Thermal-economic multi-objective optimization of plate fin heat exchanger using genetic algorithm

Thermal modeling and optimal design of compact heat exchangers are presented in this paper. ε–NTU$\epsilon ''–''\mathit{NTU}$ method was applied to estimate the heat exchanger pressure drop and effectiveness. Fin pitch, fin height, fin offset length, cold stream flow length, no-flow length and hot stream flow length were considered as six design parameters. Fast and elitist non-dominated sorting genetic-algorithm (NSGA-II) was applied to obtain the maximum effectiveness and the minimum total annual cost (sum of investment and operation costs) as two objective functions. The results of optimal designs were a set of multiple optimum solutions, called ‘Pareto optimal solutions’. The sensitivity analysis of change in optimum effectiveness and total annual cost with change in design parameters of the plate fin heat exchanger was also performed and the results are reported. As a short cut for choosing the system optimal design parameters the correlations between two objectives and six decision variables with acceptable precision were presented using artificial neural network analysis.     

Modeling and effect of leakages on heat transfer performance of fixed matrix regenerators

The following undesired leakages are inherent in operation of fixed matrix regenerators: gas pressure leakages due to pressure difference such as leakages through the valves and through cracks in regenerator housing for very high temperature heat recovery, and carryover leakages from the hot gas to cold gas and vice versa. The objective of this paper is to present a methodology for evaluation of the leakages and to determine quantitatively the detrimental influence of pressure leakages on the regenerator heat transfer performance. In this respect, a drop (reduction) in actual regenerator heat transfer effectiveness due to various leakages is presented in the paper. The results clearly suggest that a drop in the effectiveness due to leakages can be significant and depends on the category of leakages. The flow leakages due to the cracks in the regenerator housing have the most impact on reducing the regenerator performance.     

Performance analysis of a closed regenerated Brayton heat pump with internal irreversibilities

This paper analyses the performance of a real heat pump plant via methods of entropy generation minimization or finite‐time thermodynamics. The analytical relations between heating load and pressure ratio, and between coefficient of performance (COP) and pressure ratio of real closed regenerated Brayton heat pump cycles coupled to constant‐ and variable‐temperature heat reservoirs are derived. In the analysis, the irreversibilities include heat transfer‐irreversible losses in the hot‐ and cold‐side heat exchangers and the regenerator, the non‐isentropic expansion and compression losses in the compressor and expander, and the pressure drop loss in the pipe and system. The optimal performance characteristics of the cycle may be obtained by optimizing the distribution of heat conductances or heat transfer surface areas among the two heat exchangers and the regenerator, and the matching between working fluid and the heat reservoirs. The influence of the effectiveness of regenerator, the effectiveness of hot‐ and cold‐side heat exchangers, the efficiencies of the expander and compressor, the pressure recovery coefficient and the temperature of the heat reservoirs on the heating load and COP of the cycle are illustrated by numerical examples. Published in 1999 by John Wiley & Sons, Ltd.     

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

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 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.     

新型档位蓄热器的开发与研究

研究开发了一种可应用在高温空气燃烧（HTAC）技术中的新型蓄热器--档位蓄热器.档位蓄热器吸收了回转式蓄热器的思想,结合了切换式蓄热器的特点,将二者的优势融合在一起,其外观类似于回转式蓄热器,但运动型式却由回转式蓄热器的连续运动变为间歇转动,且具有了新型的密封结构.对档位蓄热器的基本工作原理、具体设计方案、实验研究及应用前景进行了详细介绍.研究结果表明档位蓄热器具有以下特点：可实现对炉窑的连续供气,保证了炉内火焰的稳定性,从而使炉内工况不易波动;另外系统的漏风率较低,阻力损失也较低,并且设备紧凑、操作安全可靠,易于实现标准化生产.实验研究的结果证明该蓄热器的温度效率可达88%,热效率可达77%.     

Multi-objective optimization of shell and tube heat exchangers

The effectiveness and cost are two important parameters in heat exchanger design. The total cost includes the capital investment for equipment (heat exchanger surface area) and operating cost (for energy expenditures related to pumping). Tube arrangement, tube diameter, tube pitch ratio, tube length, tube number, baffle spacing ratio as well as baffle cut ratio were considered as seven design parameters. For optimal design of a shell and tube heat exchanger, it was first thermally modeled using ε–NTU method while Bell–Delaware procedure was applied to estimate its shell side heat transfer coefficient and pressure drop. Fast and elitist non-dominated sorting genetic algorithm (NSGA-II) with continuous and discrete variables were applied to obtain the maximum effectiveness (heat recovery) and the minimum total cost as two objective functions. The results of optimal designs were a set of multiple optimum solutions, called ‘Pareto optimal solutions’. The sensitivity analysis of change in optimum effectiveness and total cost with change in design parameters of the shell and tube heat exchanger was also performed and the results are reported.     

Explicit Design of Balanced Regenerators

An explicit procedure for the design and sizing of balanced regenerators has been developed. A set of performance curves relating the thermal ratio, harmonic mean reduced length and period, and minimum cold fluid outlet temperature is presented. The specific characteristics of the regenerator's matrix including the heat transfer and pressure drop correlations are used to develop interrelations, represented by a set of three design curves, between these quantitites and the operating characteristics of the regenerator. The performance and design curves are used in the design procedure to determine the dimensions of the regenerator for the specified operating conditions.     

Linear analysis of rapidly switched heat regenerators in counterflow

This paper is intended to provide an accurate analytical solution to the 1D differential equations modelling cyclic steady heat transfer processes in rapidly switched heat regenerators for any value of the flush ratio. The temperature solution for the fluid is initially given in an integral form along the path of a gas particle as a function of the matrix temperature for different space and time intervals. In particular, as a Lagrange system of reference is assumed, the above solution deals separately with gas particles of three possible types (‘cold’, ‘hot’ and ‘internal’) according to Organ’s concept of independent flow regimes. Also, it accounts for the possible superposition of the so-called hot and cold zones of the regenerative matrix depending on the value of the flush ratio. Then, assuming a linear distribution for the matrix temperature, the fluid temperature may analytically be calculated. A closed-form expression for the regenerator effectiveness as a function of NTU and flush ratio is given. It provides a simple but accurate tool to estimate the regenerator effectiveness in rapid cyclic flow situations and the deriving results indicate that it is underestimated by the conventional regenerator theory.     

Thermodynamic and Economic Optimization of Plate Fin Heat Exchangers Using the Bees Algorithm

This study presents the successful application of the bees algorithm (BA) for optimal design of a cross‐flow plate fin heat exchanger by offset strip fins. The ε – NTU method is used to approximate the heat exchanger effectiveness and pressure drop. Two different objective functions including the minimization of total annual cost (sum of investment and operational costs) and total number of entropy generation units for certain heat duty required under given space constraints are considered as targets of optimization separately. Based on the applications, seven design parameters (heat exchanger length at hot and cold sides, fin height, fin frequency, fin thickness, fin‐strip length, and number of hot side layers) are selected as optimization variables. Two examples from the literature are presented to illustrate the efficiency and accuracy of the proposed algorithm. Results showed that the BA can detect an optimum configuration with higher speed (short computational time) and accuracy compared to the imperialist competitive algorithm (ICA) and the genetic algorithm (GA). © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 427–446, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21087     

Some Essential Principles for Adjustment of Seal Clearances in Rotary Regenerators

Abstract

In the present study, attention is paid to some indispensable principles for making a useful adjustment of seal clearances in a rotary regenerator, illustrated by means of examples. First, the effect of leakages and their distribution within such a heat exchanger on the efficiency of a steam power plant is presented. In this way it is shown that not only total leakage but also the distribution of the leakages within the rotary regenerator have an important influence on the efficiency. An interesting conclusion appears here—reduction in total leakage may even bring about a drop in power plant efficiency if distribution of leakages changes unfavorably. Second, in order to show in which rotor state seal clearances should be adjusted, appropriate examples of experimental results concerning radial seal clearances in the hot and cold rotor state are compared. Next, on the basis of a leakage network and some experimental data before and after reduction in radial seal clearances, the effect of reduction in seal clearances on the total leakage and its distribution within a rotary regenerator is shown. Thus the value of such a reduction for the efficiency of a steam power plant is evaluated.     

Empirical estimation of regenerator efficiency for a low temperature differential Stirling engine

An experimental method of regenerator evaluation is proposed in this paper. The configuration of the experimental equipment used in the method is similar to that of an alpha-configuration Stirling engine with a phase angle of 180°. The temperature of the hot side heat exchanger is controlled by an electric heater, and the heat sink was room air. An air conditioner controlled the temperature of the room air. The temperature and pressure of the working fluid were measured during the piston motion. A #18 stainless steel mesh was used as a regenerator matrix for a low temperature differential Stirling engine (LTDSE). The regenerator efficiency can be calculated based on the measurement results. The product of the swept volume, the density of the working fluid, the specific heat and the difference in the working fluid temperatures between the hot side and the cold side is greater than the amount of the internal energy fluctuation. The reason for this is assumed to be the temperature fluctuation in the region between the two heat exchangers. The walls of the region are made of acrylic resin. The amount of the temperature fluctuation in the region is assumed to be uniform. The regenerator efficiency is calculated as a function of the temperature fluctuation in the region. The evaluation method does not require a fast-response thermocouple. The prediction of the regenerator efficiency is possible basted on some experimental results of same matrix. Polyurethane foam and #18 stainless steel mesh, layered parallel to the stream line of the working fluid, were each tested. These materials can realize a non-rectangular regenerator without the generation of waste. Non-rectangular regenerator includes regenerator that can be installed into narrow gaps. The regenerator efficiency of the stainless steel mesh layered parallel to the stream line of the working fluid was significantly less in comparison to that of the normal mesh layers. In the polyurethane foam case, a pressure loss was observed.     

Conceptual optimization of a rotary heat exchanger with a porous core

The present article numerically optimizes the thermal performance of a rotary heat exchanger (RHEx) where its internal structure is modeled as a porous medium. The objective is to maximize the RHEx's heat transfer rate per unit of frontal surface area (q″). The flow velocity through the porous matrix respects Darcy's law. Two thermal conditions between the solid matrix and the fluid are considered: (i) local thermal equilibrium – LTE and (ii), non-local thermal equilibrium – NLTE. The numerical calculations, which are implemented using a finite volume formulation, allow us to optimize two design variables, the length L of the heat exchanger and the porosity φ. The numerical results show that the figure of merit is substantially affected by both design variables and that optimal values of L and φ can be obtained. The numerical experiments also show that the optimum porosity is not a function of the pressure difference driving the flow across the RHEx. The study ends by addressing the effects of the porosity distribution and differential periods between the hot and cold sides of RHEx on the figure of merit. The numerical results are supported by a scale analysis.     

Cooling load density characteristics of an endoreversible variable‐temperature heat reservoir air refrigerator

The performance optimization of an endoreversible air refrigerator with variable‐temperature heat reservoirs is carried out by taking the cooling load density, i.e. the ratio of cooling load density to the maximum specific volume in the cycle, as the optimization objective in this paper. The analytical relations of cooling load, cooling load density and coefficient of performance are derived with the heat resistance losses in the hot‐ and cold‐side heat exchangers. The maximum cooling load density optimization is performed by searching the optimum pressure ratio of the compressor, the optimum distribution of heat conductance of the hot‐ and cold‐side heat exchangers for the fixed total heat exchanger inventory, and the heat capacity rate matching between the working fluid and the heat reservoirs. The influences of some design parameters, including the heat capacitance rate of the working fluid, the inlet temperature ratio of heat reservoirs and the total heat exchanger inventory on the maximum cooling load density, the optimum heat conductance distribution, the optimum pressure ratio and the heat capacity rate matching between the working fluid and the heat reservoirs are provided by numerical examples. The refrigeration plant design with optimization leads to a smaller size including the compressor, expander and the hot‐ and cold‐side heat exchangers. Copyright © 2002 John Wiley & Sons, Ltd.     

Thermodynamic analysis of a Stirling engine including dead volumes of hot space, cold space and regenerator

This paper provides a theoretical investigation on the thermodynamic analysis of a Stirling engine. An isothermal model is developed for an imperfect regeneration Stirling engine with dead volumes of hot space, cold space and regenerator that the regenerator effective temperature is an arithmetic mean of the heater and cooler temperature. Numerical simulation is performed and the effects of the regenerator effectiveness and dead volumes are studied. Results from this study indicate that the engine net work is affected by only the dead volumes while the heat input and engine efficiency are affected by both the regenerator effectiveness and dead volumes. The engine net work decreases with increasing dead volume. The heat input increases with increasing dead volume and decreasing regenerator effectiveness. The engine efficiency decreases with increasing dead volume and decreasing regenerator effectiveness.     

Exergy transfer effectiveness on heat exchanger for finite pressure drop

In this paper, exergy transfer effectiveness is defined to describe the performance of heat exchangers operating above/below the surrounding temperature with/without finite pressure drop. It is discussed systemically that the effects of heat transfer units number, the ratio of the heat capacity of cold fluids to that of hot fluids and flow patterns on exergy transfer effectiveness of heat exchangers. Furthermore, the results of exergy transfer effectiveness with a finite pressure drop are compared with those without pressure drop when different objective media, such as ideal gas and incompressible liquid, etc. are applied. The detailed comparisons of the exergy transfer effectiveness with heat transfer effectiveness are also performed for the parallel flow, counter flow and cross flow heat exchangers operating above/below the surrounding temperature.     

Analysis of effectiveness and pressure drop in micro cross-flow heat exchanger

A theoretical model that predicts the thermal and fluidic characteristics of a micro cross-flow heat exchanger is developed in this study. The theoretical model is validated by comparing the theoretical solutions with the experimental data from the relative literature. This model describes the interactive effect between the effectiveness and pressure drop in the micro heat exchanger. The analytical results show that the average temperature of the hot and cold side flow significantly affects the heat transfer rate and the pressure drop at the same effectiveness. Different effectiveness has a great influence upon the heat transfer rate and pressure drop. When the micro heat exchanger material is changed from silicon to copper, the thermal conductivity changes from 148 to 400 W/m K. The heat exchanger efficiency is also similar. Therefore, the (1 1 0) orientation silicon based micro heat exchanger made using the MEMS fabrication process is feasible and efficient. Furthermore, the dimensions effect has a great influence upon the relationship between the heat transfer rate and pressure drop. Therefore, the methodology presented in this paper can be used to design a micro cross-flow heat exchanger.     

新型回热器结构设计及换热特性研究

回热器作为斯特林热机的关键部件,对于太阳能斯特林热机整机性能有着重要影响。为克服传统金属丝网回热器结构存在的填料单一,制造成本较高,工艺复杂问题,采用实用等温分析法,以回热器的长径比、通流面积、填料种类以及孔隙率各项回热器参数为基础,设计了一种新型斯特林热机回热器,该回热器具有轴向压降小,换热性能高,结构稳定,加工制造简单的特点。开展了新型回热器和传统金属丝网回热器的换热性能对比研究,采用振荡条件下的局部热平衡方法研究回热器的传热过程,对比传统金属丝网回热器和新型回热器的温度变化,速度变化以及压力变化。结果表明:在整体孔隙率相同的条件下,新型回热器和传统金属丝网回热器相比,整体启动速率相似,但新型回热器压降减少0.04 MPa,速度出现分段式变化,有利于回热器的换热和结构稳定。因此,新型回热器不但在结构上优于传统金属丝网回热器,在换热特性上也优于传统金属丝网回热器。     

Multi-Objective Optimization of R-404A Vapor Condensation in Swirling Flow Using Genetic Algorithms

Applying twisted tape inserts as a passive improvement technique increases both pressure drop and heat transfer coefficient. In the design of heat exchangers, decreasing of pressure drop and increasing of heat transfer coefficient simultaneously comprise an important aim. In this study, multi-objective optimization is used to find optimum combinations of heat transfer coefficient and pressure drop during condensation of R404A vapor inside twisted-tape-inserted tubes. At first, Pareto-based multi-objective optimization is used to find the proper artificial neural networks based on the experimental data for prediction of heat transfer coefficient and pressure drop. In the next step, Pareto-based multi-objective optimization and previously obtained artificial neural networks are used to find optimal operation conditions that lead to optimum combinations of heat transfer coefficient and pressure drop. The corresponding optimal set of design variables, namely, mass velocity, vapor quality, and dimensional parameters of tubes, show the important design aspects.     

Minimization of entropy generation in flat heat pipe

A thermodynamic model of flat heat pipe is developed based on the laws of thermodynamics. Major reasons for entropy generation, which is considered as a significant parameter on heat pipe performance, are temperature difference between hot and cold reservoirs, frictional losses in the flow of working fluid, and vapor temperature and pressure drop along heat pipe. The objective of the present work is to minimize the entropy generation in a flat heat pipe. The physical situation is formulated as a non-linear programming problem with non-linear objective function and constraints. Using available software, the optimum values of selected design variables are arrived. The effect of heat load, adiabatic length, etc. on the optimum design variables and corresponding entropy generation are studied.     

应用遗传算法优化设计紧凑式换热器

应用遗传算法对锯齿型板翅式换热器的结构进行了优化设计.以预定的传热量、两侧压降、体积等设计要求为适应度函数,通过对设计变量构成的种群个体进行适应度评估以及选择、交叉、变异等遗传操作,得到符合设计约束的换热器最优结构参数(如翅高、翅长、间距,以及长、宽、高等).此外,对10次计算得到的设计参数进行了统计分析.结果表明:相关结构参数的不确定度很小,应用遗传算法可以快速方便地对紧凑式换热器的几何结构参数作出符合设计要求的选择.