CHAPTER 9

Design Optimization and Performance Prediction of Compact Heat Exchangers

Q. Wang1, G. Xie2 & Bengt Sunden31State Key Laboratory of Multiphase Flow in Power Engineering, Xian Jiaotong University, China.2School of Mechantronics, Northwestern Polytechnical University, China.3Department of Energy Sciences, Lund University, Sweden.

Abstract

Applications of genetic algorithms (GAs) and artifi cial neural networks (ANNs) in thermal engineering have received much attention. Compact heat exchangers (CHEs) have special merits of high-performance and compactness and are widely used in various applications of energy and power engineering. This chapter demonstrates optimization design of a plate-fi n heat changer and per-formance prediction of three kinds of tube-fi n heat exchangers by a GA and an ANN, respectively. The successful applications of optimization and prediction of CHEs suggest that GAs and ANNs have strong ability of intelligent design and prediction of CHEs.

Keywords: ANN; compact heat exchanger; GA; optimization; prediction

1 Introduction

Compact heat exchangers (CHEs), including two types of heat exchangers namely, plate-fi n types and fi n-and-tube tube-fi n types, are widely used for gasgas or gasliquid applications as shown in Fig. 1. CHEs are used in many industrial processes in chemical and petroleum engineering, refrigeration and cryogenics, heating and ventilation, air-conditioning heating, ventilation, air-conditioning (HVAC), aeronautics and astronautics, automotive, electric and electronic equipments, etc. CHEs own merits of compactness, small volume, low weight, high effectiveness, and low cost. CHEs have high thermal effectiveness, because some augmented

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302 EMERGING TOPICS IN HEAT TRANSFER

devices such as fi ns, ribs, dimples are used on primary surfaces to interrupt boundary layer growth due to the disturbance of the fl ow, and has high thermal conductivity due to the thin thickness of surface walls. Many high-performance augmented structures have been developed and applied to industrial engineering applications successfully.

Heat exchanger optimization is an important fi eld and full of challenges. The task of optimization may be considered as a design process, in which any possible candidates will be evaluated based on requirements. Savings of materials or energy, as well as capital cost and operating cost, are common objectives for industrial applications of heat exchangers. By contrast, heat exchanger design involves complex processes, including selection of geometrical parameters and operating dynamic parameters for the design, cost estimation, and optimization. Generally, the design task is a complex trial-and-error process, because all possi-ble values of the geometrical parameters are combined and in turn the designed heat exchanger is evaluated with respect to the conditions of specifi ed require-ments, that is, outlet temperature, heat duty, and pressure drop. In this sense, there is always the possibility that the designed results are not the optimum. Therefore, researchers try to optimize thermal devices by means of optimization techniques, and many interesting and well-organized works have been presented. In recent years, much additional literature has appeared on optimization of heat exchangers, for example [113].

In recent years, applications of various genetic algorithms (GAs) in thermal engineering have received much attention for solving real-world problems [14]. Applications of GAs into heat exchangers optimizations have suggested that GAs have a strong ability of search and combined optimization and can success-fully optimize and predict thermal problems. Thus, applications of GAs in the fi eld of thermal engineering are new challenges. At this point, the GA technique may be used in the geometrical optimization of heat exchangers in order to obtain optimal results under specifi ed design objectives within the allowable pressure drops. Several examples of optimizations of heat exchangers are pre-sented in [1525].

Figure 1: Compact heat exchangers: plate-fi n type, tube-fi n type.

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DESIGN OPTIMIZATION AND PERFORMANCE PREDICTION OF COMPACT HEAT EXCHANGERS 303

By contrast, to evaluate the heat exchanger performances, effi cient and accurate methods for prediction of heat transfer and pressure drop have to be developed. Artifi cial neural networks (ANNs) have been developed for about two decades and are now widely used in various application areas such as performance prediction, pattern recognition, system identifi cation, and dynamic control and so on, because ANNs provide better and more reasonable solutions. ANNs have more attractive advantages. It can approximate any continuous or nonlinear function using certain network confi guration. It can be used to learn complex nonlinear relationship from a set of associated inputoutput vectors. It can be implemented to dynamically simulate and control unknown or uncertain processes. In recent years, ANNs have been used in thermal systems for heat transfer analysis, performance prediction, and dynamic control of heat exchangers [2650].

This chapter demonstrates optimization design and performance prediction of CHEs using a GA and an ANN, respectively. Such demonstrations intend to encourage researchers to extend relevant works through GAs and ANNs.

2 Design Optimization of a Plate-Fin Heat Exchanger

In this section, geometrical optimization of a plate-fi n under different objectives using GA is described. More details can be found in [23].

2.1 Physical model

A microturbine recuperator is considered [51]. A typical core of a plate-fi n heat exchanger is shown in Fig. 2. For such a plate-fi n compact heat exchanger (PFCHE), two streams are in cross-fl ow with different mass fl ow rates under specifi ed per-formances, for example, given duty, allowable drops. There are many geometrical parameters, which may be taken as optimization variables such as shape length L1, L2, L3, fi n pitch fi n density Fp, fi n height plate height Fs, fi n thickness df, and number of fl ow arrangements N. In this work, the thickness of the plate and fi ns are assumed to be constant, and thus are not to be optimized as they satisfy initial requirements, and almost do not affect the performance of the heat exchanger. The

Figure 2: A plate-fi n heat exchanger core.

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304 EMERGING TOPICS IN HEAT TRANSFER

materials of plate and fi n are aluminum with a thermal conductivity of 190 W/m K, density of 2,790 kg/m3. Plain triangular fi ns and offset strip fi ns are used on each side, and the fi n parameters are taken from Kays and London [52].

2.2 Brief description of GA and optimization process

The GA is maintained by a population of parent individuals that represent the latent solutions of a real-world problem. For example, the designer might encode the design parameters into corresponding binary strings, and then all the binary strings are connected into a binary string, which is represented as an individual. A certain number of sets of design parameters accordingly become a population of parent individuals. Figure 3 shows the fl ow chart of the GA for optimizing heat exchangers. Each individual is assigned a fi tness based on how well each indi-vidual fi ts a given environment and is then evaluated by survival of the fi tness. Fit individuals go through the process of survival selection, crossover, and mutation, resulting in creating next generation, called child individuals. A new population is therefore formed by selecting good individuals from parent and child individuals. After some generations, the algorithm converges to a best individual, which prob-ably represents the best solution of the given problem.

Once the geometrical structure sizes have been obtained by the GA-based individuals decoded, rating performance can be carried out under the specifi ed

Figure 3: Flowchart of optimization process.

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DESIGN OPTIMIZATION AND PERFORMANCE PREDICTION OF COMPACT HEAT EXCHANGERS 305

requirements. The heat exchanger effi ciency versus number of transfer units (e-NTU) method is used. For the rating performance of a heat exchanger, the data of heat transfer, j factors, and friction factors, f factors, are required for various Reynolds numbers. This is because in the optimization process, the shape param-eters vary as GA searches and combines, in return leading to changing Reynolds numbers, fi xed fl ow rate, while cross-section of passage is changed. Therefore, it is diffi cult and inconvenient to look for j and f from the fi gure of the reference as there are many possible combinations in the search process of GA. Fortunately, ahead of GA search relations among j and f versus Re are in-house obtained by curve-fi tting experimental data from Kays and London [52]. In this study, a fi ve-order polynomial relation is used to correlate the data. Thus, once the relations have been built, the computer-aided search and acquisition can be conducted.

2.3 Optimization results and discussion

2.3.1 Minimum annual costThe objective function of minimum annual cost is expressed as

Total annual cost = annualized cost of heat transfer area +