Temperature-Constrained Topology Optimization of Transient Heat Conduction Problems

A regional temperature measure model is constructed to obtain a small number of temperature constraints for local transient temperature control. The temperature sensitivity is derived using the adjoint variable method. The multiple temperature criteria and three-phase topology optimization are further investigated for transient heat conduction design. The material layout design of transient heat conduction is replaced by a static optimization problem, which is subsequently solved by the method of moving asymptotes. Finally, several numerical examples are provided to demonstrate the feasibility and validity of the proposed topology optimization for transient heat conduction problems.     

Stress constrained thermo-elastic topology optimization based on stabilizing control schemes

Abstract

This article proposes two effective stabilizing control schemes for addressing the stress constrained thermo-elastic topology optimization in a non-uniform temperature field. Based on the density interpolation scheme, two linear elastic equations for coupling a thermo-elastic problem are considered. For comparison, different topology problem formulations for minimizing compliance or volume subject to stress constraints are solved. By virtue of a stabilization transform method, two stabilizing control schemes combined with the grouped aggregation method are developed to handle the challenging difficulties stemming from the local nature of highly nonlinear stress constraints. Moreover, the adjoint method is adopted to perform the sensitivity analysis. The design variables are updated by utilizing the method of moving asymptotes. The results of several typical numerical examples verify the validity of the proposed methodology, including the present stabilizing control schemes which can be employed to obtain clear topological design and fast convergence rate for thermo-elastic coupling problems. Meanwhile, compliance minimization design with stress constraints is appropriate to achieve balance between stress level and stiffness.     

Topology Optimization of Heat and Mass Transfer Problems: Laminar Flow

The design of efficient structures for heat and mass transfer problems involves the implementation of an appropriate topology optimization strategy in order to fully take into account the bi-objective nature of the problem. This article couples the finite-volume method (FVM), for the direct solver, with the discrete adjoint approach, for the sensitivity analysis, in order to tackle both fluid dynamic and heat transfer optimization in the frame of laminar flows. Details are provided about the sparsity pattern of the discrete adjoint system, which requires special attention to select a suitable matrix iterative solver. Several examples underline the adequacy of topology optimization in conjunction with the FVM for the minimization of the power dissipated by the fluid. Then, a bi-objective problem aiming at minimizing the pressure drop while maximizing the recoverable thermal power is solved by the identification of its Pareto frontier, thanks to an aggregate objective function (AOF) method. The main conclusion deals with the possibility of finding an acceptable trade-off between both objectives and the potential of topology optimization for heat and mass transfer optimization.     

Computational Design of Microstructural Composites with Tailored Thermal Conductivity

This article presents a numerical procedure to design two-phase periodic microstructural composites with tailored thermal conductivities, which is generalized as a topology optimization problem. The objective function is formulated in a least-square of the difference between the target and effective conductivities. The effective values are derived from homogenization method with periodic boundaries; whereas, the target points locate in the Milton-Kohn bounds. The bound-based interpolation scheme and nonlinear diffusion technique are explored to regularize the original problem for attaining mesh-independent, edge-preserving, and checkerboard-free results. Various microstructures both in 2- and 3-dimensions are presented to demonstrate such a systematic procedure of conductive material design.     

Power generation enhancement of solid oxide fuel cell by cathode-electrolyte interface modification in mesoscale assisted by level set-based optimization calculation

To explore potential for the power density enhancement of solid oxide fuel cells by controlling the cathode-electrolyte interface in mesoscale, two-dimensional numerical simulations were conducted. In the simulation, a level set-based topology optimization technique was successfully coupled with the SOFC simulation based on a microscale model and was applied for the local optimization of the interface shape. The numerical results showed that the optimized shape of the cathode-electrolyte interface varied depending on the simulation conditions and that the cell performance could be improved by applying non-flat design to the cathode-electrolyte interface for the same amount of cathode/electrolyte materials.     

Evolutionary topology optimization for temperature reduction of heat conducting fields

This paper aims at developing an efficient finite element based computational procedure for the topology design of heat conducting fields. To evaluate the temperature change in a specific position, due to varying the conducting material distribution in other regions, a discrete temperature sensitivity is derived for an evolutionary topology optimization method. In the topology optimization of the conducting fields, the thermal conductivity of an individual finite element is considered as the design variable. By removing or degenerating the conductive material of the elements with the most negative sensitivity, the temperature objective at the control point can be most efficiently reduced. Illustrative examples are presented to demonstrate this proposed approach.     

西门子V94.3A型燃气轮机运行优化浅析

本文简要介绍了国内5家采用西门子V94.3A型燃气轮机的发电厂在燃机日常运行中所遇到的一些问题,诸如:点火失败,燃烧不稳定,锅炉过热蒸汽超温限制燃气轮机OTC等;并结合国外同类机组的运行经验,分别从改进控制策略、优化系统设计、增加测量手段等方面提出了一些建议与措施。     

Topology optimization for thermal conductors considering design-dependent effects,including heat conduction and convection

In structural designs considering thermal loading, in addition to heat conduction within the structure, the heat convection upon the structure’s surface can significantly influence optimal design configurations. In this paper, we focus on the influence of design-dependent effects upon heat convection and internal heat generation for optimal designs developed using a topology optimization scheme. The method for extracting the structural boundaries for heat convection loads is constructed using a Hat function, and heat convection shape dependencies are taken into account in the heat transfer coefficient using a surrogate model. Several numerical examples are presented to confirm the usefulness of the proposed method.     

Optimal design of heat exchangers using the progressive quadratic response surface model

The optimal values of the design variables which minimize the pressure loss under the required temperature rise are obtained numerically in a plate-fin heat sink. In thermal/fluid systems, three fundamental difficulties such as a high computational cost for function evaluations (i.e., pressure drop and thermal resistance), the absence of design sensitivity information, and the occurrence of numerical noise are commonly confronted. Thus, sequential approximate optimization (SAO) algorithms have been used to overcome the above mentioned problems. In the present work, the progressive quadratic response surface method (PQRSM), which is one of the SAO algorithms, is proposed for constrained nonlinear optimization problems and is coupled with the computational fluid dynamics (CFD) for the optimization of heat sink. The optimal solutions obtained from the PQRSM are also compared with those of the sequential quadratic programming (SQP) method, which is one of the gradient-based optimization algorithms, to validate the efficiency and fidelity of the PQRSM.     

Generating optimal heat conduction paths based on bionic growth simulation

This paper proposes a novel topology optimization method for designing the best-possible heat conduction paths. The design idea is originated from the natural observation that plant roots or leaf veins care by self-adaptive growth to minimize the flow resistance through the whole networks. Based on the analogy between fluid flow and heat flow problems, the natural growth rule is systematically transformed into a mathematical model and written as an algorithm, where the high conductivity material is treated as being alive and the topology optimization process is viewed as plant morphogenesis process. Specifically, a new treatment called ‘conductivity spreading approach (CSA)’ is proposed to transform nodal temperatures of cooling channels into those of the background mesh, by which cooling channels can be separated from the underlying grid so that they can branch and extend freely along any direction. The growth method is used to construct the heat conduction paths for a fundamental ‘volume-to-point’ problem. Unlike other methods, layout solution produced by the suggested method is favorable to practical problems because it provides clear information about the location, orientation and dimensions of each cooling channel. In addition, the growth method requires little of human involvement and is easily delegated to computers, offering great advantage of automated design for large-scale cooling channel layouts in heat conduction systems.     

Multi-objective topology optimization of end plates of proton exchange membrane fuel cell stacks

End plates of the proton exchange membrane fuel cell (PEMFC) need to be well designed because their strength and rigidity directly affect the clamping pressure distribution and thus affect the performance and lifetime of fuel cell stacks. In this paper, a multi-objective topology optimization model of the end plates in a PEMFC stack with nonlinear contact boundary conditions was established to obtain an optimized structural design. It was found that the design improved with topology optimization is not only light but also meets manufacturability requirements. This provides good guidance for the design of a high-performance end plate.     

基于HyperWorks的柴油机油底壳拓扑优化设计

油底壳是柴油机的主要结构噪声辐射部件,也是最具结构减重潜力的关键部件之一。针对某型大功率柴油机,运用特征化实体建模技术,利用HyperWorks-Optistruct软件平台,开展了基于拓扑优化的该柴油机油底壳模态分析和结构改进设计。为有效提高其结构刚度,建立了以结构质量最轻为优化目标、油底壳固有频率提高20%为约束函数的拓扑优化设计模型。优化后的油底壳重量有了明显降低,前5阶固有频率也有了不同程度的提高,实现了移频和减重的结构改进设计目标,并给出了油底壳结构材料的最优分布图。为有效提高油底壳的结构刚度,进而改善柴油机整机的结构辐射噪声,奠定了基础。     

A GENETIC ALGORITHM FOR THE SHAPE OPTIMIZATION OF PARTS SUBJECTED TO THERMAL LOADING

In many technical situations, the optimization of the mechanical behavior of structures proceeds from the search for the ideal shape satisfying thermal, mechanical, technological, and geometrical constraints. In this article, the shape optimization of mono- and two-dimensional structures is handled by means of a new genetic algorithm (GA). The method is in general well suited to the resolution of nonconstrained optimization problems: The algorithm presented here has been modified by taking into account the imposed design constraints in the selection of the "individuals" belonging to a given population. The crossover operation between individuals and the mutation process in their original forms are applied to derive the optimal shape of parts subjected to thermal loadings. The algorithm exhibits a good convergence toward the optimal solution and the numerical results of its application show a good numerical accuracy.     

THERMOELASTIC TOPOLOGY OPTIMIZATION FOR PROBLEMS WITH VARYING TEMPERATURE FIELDS

Elastic structures that exist in a thermal environment usually experience complex steady-state or transient heat conduction, whereby operational temperatures and stresses may change with time, heat sources, and thermal or kinematic boundary conditions. This article proposes an evolutionary optimization procedure for topology design involving thermoelasticity in which finite element heat analysis, finite element thermoelastic analysis, and subsequently design modification are iteratively carried out. To achieve as efficacious a material usage as possible, the relative efficiency of an element is defined in terms of its thermal stress level. In this article, design cases with uniform temperature fields, nonuniform temperature fields subjected to single or multiple heat load cases, and transient temperature fields are studied. The examples presented show the capabilities of the proposed procedure to solve various thermoelastic problems under varying temperature fields.     

Multi-objective optimization of internal combustion engine by means of 1D fluid-dynamic models

The definition of an efficient optimization methodology for internal combustion engine design using 1D fluid dynamic simulation models is presented. This work aims at discussing the fundamental numerical and fluid dynamic aspects which can lead to the definition of a best practice technique, depending on the complexity of the problem to be dealt with, on the number of design parameters, objective variables and constrains. For these reasons, both single-and multi-objective problems will be addressed, where the former are still of relevant interest (i.e. optimization of engine performances), while the latter have a much wider range of applications and are often characterized by conflicting objectives.     

Inverse boundary design of square enclosures with natural convection

An optimization technique is applied to design of heat transfer systems in which the natural convection is important. The inverse methodology is employed to estimate the unknown strengths of heaters on the heater surface of a square cavity with free convection from the knowledge of the desired temperature and heat flux distributions over a given design surface. The direct and the sensitivity problems are solved by finite volume method. The conjugate gradient method is used for minimization of an objective function, which is expressed by the sum of square residuals between estimated and desired heat fluxes over the design surface. The performance and accuracy of the present method for solving inverse convection heat transfer problems is evaluated by comparing the results with a benchmark problem and a numerical experiment.     

Sidewall effects on heat transfer in narrow backward facing step in transitional regime

In this work, we study numerically with large eddy simulation, the effects induced by the three-dimensional geometry of the channel on the flow topology that exists when the three-dimensional intrinsic instabilities appear in a backward facing step flow with low aspect ratio for Reynolds in the transitional regime (Re = 1,000–1,600), and its impact on the heat flux in the lower wall. Under the transitional regime, the three-dimensional instabilities begin to appear, but they can be masked by the flows due to the presence of the side walls. The study is carried out with two boundary conditions in the sidewalls, slip, and no-slip, to discriminate between the three-dimensionality induced by the geometry and the intrinsic three-dimensional instabilities. The results obtained are compared between the two boundary conditions, establishing what type of flow prevails and its influence on time-averaged mean Nusselt number for all Reynolds.     

Level Set–Based Topological Shape Optimization of Heat Conduction Problems Considering Design-Dependent Convection Boundary

A level set–based topological shape optimization method considering design-dependent convection boundaries is developed for steady-state heat conduction problems. We embed the level set function obtained from a Hamilton-Jacobi type of equation into a fixed initial domain to implicitly represent thermal boundaries. The effects of the implicit convection boundary obtained from topological shape variations are represented by numerical Dirac delta and Heaviside functions. The method minimizes the thermal compliance of systems by varying the implicit boundary, satisfying the constraint of allowable material volume. During design optimization, the boundary velocity to integrate the Hamilton-Jacobi equation is derived from an optimality condition.     

Energy management strategy and capacity optimization for CCHP system integrated with electric-thermal hybrid energy storage system

In order to improve the comprehensive energy utilization rate of combined cooling, heating, and power (CCHP) system, a hybrid energy storage system (HESS) is proposed in this paper consisting of electric and thermal energy storage systems. And the overall optimization design and operation of CCHP system with HESS are the main problems to be solved in application. Therefore, the topology and the energy flow model of CCHP system with HESS are established and analyzed according to the energy conversion characteristics of the component equipment. Moreover, combined with five evaluative restrictions for HESS system, a rule-based energy management strategy is designed to realize the decoupling regulation of electric energy and thermal energy in CCHP system. On this basis, a multi-objective optimization model is studied by taking the indicators of annual cost ratio, the primary energy consumption ratio, and loss energy ratio, and then the capacity parameters are optimized by particle swarm optimization algorithm (PSOA). Finally, a case is carried out to compare the energy allocation situations and capacity optimization results between CCHP system with HESS and CCHP system with single thermal energy storage system (ST). Results show that the capacity of ICE is reduced by 34%, and the annual cost and the primary energy consumption are saved about 7.69% and 18.47%, respectively, demonstrating that HESS has better optimization effect and applicable for small-scale CCHP system.