Optimal shape design for packaging containing heating elements by inverse heat transfer method

The present study is concerned with the determination of the optimal shape for a package containing multiple heating elements. The optimization tool has been developed based on the inverse heat transfer (IHT) approach, incorporating a direct problem solver, a numerical grid generator, a direct-differentiation sensitivity analyzer, and the conjugate gradient method. Shape design that leads to a specified outer surface temperature distribution is predicted by the approach. In this study, the effects of internal heat generation on optimal shapes of the packagings have also been evaluated. Several practical cases with various imbedded heating elements and thermal conditions are studied. Results show that the approach provides an efficient computer-aided design scheme for the shape profile determination.     

Improved non-dominated sorting genetic algorithm （NSGA）-II in multi-objective optimization studies of wind turbine blades

The non-dominated sorting genetic algorithm (NSGA) is improved with the controlled elitism and dynamic crowding distance. A novel multi-objective optimization algorithm is obtained for wind turbine blades. As an example, a 5 MW wind turbine blade design is presented by taking the maximum power coefficient and the minimum blade mass as the optimization objectives. The optimal results show that this algorithm has good performance in handling the multi-objective optimization of wind turbines, and it gives a Pareto-optimal solution set rather than the optimum solutions to the conventional multiobjective optimization problems. The wind turbine blade optimization method presented in this paper provides a new and general algorithm for the multi-objective optimization of wind turbines.     

Thermal-economic multi-objective optimization of shell and tube heat exchanger using particle swarm optimization (PSO)

Many studies are performed by researchers about shell and tube heat exchanger (STHE) but the multi-objective particle swarm optimization (PSO) technique has never been used in such studies. This paper presents application of thermal-economic multi-objective optimization of STHE using PSO. For optimal design of a STHE, it was first thermally modeled using e-number of transfer units method while Bell–Delaware procedure was applied to estimate its shell side heat transfer coefficient and pressure drop. Multi objective PSO (MOPSO) method was 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’. In order to show the accuracy of the algorithm, a comparison is made with the non-dominated sorting genetic algorithm (NSGA-II) and MOPSO which are developed for the same problem.     

Three-dimensional analysis of fluid flow and heat transfer in single- and two-layered micro-channel heat sinks

A three-dimensional numerical analysis of laminar fluid flow and conjugate heat transfer has been conducted for single- and two-layered micro-channel heat sinks. The validity of the numerical model has been confirmed by comparison with available experimental data. Results for the overall thermal resistance, pumping power, the maximum temperature difference on the heat-sink surface where the heat flux is applied, and an overall performance parameter were obtained for single- and two-layered sinks. The effects of Reynolds number, inlet velocity profile, and flow arrangement in the channels (parallel and counter) on these results are presented and discussed. A special emphasis was placed on the comparison between the thermal performances of the parallel and counter flow arrangements and further results were obtained in order to quantify and explain the relative performance under these flow arrangements.     

Multi-objective optimization of a dimpled channel for heat transfer augmentation

Staggered arrays of dimples printed on opposite surfaces of a cooling channel is formulated numerically and optimized with hybrid multi-objective evolutionary algorithm and Pareto optimal front. As Pareto optimal front produces a set of optimal solutions, the trends of objective functions with design variables are predicted by hybrid multi-objective evolutionary algorithm. The problem is defined by three non-dimensional geometric design variables composed of dimpled channel height, dimple print diameter, dimple spacing, and dimple depth, to maximize heat transfer rate compromising with pressure drop. Twenty designs generated by Latin hypercube sampling were evaluated by Reynolds-averaged Navier–Stokes solver and the evaluated objectives were used to construct Pareto optimal front through hybrid multi-objective evolutionary algorithm. The optimum designs were grouped by k-means clustering technique and some of the clustered points were evaluated by flow analysis. With increase in dimple depth, heat transfer rate increases and at the same time pressure drop also increases, while opposite behavior is obtained for the dimple spacing. The heat transfer performance is related to the vertical motion of the flow and the reattachment length in the dimple.     

传热结构的多目标拓扑优化设计研究

深入分析了传热结构多目标拓扑优化设计中的几个关键问题。提出了基于结构柔度最小化和结构散热弱度最小化的多目标拓扑优化设计方法,建立了传热结构的多目标拓扑优化设计模型,推导了传热结构多目标拓扑优化中用于迭代分析求解的优化准则算法和敏度分析方程。通过数值计算验证了理论和算法的有效性。     

Multi-objective optimization of discrete film hole arrangement on a high pressure turbine end-wall with conjugate heat transfer simulations

This paper discussed a method of combining a full automatic multi-objective optimization and conjugate heat transfer calculation to obtain optimal cooling layouts on a transonic high pressure guide vane under a realistic turbine working condition. The improvement in cooling design from the optimized models was analyzed in detail, along with a discussion of sensitivities of two objective functions to five design variables. The full automatic method comprises the process of geometry creation, mesh generation, numerical solution and post data analysis. The vane is solid and the end-wall is arranged in a linear cascade. On the end-wall, film holes are all cylindrical and classified in five regions, with region A near the leading edge of the vane, region B near the suction side, regions C and D near the pressure side, and region E for the rest. Five design variables are three pitch-to-hole ratios in regions B, D, E and two compound angles of film holes in regions A and D. Two selected objective functions are area averaged overall cooling effectiveness of the end-wall and aerodynamic losses in a cross-plane at x/C_ax = 1.06 just downstream of the outlet of the cascade. For the optimization process, the multi-objective genetic algorithm based on the Non-dominated Sorted Genetic Algorithm-II was applied. The Latin hypercube sampling method was used to choose 21 experimental design points in the design space, which are also the sources for constructing the surrogate models with the Kriging model. The results demonstrate that the method using full automatic optimization and conjugate heat transfer calculation has achieved an increase of 8.7%–9.5% in area-averaged overall cooling effectiveness and a reduction of about 4.8%–6.1% in aerodynamic losses. The highest increase in cooling effectiveness exists in the region near the pressure side with a mild increase in the middle of the passage. The largest heat flux reduction exists in the regions near the pressure side and the crown of the suction side. The change of compound angle in region A near the leading edge has a negligible influence on overall cooling effectiveness but a high impact on aerodynamic losses. It's advisable to maintain the compound angle and pitch-to-diameter ratio at low values in region D near the pressure side to obtain high cooling performance.     

Flow and heat transfer over hyperbolic stretching sheets

The boundary layer flow and heat transfer analysis of an incompressible viscous fluid for a hyperbolically stretching sheet is presented. The analytical and numerical results are obtained by a series expansion method and a local non-similarity (LNS) method, respectively. The analytical and numerical results for the skin friction and the Nusselt number are calculated and compared with each other. The significant observation is that the momentum and the thermal boundary layer thickness decrease as the distance from the leading edge increases. The well-known solution of linear stretching is found as the leading order solution for the hyperbolic stretching.     

Mass and heat transfer modeling of bio-substrates during packaging

Perishable bio-substrate behavior can be modeled during packaged storage. Local mass and heattransfer have been coupled to respiration rate and microbial growth. Validating measurements have also been performed, and a multi-objective optimization was employed to tune the model. The model is able to simulate gas composition history and local bacteria spoilage in storage modes commonly adopted by the food industry, depending on product features and temperature. Exploitation of this mathematical tool would allow for informed technical and management decisions.     

A modified multi-objective particle swarm optimization approach and its application to the design of a deepwater composite riser

A modified multi-objective particle swarm optimization method is proposed for obtaining Pareto-optimal solutions effectively. Different from traditional multi-objective particle swarm optimization methods, Kriging meta-models and the trapezoid index are introduced and integrated with the traditional one. Kriging meta-models are built to match expensive or black-box functions. By applying Kriging meta-models, function evaluation numbers are decreased and the boundary Pareto-optimal solutions are identified rapidly. For bi-objective optimization problems, the trapezoid index is calculated as the sum of the trapezoid’s area formed by the Pareto-optimal solutions and one objective axis. It can serve as a measure whether the Pareto-optimal solutions converge to the Pareto front. Illustrative examples indicate that to obtain Pareto-optimal solutions, the method proposed needs fewer function evaluations than the traditional multi-objective particle swarm optimization method and the non-dominated sorting genetic algorithm II method, and both the accuracy and the computational efficiency are improved. The proposed method is also applied to the design of a deepwater composite riser example in which the structural performances are calculated by numerical analysis. The design aim was to enhance the tension strength and minimize the cost. Under the buckling constraint, the optimal trade-off of tensile strength and material volume is obtained. The results demonstrated that the proposed method can effectively deal with multi-objective optimizations with black-box functions.     

考虑破损-安全的连续体结构拓扑优化ICM方法

本文瞄准连续体在破损-安全考虑下的结构拓扑优化问题,旨在克服传统模型求解所得最终构型存在的弊病,避免结构因缺乏合理的冗余结构而敏感于局部破坏,实现破损-安全的目标. 首先,梳理了以往虽然用到却并不明晰的4个概念:结构局部破损模式、结构局部破损区域、结构破损状况、结构破损状况的预估分布. 之后,基于独立连续映射(ICM)方法,对该问题建立了力学性能约束下结构体积极小化的模型. 建立目标函数时,利用Minimax的概念将可能出现的结构破损状况对应的所有结构体积目标转化为原结构的唯一结构体积目标,克服了多目标问题的困难. 建立近似约束函数时,将可能出现的所有结构破损状况对应的力学性能的约束皆考虑进去,既能处理载荷单工况也能处理载荷多工况. 最后,以位移约束为例,建立了优化模型并求解. 单工况及多工况位移约束拓扑优化算例验证了算法的有效性. 结果表明:本方法相比于不考虑破损-安全的拓扑优化设计,得到的最优拓扑更复杂,体积比更大即所用材料更多,亦即最优结构具有更多的冗余,此正是考虑破损-安全设计原则的结果. 本文的研究对于航空、航天、其他水、陆等领域运载工具以及其他工程结构在意外破坏、战争创伤或恐怖袭击下的结构设计,乃是非常重要的进展.      

一种基于路径优化的非平衡自由能预测方法

提出一种基于路径优化的非平衡自由能预测方法。首先,通过建立蛋白质复合物解离的多目标优化模型找出一条能耗小、速度快的拉伸分子动力学SMD(Steered Molecular Dynamics)解离路径,然后,沿此路径计算解离自由能。与Jarzynski按平均力势PMF(Potentials of Mean Force)的外推方法相比,本文方法有较高的预测效率,数值算例也给出了与实验值比较的预测精度。通过拉伸分子动力学模拟还可以揭示小配体与蛋白质之间的解离全过程,为药物设计提供重要的结构信息。     

采用包络-准则法优化考虑瞬态传热的薄板结构

刚度和强度是薄板结构的两个主要性能。在瞬态传热过程中,考虑热-力耦合,随时间和空间变化的非均匀温度场在结构中会引起热变形和热应力,温度场随时间变化的规律和空间分布依赖于板的厚度变化,进而影响板的刚度和强度。因此,考虑瞬态传热的薄板优化问题具有更强的非线性,更加难以求解。本文给出一种包络-准则方法处理这类结构优化问题。首先,针对外力荷载,进行一个结构柔顺性的优化设计;以这一设计为基础,通过瞬态热-力耦合分析及优化准则,计算多个时刻的优化设计变量并取其包络,对上述优化结果进行迭代修正,以消除瞬态温度场作用下较高的局部应力。优化算例表明,该方法对于考虑瞬态传热薄板优化问题有效。     

基于多目标优化策略的结构可靠性稳健设计

应用可靠性稳健优化设计理论和多目标决策方法,将结构可靠性稳健优化设计转化为多目标优化问题。运用灰色理论中的关联分析法,选取粒子群算法中的全局极值和个体极值,提出了灰色粒子群算法求解可靠性稳健优化设计问题。与传统方法相比,该方法简便易行并能迅速准确地得到结构可靠性稳健优化设计信息。     

A computational method for geometric optimization of enhanced heat transfer devices based upon entropy generation minimization

A computational fluid dynamics‐based optimization methodology is developed, appropriate for the geometric optimization of enhanced heat transfer devices based upon the principle of entropy generation minimization, in which the objective function is evaluated from a flow field obtained by computational simulation. A quasi‐Newton optimization procedure is employed, with computation of the objective function gradients based upon a finite difference approach. The optimization procedure is developed to be general with regard to the choice of objective function, the details of the problem under consideration, and the computational methodology employed in solving the fluid flow and heat transfer problems. A novel implementation of a Taylor series‐based procedure for the fast solution of nearby problems is presented, which is found to greatly benefit the efficiency of the present methodology. Finally, a numerical experiment is presented, illustrating the use of the present method in the geometric optimization of a practical enhanced heat transfer device on the basis of the criterion of entropy generation minimization. The optimization of the fin spacing of a simple plate fin heat sink is considered, and a comparison of the computational results with results obtained by analytical optimization based upon empirical friction factor and Nusselt number correlations is given. Copyright © 2012 John Wiley & Sons, Ltd.     

A Comparison of Deterministic,Reliability-Based Topology Optimization under Uncertainties

Reliability and optimization are two key elements for structural design. The reliabilitybased topology optimization(RBTO) is a powerful and promising methodology for finding the optimum topologies with the uncertainties being explicitly considered, typically manifested by the use of reliability constraints. Generally, a direct integration of reliability concept and topology optimization may lead to computational difficulties. In view of this fact, three methodologies have been presented in this study, including the double-loop approach(the performance measure approach, PMA) and the decoupled approaches(the so-called Hybrid method and the sequential optimization and reliability assessment, SORA). For reliability analysis, the stochastic response surface method(SRSM) was applied, combining with the design of experiments generated by the sparse grid method, which has been proven as an effective and special discretization technique.The methodologies were investigated with three numerical examples considering the uncertainties including material properties and external loads. The optimal topologies obtained using the deterministic, RBTOs were compared with one another; and useful conclusions regarding validity,accuracy and efficiency were drawn.     

带有圆弧形凹槽金属薄壁圆管抗撞性优化设计

在金属薄壁圆管的基础上,引入圆弧形凹槽诱导结构并以其为研究对象,建立以凹槽数量及其半径为优化参数,以比吸能和压溃力效率为评价指标的多目标优化模型。分析研究均布设置诱导凹槽对结构吸能、最大峰值压溃力及压溃力曲线平稳性的影响。采用有限元软件LS-DYNA得到不同几何参数模型的碰撞响应,结合径向基函数法构造近似函数,并采用理想点法进行优化设计,得出使结构最优时的凹槽数量和半径,从而得到了理想的诱导凹槽优化结构。     

特定方向"零膨胀"的最小柔顺性结构优化设计

工程中很多承载结构必须面对苛刻的温度变化工作环境,如卫星天线、太空照相机和电子器件等。剧烈的温度变化引起较大的热变形,造成仪器信号失真,精度下降;同时温度应力也会造成结构破坏甚至失效,因此零膨胀材料的研制备受关注。近年来国内外很多学者对此进行了研究,设计出具有特定等效膨胀系数的微结构,但考虑到制备工艺的限制,这类具有复杂微结构的材料制备起来比较困难,成本较高;同时这类材料一般不具备足够的刚度,难以满足承载性能的要求。本文基于结构优化设计技术,采用拓扑优化方法直接设计出具备较高的承载性能和特定方向变形较少受热载荷影响的结构。本文提出采用多目标优化的方法设计圆环结构,使其具有较高的刚度和在热载荷下圆环内表面具有较好的热几何稳定性。由于用单相材料无法同时满足高刚度和低热膨胀的要求,因此假设结构由两种不同的材料构成,用连续体拓扑优化的方法设计三相材料(两种实体材料MAT-I、MAT-II和空材料)在设计域上的最优分布,使结构满足设计要求。由对称性,设计域取为圆环的一个扇面,将设计域离散成有限元网格,每个单元具有两个设计变量:实体材料的体分比和MAT-I在实体材料中所占的体分比,采用伴随法进行灵敏度分析,用GCMMA方法求解此问题,采用体积守恒的Heaviside密度过滤函数保证获得清晰的最优拓扑构型以及避免棋盘格式的出现。通过两个数值算例,表明使用本文提出的多目标优化模型能够得到特定方向"零膨胀"同时具有一定刚度的结构设计,且这种宏观结构尺度上的两种材料组成的拓扑构型相对易于制造。     

Multi-objective optimization of a guide vane in the turning region of a rotating U-duct to enhance heat transfer performance

An optimization has been performed for the design of a guide vane in the turning region of a rotating U-duct using the Kriging meta-model and a hybrid multi-objective evolutionary algorithm. Rotation of the U-duct is accompanied by the Coriolis force that causes a discrepancy in heat transfer between the trailing (pressure) and leading (suction) surfaces of the duct. For the optimization, three geometric variables related to the thickness, angle, and location of the guide vanes are selected as the design variables. A Kriging model is constructed to obtain a Pareto-optimal front through a multi-objective evolutionary algorithm. The values of the objective function at the design points are evaluated by Reynolds-averaged Navier–Stokes analysis. The shear stress transport model is used as the turbulence closure model in the analysis. The tradeoff between the two competing objective functions is discussed for Pareto-optimal solutions in the design space. The optimized guide vanes show an increase in heat transfer performance with a decrease in the friction loss in the turning region and downstream straight passage in comparison with the reference design.     

Multi-objective optimization of a plate and frame heat exchanger via genetic algorithm

In the present paper, a plate and frame heat exchanger is considered. Multi-objective optimization using genetic algorithm is developed in order to obtain a set of geometric design parameters, which lead to minimum pressure drop and the maximum overall heat transfer coefficient. Vividly, considered objective functions are conflicting and no single solution can satisfy both objectives simultaneously. Multi-objective optimization procedure yields a set of optimal solutions, called Pareto front, each of which is a trade-off between objectives and can be selected by the user, regarding the application and the project’s limits. The presented work takes care of numerous geometric parameters in the presence of logical constraints. A sensitivity analysis is also carried out to study the effects of different geometric parameters on the considered objective functions. Modeling the system and implementing the multi-objective optimization via genetic algorithm has been performed by MATLAB.