This work develops a new and effective method to predict the 2-D cooling effectiveness distribution. The assumption in the existing 1-D method is abandoned and replaced by a scalar diffusion equation to model the lateral spreading of the coolant. The proposed model can be used for predicting 2-D multi-row cooling performance and is validated over four arrangements of double-row cooling holes against in-house experimental data. The paper further presents the advantages of the current method over the classic 1-D method. 2-D distributions for different multi-row configurations are successfully obtained and the relative error is reduced to 19.77% as opposed to that of 45.65% with the 1-D model. The time consumption by the proposed method is on the order of $1\times 10^{-3}$ s which is exceedingly efficient for the cooling design process. To sum up, the proposed method is accurate, capable of 2-D multi-row modeling and of simple form and high efficiency. Hence it is potentially an effective tool for film cooling design.

这项工作开发了一种新的有效方法来预测二维冷却效率分布。现有一维方法中的假设被放弃，取而代之的是标量扩散方程，以模拟冷却剂的横向扩散。所提出的模型可用于预测二维多排冷却性能，并根据内部实验数据对四种双排冷却孔布置进行了验证。本文进一步介绍了当前方法相对于经典一维方法的优势。成功获得了不同多行配置的二维分布，相对误差降低到 19.77%，而一维模型为 45.65%。所提出的方法的时间消耗约为$1\times 10^{-3}$s 这对于冷却设计过程非常有效。综上所述，该方法准确，能够进行二维多行建模，形式简单，效率高。因此，它可能是薄膜冷却设计的有效工具。