Control of the freezing interface motion in two‐dimensional solidification processes using the adjoint method
Control of the freezing interface motion in two‐dimensional solidification processes using the adjoint method
复制标题
伴随法控制二维凝固过程中的凝固界面运动
DOI：
10.1002/nme.1620380105
复制
发表时间：
1995
影响因子：
2.9
通讯作者：
N. Zabaras
中科院分区：
文献类型：
--
作者：
Shinill Kang;N. Zabaras
这项工作的目的是计算边界冷却条件的最佳历史，在二维传导驱动的凝固过程中，在所需的历史的冻结界面的位置/运动的结果。凝固前沿速度和前沿的固体侧上的热通量限定了所获得的凝固微观结构，可以选择所述凝固微观结构，使得实现最终铸造产品的所需宏观机械性能和坚固性。
所谓的二维Stefan逆设计问题被表述为一个无限维的最小化问题。共轭梯度法结合共轭梯度法的解决方案，这个最小化问题的伴随方法。导出了运动区域中的灵敏度方程和伴随方程。通过在时间上向后求解伴随方程得到代价泛函的梯度。灵敏度方程在时间上向前求解，以计算梯度法的最佳步长。二维数值算例分析表明，本方法的性能。
The aim of this work is to calculate the optimum history of boundary cooling conditions that, in two-dimensional conduction driven solidification processes, results in a desired history of the freezing interface location/motion. The freezing front velocity and heat flux on the solid side of the front, define the obtained solidification microstructure that can be selected such that desired macroscopic mechanical properties and soundness of the final cast product are achieved.
The so-called two-dimensional inverse Stefan design problem is formulated as an infinite-dimensional minimization problem. The adjoint method is developed in conjunction with the conjugate gradient method for the solution of this minimization problem. The sensitivity and adjoint equations are derived in a moving domain. The gradient of the cost functional is obtained by solving the adjoint equations backward in time. The sensitivity equations are solved forward in time to compute the optimal step size for the gradient method. Two-dimensional numerical examples are analysed to demonstrate the performance of the present method.