Exergetic Optimization of Shell-and-Tube Heat

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Exergetic Optimization of Shell-and-Tube Heat Exchangers Using NSGA-II a

b

Hassan Hajabdollahi , Pouria Ahmadi & Ibrahim Dincer a

b

Young Researchers Club, Islamic Azad University, Zahedan Branch, Iran

b

Department of Mechanical Engineering, University of Ontario Institute of Technology (UOIT), Oshawa, Ontario, Canada Available online: 17 Oct 2011

To cite this article: Hassan Hajabdollahi, Pouria Ahmadi & Ibrahim Dincer (2012): Exergetic Optimization of Shell-and-Tube Heat Exchangers Using NSGA-II, Heat Transfer Engineering, 33:7, 618-628 To link to this article: http://dx.doi.org/10.1080/01457632.2012.630266

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Heat Transfer Engineering, 33(7):618–628, 2012 C Taylor and Francis Group, LLC Copyright ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457632.2012.630266

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Exergetic Optimization of Shell-and-Tube Heat Exchangers Using NSGA-II HASSAN HAJABDOLLAHI,1 POURIA AHMADI,2 and IBRAHIM DINCER2 1 2

Young Researchers Club, Islamic Azad University, Zahedan Branch, Iran Department of Mechanical Engineering, University of Ontario Institute of Technology (UOIT), Oshawa, Ontario, Canada

In this article, a multi-objective exergy-based optimization through a genetic algorithm method is conducted to study and improve the performance of shell-and-tube type heat recovery heat exchangers, by considering two key parameters, such as exergy efficiency and cost. The total cost includes the capital investment for equipment (heat exchanger surface area) and operating cost (energy expenditures related to pumping). The design parameters of this study are chosen as tube arrangement, tube diameters, tube pitch ratio, tube length, tube number, baffle spacing ratio, and baffle cut ratio. In addition, for optimal design of a shell-and-tube heat exchanger, the ε − NT U method and Bell–Delaware procedure are followed to estimate its pressure drop and heat transfer coefficient. A fast and elitist nondominated sorting genetic algorithm (NSGA-II) with continuous and discrete variables is applied to obtain maximum exergy efficiency with minimum exergy destruction and minimum total cost as two objective functions. The results of optimal designs are a set of multiple optimum solutions, called “Pareto optimal solutions.” The results clearly reveal the conflict between two objective functions and also any geometrical changes that increase the exergy efficiency (decrease the exergy destruction) lead to an increase in the total cost and vice versa. In addition, optimization of the heat exchanger based on exergy analysis revealed that irreversibility like pressure drop and high temperature differences between the hot and cold stream play a key role in exergy destruction. Therefore, increasing the component efficiency of a shell-and-tube heat exchanger increases the cost of heat exchanger. Finally, the sensitivity analysis of change in optimum exergy efficiency, exergy destruction, and total cost with change in decision variables of the shell-and-tube heat exchanger is also performed.

INTRODUCTION The shell-and-tube heat exchanger, as shown in Figure 1, is widely used in many industrial power generation plants, as well as in chemical, petrochemical, and petroleum industries. These exchangers are used to transfer heat between two or more fluids, between a solid surface and a fluid, or between solid particulates and a fluid, at different temperatures and in thermal contact. In heat exchangers, there are usually no external heat and work interactions. There are some effective parameters in shell-and-tube heat exchanger design, such as tube numbers, tube length, tube arrangement, and baffle spacing. Some researchers consider only Address correspondence to Professor Ibrahim Dincer, Department of Mechanical Engineering, Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, 2000 Simcoe St. North, Oshawa, ON L1H 7K4, Canada. E-mail: [email protected]

the cost of heat transfer surface area or capital investment as an objective function [1, 2], while others assumed entropy generation [3–5]. Ahmadi et al. [6] conceptually discussed exergy from several perspectives and introduced the exergy analysis method as a useful tool for furthering the goal of more efficient use of energy resources. Bejan [7] demonstrated the use of irreversibility as a criterion for evaluation of the efficiency of a heat exchanger. The purpose was to minimize the wasted energy by optimum design of fluid passages in a heat exchanger. Johannessen et al. [8] proved that the entropy production due to heat transfer in a heat exchanger is a minimum when the local entropy production is constant throughout all parts of the system. A new design strategy, involving losses due to fluid and heat transfer irreversibilities that lead to production of entropy, has recently been presented by Lerou et al. [9] and applied to the thermal design of a counterflow heat exchanger through minimization of entropy generation. Haseli et al. [10]

618

H. HAJABDOLLAHI ET AL.

619


Figure 1 Schematic of TEMA E shell-and-tube heat exchanger.

optimized the temperatures in a shell-and-tube condenser with respect to exergy. The optimization problem is defined subject to condensation of the entire vapor mass flow and it is solved based on the sequential quadratic programming (SQP) method. Also it was concluded that optimization results revealed new characteristics for the cooling water, with respect to the minimization of exergy destruction of the condensation process. Thus, these papers show that exergy analysis and optimization based on the second law of thermodynamics is an important tool for design, analysis, and improvement of heat exchangers and their networks. Moreover, in reference [11] the capital cost of the heat exchanger was considered as an objective function, while another group of researchers [12–16] considered the sum of capital/investment costs (related to the heat transfer area and energy-related costs of friction losses in the fluid flow) as an objective function to optimize shell-and-tube heat exchanger. Two objective functions (minimization of the total annualized cost and the amount of cooling water required) were also studied in reference [17]. In this study, after thermal modeling of an industrial shelland-tube heat recovery heat exchanger using the ε − NT U method and the Bell–Delaware approach [18], the exchanger is optimized by maximizing the exergy efficiency and minimizing the total cost and exergy destruction. A genetic algorithm technique is then employed to provide a set of the Pareto optimal solutions. The sensitivity analysis of change in optimum values of exergy efficiency (and exergy destruction) and total cost with change in design variables is performed and the results are discussed. In this analysis, an earlier study [10] is greatly enhanced by the following specific objectives: • To conduct a multi-objective optimization of shell-and-tube heat exchangers with respect to exergy efficiency (exergy destruction) and total cost. • To find the best and optimal design parameters such as tube configuration, tube diameter, tube pitch ratio, tube length, baffle spacing ratio, and baffle cut ratio using genetic algorithm. • To propose a closed-form equation for the total cost in term of exergy efficiency (exergy destruction) at the optimal design point. • To perform sensitivity analysis for the objective functions when the optimum design parameters vary. heat transfer engineering

ANALYSIS Heat Transfer Analysis An E-type TEMA shell is considered for this case study as shown in Figure 1. The heat-exchanger effectiveness for this type of shell is estimated from [18] using ε=

(1 +

C ∗)

+ (1 +

2 (1) coth N T2 U (1 + C ∗2 )0.5

C ∗2 )0.5

where the heat capacity ratio (C ∗ ) and the number of transfer units (NTU) are defined as N T Umax =

U At Cmin

(2) .

C∗ =

.

min((m c p )c , (m c p )h ) Cmin min(Cc , C h ) = = . . Cmax max(Cc , C h ) max((m c p )c , (m c p )h ) (3)

where At is the total heat transfer surface area and U is the overall heat transfer coefficient, defined as At = πLdo Nt U =

(4) 1

1 ho

+ Ro, f +

do ln(do /di ) 2kw

+ Ri, f

do di

+

1 do h i di

(5)

Here, L, Nt , di , do , Ri, f , Ro, f , and kw are tube length, tube number, tube inside and outside diameter, fouling resistance in tube and shell side, and thermal conductivity of tube wall, respectively. The tube-side heat transfer coefficient (h i ) is applied in form of [18]: 0.4 for 2500 < Ret < 1.24×105 h i = h t = (kt /di ) 0.024Re0.8 t Prt (6) where kt and Prt are tube-side fluid thermal conductivity and Prandtl number, and Ret is

Ret = vol. 33 no. 7 2012

. t mdi

µt Ao,t

(7)

620


Here, m˙ t is the mass flow rate and Ao,t is the tube-side flow cross-section area per pass, defined as Ao,t = 0.25πdi2 Nt /n p

(8)


Also n p is the number of tube passes. The shell diameter can be estimated from [19]: Ds = 0.637 pt (πNt )C L/C T P (9) where pt is tube pitch and C L is the tube layout constant, which is unity for 45◦ and 90◦ tube arrangement and 0.87 for 30◦ and 60◦ tube arrangement. Also, CTP is the tube count calculation constant, which is 0.93, 0.9, and 0.85 for a single pass, two passes, and three passes of tube, respectively [20]. Furthermore, the Bell–Delaware method was used to compute the shell-side heat transfer and friction factor coefficients in the form of h o = h s = h id Jc Jl Jb Js Jr

(10)

where h id is the heat transfer coefficient for the pure cross-flow stream over tube bundle evaluated at a Reynolds number at or near the center line of the shell in the form of [20]: . 2/3 ks µs 0.14 ms (11) h id = js c p,s As c p,s µs µs,w Here, js is the ideal tube bank Colburn factor, As is the crossflow area at or near the shell center line, and µs /µs,w is the ratio between viscosity in average temperature and wall temperature in the shell side. The shell-side pressure drop is computed as three terms including cross-flow section pressure drop, inlet and outlet pressure drop and window section pressure drop. The details of computing Colburn factor, friction factor, and cross-flow area at or near the shell center line can be found in reference [20]. These factors depend on tube arrangement and Reynolds number. Jc is the correction factor for baffle configuration (baffle cut and spacing) and takes into account the heat transfer in the window. Jl is the correction factor for baffle leakage effects and takes into account both the shell-to-baffle and tube-to-baffle hole leakages. Jb is the correction factor for bundle and pass partition bypass streams and depends on the flow bypass area and number of sealing strips. Js is the correction factor for bigger baffle spacing at the shell inlet and outlet sections. Jr is the correction factor for the adverse temperature gradient in laminar flows (at low Reynolds numbers) [18]. Furthermore, the pressure drop in tube side was also estimated from .

4 ft L + (1 − σ2 + K c ) − (1 − σ2 − K e ) n p di (12) where K c and K e are entrance and exit pressure loss coefficient for a multiple circular tube core, respectively, and σ is defined as the ratio of minimum free flow area to frontal area (Table 1). The term f t is the friction factor obtained from the following m 2t Pt = 2ρt A2o,t

heat transfer engineering

Table 1 The ratio of minimum free flow area to frontal area Square

σ

30◦ Triangular staggered array

45◦ Rotated square staggered array √ pt 2 pt − d o f or ≥ 1.707 √ do 2 pt

pt − do pt

2( pt − do ) pt f or ≤ 1.707 √ do 2 pt

90◦ Rotated staggered array

p t − do pt

equation [18]: f t = 0.00128 + 0.1143(Ret )−0.311

(13)

for 4000 < Ret < 10 range with ±2%. 7

Exergy Analysis Exergy is a measure of the departure of the state of a system from that of the environment. It can be defined as the maximum obtainable work from the combination of the system and environment. Unlike energy, exergy is not conserved; indeed, it is destroyed by irreversibilities. The exergy destruction during a process is proportionally associated with entropy generation due to these irreversibilities [21, 22]. The steady-state exergy rate balance for a control volume can be written as T0 ˙ ˙ cv + 1− Qj − W m˙ i ei − m˙ e ee − E˙ x D = 0 Tj e j i (14) ˙ j represents the heat transfer rate at the location where Q on the boundary where the instantaneous temperature is T j , ˙ cv represents the energy transfer by work, other than andW flow work. The specific flow exergy, e, is evaluated as follows: V2 + gz (15) 2 where h and S denote, respectively, enthalpy and entropy of the system and ho and So are the values of the same properties if the system was at the dead state. Also, To refers to the dead state (environment) temperature. Therefore, the exergy destruction for a heat exchanger is calculated as follows: E˙ x D,H E = (16) m˙ i ei − m˙ e ee e = (h − h ◦ ) − T◦ (S − S◦ ) +

e

i

The exergy efficiency of a heat exchanger is calculated as .

E x D,H E x ηex,A P = 1 − Ex i,H E x

vol. 33 no. 7 2012

(17)


MULTI-OBJECTIVE OPTIMIZATION USING GENETIC ALGORITHM A multi-objective problem consists of optimizing (i.e., minimizing or maximizing) several objectives simultaneously, with a number of inequality or equality constraints. The problem can formally be written to find: Find x = (xi )∀i = 1, 2, . . . , N param

(18)


such that f i (x) is a minimum(respectively maximum) ∀i = 1, 2, . . . , Nobj , subject to: g j (x) = 0 ∀ j = 1, 2, . . . , M,

(19)

h k (x) ≤ 0

(20)

∀k = 1, 2, . . . , K ,

where x is a vector containing the N param design parameters, ( f i )i=1,....,N obj the objective functions, and Nobj the number of objectives. The ( f i )i=1,....,N obj returns a vector containing the set of Nobj values associated with the elementary objectives to be optimized simultaneously. The genetic algorithms are semistochastic methods, based on an analogy with Darwin’s laws of natural selection [23]. The first multi-objective genetic algorithm (GA), called vector-evaluated GA (or VEGA), was proposed by Schaffer [24]. An algorithm based on nondominated sorting was proposed by Srinivas and Deb [25] and called nondominated sorting genetic algorithm (NSGA). This was later modified by Deb et al. [26], which eliminated higher computational complexity, lack of elitism, and the need for specifying the sharing parameter. This algorithm is called NSGA-II and is coupled with the thermal modeling programming for optimization.

Nondominated Sorting Following the definition by Deb and Goel [27], an individual X (a) is said to constrain-dominate an individualX (b) if any of the following conditions are true: 1. X (a) and X (b) are feasible, with (a) X (a) is no worse than X (b) in all objective, and (b) X (a) is strictly better thanX (b) in at least one objective. 2. X (a) is feasible while individualX (b) is not. 3. X (a) andX (b) are both infeasible, but X (a) has a smaller constraint violation. Here, the constraint violation (X ) of an individual X is defined to be equal to the sum of the violated constraint function values, (X ) = Bj=1 γ(g j (X ))g j (X ), where γ is the Heaviside step function. heat transfer engineering

621

Tournament Selection Each two individuals compete in a tournament with randomly selected individuals, a procedure that imitates survival of the fittest in nature.

Controlled Elitism Sort To preserve diversity, the influence of elitism is controlled by choosing the number of individuals from each subpopulation, according to the geometric distribution [28]: Sq = S

1 − c q−1 c , 1 − cw

(21)

to form a parent search population, Pt+1 (t denote the generation), of size S, where 0 < c < 1 and w is the total number of ranked nondominated individuals.

Crowding Distance The crowding distance metric proposed by Deb and Goel [27] is utilized, where the crowding distance of an individual is the perimeter of the rectangle with its nearest neighbors at diagonally opposite corners. Thus, if individual X (a) and individual X (b) have the same rank, each one that has a larger crowding distance is better.

Crossover and Mutation Uniform crossover and random uniform mutation are employed to obtain the offspring population, Q t+1 . The integerbased uniform crossover operator takes two distinct parent individuals and interchanges each corresponding binary bit with a probability 0 < pc ≤ 1. Following crossover, the mutation operator changes each of the binary bits with a mutation probability, 0 < pm < 0.5.

Objective Functions, Design Parameters, and Constraints In this study, the exergy efficiency (and exergy destruction) and total cost are considered as two objective functions. The total cost includes the cost of heat transfer area and the operating cost for the pumping power: Ctotal = Cin + Cop

(22)

The investment cost for both the stainless steel-made shell and tube is considered as [29]: Cin = 8500 + 409A0.85 t where At is the total tube outside heat transfer area. vol. 33 no. 7 2012

(23)

622


Table 2 The operating conditions of the shell-and-tube heat exchanger (input data for the model)

Table 4 Comparison of modeling output and the corresponding results from reference [18]

Properties

Variables

Shell side (hot water) Tube side (cold water)

Density (kg/m3) Specific heat (J/kg-K) Viscosity (Pa-s) Fouling factor (m2-W/K) Thermal conductivity (W/m-K)

980 4180 0.000672 0.000065 0.56

995 4120 0.000695 0.000074 0.634

C total Pt Ps q ht hs


The total discounted operating cost related to pumping power to overcome friction losses is computed from the following equations [29]: Cop =

ny k=1

Co (1 + i)k

Unit

Reference [15]

Present article

Difference (%)

— $ kPa kPa kW W/m2–K W/m2–K

0.1555 74598 17.58 112 393.6 7837 698.8

0.1599 74112 17.660 111.02 404.63 7838.2 730.226

2.83 0.65 0.45 −0.875 2.78 0.0153 4.497

tubes with definite inner and outer diameter listed in Table 3 are considered as discrete design variables [30].

(24) RESULTS AND DISCUSSION

Co = H kel τ

(25)

1 m˙ t m˙ s H = Pt + Ps η ρt ρs

(26)

Modeling Verifications and Optimization Results

where ny is the equipment lifetime per year, i is annual discount rate, and kel , τ, and η are price of electrical energy, hours of operation per year, and pump efficiency, respectively. In this study tube arrangement, tube diameters, tube pitch ratio pt /do , tube length, tube number, baffle spacing ratio(L bc /Ds,i ), and baffle cut ratio (BC/Ds,i ) were considered as seven decision variables. The following constraints are introduced to insure to satisfy that the ratio of L/Ds is in the range of 3 < L/Ds < 12.

CASE STUDY The optimum heat exchanger configurations were obtained for an oil cooler shell-and-tube heat recovery heat exchanger in the Sarcheshmeh cupper production power plant located in the south of Kerman city. The goals in this study were to maximize exergy efficiency (minimize exergy destruction) while minimizing the total cost. The hot water (hot stream) with 8.1 kg/s mass flow rate passes through the shell side of heat exchanger at 78.3◦ C. The fresh water (cold stream) with 12.5 kg/s mass flow rate passes through the tube side at 30◦ C. The operating conditions are listed in Table 2. In this study, the equipment life assigned ny = 10yr , the rate of annual discount assigned i = 10%, price of electrical energy considered kel = 0.15/kW h, and hours of operation and pump efficiency considered are τ = 7500h/yr and η = 0.6, respectively. Three tube arrangements (30◦ , 45◦ , 90◦ ) and the number of 20 standard

To verify the modeling results, the simulation output were compared with the corresponding reported results given in literature. The comparison of our modeling results and the corresponding values from reference [18], for the same input values, is shown in Table 4. Results show that the difference percentage points of modeling output results are acceptable.

Optimization Results To maximize the exergy efficiency and minimize the total cost, and the exergy destruction, seven design parameters including tube arrangement, tube diameters, tube pitch ratio, tube length, tube number, baffle spacing ratio, and baffle cut ratio were selected. The design parameters (as decision variables) and the range of their variations are listed in Table 5 according to reference [31]. The number of iterations for finding the global optimum in the whole searching domain is 8.2 × 1015. Also, the running time of the CPU for this condition for 200 generations is about 10 minutes.

Multi-Objective Optimization of Exergy Efficiency and Total Cost The genetic algorithm optimization is performed for 100 generations, using a search population size of M = 100 individuals, crossover probability of pc = 0.9, gene mutation probability of pm = 0.035, and controlled elitism value of c = 0.65. The results for a Pareto-optimal front are shown in

Table 3 Inner and outer diameters of 20 standard tubes Inner diameter (in) 0.444 0.407 0.435 0.481 0.495 0.509 0.527 0.541 0.555 0.482 0.510 0.532 0.560 0.584 0.606 0.620 0.634 0.352 0.680 0.607 Outer diameter (in) 1/2 5/8 5/8 5/8 5/8 5/8 5/8 5/8 5/8 3/4 3/4 3/4 3/4 3/4 3/4 3/4 3/4 3/4 3/4 7/8


vol. 33 no. 7 2012

H. HAJABDOLLAHI ET AL. Table 5

The design parameters, their range of variation, and their change step

Variables


Tube arrangement Tube inside diameter, m Tube outside diameter, m pt /do Tube length, m Tube number Baffle cut ratio Baffle spacing ratio

From (30◦ ,

90◦ )

45), 0.0112 0.0126 1.25 3 100 0.19 0.2

To

Step of change

(—) 0.0153 0.022 2 8 600 0.32 1.4

1 — — 0.001 0.001 1 0.001 0.001

Figure 2, which clearly reveal the conflict between two objectives, exergy efficiency versus total cost. Any geometrical change that increases the exergy efficiency leads to an increase in the total cost, and vice versa. This shows the need for multiobjective optimization techniques in optimal design of a shelland-tube heat exchanger. It is shown in Figure 2 that the maximum exergy efficiency appears at design point A (0.9249), while the total cost is the biggest at this point. On the other hand, the minimum total cost occurs at design point C (14340 $), with a smallest exergy efficiency value (0.7654) at that point. Design point A is the optimal situation at which,\ exergy efficiency is a single objective function, while design point C is the optimum condition at which total cost is a single objective function. To provide a useful tool for the optimal design of the shelland-tube heat exchanger, the following equation for exergy efficiency versus the total cost was derived for the Pareto curve (Figure 2): −94.96η3ex + 4.082η2ex + 144.4ηex − 61.56 × 105 η2ex − 397.8ηex + 367.8 (27) which is valid in the range of 0.7654 < ηex < 0.9249 for Ctotal ($) =

Table 6 The optimum values of exergy efficiency, total cost, and exergy destruction for the design points A to F in Pareto-optimal fronts for input values given in Table 2 A


B

C

D

E

F

Exergy efficiency 0.9249 0.8889 0.7654 0.7686 0.8675 0.9246 Total cost ($) 57,359 22,090 14,337 14,397 19,995 43,959 Exergy destruction (kW) 12.154 17.971 37.959 37.447 21.435 12.192

exergy efficiency. The interesting point here is that considering a numerical value for the exergy efficiency in the mentioned range provides the minimum total cost for that optimal point along with other optimal design variables.

Multi-Objective Optimization of Exergy Destruction and Total Cost The genetic algorithm optimization was performed for 100 generations, using a search population size of M = 100 individuals, crossover probability of pc = 0.9, gene mutation probability of pm = 0.035, and controlled elitism value c = 0.55. The results for the Pareto-optimal front are shown in Figure 2, which clearly reveal the conflict between two objectives (exergy destruction versus total cost). Any geometrical change that decreases the exergy destruction leads to an increase in the total cost and vice versa. It is shown in Figure 2 that the minimum exergy destruction exists at design point F (12.19 kW), while the total cost is the biggest at this point. On the other hand, the minimum total cost occurs at design point D ($14,397), with a biggest exergy destruction value (37.447 kW) at that point. Design point F is the optimal situation at which exergy destruction is a single objective function, while design point D is the optimum condition at which total cost is a single objective function. To provide a useful tool for the optimal design of the shelland-tube heat exchanger, the following equation for exergy destruction versus the total cost was derived for the Pareto curve (Figure 2): Ctotal ($) =

Figure 2 The distribution of Pareto-optimal points solutions using NSGA-II. (Color figure available online.)

623

5.848E 2D + 384E D − 5215 × 103 E 2D − 3.483E D − 97.95

(28)

which is valid in the range of 12.19 < E D < 37.45 (kW ) for exergy destruction. The key point here is that considering a numerical value for the exergy destruction in the mentioned range provides the minimum total cost for that optimal point along with other optimal design variables. Optimum objectives for six typical points from A to F Paretooptimal fronts for input values given in Table 2 are listed in Table 6. The variation of optimum values of exergy efficiency with the total cost for various values of optimum design variables in A–C cases (Pareto front) and exergy destruction with the total cost for various values of optimum design parameters in D–F are shown in Figures 3a–e and Figures 4a–e, respectively. vol. 33 no. 7 2012



624

Figure 3 The variation of exergy efficiency with total cost for five optimum design parameters in three cases of A–C where exergy efficiency and total cost are given as objective functions.(Color figure available online.)

The effect of tube diameter is not considered because there is no direct relation between tube diameter and tube thickness in the existing tubes. In addition, the optimal tube pitch for two optimization methods was fixed at 45 degrees. It was observed that the variation of two objective functions at other points on a Pareto optimal front had the same trend as the six points (A–F). The effect of design variables on objective functions are investigated and explained as follows.


Effect of Decision Variables on Objective Functions Tube Pitch Ratio By increasing the pt /do , both exergy efficiency and total cost decreased for all design points A-C (Figure 3a). Also, increase in this parameter results in increment of exergy destruction in all points from D to F in Figure 4a. Therefore, variations of tube pitch ratio cause a conflict between two objectives.

vol. 33 no. 7 2012



625

Figure 4 The variation of exergy destruction with total cost for five optimum design parameters in three cases of D–F where exergy destruction and total cost are given as objective functions. (Color figure available online.)

Tube Length By increasing the tube length, both exergy efficiency and total cost increases for all design points A–C (Figure 3b). In addition, this parameter results in decrease in exergy destruction in all points from D to F in Figure 4b. Therefore, variations of tube length cause a conflict between two objective functions. Tube Number Like tube length, both exergy efficiency and total cost increase with increasing the tube number (Figure 3c). Moreover, heat transfer engineering

increment of this parameter leads to decrease in exergy destruction for all points from D to F in Figure 4c. Therefore, the tube number causes a conflict between these two objective functions.

Baffle Spacing Ratio As shown in Figures 3d and 4d, an increase in the baffle spacing ratio (L bc /Ds,i ) creates a conflict between two objective functions (exergy efficiency and total cost, exergy destruction, and total cost). vol. 33 no. 7 2012

626


Baffle Cut Ratio Increase in baffle cut ratio (BC/Ds,i ) decreases both exergy efficiency and total cost (Figure 3e) but not directly. However the effect is not considerable. Also, increase in this parameter changes exergy destruction a little for all points in Figure 4e.


CONCLUSIONS In this work, a multi-objective exergy-based optimization through a genetic algorithm method has been conducted to study and improve the performance of shell-and-tube type heat recovery heat exchangers, by considering two key parameters, such as exergy efficiency and cost. The design parameters (decision variables) were tube arrangement, baffle cut ratio, tube pitch ratio, tube length, tube number, and baffle spacing ratio, as well as 20 standard tubes with definite inner and outer diameter. In the presented optimization problem, the exergy efficiency (and exergy destruction) and the total cost were considered two objective functions. Therefore exergy efficiency was maximized, while minimizing the exergy destruction, and the total cost was minimized. Here are some of the concluding remarks: • When the exergy efficiency of a shell-and-tube heat exchanger increases, the total cost of the heat exchanger increases respectively. • Increasing heat exchanger exergy efficiency leads to a more efficient heat exchanger both thermodynamically and thermoeconomically. • Decreasing exergy destruction increases the total cost. • Irreversibility, like pressure drop and high temperature difference between cold and hot stream, plays a key role in exergy destruction. • Tube pitch ratio, tube length, tube number, and baffle spacing ratio appear to be important design parameters, while tube arrangement indicates no effect on the conflict between two optimized objective functions. NOMENCLATURE Ao,t At As BC cp C Cmin Cmax C∗ Cin Cop Co Ctotal CL

tube side flow area per pass (m2) total tube outside heat transfer area (m2) cross flow area at or near the shell center line baffle cut (m) specific heat at constant pressure (J/kg-K) flow stream heat capacity rate (W/k) minimum of C h and Cc (W/K) maximum of C h and Cc (W/K) heat capacity rate ratio (Cmin /Cmax ) investment cost ($) operational cost ($) annual operating cost ($/yr) total cost ($) tube layout constant(−) heat transfer engineering

CT P di do Ds ED f h h id hi ho H i j k Kc Ke kel L L bc . m np ny Nt NTU pt Pr q Ro, f Ri, f Re T U

tube count calculation constant(−) inner tube diameter (m) outer tube diameter (m) shell diameter (m) exergy destruction (kW) friction factor (−) heat transfer coefficient (W/m2-K) ideal heat transfer coefficient in shell side tube-side heat transfer coefficient (W/m2-K) shell-side heat transfer coefficient (W/m2-K) pumping power (W) annual discount rate (%) Colburn number (−) thermal conductivity (W/m-K) entrance pressure loss coefficient (−) exit pressure loss coefficient (−) price of electrical energy ($/kWh) tube length (m) baffle spacing (m) mass flow rate (kg/s) number of tube pass(−) equipment life (yr) number of tubes (−) number of transfer units (−) tube pitch (m) Prandtl number (−) heat transfer rate (kW) shell-side fouling resistance (m2-K/W) tube-side fouling resistance (m2-K/W) Reynolds number (−) temperature (◦ C) overall heat transfer coefficient (W/m2-K)

Greek Symbols σ ε P ρ µ η ηex τ

ratio of minimum free flow area to frontal area (−) thermal effectiveness(−) pressure drop (Pa) density (kg/m3) viscosity (Pa-s) pump efficiency (−) exergy efficiency (−) hours of operation per year (h/yr)

Subscripts c h i o s t w

cold stream hot stream inner or inlet outer or outlet shell-side tube side tube wall vol. 33 no. 7 2012



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[31] Saunders, E. A. D., Heat Exchangers—Selection, Design and Construction, Wiley, New York, 1988. Hassan Hajabdollahi received his B.Sc. degree in mechanical engineering in 2006 from Sistan and Balochestan University, Zahedan, Iran. He received his master’s degree in mechanical engineering from Iran University of Science and Technology Tehran, Iran, in 2009. Now he is a Ph.D. student at Iran University of Science and Technology. His research interests are heat exchangers optimization, power plant optimization, combined heat and power generation optimization, central heating, nondominated sorting genetic algorithm for multi-objective optimization (NSGA-II), artificial neural networks, and fuzzy logic. He has published more than 32 articles in journals and conference proceedings. He has also been a reviewer for Energy Conversion and Management, Heat Transfer Engineering, Energy and Building, and International Journal of Greenhouse Gas Control. Pouria Ahmadi received his B.Sc. degree in mechanical engineering in 2006 from Power and Water University of Technology (PWUT), Tehran, Iran. He received his master’s degree in mechanical engineering from Iran University of Science and Technology, Tehran, Iran in 2009. In 2009 he was accepted for his Ph.D. at Sharif University of Technology, where he studied for one year as a research assistant at the Advanced Heat Transfer Laboratory. Currently he is a Ph.D. student at the University of Ontario Institute of Technology, Canada. His research interests are second law analysis (exergy)


of energy systems, renewable energies, optimization of thermal systems and thermodynamic modeling of integrated gas turbine SOFC power plants, advanced power plant technology, green energies, and heat exchanger design and optimization. He has published more than 50 articles in journals and conference proceedings as well as two books in translation and three books published for Prdazesh Isituations, Tehran, Iran. He has also been a reviewer for International Journal of Energy Research, International Journal of Exergy, Energy Conversion and Management, Applied Thermal Engineering Journal, and numerous national conferences in Iran. Ibrahim Dincer is a full professor at the Faculty of Engineering and Applied Science at the University of Ontario Institute of Technology (UOIT), Canada. He is the author of more than 700 journal and conference publications, 9 books, 12 edited books, and 33 book contributions; editor-in-chief of International Journal of Energy Research, International Journal of Exergy, International Journal of Global Warming, and The Open Environmental Engineering Journal, and is associate editor, regional editor, and has editorial board member responsibilities for a number of international reputable journals. He has been keynote speaker in several prestigious conferences; he has been chair of a number of international conferences, symposia, and workshops; served as executive/scientific committee member of various organizations and conferences; is an inventor of various new thermal equipment configurations, systems and designs, and new models, correlations, and graphs for heat and mass transfer parameters; and is the recipient of various research excellence awards, including the Premier’s Research Excellence Award in Canada more recently. His research interests cover many topics, particularly on sustainable energy technologies.

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