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The adjoint method for the design of directional binary alloy solidification processes in the presence of a strong magnetic field.

机译：在强磁场存在下设计定向二元合金凝固过程的辅助方法。

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摘要

An adjoint method formulation and numerical implementation is presented for a specific class of inverse design solidification problems. In particular, a method is developed to calculate the thermal boundary conditions on the mold walls for directional solidification processes under the influence of an external magnetic field such that a desired stable solid-liquid interface growth is achieved throughout solidification. Achieving a stable interface growth has profound implications on the obtained cast microstructures and is directly related to the quality of the solidified product.; The considered inverse solidification design problem belongs to a typical class of inverse heat transfer problems, in which, incomplete conditions are provided on one part of the boundary, whereas over-specified conditions are given on another part of the boundary. The design problem is mathematically posed as a functional optimization problem. The unknowns of the design problem are thermal boundary conditions on part of the mold walls. The cost functional is defined so as to represent the deviation of the freezing interface thermal conditions from local thermodynamic equilibrium. A continuum adjoint based method for gradient computations coupled with a conjugate-gradient optimization solver is employed to solve the inverse problem.; The design method is developed in two stages. First, the adjoint method is formulated for an inverse magneto-convection problem in a fixed domain with convection driven by buoyancy effects as well as a Lorentz force generated due to the applied magnetic field. The developed methods are demonstrated using various examples in which the exact solution to the inverse problem is known a priori. The examples demonstrate the accuracy and convergence behavior of the method in the framework of the conjugate gradient algorithm. The need for regularization is identified in one of the examples with uniformly distributed random errors in the input/measured temperature data where a H 1 regularized formulation is introduced in order to obtain stable solutions. The method is shown to be very robust and to work well for various problems including 3D applications. Secondly, the above developed adjoint technique is applied to the design of two typical solidification design problems. A directional binary alloy solidification process is examined in which melt convection is induced due to the combined action of buoyancy as well as Lorentz forces due to an external magnetic field. The goal of the inverse design problem is to identify the thermal conditions on the mold walls so that a desired stable flat-interface growth is realized throughout solidification. The above method is then extended to the design of a directional solidification process of a near-eutectic binary alloy in which convection is driven by the coupled action of buoyancy, thermocapillary and electromagnetic convection. Finally, the thesis concludes with a discussion of possible extensions to the proposed method.
机译：针对特定类型的逆向设计凝固问题，提出了一种伴随方法的公式化和数值实现。特别地，开发了一种方法，用于在外部磁场的影响下计算用于定向凝固过程的模具壁上的热边界条件，从而在整个凝固过程中实现所需的稳定的固液界面生长。实现稳定的界面生长对所获得的铸件微观结构具有深远的影响，并且与固化产品的质量直接相关。所考虑的逆凝固设计问题属于一类典型的逆传热问题，其中边界的一部分提供了不完整的条件，而边界的另一部分则给出了过度指定的条件。在数学上将设计问题视为功能优化问题。设计问题的未知数是部分模具壁上的热边界条件。定义成本函数，以表示冻结界面热条件与局部热力学平衡的偏差。结合梯度共轭梯度优化求解器，采用基于连续伴随的梯度计算方法来求解反问题。设计方法分两个阶段开发。首先，针对在固定域中具有浮力效应以及由于施加磁场而产生的洛伦兹力驱动的对流的逆磁对流问题，制定了伴随法。使用各种示例演示了开发的方法，其中先验地知道了反问题的确切解决方案。实例证明了该方法在共轭梯度算法框架内的准确性和收敛性。在输入/测量温度数据中均匀分布随机误差的示例中，确定了对正则化的需求，其中引入了 H 1 正则化公式以获得稳定解决方案。该方法显示出非常强大的功能，并且可以很好地解决包括3D应用程序在内的各种问题。其次，将上述开发的伴随技术应用于两个典型的凝固设计问题的设计。研究了定向二元合金的凝固过程，在该过程中，由于浮力和外磁场引起的洛伦兹力的共同作用，引起了熔体对流。反设计问题的目的是确定模具壁上的热条件，以便在整个固化过程中实现所需的稳定平面界面生长。然后将上述方法扩展到近共晶二元合金的定向凝固过程的设计，在该过程中，对流是由浮力，热毛细管和电磁对流的耦合作用驱动的。最后，本文以对所提出方法的可能扩展进行了讨论。

著录项

  • 作者

    Sampath, Rajiv.;

  • 作者单位

    Cornell University.;

  • 授予单位 Cornell University.;
  • 学科 Engineering Mechanical.; Applied Mechanics.
  • 学位 Ph.D.
  • 年度 2001
  • 页码 187 p.
  • 总页数 187
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 机械、仪表工业;应用力学;
  • 关键词

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