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An implicit and explicit BEM sensitivity approach for thermo-structural optimization

机译：隐式和显式BEM灵敏度方法用于热结构优化

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A computer-automated shape optimization methodology has been developed for the purpose of providing internal cooling systems designers the ability to optimize the internal cooling configuration, geometry and heat transfer enhancements for greater cooling efficiency and more durable turbine airfoils. The methodology presents the theory and practical programming requirements for coupling existing computer design and analysis tools together into a new and powerful design system. The goal of this paper is to demonstrate the computational advantages of using implicit sensitivity with the boundary element method (BEM) within this system over other more brute force methods. For this research, BEM algorithms for nonlinear heat conduction and thermo-elasticity were developed and coupled to an unstructured finite volume CFD code for the hot gas flow and a quasi-one-dimensional thermo-fluid system for the analysis of the internal coolant network. These computational tools were controlled by a constrained hybrid optimization algorithm to provide aerodynamic, thermal and internal fluid flow analyses on modified designs. The coolant supply total pressure, turbine inlet temperature, coolant wall thickness, thickness of ribs, rib positions, rib orientations, pin fin diameters and trip strip heights were incorporated into the set of optimization design variables. In order to improve performance, sensitivity gradients of the objective and constraint functions with respect to the geometric and heat transfer enhancement design variables were obtained using implicit differentiation of the boundary element system of equations. A three-to-one improvement in the optimization convergence rate and greater gradient accuracy were obtained for the two-dimensional thermal optimization problems. An order of magnitude larger computing time reduction was realized for three-dimensional thermal optimizations at the expense of additional memory, and another order of magnitude is expected for thermo-elastic optimization problems. Examples include studies of the accuracy of the design sensitivities with respect to forward and central finite differences, and validation of the optimization process using a symmetric cooled configuration.
机译：为了使内部冷却系统设计人员能够优化内部冷却配置，几何形状和传热增强能力，从而获得更高的冷却效率和更耐用的涡轮机翼型，已经开发了一种计算机自动形状优化方法。该方法论提出了将现有计算机设计和分析工具耦合到一个新的功能强大的设计系统中的理论和实际编程要求。本文的目的是证明在该系统内使用隐式灵敏度与边界元方法（BEM）相比其他更强力的方法的计算优势。为了进行这项研究，开发了用于非线性热传导和热弹性的BEM算法，并将其与用于热气流的非结构化有限体积CFD代码以及用于分析内部冷却剂网络的准一维热流体系统相结合。这些计算工具受约束的混合优化算法控制，可在修改后的设计上提供空气动力，热力和内部流体流动分析。冷却剂供应的总压力，涡轮机入口温度，冷却剂壁厚，肋板的厚度，肋板的位置，肋板的方向，销钉翅片的直径和脱模带的高度都被整合到优化设计变量集中。为了提高性能，使用边界元方程组的隐式微分，获得了目标函数和约束函数相对于几何和传热增强设计变量的灵敏度梯度。对于二维热优化问题，优化收敛速度和梯度精度获得了三对一的提高。对于三维热优化，以减少额外的内存为代价，实现了较大数量级的计算时间减少，而对于热弹性优化问题，则有望达到另一个数量级。实例包括关于前向和中心有限差的设计灵敏度的准确性研究，以及使用对称冷却配置验证优化过程。

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