Predicting method of film cooling effectiveness distribution based on constrained neural network
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摘要:
为提高涡轮叶片气膜冷却设计效率，提出以高斯函数约束的单排气膜冷效分布神经网络预测方法，并结合修正叠加原理预测多排气膜冷效分布。针对平板单排气膜，以主流湍流度、密度比、吹风比、气膜入射角和长径比以及无量纲流向距离为输入预测高斯函数的3个系数，再将无量纲横向距离代入预测的高斯函数计算得到冷效。高斯函数约束的神经网络对测试集的面平均冷效预测误差仅为5.70%，比直接预测的误差低67%。基于单排气膜预测模型，再根据吹风比和无量纲坐标预测多排气膜叠加原理修正系数，从而计算多排气膜冷效。在吹风比为0.5和1时，多排叉排气膜的面平均冷效预测误差分别仅为6.19%和12.19%。结果说明该方法具有较强的气膜冷效分布预测能力。
Abstract:To improve the design efficiency of film cooling in turbine vane, a neural network constrained by Gaussian function was proposed to predict the cooling effectiveness distribution of single film row, and the distribution of multi film rows was predicted by combining the modified superposition principle. For a single film row on the flat-plate, three coefficients of the Gaussian function were predicted with the main flow turbulence degree, density ratio, blowing ratio, film inclined angle, length-width ratio and dimensionless flow direction distance taken as inputs, and then the dimensionless lateral distance was substituted into the predicted Gaussian function to calculate the cooling effectiveness. The prediction error of the Gauss function constrained neural network for the average cooling effectiveness of the test samples was only 5.70%, which was 67% lower than that of network without constraints. Based on the model of single film row and the correction coefficient of multi film rows superposition principle predicted according to the blowing ratio and dimensionless coordinates, the cooling effectiveness distribution of multi film rows was calculated. The prediction errors of the average cooling effectiveness were only 6.19% and 12.19% with the blowing ratio at 0.5 and 1, respectively. According to the results, the proposed method can predict the film cooling effectiveness distribution accurately.
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图 1 高斯函数约束的单排气膜冷效神经网络
Figure 1. Gaussian function restricted neural network for cooling effectiveness prediction of a single film row
图 3 不同湍流模型计算得到的中心线冷效对比
Figure 3. Comparison of centerline cooling effectiveness calculated by different turbulence models
图 4 中心线冷效随网格数量的变化
Figure 4. Variation of centerline cooling effectiveness with respect to mesh size
图 5 对不同样本两种ANN预测得到的面平均冷效相对误差对比
Figure 5. Comparison of relative errors of surface average cooling effectiveness predicted by two ANNs for different samples
图 6 吹风比为0.25和1时两种ANN预测得到的气膜冷效云图对比
Figure 6. Comparison of cooling effectiveness contour predicted by two ANNs at blowing ratio of 0.25 and 1 respectively
图 7 吹风比为0.25和1时两种ANN预测值的冷效绝对误差云图对比
Figure 7. Comparison of absolute error contour of cooling effectiveness predicted by two ANNs at blowing ratio of 0.25 and 1 respectively
图 8 吹风比为0.25时双排顺排结构修正前后冷效预测云图和数值计算的对比
Figure 8. Comparison of predicted cooling effectiveness contours with and without correction to the numerical results when two film rows are in line at blowing ratio of 0.25
图 9 吹风比为1时双排叉排结构修正前后冷效预测云图和数值计算的对比
Figure 9. Comparison of predicted cooling effectiveness contours with and without correction to numerical results when two film rows are staggered at blowing ratio of 1
图 10 吹风比为0.5和1时修正前后多排气膜冷效分布云图
Figure 10. Contours of cooling effectiveness of multi film rows with and without correction at blowing ratio of 0.5 and 1 respectively
表 1 两种神经网络训练时间对比
Table 1. Comparison of training time between two neural networks
预测模型 每个训练样本
包含的点所有样本
Eave/%平均训练
时间/s直接预测 500 35.72 7.3 直接预测 1000 31.01 21.5 直接预测 5000 19.35 235.8 直接预测 10000 17.27 640.5 高斯函数约束 61 5.70 0.99 
下载: 导出CSV
表 2 双排顺排结构修正前后预测误差对比
Table 2. Comparison of prediction error with and without correction when two film rows are in line
吹风比M 修正前Eave/% 修正后Eave/% 0.25 9.18 1.85 0.5 4.15 0.28 0.6 1.55 1.47 0.8 1.15 1.15 1 5.69 2.83
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表 3 双排叉排结构修正前后预测误差对比
Table 3. Comparison of prediction error with and without correction when two film rows are staggered
吹风比M 修正前Eave/% 修正后Eave/% 0.8 17.61 0.07 1 35.94 3.96
下载: 导出CSV
表 4 多排结构修正前后预测误差对比
Table 4. Comparison of prediction error with and without correction when there are multi film rows
吹风比M 修正前Eave/% 修正后Eave/% 0.5 15.85 6.19 1 28.05 12.19
下载: 导出CSV
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