Objective function proposed for optimization of convective heat transfer devices

In this work, a general method using exergy analysis has been proposed to achieve a compromise between heat transfer effectiveness and pressure loss in heat transfer optimization problems involving internal channels. The proposed method is applied to the design optimization of a channel roughened by staggered arrays of dimples for heat transfer augmentation. Optimization is performed using surrogate-based optimization techniques and three-dimensional Reynolds-averaged Navier–Stokes analysis. Three nondimensional design variables are defined using the dimpled channel height, dimple print diameter, dimple spacing, and dimple depth. The objective function is defined as the net exergy gain considering the exergy gain by heat transfer, and exergy losses generated by friction and heat transfer. Twenty design points are generated using Latin hypercube sampling, and the Kriging model is used as a surrogate model to approximate the objective function values in the design space. Through optimization, the objective function is successfully improved with respect to the reference geometry.     

Optimal design of plate-fin heat exchangers by a hybrid evolutionary algorithm

This study explores the first application of a Genetic Algorithm hybrid with Particle Swarm Optimization (GAHPSO) for design optimization of a plate-fin heat exchanger. A total number of seven design parameters are considered as the optimization variables and the constraints are handled by penalty function method. The effectiveness and accuracy of the proposed algorithm is demonstrated through an illustrative example. Comparing the results with the corresponding results using GA and PSO reveals that the GAHPSO can converge to optimum solution with higher accuracy.     

The application of field synergy number in shell-and-tube heat exchanger optimization design

In the present work the field synergy principle is applied to the optimization design of the shell-and-tube heat exchanger with segmental baffles. The field synergy number which is defined as the indicator of the synergy between the velocity field and the heat flow is taken as the objective function. The genetic algorithm is employed to solve the heat exchanger optimization problems with multiple design variables. The field synergy number maximization approach for heat exchanger optimization design is thus formulated. In comparison with the initial design, the optimal design leads to a significant cost cut on the one hand and an improvement of the heat exchanger performance on the other hand. The comparison with the traditional heat exchanger optimization design approach with the total cost as the objective function shows that the field synergy number maximization approach is more advantageous.     

Optimization of plate-fin heat exchangers by an improved harmony search algorithm

This study explores the use of a proposed variant of harmony search algorithm for design optimization of plate-fin heat exchangers. The algorithm deals with a large number of continuous and discrete variables. To handle the constraints in the optimization problem, a self-adaptive penalty function scheme is used. The efficiency and accuracy of the proposed method are demonstrated through an illustrative example taken from previous studies. Numerical results indicate that the presented approach can generate optimum solutions with higher accuracy when compared to Genetic algorithms (GAs), Particle Swarm Optimization (PSO) and GA hybrids with PSO (GAHPSO).     

Application of a Genetic Algorithm for Thermal Design of Fin-and-Tube Heat Exchangers

Instead of the traditional trial-and-error process, a genetic algorithm (GA) is successfully applied to thermal design of fin-and-tube heat exchangers (FTHEs). The design method uses a GA to search and optimize structure sizes of FTHEs. The minimum total weight or total annual cost of FTHEs is taken as the objective function in the GA, respectively. Seven design parameters are varied for the optimization objectives. The implementation of the design method consists of a GA routine and a thermal design routine. In the GA routine, binary coding for tournament selection, uniform crossover, and one-point mutation is adopted. In the thermal design routine, thermal design of the FTHE is carried out according to the conditions of the structure sizes that the genetic algorithm generated, and the log-mean temperature difference method is used to determine the heat transfer area under the combined structure sizes for a given heat duty. Optimization shows that it is possible to achieve a great reduction in cost or weight, whenever such objectives have been chosen for minimization. The method is universal and may be used for thermal design and optimization of FTHEs under different specified duties.     

Exergetic optimization of shell and tube heat exchangers using a genetic based algorithm

In the computer-based optimization, many thousands of alternative shell and tube heat exchangers may be examined by varying the high number of exchanger parameters such as tube length, tube outer diameter, pitch size, layout angle, baffle space ratio, number of tube side passes.In the present study, a genetic based algorithm was developed, programmed, and applied to estimate the optimum values of discrete and continuous variables of the MINLP (mixed integer nonlinear programming) test problems. The results of the test problems show that the genetic based algorithm programmed can estimate the acceptable values of continuous variables and optimum values of integer variables. Finally the genetic based algorithm was extended to make parametric studies and to find optimum configuration of heat exchangers by minimizing the sum of the annual capital cost and exergetic cost of the shell and tube heat exchangers. The results of the example problems show that the proposed algorithm is applicable to find optimum and near optimum alternatives of the shell and tube heat exchanger configurations.     

基于CFO的海上风电场微观选址优化算法研究

海上风电场用海面积有限,尾流影响比陆上大,微观选址是其规划设计的关键技术。传统优化算法大多采用离散化变量,使得潜在解空间减少到有限个,难以达到最优化的效果。为了提高海上风电场微观选址优化效率,文章提出了一种基于中心引力优化(CFO)算法的海上风电场微观选址方法。该算法使用实数编码,通过将微观选址优化的变量假设为天体,各个天体之间相互作用,达到平衡的原理,具有可能得到全局最优解和效率高的优点。使用该算法对海上风电场微观选址优化进行仿真,并与现有方法比较。结果表明,所提出的算法得到的排布方式发电量最高,并具有优化精度高、速度快和优化排布较为均匀的特点。该研究结果可以为实际工程应用提供参考。     

Enhanced multi-objective optimization of a microchannel heat sink through evolutionary algorithm coupled with multiple surrogate models

A liquid flow microchannel heat sink has been optimized with the help of three-dimensional numerical analysis and multiple surrogate methods. Two objective functions, thermal resistance and pumping power have been selected to assess the performance of the microchannel heat sink. The design variables related to the width of the microchannel at the top and bottom, depth of the microchannel, and width of fin, which contribute to objective functions, have been identified and a three-level full factorial design was selected to exploit the design space. The numerical solutions obtained at these design points were utilized to construct surrogate models, namely Response Surface Approximations, Kriging and Radial Basis Neural Network. A hybrid multi-objective evolutionary algorithm coupled with surrogate models is applied to find out global Pareto-optimal solutions. The accuracy of the surrogate models has been discussed in view of their predictions and trade-off analysis was performed in view of conflicting nature of the two objectives. The Pareto-optimal sensitivity of the design variables has been found out to economically compromise with the design variables. The application of the multiple surrogate methods not only improves quality of multi-objective optimization but also gives the feedback of the fidelity of the optimization model.     

Comprehensive optimization of a heat pipe radiator assembly filled with ammonia or acetone

Optimal mass characteristics for a heat pipe radiator assembly for space application are investigated. The assembly consists of the heat pipe itself, an evaporator saddle and a radiator. The internal HP geometry and the dimensions of the saddle and radiator panel are the variables to be optimized. Operational and structural constraints are considered and the assembly is optimized for different operational modes in 0g and 1g gravity conditions. A new global search metaheuristic, called generalized extremal optimization, was used as the optimization tool. The results show that under certain combinations of input parameters the assembly with acetone HP can be more weight effective than the one with ammonia, in spite of the liquid transport factor criterion indicates an opposite trend.     

Contribution for optimal sizing of grid-connected PV-systems using PSO

Particle Swarm Optimization (PSO) is an optimization algorithm considered to be highly efficient for the solution of complicated problems. This paper presents the application of this method for the design optimization of photovoltaic grid-connected systems (PVGCSs). The purpose of the proposed methodology is to locate the optimal number of system devices and the optimal values of the PV module installation details, such that the total net economic benefit achieved during the system operational lifetime period is maximized. The optimization's decision variables are the optimal number of the PV modules, the PV modules optimal tilt angle, the optimal placement of the PV modules within the available installation area and the optimal distribution of the PV modules among the DC/AC converters. The objective function of the proposed optimization process is the lifetime system's total net profit which is calculated according to the method of the Net Present Value (NPV). The methodology's resulting system structures are economically evaluated through the methods of the discounted payback time and the Internal Rate of Return (IRR). The PSO algorithm is compared to the application of Genetic Algorithms (GAs) in terms of efficiency for the current problem.     

离心压气机的初步设计及其优化方法

提出了一种对工程实际设计具有指导意义的离心压气机初步设计及其优化计算方法。这种方法把离心压气机划分成几个截面进行迭代计算,使用完善的损失模型对离心压气机中出现的各种流动损失进行模拟,为了保证计算精度,该数学模型中对叶轮出口和扩压器入口区域采用交错网格方法对压力分布和速度分布进行求解。程序中可以优化的参数有6个,可在这6个参数中任意选取2个或3个参数进行优化计算,为了验证这种方法的可行性,对比了采用一般方法和采用本方法进行初步设计的计算结果。最后,对离心压气机初步设计及其优化方法中的几个问题进行了探讨,如不同叶轮后弯角对优化结果的影响,叶片入口平均宽度对优化结果的影响。部分损失系数随后弯角变化的趋等。     

Shape Optimization of a Dimpled Channel to Enhance Heat Transfer Using a Weighted-Average Surrogate Model

Shape optimization of a rectangular channel with the opposite walls roughened by staggered arrays of dimples has been performed not only to enhance turbulent heat transfer but also to reduce friction loss. The dimpled channel shape is defined by three geometric design variables, and the design points within design space are selected using Latin hypercube sampling. The shape of the channel is optimized with three-dimensional (3-D) Reynolds-averaged Navier–Stokes analysis and surrogate approximation methods. A weighted-sum method for multi-objective optimization is applied to integrate multiple objectives related to heat transfer and friction loss into a single objective. A weighted-average surrogate model is employed for this optimization. By the optimization, the objective function value is improved largely and heat transfer rate is increased much higher than pressure loss increase due to shape deformation. The optimum design results in lower channel height, wider dimple spacing, and deeper dimple. The flow mechanism shows the heat transfer rate is increased mainly in the rear portion of the dimple.     

Multi-Objective Optimization of an Inverse Trapezoidal-Shaped Microchannel

The microchannel with inverse trapezoidal cross section in a micro heat sink has been optimized using three-dimensional Navier–Stokes analysis and a multi-objective evolutionary algorithm. Thermal resistance and pressure drop were selected as objective functions to evaluate the performance of the microchannel heat sink. Three design variables related to the width, depth, and angle of the channel, respectively, were selected for optimization. Parametric study has been performed with the three design variables prior to the optimization to analyze the variation of objective functions with the design variables, and thus to determine the design space for the optimization. Using a finite-volume solver, Navier–Stokes and energy equations for laminar flow and conjugate heat transfer were solved for the constant mass flow rate of 0.000598 kg/s. Latin hypercube sampling was utilized to select the design points. A surrogate model for each objective function was constructed using the values of the objective function calculated at the design points. Pareto-optimal solutions were obtained to find the optimal designs of the microchannel. Pareto sensitivity analysis was performed for the design variables along the Pareto optimal front, and it was found that both the objective functions were most sensitive to the design variable that is related to the width of the microchannel.     

Air-Cooled Heat Exchanger Design Using Successive Quadratic Programming (SQP)

A nonlinear optimization algorithm is applied to the design of air-cooled heat exchangers. In such equipment, the cold fluid (air) is impelled across banks of finned tubes by means of fans in forced or induced draft. The hot stream flows inside the tubes in one or more passes, and the process that takes place may be cooling of either a gas or a liquid, or condensation of either a pure vapor or a mixture. The objective function is the minimum cost of the unit (investment and operation), subject to certain geometric and thermohydraulic constraints. The optimization algorithm used is that developed by Biegler and Cuthrell [1], and programmed by them in the OPT package. The problem posed in this case is made of 10 optimization variables, subject to five constraints related to geometric and operational parameters of the heat exchanger.     

Optimization design of shell-and-tube heat exchanger by entropy generation minimization and genetic algorithm

In the present work, a new shell-and-tube heat exchanger optimization design approach is developed, 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 is employed as the objective function, some geometrical parameters of the shell-and-tube heat exchanger are taken as the design variables and the genetic algorithm is applied to solve the associated optimization problem. It is shown that for the case that the heat duty is given, not only can the optimization design increase the heat exchanger effectiveness significantly, but also decrease the pumping power dramatically. In the case that the heat transfer area is fixed, the benefit from the increase of the heat exchanger effectiveness is much more than the increasing cost of the pumping power.     

基于改进拉格朗日算法的风光互补系统优化设计研究

从风光互补系统的经济性出发研究了风光互补系统的优化设计问题。以年度平均电量成本最小化作为目标,将太阳能光伏板面积、风电机组额定功率和蓄电池最大储能容量作为决策变量,构建了风光互补系统优化设计模型,并通过引入互补约束条件,将分段函数转化为连续函数,利用改进的拉格朗日分解法,由上而下分阶段求解模型。实例应用结果表明,利用优化模型计算所得结果在经济性和运算效率上有明显提高,验证了模型的可行性和算法的有效性。     

Multiobjective Particle Swarm Optimization for the optimal design of photovoltaic grid-connected systems

Particle Swarm Optimization (PSO) is a highly efficient evolutionary optimization algorithm. In this paper a multiobjective optimization algorithm based on PSO applied to the optimal design of photovoltaic grid-connected systems (PVGCSs) is presented. The proposed methodology intends to suggest the optimal number of system devices and the optimal PV module installation details, such that the economic and environmental benefits achieved during the system’s operational lifetime period are both maximized. The objective function describing the economic benefit of the proposed optimization process is the lifetime system’s total net profit which is calculated according to the method of the Net Present Value (NPV). The second objective function, which corresponds to the environmental benefit, equals to the pollutant gas emissions avoided due to the use of the PVGCS. The optimization’s decision variables are the optimal number of the PV modules, the PV modules optimal tilt angle, the optimal placement of the PV modules within the available installation area and the optimal distribution of the PV modules among the DC/AC converters.     

Optimization of fractal-like branching microchannel heat sinks for single-phase flows

Fractal-like branching flow networks in disk-shaped heat sinks are numerically optimized to minimize pressure drop and flow power. Optimization was performed using a direct numerical search, gradient-based optimization, and genetic algorithm. A previously validated one-dimensional pressure drop and heat transfer model, with water as the working fluid, is employed as the objective function. Geometric constraints based on fabrication limitations are considered, and the optimization methodology is compared with results from a direct numerical search and a genetic algorithm.The geometric parameters that define an optimal flow network include the length scale ratio, width scale ratio, and terminal channel width. Along with disk radius, these parameters influence the number of branch levels and number of channels attached to the inlet plenum. The geometric characteristics of the optimized flow networks are studied as a function of disk radius, applied heat flux, and maximum allowable wall temperature. A maximum inlet plenum radius, minimum interior channel spacing, and ranges of terminal channel widths and periphery channel spacing are specified geometric constraints. In general, all geometric constraints and the heat flux have a significant influence on the design of an optimal flow network. Results from a purely geometrically derived network design are shown to perform within 15% of the direct search and gradient-based optimized configurations.     

Analysis and optimization of electrokinetic microchannel heat sink

A mixed (electroosmotic and pressure-driven) flow microchannel heat sink has been studied and optimized with the help of three-dimensional numerical analysis, surrogate methods, and the multi-objective evolutionary algorithm. Two design variables; the ratio of the microchannel width-to-depth and the ratio of fin width-to-depth of the microchannel are selected as the design variables while design points are selected through a four-level full factorial design. The single-objective optimization is performed taking overall thermal resistance as the objective function and Radial Basis Neural Network as the surrogate model while for multi-objective optimization pumping power is considered as the objective function along with the thermal resistance. It is observed that the optimum design shifted towards the lower values of the ratio of the channel width-to-depth and the higher values of the ratio of fin width-to-depth of channel with increase of the driving source. The trade-off between the two conflicting objectives has been found and discussed in detail in light of the distribution of Pareto-optimal solutions in the design space. The ratio of channel width-to-depth is found to be higher Pareto-sensitive (sensitivity along the Pareto-optimal front) than the ratio of fin width-to-depth of the channel.     

Design and economic optimization of shell and tube heat exchangers using Artificial Bee Colony (ABC) algorithm

In this study, a new shell and tube heat exchanger optimization design approach is developed. Artificial Bee Colony (ABC) has been applied 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 such as tube length, tube outer diameter, pitch size, baffle spacing, etc. Finally, the results are compared to those obtained by literature approaches. The obtained results indicate that Artificial Bee Colony (ABC) algorithm can be successfully applied for optimal design of shell and tube heat exchangers.