采用二维贝叶斯方法求解旋转盘腔导热反问题

为了研究压气机旋转盘腔换热特性,实现准确求解转盘表面传热系数,引入二维贝叶斯方法,此方法采用先验分布优化测温误差,并且更加符合转盘的二维特性。通过加入噪声的模拟数据验证方法的可行性,结果表明无测温误差时方法的平均误差是3.2%,有测温误差时方法的平均误差是10.6%,并分析了误差来源。通过与已有实验结果对比,发现方法更适用于计算转盘迎风面与背风面传热差异较大时的表面传热系数,平均相对误差为9.6%,满足实际工程精度的要求。通过改变盘面温度测点数量,发现测点增加会提升计算精度,并采用统计抽样理论分析原因,发现在可接受误差为10%时,所需要的测点数量比较合理。

Use two-dimensional Bayesian method to solve inverse heat conduction problem for rotating disc cavity

In order to study the heat transfer characteristics of compressor rotating disc cavity, and calculate the surface heat transfer coefficient on rotating disc accurately, a two-dimensional Bayesian method was introduced. Using prior distribution to optimize temperature measurement error, this method agreed well with the two-dimensional characteristics of rotating disc. Using simulation data with noise to verify the feasibility of method, the results showed that the average error without temperature measurement error was 3.2% and the average error with temperature measurement error was 10.6%.The error source was analyzed too. By comparing with existing experimental data, results showed that the method was more suitable for calculating surface heat transfer coefficient when the windward and leeward surfaces had a large difference in heat transfer. The average relative error was 9.6%, meeting actual engineering accuracy requirements. By changing the number of temperature measurement points on disc surface, it was found that the increase in measurement points could improve calculation accuracy, and the statistical sampling theory was used to analyze the phenomenon. It was found that when the acceptable error was 10%, the number of measuring points required was reasonable.