合成氨裝置-五級(jí)閃蒸汽熱交換器設(shè)計(jì)含10張CAD圖

合成氨裝置-五級(jí)閃蒸汽熱交換器設(shè)計(jì)含10張CAD圖,合成氨,裝置,閃蒸,熱交換器,設(shè)計(jì),10,cad tube India Many-objective optimization Effectiveness Total cost objective space. These six Pareto fronts are compared with their corresponding two-objective Pareto through one [1].STHEs power 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 as objective teaching learning based optimization (TLBO) algorithm as an optimization tool. Wen et al. [8] obtained a Pareto front between heat transfer and total cost of the helical baffle 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 field synergy principle to opti- mized STHE design. The authors had considered field 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 ? Corresponding author. E-mail addresses: bansi14.raja@ (B.D. Raja), ramdevsinh.jhala@ marwadieducation.edu.in (R.L. Jhala), viveksaparia@ (V. Patel). Thermal Science and Engineering Progress 2 (2017) 87–101 Contents lists available Thermal Science and Engin STHE is time-consuming, and does not guarantee an optimal solu- tion. Hence, application of evolutionary and swarm intelligence heat transfer rate and total cost of the heat exchanger functions. The authors used modified version of http://dx.doi.org/10.1016/j.tsep.2017.05.003 2451-9049/C211 2017 Published by Elsevier Ltd. rate ation, heating and air conditioning and medical applications. Design-optimization of STHE requires an integrated under- standing of thermodynamics, fluid 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 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 Pressure drop Number of entropy generation units 1. Introduction Heatexchangersareoneoftheimportant vers the purpose of energy conservation Out of various types of heat exchangers, isshellandtubeheatexchanger(STHE) refineriesandpetrochemicalindustries, fronts. Different decision making approaches that include LINMAP, TOPSIS and fuzzy are used to select the final optimal solution from the Pareto optimal set of the many-objective optimization. Finally, to reveal the level of conflict between these objectives, the distribution of each design variables in their allowable range is also shown in two dimensional objective spaces. C211 2017 Published by Elsevier Ltd. equipmentswhichser- energy recovery. of the important types arewidelyusedin generation,refriger- 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] consideredincrement in heat transfer rate and decrement in total cost of the heat exchange as objective Keywords: Shell and tube heat exchanger 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 Many-objective optimization of shell and Bansi D. Raja a , R.L. Jhala b , Vivek Patel c,? a Department of Mechanical Engineering, Indus University, Gujarat, India b Department of Mechanical Engineering, Gujarat Technological University, Gujarat, India c Department of Mechanical Engineering, Pandit Deendayal Petroleum University, Gujarat, article info Article history: Received 28 February 2017 Received in revised form 5 May 2017 Accepted 7 May 2017 abstract This paper presents a rigorous tube heat exchangers. Many-objective effectiveness and minimization heat exchanger. Multi-objectiv obtain a set of Pareto-optimal journal homepage: www.else heat exchanger investigation of many-objective (four-objective) optimization of shell and optimization problem is formed by considering maximization of of total cost, pressure drop and number of entropy generation units of e heat transfer search (MOHTS) algorithm is proposed and applied to points. Many objective optimization results form a solution in a four at ScienceDirect eering Progress Engineering Nomenclature A heat transfer area (m 2 ) A t tube outside heat transfer area (m 2 ) A o,cr flow area at or near the shell centerline for one cross- flow section (m 2 ) A o,w net flow area in one window section a,a 1 ,a 2 co-efficient to obtain shell side Colburn factor a d annual discount rate (%) bc baffle cut ratio bs baffle spacing ratio b,b 1 ,b 2 co-efficient to calculate shell side friction factor C p specific heat (J/kg K) CL tube layout constant CPT tube count constant C inv investment cost ($) C ope operating cost ($) C o annual operating cost ($/year) d tube diameter (m) D s shell diameter (m) F c fraction of the total number of tubes in the cross flow section f friction factor G mass velocity (kg/m 2 s) h heat transfer coefficient (W/m 2 K) j colburn factor K c ,K e entrance and exit pressure loss coefficient k thermal conductivity (W/m K) 88 B.D. Raja et al./Thermal Science and 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 nanofluid based heat recovery systems. Several other investigators [17–25] 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. [26–30] implemented evolutionary algorithms for the optimization of compact heat exchangers. Patel et al. [31,32] inves- tigate optimization of plate-fin heat exchanger for thermo eco- nomic objectives. Raja et al. [33] perform multi-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, k el price of electrical energy ($/kWh) L tube length (m) L bi , L bo , L bc inlet, outlet and center baffle spacing (m) m mass flow rate (kg/s) N b number of baffle N t number of tubes Ns number of entropy generation units n p number of tube passes ny equipment life time (year) p t tube pitch (m) Pr Prandtl number P pressure (Pa) DP pressure drop (Pa) Re Reynolds number R fs shell side fouling resistance (m 2 K/W) R ft tube side fouling resistance (m 2 K/W) r s , r lm co-efficient to obtain shell side Colburn factor Q heat transfer rate (kW) T temperature (K) U overall heat transfer coefficient (W/m 2 K) V volumetric flow rate (m 3 /s) Greek symbols q density (kg/m 3 ) l dynamic viscosity (Pa s) r ratio of minimum free flow area to frontal area g p overall pumping efficiency e effectiveness ?? hours of operation per year Subscripts Progress 2 (2017) 87–101 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) optimization and multi- objective (i.e. two-objective) optimization. (v) Select the final opti- mal solution from the Pareto optimal set of the many-objective i inner or inlet o outer or outlet s shell side t tube side w wall 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- where, DP t and DP s are tube side and shell side pressure drop respectively. Likewise T t,i , T s,i , P t,i , and P s,i are the inlet temperature and pressure of the tube side and shell side fluid respectively which are found by utilizing the thermal-hydraulic model of STHE given in Table 1. C15 Economic objective An economic objective function is formulated by considering the total annual cost (C tot ) of the STHE which is composed by con- sidering the investment cost and operating cost of STHE and given by [7,24], C tot ? C inv t C ope e20T where, C inv and C ope are the total investment cost and operating cost B.D. Raja et al./Thermal Science and Engineering Progress 2 (2017) 87–101 89 tribution and heat transfer coefficient are assumed uniform and constant. Furthermore, Bell–Delaware 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- flicting thermodynamic and economic objectives is carried out. The considered thermodynamic and economic objectives are listed below. C15 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 1t CeTt1 t C 2 C16C17 0:5 coth NTU 2 1t C 2 C16C17 0:5 C18C19e17T where, C ? and 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], DP total ? DP t tDP s e18T N s ? Cp;s Cmax ln 1C0e C min Cp;s 1C0 T t;i T s;i C16C17C16C17 C0 Rs Cp;s ln 1C0 DPs P s;i C16C17hi t C p;t Cmax ln 1 te C min Cp;t T s;i T t;i C01 C16C17C16C17 C0 Rt Cp;t ln 1 C0 DPt P t;i C16C17 e19T Fig. 1. Shell and tube heat of the STHE and defined as [7,24], C inv ? 8500 t409A 2 t e21T C ope ? X ny ti?1 C o 1t a d eT ti e22T C o ? Wk el s e23T where, a d , ny, k el , 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=Minimise f XeT?f 1 XeT;f 2 XeT;f 3 XeT;f 4 XeT X ? x 1 ;x 2 ; ...x k ?C138 e24T where, f 1 (X), f 2 (X), f 3 (X), f 4 (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, g i XeTC200; i ? 1;2; ...;nc e25T x j;min C20 x j C20 x j;max ; j ? 1;2; ...;nd e26T 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 exchanger geometry. Table 1 Modeling equations for STHE [7.24]. Equations h t ? 0:024 kt d i Re 0:8 t Pr 0:4 t l t l w C16C17 0:14 For2500 C20 Ret C20 1:24C2 10 5 Re t ? mtd i l t At A t ? 0:25pd 2 i N t =n p 3 Tube side cross section area per pass ?????????????p 2q t A t i f ? 0:00128 t 0:1143 Re t eT C00:311 DP b;id ? 4f s G 2 s Nr;cc 2q l sw l C16C17 0:25 ; DP w;id ? 2t0:6Nr;cweTm 2 s Nr;cc 2q A A : 90 B.D. Raja et al./Thermal Science and Engineering includes: (i) tube diameter (ii) number of tubes (iii) tube length (iv) s s s o;cr o;w c b ? 1 c 0 ? exp C01:33 1tr s eTr s lm C0C1 ; c s ? L b;c L b;o C16C17 1:8 t L b;c L b;i C16C17 1:8 ( f s ? b 1 1:33 p t =do C16C17 b Re s eT b2 W ? DPtVt g p t DPsVs g p C16C17 t DP s ? N b C0 1eTDP b;id c b t N b DP w;id C2C3 c 0 t 2DP b;id 1 t Nr;cw Nr;cc C16C17 c b c s 8 > > > > : U ? 1 1 hs C0C1 tR fs t do ln do=d i eT 2kw C0C1 t do d i R ft t 1 h t C16C17 A ? pLd o N t C C3 ? C p;min Cp;max 1 NTU ? C min UA DP t ? m 2 t 2 4L d f t t 1C0r 2 tK c C0C1 C0 1C0r 2 C0 K e C0C1 C16C17 n p tube pitch ratio (v) baffle cut ratio (vi) baffle 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 < L D s < 12 e27T DP s < DP s;max e28T DP t fX k eT lX new ? X old t r X old C0 X old If f X C0C1 > fXeT > fX j C0C1 > : ; If g > g max =RDF e35T where, j =1,2,..., n, j–k, k e (1, 2, ..., n) and i e (1, 2, ..., m). Fur- where,j= 1, 2, ..., n, i = 1, 2, ..., m. X s is the temperature of sur- rounding and X ms is mean temperature of the system. R 2 [0.3333,0.6666] is the probability for selection of convection phase; r i 2 [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]. X new j;i ? X old j;i t RX old k;i C0 X old j;i C16C17 If f X j C0C1 > fX k eT X new j;i ? X old j;i t RX old j;i C0 X old k;i C16C17 If f X k eT> fX j C0C1 8 > : ; If g C20 g max =RDF e34T C16C17 8 j;i k;i k;i X new k;i ? X old j;i C0 r i X old j;i If f X k eT> fX j C0C1 ; If g > g max =CDF e31T 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; r i 2 [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]. X new j;i ? X old j;i t RX s C0 X ms TCFeT e32T TCF ? abs R C0 r i eTIf g C20 g max =COF TCF ? round 1t r i eTIf g > g max =COF C26 e33T conduction phase, solutions are updated according to the following equations [34]. X new j;i ? X old k;i C0 R 2 X old k;i If f X j C0C1 > fX k eT X new k;i ? X old j;i C0 R 2 X old j;i If f X k eT> fX j C0C1 ( ; If g C20 g max =CDF e30T C0C1( B.D. Raja et al./Thermal Science and ther, k is a randomly selected solution. R e [0.6666, 1] is the proba- bility for selection of radiation phase; r i e [0, 1] is a uniformly distributed random number and RDF is the radiation factor. tion of STHE is taken from the Ref. [7,24]. So, the objectives are to find out the design parameter of STHE (i.e. tube diameter, num- ber of tubes, length of tubes, tube pith ratio, baffle cut ratio and baffle spacing ratio) for maximum effectiveness and minimum total cost, pressure drop and number of entropy generation units. 6. Results and discussion Initially, single objective optimization of each objective function is carried out to identify the behaviour of objective function with respect to each other. The control parameters of HTS and MOHTS algorithm used in the present investigation are listed in Table 3. The results of the single objective optimization are demonstrated in Table 4. It is observed form the result that when effectiveness is maximum (i.e. maximum effectiveness consideration) at that time other three objective functions are not at their optimum value. Similar situation is observed when we consider other objec- tives (i.e. total cost, pressure drop and number of entropy genera-