A Bayesian model to solve a two-dimensional inverse heat transfer problem of gas turbine discs
A Bayesian model to solve a two-dimensional inverse heat transfer problem of gas turbine discs
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求解燃气轮机圆盘二维逆传热问题的贝叶斯模型
DOI：
10.1016/j.applthermaleng.2022.118762
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发表时间：
2022
影响因子：
6.4
通讯作者：
Cao N
中科院分区：
文献类型：
--
作者：
Cao N
燃气涡轮机发动机中的叶尖间隙受到旋转盘表面上的热传递的强烈影响，因为它决定了温度，进而决定了旋转盘的径向生长。在实验中，圆盘传热通常由圆盘温度测量值计算。这就产生了一个典型的不适定反问题，其中温度测量的小不确定性会导致计算的热通量的大不确定性。在本文中，贝叶斯方法被建立来计算在上游和下游表面的圆盘模拟温度测量的传热，减少不适定性的问题。在高斯先验分布中采用Matérn协方差矩阵，并进行参数研究，以研究贝叶斯方法的准确性，稳定性和鲁棒性。结果表明，与传统的曲线拟合方法相比，贝叶斯方法提供了更好的准确性，鲁棒性和稳定性。在温度不确定度为5e-3时，用贝叶斯方法计算的毕奥数的相对误差小于10%，而用曲线拟合方法计算的相对误差在40- 90%之间。采用不同的毕奥数初始猜测，相对误差的变化小于0.8%.贝叶斯方法的准确性取决于在先验分布中的标准差的选择，并且它示出了在毕奥数最大值的两倍处的值给出了最佳的准确性。该研究为后续燃气涡轮机轮盘传热的实验研究和数据处理提供了指导。
Blade tip clearances in gas turbine engines are strongly affected by heat transfer on rotating disc surfaces as it determines the temperature and in turn the radial growth of rotating discs. In experiments, disc heat transfer is often calculated from disc temperature measurements. This creates a typical ill-posed inverse problem where small uncertainties of temperature measurements can cause large uncertainties of the calculated heat fluxes. In this paper, a Bayesian method is built to calculate heat transfer on both the upstream and downstream surfaces of discs from simulated temperature measurements, reducing the ill-posedness of the problem. A Matérn covariance matrix is employed in the Gaussian prior distribution, and parametric studies are conducted to investigate the accuracy, stability and robustness of the Bayesian method. It is shown that, compared to the traditional curve-fitting methods, the Bayesian method offers better accuracy, robustness, and stability. With a temperature uncertainty of 5e-3, the relative errors of the calculated Biot number from the Bayesian method are less than 10%, whereas those from the curve-fitting methods are in the range of 40-90%. Using different initial guesses of the Biot number, the variations of the relative errors are less than 0.8%. The accuracy of the Bayesian method depends on the selection of the standard deviation in the prior distribution, and it is shown that a value at twice of the Biot number maximum value gives the best accuracy. This study provides guidelines for subsequent experimental research on gas turbine disc heat transfer and data processing.
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