) 220 Condensng temperature ( 0 C) Vapor qualty V. DATA COLLECTION AND DATA REDUCTION The expermentaton was carryout for the condensaton of R-245fa wth refrgerant mass fluxes 100, 150, 200 and 250 kg/m 2 -s and vapor qualty range from 0.1 to 0.8. The vapor qualty at entry and ext of each test secton was calculated through energy balance along the test condenser and evaporator. The test secton vapor qualty was consdered as the average of ts entry and ext values. The heat transfer coeffcent of each test secton was calculated by applyng energy balance between refrgerant vapor and water usng Eq. 4. The overall heat transfer coeffcent for each test run was consdered as the average of two test sectons. Π D l (T-T s wo) D ln(d o/d) h = - 0 m 2 k w wc pw(tc,o-t c,n) -1 (4) The two phase flow frctonal pressure drop durng condensaton of R-245fa nsde a plan horzontal tube was calculated by Eq. 5. ΔP fr = ΔPtot - ΔP (5) mom Where ΔP fr, ΔP tot and ΔP mom are frctonal pressure drop, total pressure drop measured by pressure gauge and momentum pressure drop respectvely. The calculaton of the momentum pressure drop was made accordng to Eq.6. DOI: /jet/2017/v91/ Vol 9 No 2 Apr-May

5 (1-x) x (1-x) x ΔP mom= G (6) ρ L(1-α) ρgα ρ(1-α) out L ρgαn Here α s the vod fracton calculated as suggested by Stener. VI. RESULTS AND DISCUSSION A. Heat transfer coeffcent Fgure 3 represents the effect of refrgerant mass flux and vapor qualty on the heat transfer coeffcent durng condensaton of R-245fa nsde a plan horzontal tube. As could be seen from the fgure, heat transfer coeffcent ncreases wth rse n vapor qualty and mass flux. The maxmum heat transfer coeffcent 3.27kW/m 2 K was reported at mass flux 250 kg/m 2 s and vapor qualty 0.8. The rse n heat transfer coeffcent s due to hgh turbulence nduced n the condensate flm at hgh mass flux and low thermal resstance offered to condensaton heat transfer coeffcent by thn vapor flm on tube wall at hgh vapour qualty [11, 12]. Expermental data of heat transfer coeffcent were compared wth several well-known correlatons to predct the heat transfer coeffcent durng condensaton of R-245fa nsde a smooth horzontal tube. The Dobson s correlaton [13] predcted the present heat transfer coeffcent data wthn an error range of ± 20% as shown n Fgure 4. The Dobson s correlaton of heat transfer coeffcent for plan flow nsde a horzontal tube s gven by Eq k 2.22 h = Re Pr 1+ (7) 0.89 D Xtt Where Xtt s known Martnell parameter computed as accordng to equaton 8. X = tt x ρ G μ L x ρl μ G (8) Fg. 3. Effect of mass flux and vapor qualty on the heat transfer coeffcent. DOI: /jet/2017/v91/ Vol 9 No 2 Apr-May

6 Fg. 4. Comparson of expermental heat transfer coeffcent wth that predcted by Dobson s correlaton. B. Frctonal pressure drop Fgure 5 shows the effect of refrgerant mass flux and vapor qualty on the frctonal pressure drop along the flow durng condensaton of R-245fa nsde aplan horzontal tube. As could be seen from the fgure, frctonal pressure drop ncreases wth mass flux and vapor qualty of refrgerant. Increasng mass flux produces greater two-phase velocty resultng n a greater frctonal pressure drop. Ths effect s more evdent n the hgh vapor qualty regon where the pattern changes nto fully developed annular regon flow. The ncrease n frctonal pressure drop wth vapor qualty at any mass flux s due to changes n flow pattern wth ncreasng vapor qualty. Fg. 5. Varaton n frctonal pressure drop wth mass flux and vapor qualty. The present frctonal pressure drop data were compared wth some well-known two phase flow frctonal pressure drop correlatons [14, 15, 16]. Fg. 6 represents the comparson of expermental frctonal pressure drop wth that of predcted by above mentoned correlatons. As could be observed from the fgure all correlatons predcted the data beyond an error range of +15%. DOI: /jet/2017/v91/ Vol 9 No 2 Apr-May

7 Fg. 6. Comparson of expermental frctonal wth dfferent correlatons. The present expermental data were used to develop an emprcal correlaton based on Cavalln [17] to predct frctonal pressure drop durng condensaton of R-245fa nsde plan horzontal tube. The Eq. 9 s the modfed correlaton of frctonal pressure drop for condensaton nsde a smooth horzontal tube. The expermental data predcted by Eq. 9 are wthn an error band of -5 % to +15%, as shown n Fgure 7. 2 dp 2 G = φ LO 2 f LO (9) dz D ρ Where, f L G D f LO = μ l (10) 2 = Z F H (11) LO 2 2 ρ L μ G Z = (1-x) +x ρg μ L F = x (1-x) (13) 0.2 (12) ρ μ μ G ρg μl μl L G H = 1- (14) Fg. 7. Comparson of expermental frctonal pressure drop wth that predcted by Eq. 9 DOI: /jet/2017/v91/ Vol 9 No 2 Apr-May

8 C. Valdaton of partcle swarm optmzaton algorthm (PSO) The partcle swarm optmzaton algorthm was executed for the maxmzaton of heat transfer coeffcent durng condensaton of R-245fa nsde a smooth horzontal tube. The Eq. 7 was consdered as a maxmzaton objectve functon. The algorthm was run ntally executed at each mass flux 100, 150, 200, and 250 kg/m 2 s. Vapor qualty of refrgerant was vared from 0.1 to 0.8 for each mass flux. The optmzed results were compared wth expermental, as shown n Table 2. The PSO algorthm was agan run for the same maxmzaton functon wth mass flux and vapor qualty varyng between 100 to 250 kg/m 2 s and 0.1 to 0.8 respectvely. Table 3 shows the comparson of PSO predcted and expermental. As could be observed from tables 3 and 4, PSO predcted values are very close to the expermental. Table 2. Comparson between PSO and expermental results. Mass flux Vapour qualty Heat transfer coeffcent (kw/m 2 K) (kg/m 2 s) Expermental PSO Expermental PSO Table 3. Comparson of optmzed results Parameters Expermental PSO Mass flux of R-245fa (kg/m 2 s) Vapor qualty Optmum heat transfer coeffcent (kw/m 2 K) Fg. 8. Varaton n optmum vapor qualty wth mass flux. D. Optmzaton of heat transfer coeffcent and frctonal pressure drop A sngle mult-objectve optmzaton problem was formulated as accordng to Eq. 3 for the maxmzaton of heat transfer coeffcent and mnmzaton of fractonal pressure drop. The PSO algorthm was ntally for mult-objectve optmzaton problem at constant refrgerant mass flux between 100 kg/m 2 s to 250 kg/m 2 s wth step sze 1 and vapor qualty was vared from 0.1 to 0.8 for each mass flux. Fg. 8 represents the optmzed refrgerant vapor qualty for each mass flux. As could be seen, up to the mass flux 139 kg/m 2 s optmzed vapor qualty predcted by PSO s And as the mass flux ncreased beyond 139 kg/m 2 s optmzed vapor qualty went on decreasng and became constant (0.1) on and after 200 kg/m 2 s. The algorthm was run agan consderng the mass flux and vapour qualty as varables. The mass flux and vapour qualty were vared from DOI: /jet/2017/v91/ Vol 9 No 2 Apr-May

9 100 to 250 kg/m 2 s and 0.1 to 0.8 respectvely. The optmum refrgerant mass flux and vapor qualty predcted by PSO was kg/m 2 -s and 0.79 respectvely. VII. CONCLUSIONS On the bass of above results followng nferences may be drawn pertanng to the condensaton heat transfer and frctonal pressure drop durng condensaton of R-245fa nsde a smooth horzontal tube and ther optmzaton usng partcle swarm optmzaton technque. 1. Refrgerant mass flux and vapor qualty have greater nfluence on the heat transfer coeffcent and frctonal pressure drop durng condensaton. Heat transfer coeffcent and frctonal pressure drop along the flow nsde tube ncrease wth ncreasng mass flux and vapor qualty. 2. The partcle swarm optmzaton technque was effectvely appled to mult-objectve optmzaton of heat transfer coeffcent and frctonal pressure drop. Refrgerant mass flux below 140 kg/m 2 s can provde maxmum heat transfer and mnmum pressured drop durng condensaton nsde plan tubes. The values of optmum mass flux and vapor qualty predcted by partcle swarm optmzaton are kg/m 2 s and 0.79 respectvely. 3. The partcle swarm optmzaton algorthm may also be used for the mult-objectve optmzaton of desgn and operatng parameters durng swrlng flow condensaton of refrgerants nsde tubes. LIST OF SYMBLOS C P Specfc heat(kj / kg K) DTube dameter (mm) G Mass flux (kg/m 2.s) h Heat transfer coeffcent (kw / m 2 K) kthermal conductvty (W / m K) x Vapor qualty µvscosty (µpa-s) ρdensty (kg/m 3 ) DIMENSIONLESS NUMBERS Re Reynolds number Pr Prandtl number Xtt Martnell parameter SUBSCRIPT L lqud G gas LO lqud only B bottom R rght nner o outer REFERENCES [1] M. Balclar et al., Investgaton of emprcal correlaton on the determnaton of condensaton heat transfer characterstcs durng downward annular flow of R-134a nsde a vertcal smooth tube usng artfcal ntellgence algorthm, Journal of Mechancal Scence and Technology, Vol.25, pp , [2] M. Balclar et al., A numercal correlaton development study for the determnaton of Nusselt number durng bolng and condensaton of R-134a nsde smooth and corrugated tube, Internatonal Communcaton n Heat and Mass Transfer, Vol. 48, pp , [3] S. Sepher, H Hajabdollah, Mult-objectve optmzaton of shell and tube heat exchanger, Appled Thermal Engneerng, Vol. 30, pp , [4] P. Ahmad et al., Thermo economc optmzaton of a shell and tube condenser usng both genetc algorthm and partcle swarm optmzaton technque, Internatonal journal of refrgeraton, Vol. 34, pp , [5] V. Patel, V. Savsan, Optmzaton of a plate-fn heat exchanger desgn through an mproved mult-objectve teachng-learnng based optmzaton algorthm, Chemcal Engneerng Research and Desgn, Vol. 92, pp , 2014 [6] R.V. Rao, V. Patel, Mult-objectve optmzaton of heat exchangers usng a modfed teachng learnng based optmzaton algorthm, Appled Mathematcal Modelng, Vol. 37, pp , [7] Ravndra Kumar, P. Kumar, Optmzaton of heat transfer coeffcent durng condensaton of refrgerant nsde plan horzontal tube usng teachng-learnng based optmzaton algorthm, Indan journal of scence and technology, Vol 9(38) October [8] J. Kennedy, R. Eberhart, Partcle swarm optmzaton, n: Proceedngs of the IEEE Internatonal Conference on Neural Networks, Perth, Australa, pp , [9] Y. Dong et al., An applcaton of swarm optmzaton to nonlnear programmng, Computer and Mathematcs wth Applcatons, Vol. 49, , DOI: /jet/2017/v91/ Vol 9 No 2 Apr-May

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