合成氨装置-五级闪蒸汽热交换器设计【机械类毕业-含CAD图纸】.zip
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合成氨装置-五级闪蒸汽热交换器设计【机械类毕业-含CAD图纸】.zip,机械类毕业-含CAD图纸,热交换器设计
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Many-objective optimization of shell and tube heat exchanger Bansi D. Raja a, R.L. Jhalab, Vivek Patelc, aDepartment of Mechanical Engineering, Indus University, Gujarat, India bDepartment of Mechanical Engineering, Gujarat Technological University, Gujarat, India cDepartment of Mechanical Engineering, Pandit Deendayal Petroleum University, Gujarat, India a r t i c l ei n f o Article history: Received 28 February 2017 Received in revised form 5 May 2017 Accepted 7 May 2017 Keywords: Shell and tube heat exchanger Many-objective optimization Effectiveness Total cost Pressure drop Number of entropy generation units a b s t r a c t This paper presents a rigorous investigation of many-objective (four-objective) optimization of shell and tube heat exchangers. Many-objective optimization problem is formed by considering maximization of effectiveness and minimization of total cost, pressure drop and number of entropy generation units of heat exchanger. Multi-objective heat transfer search (MOHTS) algorithm is proposed and applied to obtain a set of Pareto-optimal points. Many objective optimization results form a solution in a four dimensional hyper objective space and for visualization it is represented on a two dimension objective space. Thus, results of four-objective optimization are represented by six Pareto fronts in two dimension objective space. These six Pareto fronts are compared with their corresponding two-objective Pareto fronts. Different decision making approaches that include LINMAP, TOPSIS and fuzzy are used to select the fi nal optimal solution from the Pareto optimal set of the many-objective optimization. Finally, to reveal the level of confl ict between these objectives, the distribution of each design variables in their allowable range is also shown in two dimensional objective spaces. ? 2017 Published by Elsevier Ltd. 1. Introduction Heatexchangersareoneoftheimportantequipmentswhichser- vers the purpose of energy conservation through energy recovery. Out of various types of heat exchangers, one of the important types isshellandtubeheatexchanger(STHE)1.STHEsarewidelyusedin refi neries and petrochemical industries, power generation, refriger- ation, heating and air conditioning and medical applications. Design-optimization of STHE requires an integrated under- standing of thermodynamics, fl uid dynamics and cost estimation 1,2. Generally, objectives involved in the design optimization of STHE are thermodynamic (i.e. maximum effectiveness, minimum entropy generation rate, minimum pressure drop etc.) and eco- nomic (i.e. minimum cost). The conventional design approach for STHE is time-consuming, and does not guarantee an optimal solu- tion. Hence, application of evolutionary and swarm intelligence based algorithms has gained much attention in the design- optimization of STHE. Previously, several investigators had used different optimiza- tion techniques with different methodologies and objective func- tions to optimize STHE. However, their investigation is focused on single objective optimization or multi-objective (i.e. two or three objective) optimization. Mohanty 3 carried out the work for economic optimization of STHE. He used gravitational search algorithm as an optimization tool and focus on optimization of total annual cost of STHE. Wong et al. 4 used NSGA-II for the simultaneous optimization of capital cost and operating cost of STHE. Amin and Bazargan 5 considered increment in heat transfer rate and decrement in total cost of the heat exchange as objective functions for multi-objective optimization of STHE. They employ eleven decision variables and pressure drop constraint in their investigation with genetic algorithm. Hadidi and Nazari 6 employed biogeography-based optimization (BBO) algorithm for cost minimization of STHE. The authors solved three test case of STHE to demonstrate the effectiveness of BBO approach. Rao and patel 7 perform the multi-objective optimization of STHE with heat transfer rate and total cost of the heat exchanger as objective functions. The authors used modifi ed version of teaching learning based optimization (TLBO) algorithm as an optimization tool. Wen et al. 8 obtained a Pareto front between heat transfer rate and total cost of the helical baffl e STHE. The authors had consid- ered three optimization variables in their investigation and demonstrate the comparison between optimized and conventional STHE design. Guo et al. 9 applied fi eld synergy principle to opti- mized STHE design. The authors had considered fi eld synergy num- ber maximization as an objective function and employed genetic algorithm to solve optimization problem. Caputo et al. 10 presented a new mathematical model for manufacturing cost /10.1016/j.tsep.2017.05.003 2451-9049/? 2017 Published by Elsevier Ltd. Corresponding author. E-mailaddresses:bansi14.raja(B.D. Raja),ramdevsinh.jhala .in (R.L. Jhala), viveksaparia (V. Patel). Thermal Science and Engineering Progress 2 (2017) 87101 Contents lists available at ScienceDirect Thermal Science and Engineering Progress journal homepage: /locate/tsep estimation of STHE. The authors had carried out the parametric analysis to obtain the optimum length to diameter ratio of STHE. Hajabdollahi et al. 11 perform economic optimization of STHE with nine decision variables and genetic algorithm as an optimiza- tion tool. The authors also present the sensitivity of design variable on optimum value of objective function. Khosravi et al. 12 inves- tigates the performance of three different evolutionary algorithms for economic optimization of STHE. Sadeghzadeh et al. 13 demonstrate techno-economical optimization of STHE design with genetic and Particle swarm optimization algorithm. Yousefi et al. 14 implemented NSGA-II to for the optimization of STHE used for exhaust heat recovery in hybrid PV-diesel power systems. Hajabdollahi and Hajabdollahi 15 investigate the effect of nanoparticles in the thermo-economic optimization of STHE. You- sefi et al. 16 perform thermo-economic optimization of STHE for nanofl uid based heat recovery systems. Several other investigators 1725 perform the single objective or multi-objective (two or three objective) optimization of STHE for the thermodynamic, eco- nomic or thermo-economic objectives with different optimization strategies. Apart from STHE, effort had been put by researchers to optimize other types of heat exchangers also. For example, You- sefi et al. 2630 implemented evolutionary algorithms for the optimization of compact heat exchangers. Patel et al. 31,32 inves- tigate optimization of plate-fi n heat exchanger for thermo eco- nomicobjectives.Rajaetal.33performmulti-objective optimization of rotary regenerator. Thus, it is observed from the literature survey that researchers had carried out the economical optimization, thermodynamic opti- mization or thermo-economic optimization of STHE for single or multi-objective (two or three objective) consideration. However, many-objective optimization of the STHE yet not observed in the literature. Considering this fact, effort has been put in the present work to perform the many-objective (i.e. four-objective) optimiza- tion of STHE. Many-objective consideration results in more realis- tic design of STHE and end user can select any optimal design from it depending on his/her requirements. Furthermore, as an optimization tool, heat transfer search (HTS) algorithm 34 is implemented in the present work. Heat transfer search is a recently developed meta-heuristic algorithm based on the natural law of thermodynamics and heat transfer 34. In this work, a multi-objective variant of the heat transfer search (MOHTS) algorithm is presented to address many-objective opti- mization problem of STHE. The proposed algorithm uses a grid- based approach in order to keep diversity in the external archive. Pareto dominance is incorporated into the MOHTS algorithm in order to allow this heuristic to handle problems with several objec- tive functions. The qualities of the solution are computed based on the Pareto dominance notion in the proposed algorithm. So, the main contributions of the present work are (i) Many- objective optimization of STHE to maximize effectiveness and min- imize total cost, pressure drop and number of entropy generation units simultaneously. (ii) Introduce multi-objective variant of the heat transfer search (MOHTS) algorithm and employed it to solve many-objective optimization problem of STHE (iii) Compare the results of many-objective (i.e. four-objective) optimization with multi-objective (i.e. two-objective) optimization. (iv) Compare the underlying relationship of the decision variables between many-objective(i.e.four-objective)optimizationandmulti- objective (i.e. two-objective) optimization. (v) Select the fi nal opti- mal solution from the Pareto optimal set of the many-objective Nomenclature Aheat transfer area (m2) Attube outside heat transfer area (m2) Ao,cr fl ow area at or near the shell centerline for one cross- fl ow section (m2) Ao,w net fl ow area in one window section a,a1,a2 co-effi cient to obtain shell side Colburn factor adannual discount rate (%) bc baffl e cut ratio bs baffl e spacing ratio b,b1,b2 co-effi cient to calculate shell side friction factor Cp specifi c heat (J/kg K) CLtube layout constant CPTtube count constant Cinvinvestment cost ($) Copeoperating cost ($) Coannual operating cost ($/year) dtube diameter (m) Dsshell diameter (m) Fc fraction of the total number of tubes in the cross fl ow section ffriction factor Gmass velocity (kg/m2s) h heat transfer coeffi cient (W/m2K) jcolburn factor Kc, Ke entrance and exit pressure loss coeffi cient kthermal conductivity (W/m K) kelprice of electrical energy ($/kWh) Ltube length (m) Lbi, Lbo, Lbc inlet, outlet and center baffl e spacing (m) m mass fl ow rate (kg/s) Nb number of baffl e Ntnumber of tubes Nsnumber of entropy generation units npnumber of tube passes nyequipment life time (year) pttube pitch (m) PrPrandtl number Ppressure (Pa) DPpressure drop (Pa) ReReynolds number Rfsshell side fouling resistance (m2K/W) Rfttube side fouling resistance (m2K/W) rs, rlm co-effi cient to obtain shell side Colburn factor Qheat transfer rate (kW) Ttemperature (K) U overall heat transfer coeffi cient (W/m2K) V volumetric fl ow rate (m3/s) Greek symbols qdensity (kg/m3) ldynamic viscosity (Pa s) r ratio of minimum free fl ow area to frontal area gp overall pumping effi ciency eeffectiveness ?hours of operation per year Subscripts iinner or inlet oouter or outlet sshell side ttube side wwall 88B.D. Raja et al./Thermal Science and Engineering Progress 2 (2017) 87101 optimization with the help of LINMAP, TOPSIS and fuzzy decision making approaches. 2. Modeling formulation This section describes the thermal hydraulic modeling of STHE, objective function formulation, design variables and constraints involved in STHE design optimization. 2.1. Thermal and hydraulic formulation Detailed geometry of the STHE is shown in Fig. 1. In the present work,e-NTU approach is utilized to predict the performance of STHE. The STHE is running under a steady state, and the area dis- tribution and heat transfer coeffi cient are assumed uniform and constant. Furthermore, BellDelaware approach 1,35,36 is used to estimate shell side heat transfer and pressure drop. Table 1 shows the thermal and hydraulic model formulation of STHE. 2.2. Objective functions In the present work, many-objective optimization between con- fl icting thermodynamic and economic objectives is carried out. The considered thermodynamic and economic objectives are listed below. ? Thermodynamic objectives In the present work, three thermodynamic objectives are for- mulated by considering the effectiveness, total pressure drop and number of entropy generation units of the STHE. Here, it is desired to maximized the heat exchanger effectiveness and minimize the total pressure drop and entropy generation units. The heat exchan- ger effectiveness for selected E type TEMA shell and tube heat exchanger is calculated by 1,7,35 e 2 1 C 1 C2 ?0:5 coth NTU 2 1 C2 ?0:5 ?17 where, Cand NTU are heat capacity ratio and number of transfer unit of STHE respectively and given Table 1. Similarly, the total pressure drop and number of entropy gener- ation units of STHE is given by 35,37, DPtotalDPtDPs18 Ns Cp;s Cmax ln 1 ?e Cmin Cp;s 1 ? Tt;i Ts;i ? ? Rs Cp;s ln 1 ? DPs Ps;i ?hi Cp;t Cmax ln 1 e Cmin Cp;t Ts;i Tt;i? 1 ? ? Rt Cp;t ln 1 ? DPt Pt;i ?hi19 where,DPtandDPsare tube side and shell side pressure drop respectively. Likewise Tt,i, Ts,i, Pt,i, and Ps,iare the inlet temperature and pressure of the tube side and shell side fl uid respectively which are found by utilizing the thermal-hydraulic model of STHE given in Table 1. ? Economic objective An economic objective function is formulated by considering the total annual cost (Ctot) of the STHE which is composed by con- sidering the investment cost and operating cost of STHE and given by 7,24, Ctot Cinv Cope20 where, Cinvand Copeare the total investment cost and operating cost of the STHE and defi ned as 7,24, Cinv 8500 409A2 t 21 Cope X ny ti1 Co 1 adti 22 Co Wkels23 where, ad, ny, kel, and ? are the annual discount rate, equipment life time in year, price of electrical energy and hours of operation per year respectively. Likewise, W is the pumping power and obtained using the thermal-hydraulic model of STHE given in Table 1. In the present work, the MOHTS algorithm is used for many- objective optimization of a STHE. The many-objective problem can generally be described as follows 38, Maximise=Minimisef X f1X ;f2X ;f3X ;f4X X x1;x2;.xk? 24 where, f1(X), f2(X), f3(X), f4(X) are effectiveness, total cost, pressure drop and number of entropy generation units of STHE for many- objective consideration. Also, the constraints are stated as, giX ? 0;i 1;2;.;nc25 xj;min? xj? xj;max;j 1;2;.;nd26 where, nc and nd are number of constraints and number of decision variables respectively. Furthermore, static penalty method is used in the present work for constrain handling. A detail review on appli- cation of constraint handling method in evolutionary algorithm is available in the literature 39. 2.3. Design variables and constraints In the present work, six design variables which affect the per- formance of STHE are considered for optimization. These variables Fig. 1. Shell and tube heat exchanger geometry. B.D. Raja et al./Thermal Science and Engineering Progress 2 (2017) 8710189 includes: (i) tube diameter (ii) number of tubes (iii) tube length (iv) tube pitch ratio (v) baffl e cut ratio (vi) baffl e spacing ratio. The design parameters variation ranges are shown in Table 2. More- over, the objective functions which are based on the thermal- hydraulic model of Table 1 should satisfy the following constraints 35,36. 3 : 6Colburn factor for shell side U 1 1 hs ? ? Rfs doln do=di 2kw ? do di Rft1 ht ?7 Overall heat transfer co-effi cient A pLdoNt8Heat exchanger surface area C? Cp;min Cp;max 9Heat capacity ratio 1 NTU Cmin UA 10Number of transfer units DPt m2t 2qtA2t 4L dift 1 ?r 2 Kc ? ? 1 ?r2? Ke ? ? np 11Tube side pressure drop ft 0:00128 0:1143 Ret?0:311 12Tube side friction factor DPsNb? 1DPb;idcb NbDPw;id ?c 0 2DPb;id 1 Nr;cw Nr;cc ? cbcs DPb;id 4fsG2sNr;cc 2qs lsw ls ?0:25 ;DPw;id 20:6Nr;cwm2sNr;cc 2qsAo;crAo;w 8 f Xk Xnew k;i Xold j;i ? R2Xold j;i If f Xk f Xj ? ( ;If g ? gmax=CDF30 Xnew j;i Xold k;i ? riXold k;i If f Xj ? f Xk Xnew k;i Xold j;i ? riXold j;i If f Xk f Xj ? ( ;If g gmax=CDF31 where, j = 1,2, ., n, j k, k 2 (1,2, ., n) and i 2 (1,2, ., m). Further, k and i are randomly selected solution and design variables. R 2 0,0.3333 is the probability for selection of conduction phase; ri2 0,1 is a uniformly distributed random number and CDF is the conduction factor. 3.2. Convection phase This phase simulates convection heat transfer between system and surroundings. In convective heat transfer, surrounding tem- perature interact with mean temperature of the system. In the course of optimization with HTS algorithm, best solution is assumed as a surrounding while rest of the solutions compose the system. So, the design variable of the best solution interacts with the corresponding mean design variable of the population. In this phase, solutions are updated according to the following equations 34. Xnew j;i Xold j;i R Xs? XmsTCF32 TCF abs R ? riIf g ? gmax=COF TCF round 1 ri If g gmax=COF ? 33 where, j = 1, 2, ., n, i = 1, 2, ., m. Xsis the temperature of sur- rounding and Xmsis mean temperature of the system. R 2 0.3333,0.6666 is the probability for selection of convection phase; ri2 0,1 is a uniformly distributed random number and COF is the convection factor. 3.3. Radiation phase This phase simulate the radiation heat transfer within the sys- tem as well as between system and surrounding. Radiation heat transfer takes place between the system and surrounding as well as within the different part of the system also. In the course of opti- mization with HTS algorithm, this situation represents the update of any solution with the help of best solution or any other ran- domly selected solution. In this phase, the solutions are updated as given below 34. Xnew j;i Xold j;i R Xold k;i ? Xold j;i ? If f Xj ? f Xk Xnew j;i Xold j;i R Xold j;i ? Xold k;i ? If f Xk f Xj ? 8 : ;If g ? gmax=RDF 34 lXnew j;i Xold j;i riXold k;i ? Xold j;i ? If f Xj ? f Xk Xnew j;i Xold j;i riXold j;i ? Xold k;i ? If f Xk f Xj ? 8 : ;If g gmax=RDF 35 where, j = 1, 2, ., n, j k, ke(1, 2, ., n) and ie(1, 2, ., m). Fur- ther, k is a randomly selected solution. Re0.6666, 1 is the proba- bili
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