Purpose

To reduce the heat load of a gas turbine blade, its surface is covered with an outer layer of ceramics with high thermal resistance. The purpose of this paper is the selection of ceramics with such a low heat conduction coefficient and thickness, so that the permissible metal temperature is not exceeded on the metal-ceramics interface due to the loss ofmechanical properties.

Design/methodology/approach

Therefore, for given temperature changes over time on the metal-ceramics interface, temperature changes over time on the inner side of the blade and the assumed initial temperature, the temperature change over time on the outer surface of the ceramics should be determined. The problem presented in this way is a Cauchy type problem. When analyzing the problem, it is taken into account that thermophysical properties of metal and ceramics may depend on temperature. Due to the thin layer of ceramics in relation to the wall thickness, the problem is considered in the area in the flat layer. Thus, a one-dimensional non-stationary heat flow is considered.

Findings

The range of stability of the Cauchy problem as a function of time step, thickness of ceramics and thermophysical properties of metal and ceramics are examined. The numerical computations also involved the influence of disturbances in the temperature on metal-ceramics interface on the solution to the inverse problem.

Practical implications

The computational model can be used to analyze the heat flow in gas turbine blades with thermal barrier.

Originality/value

A number of inverse problems of the type considered in the paper are presented in the literature. Inverse problems, especially those Cauchy-type, are ill-conditioned numerically, which means that a small change in the inputs may result in significant errors of the solution. In such a case, regularization of the inverse problem is needed. However, the Cauchy problem presented in the paper does not require regularization.

中文翻译：

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两层区域的柯西型非线性逆问题

目的

为了降低燃气轮机叶片的热负荷，其表面覆盖有高耐热陶瓷外层。本文的目的是选择具有如此低导热系数和厚度的陶瓷，使金属-陶瓷界面上不会因机械性能损失而超过允许的金属温度。

设计/方法/方法

因此，对于给定的金属-陶瓷界面随时间的温度变化、叶片内侧的温度随时间的变化以及假定的初始温度，应确定陶瓷外表面上随时间的温度变化。以这种方式提出的问题是一个柯西型问题。在分析问题时，考虑到金属和陶瓷的热物理特性可能取决于温度。由于与壁厚相关的陶瓷薄层，问题被考虑在平坦层的区域中。因此，考虑一维非平稳热流。

发现

检查了作为时间步长、陶瓷厚度以及金属和陶瓷的热物理特性的柯西问题的稳定性范围。数值计算还涉及温度扰动对金属-陶瓷界面的影响对逆问题的求解。

实际影响

该计算模型可用于分析具有热障的燃气轮机叶片中的热流。

原创性/价值

文献中提出了许多论文中考虑的类型的逆问题。逆问题，尤其是那些柯西类型的，在数值上是病态的，这意味着输入的微小变化可能会导致解决方案的重大错误。在这种情况下，需要对逆问题进行正则化。但是，论文中提出的柯西问题不需要正则化。