Application of firefly algorithm for design optimization of a shell and tube heat exchanger from economic point of view

https://doi.org/10.1016/j.ijthermalsci.2015.12.002Get rights and content

Highlights

  • A comprehensive design procedure for a shell and tube heat exchanger is provided.

  • The firefly algorithm is applied for economic optimization with total annual cost as objective function.

  • Two different case studies have been considered for application of the Firefly algorithm.

  • The results are compared with the original design and other optimization methods available in literature.

  • The results of this work are found to be most economical as compared to other optimization methods.

Abstract

In the present work, a shell and tube heat exchanger optimization design approach is developed with respect to the total annual cost by application of Firefly algorithm. The total annual cost including the investment cost and the operating cost is considered to be the objective function of the optimization process. The developed algorithm is applied to two case studies and the results show that the operating cost can be reduced by 77% while the total cost can be reduced by 29% as compared to the original design. Further the outcome of the Firefly algorithm is compared with various design optimization algorithms and the results show a much better solution to the problem of economic optimization for the design of a shell and tube heat exchanger. Simultaneously, the present method shows a marginal development in increase of overall heat transfer coefficient and decrease of heat exchanger area corresponding to same heat duty as compared to other optimization methods.

Introduction

A heat exchanger is a device in which two fluid streams, one hot and one cold, are brought into thermal contact with each other in order to transfer heat from the hot fluid stream to the cold one. It provides a relatively large surface area of heat transfer for given volume of the equipment. The specific applications of heat exchangers are most frequently found in chemical process industries as well as power production, waste heat recovery, cryogenic, air conditioning and petrochemical industries. Among the various types of heat exchangers, the shell and tube type heat exchangers are the most widely used heat exchangers which contribute approximately more than 65% of the exchangers in chemical process industries [1]. This is due to the fact that they provide area density greater than 700 m2/m3 for gases and greater than 300 m2/m3 for liquids. Besides higher efficiency, reduced volume, weight and cost for specific heat duty justify shell and tube heat exchangers to be the best among all other kinds of heat exchange equipments. This exchanger is generally built of a bundle of round tubes mounted in a cylindrical shell with the tube axis parallel to that of the shell. The major components of this exchanger are tubes, shell, front end head, rear end head, baffles and tube sheet. The selection criteria for a proper combination of these components depend upon the operation pressures, temperatures, thermal stress, corrosion characteristics of fluids, fouling, cleanability and cost. Fig. 1 shows the schematic diagram of a typical single pass heat exchanger [2].

The design of shell-and-tube heat exchangers involves a large number of geometric and operating variables as part of the search for an exchanger geometry that meets the heat duty requirement and a given set of design constraints. Efforts have been made by various researchers to develop systematic design approaches for seeking the best possible heat exchanger that provides the optimum heat duty while meeting a set of specified constraints. In the pursuit of improved designs, much research has been carried out with objective functions aimed at decreasing total cost and heat transfer area. Over the past few years, genetic algorithms (GAs) have been used by many researchers as an optimization method in shell and tube heat exchanger design [3], [4], [5], [6], [7], [8], [9], [10], [11], [12]. Selbas et al. provided an optimal design for a shell and tube heat exchanger by using genetic algorithm for finding the global minimum heat transfer area and economic cost [3]. Guo et al. developed a new shell-and-tube heat exchanger optimization design approach wherein the dimensionless entropy generation rate obtained by scaling the entropy generation on the ratio of the heat transfer rate to the inlet temperature of cold fluid was employed as the objective function and the genetic algorithm was applied to solve the associated optimization problem [4]. Sanaye and Hajabdollahi developed an optimum design for a STHE in order to obtain the maximum effectiveness and minimum total cost based on multi-objective functions [13]. Fettaka et al. [6] presented the multiobjective optimization for a shell and tube heat exchanger based on heat transfer area and pumping power. This provided a design with multiple Pareto-Optimal solutions which was able to capture the trade-off between the two objectives. Sadeghzadeh et al. [12]. used a combination of genetic and particle swarm algorithms for the design of techno-economically optimum shell and tube heat exchangers. This design considered cost of the heat exchanger based on surface area and power consumption to overcome pressure drops as the objective function.

Several researchers have introduced different optimization methods in recent years that outperform genetic algorithm in terms of optimization results. Yang et al. [14]. proposed a general optimization design method for heat exchangers motivated by constructal theory. In this method, a global heat exchanger was divided into several sub-heat exchangers in series-and-parallel arrangement and the Tubular Exchanger Manufacturers Association (TEMA) standards were rigorously followed for all design parameters. The objective was to minimize the total cost of the shell-and-tube heat exchanger including the investment cost for initial manufacture and the operational cost involving the power consumption to overcome the frictional pressure loss. Asadi et al. [15]. used the cuckoo search algorithm to develop an optimal design of a shell and tube heat exchanger with respect to total annual cost. This optimization process was based on the minimization of the total annual cost including the capital investment and operating expenses. The case studies show that the operating costs can be reduced by 77% and 48% compared to the results obtained from Particle Swarm Optimization and Genetic Algorithm. Hadidi and Nazari [16] developed an improved optimization design approach for shell and tube heat exchangers based on biogeography based optimization (BBO) algorithm. The BBO algorithm has some improved features in reaching to the global minimum as compared to other evolutionary algorithms. In this study, the BBO technique was applied to minimize the total cost of the equipment by varying various design variables such as tube length, tube outer diameter, pitch size, baffle spacing, etc. The obtained results indicated that the BBO algorithm can be successfully applied for optimal design of shell and tube heat exchangers in comparison to other optimization algorithms such as Genetic Algorithm or Particle Swarm Optimization. Sahin et al. [17]. applied the Artificial Bee Colony (ABC) to minimize the total cost of the equipment including capital investment and the sum of discounted annual energy expenditures related to pumping of shell and tube heat exchanger by varying various design variables. The Artificial Bee Colony (ABC) method was found to be the most accurate and quick according to other traditional methods. Patel and Rao [18] used a non-traditional particle swarm optimization technique for design optimization of shell-and-tube heat exchangers from economic view point. Three design variables such as shell internal diameter, outer tube diameter and baffle spacing were considered for minimization of the total annual cost. A new shell and tube heat exchanger optimization design approach was developed by Hadidi et al. [19]. based on imperialist competitive algorithm (ICA). The ICA algorithm was found to be having some good features in reaching to the global minimum as compared to other evolutionary algorithms. Referring to the literature test cases, reduction of capital investment up to 6.1% and savings in operating costs up to 94% were obtained by this method. The total cost up was decreased to 53%, which shows the improvement potential of the proposed method. Furthermore, the ICA technique allows for rapid solution of the design problem and enables to examine a number of alternative solutions of good quality. This provides the designer more degrees of freedom in the final choice as compared to other traditional methods. Fessnghary et al. [20]. explored the use of global sensitivity analysis (GSA) and harmony search algorithm (HSA) for design optimization of shell and tube heat exchangers (STHXs) from the economic viewpoint. To reduce the size of the optimization problem, non-influential geometrical parameters which have the least effect on total cost of STHXs were identified using GSA. The meta-heuristic based algorithm HSA was then applied to optimize the influential geometrical parameters. To demonstrate the effectiveness and accuracy of the proposed algorithm, an illustrative example was studied. Comparison of the HSA results with those obtained using genetic algorithm (GA) revealed that the HSA can converge to optimum solution with higher accuracy.

In this study, a firefly algorithm was selected for optimization of a shell and tube heat exchanger. The objective function is the minimization of total annual cost. As seen above, studies on optimization of heat exchangers with firefly algorithm in the literature was not found much. This algorithm was successfully applied for design and economic optimization of shell and tube heat exchangers. This study has provided new and powerful methodology in the optimization of shell and tube heat exchangers. Based on proposed method, a full computer program was developed for optimal design of shell and tube heat exchangers and two different test cases were taken into consideration to demonstrate the effectiveness and accuracy of the proposed algorithm. The results of the proposed algorithms are compared with the results available in literature obtained by using various other optimization techniques. It is found that the proposed method is very accurate, quick and reliable for economically optimal design of shell and tube heat exchangers.

Section snippets

Heat exchanger design model

For sensible heat transfer, the heat transfer rate is calculated asQ=mhCph(ThiTho)=mcCpc(TcoTci)

For n number of tube passes, the number of tubes Nt can be determined as [1], [2].Nt=K1(Dsdo)n1where K1 and n1 are numerical coefficients depending on flow arrangement and number of tube passes. These coefficients are presented in Table 1 for different combinations of flow arrangement and tube passes [3].

Firefly algorithm

The bio-inspired optimization techniques have successfully been applied in the recent past in various optimization problems related to real life and industrial applications due to their simplicity, robustness and ability to solve complex optimization problems efficiently. Among the different algorithms, the metaheuristic algorithms are most suitable for global optimization as metaheuristic uses certain tradeoff a randomization and local search, as randomization provides a good way to move away

Results and discussion

In this work, a Firefly algorithm is adopted for finding out optimal design of a shell and tube heat exchanger from economic point of view. In order to estimate the suitability and reliability of the proposed methodology, two case studies were taken into considerations which were analyzed previously by Asadi et al. using cuckoo search algorithm [15], Hadidi and Nazari using BBO [16], Sahin et al. using ABC [17], Patel and Rao using PSO [18], Hadidi et al. using ICA [19] and Caputo et al. using

Conclusion

In the present work, the Firefly algorithm is applied to obtain an optimal design for a shell and tube heat exchanger. The objective of the optimization process is minimization of the total cost which includes both the investment cost and the total discounted annual operating cost. The proposed methodology is applied to two case studies and the results are compared with other design optimization methods and the original design. As observed in both the case studies, it is found that the

References (35)

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