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中文核心期刊

考虑变边界热对流的轴对称涡轮盘热力耦合拓扑优化

THERMOMECHANICAL TOPOLOGY OPTIMIZATION OF AXISYMMETRIC TURBINE DISKS UNDER BOUNDARY-DEPENDENT CONVECTION

  • 摘要: 随着航空发动机朝着高推重比、高可靠性的方向发展, 涡轮盘作为发动机的核心部件之一, 其在复杂热力耦合条件下的轻量化、高性能设计至关重要. 针对变密度拓扑优化中无显式边界描述而难以施加热对流等变边界载荷的难题, 本文提出了基于对流-扩散方程和密度梯度的涡轮盘内外部热对流边界识别和加载方法. 通过求解对流-扩散方程获得盘体两侧光照下的阴影区域, 建立结构内部空腔区域和外部区域的指示函数, 然后结合密度梯度分别识别内部和外部边界, 并基于密度梯度将热对流边界载荷转化为体载荷隐式施加. 在优化建模方面, 借助阶跃函数映射构建了考虑热对流、热力耦合和离心力等设计相关载荷的总体应力约束, 并采用伴随法进行了灵敏度分析. 基于所建立的轴对称问题热力耦合拓扑优化模型, 对典型涡轮盘构型进行了数值求解, 详细分析了不同对流边界条件对最优拓扑构型及应力分布的影响规律, 并对优化结果进行了交叉验证. 算例结果表明, 在涡轮盘拓扑优化中考虑热对流散热具有显著必要性, 所提出的变边界热对流加载方法有效且可行.

     

    Abstract: With the relentless pursuit of higher thrust to weight ratios and superior operational reliability in modern aero engine development, the turbine disk, being one of the most critical rotating components of the engine, has drawn ever increasing research attention. Given its severe service environment involving complex thermomechanical coupling effects, the structural design of the turbine disk light weight and high performance is of paramount importance for ensuring overall engine efficiency, durability, and safety. In the density-based topology optimization, it is challenging to impose boundary dependent loads, such as convection, due to the lack of explicit boundary representation. To solve this issue, this paper proposes a method for identifying internal and external boundaries of turbine disks and imposing convection through the advection diffusion equation and density gradients. By solving the advection diffusion equation under lighting on both sides of the disk, the obtained shadow regions are used to indicate both internal cavities and external regions of the structure. Subsequently, the internal and external boundaries are identified in conjunction with density gradients. Through the use of density gradient information, the convective heat transfer loads on the boundaries are transformed into body-wise heat source terms and imposed in an implicit manner, which completely eliminates the requirement for explicit boundary tracking. In the optimization modeling, a global stress constraint that accounts for design dependent loads including thermal convection, thermomechanical coupling, and centrifugal force is constructed via Heaviside function projection, and the adjoint method is employed for sensitivity analysis. Based on the established topology optimization model for the axisymmetric thermomechanical coupling problem, numerical solutions are obtained for a typical turbine disk configuration. The effects of varying convective boundary conditions on the optimal topological layouts and stress distributions are analyzed in detail, and cross validation of the optimization results is performed. Numerical results demonstrate that it is imperative to consider thermal convection in turbine disk topology optimization, and the proposed boundary dependent thermal convection loading method proves to be effective and feasible.

     

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