对流换热是能量传递与转换中的关键过程，强化对流换热过程、实现热沉结构的优化设计，有利于提升能源利用效率、推动国家战略产业发展。本文首先分析对流换热过程，揭示对流换热过程性能最佳时的均匀性原理，导出求解热沉最优结构分布的不动点迭代格式，建立了基于优化准则法的对流换热热沉的拓扑优化框架；采用商业有限元软件COMSOL验证该框架的正确性，发现优化准则法的优化结果与移动渐进线算法一致，且迭代次数更少、计算效率更高。针对层流问题和封闭空间问题，相应伴随方程易于导出并求解，本文结合变分原理，采用连续伴随法对对流换热问题进行灵敏度分析。基于开源计算流体力学软件OpenFOAM，编写伴随方程求解器，开发拓扑优化程序。应用该程序，对二维层流强制对流和二维封闭空间层流自然对流问题进行拓扑优化研究。结果显示，二维层流强制对流换热问题的最优热沉为楔形台阶结构，相比参考结构平均温差下降34.6%；二维封闭空间层流自然对流的最优热沉在Gr数较低时呈树状分叉结构，相比参考结构平均温差下降8.7%，在Gr数较高时呈尖峰状结构，相比参考结构平均温差下降6.8%。针对湍流问题和开放空间问题，解析形式的伴随方程难以导出，本文结合自动微分技术，采用离散伴随法对其进行灵敏度分析。基于开源计算流体力学软件OpenFOAM，编写自动微分求解器，开发拓扑优化程序。在此基础上，对二维湍流强制对流和二维开放空间层流自然对流问题进行拓扑优化研究。结果显示，二维湍流强制对流换热问题的最优热沉为波浪结构，通过增强壁面附近流体扰动，减少层流底层厚度实现换热强化；二维开放空间层流自然对流换热拓扑优化问题的最优热沉为上侧平滑、下侧分叉的结构，相比参考结构平均温差下降7.1%。最后，针对实际应用中的三维对流换热模型，应用上述拓扑优化程序进行拓扑优化研究。三维方管层流对流换热模型最优热沉为多花瓣状结构，对应流场为对称的多纵向涡结构。当截面形状长宽比增加时，截面上纵向涡数量也会增加。三维开放空间层流自然对流模型最优热沉为整体向上游发展的分叉结构，相比参考结构平均温差下降25.8%。
Convective heat transfer is a key process in energy transfer and conversion. The enhancement of convection heat transfer and the optimal design of heat sink structure are of great importance for energy efficiency improvement and the development of strategic industries. First, the convective heat transfer process is analyzed, and the uniformity principle of optimal convective heat transfer process is revealed. Besides, the fixed point iteration scheme for solving the optimal heat sink structure is derived, and the topology optimization framework of the convective heat transfer heat sink based on the optimization criterion method is established. At the same time, the correctness of the topology optimization framework is verified by the commercial finite element software COMSOL, and it is found that the optimization results of the optimization criterion are consistent with the method of moving asymptotes, with fewer iterations and higher computational efficiency.For laminar flow problems in closed space, the adjoint equations of which are easy to be derived analytically and solved numerically. Combined with the variational principle, the sensitivity analysis of convective heat transfer process is carried out by continuous adjoint method. Based on the open source computational fluid dynamics software OpenFOAM, an adjoint equation solver and a topology optimization program are developed. The program is used to study the topology optimization of the two-dimensional laminar forced convection and the two-dimensional laminar natural convection in closed space. The results show that the optimal heat sink of the two-dimensional laminar forced convection is a wedge step structure, whose average temperature difference is 23.1% lower than reference structure; the optimal heat sink of the two-dimensional laminar natural convection heat transfer showing a tree bifurcation structure at low Gr number, whose average temperature difference is 8.7% lower than reference structure, and a tree peaking structure at high Gr number, whose average temperature difference is 6.0% lower than reference structure.For turbulence and flow problems with open boundary, the analytical adjoint equations of which are difficult to derive. Combined with automatic differentiation technique, the sensitivity analysis of convective heat transfer process is carried out by discrete adjoint method. Based on the open source computational fluid dynamics software OpenFOAM, an automatic differentiation solver and a topology optimization program are developed. On this basis, the topology optimization of the two-dimensional turbulent forced convection and the two-dimensional laminar natural convection with open boundary are studied. The results show that the optimal heat sink of the two-dimensional turbulent forced convection heat transfer showing a wave structure, which enhance heat transfer by enhancing the fluid disturbance near the wall and reducing the thickness of the laminar bottom layer; the optimal heat sink of the two-dimensional laminar natural convection with open boundary showing a smooth downstream and bifurcated upstream structure, whose average temperature difference is 7.1% lower than reference structure.Finally, the above topology optimization program is used for topology optimization of the three-dimensional convective heat transfer model in practical applications. The optimal heat sink of the three-dimensional square tube laminar convection heat transfer model is multi petal structure, and the corresponding flow field is symmetric multi-longitudinal vortex structure. When the aspect ratio of cross-section increases, the number of longitudinal vortices increases. The optimal heat sink of the three-dimensional open space laminar natural convection model is a bifurcated structure that develops upstream , whose average temperature difference is 25.8% lower than reference structure.
