Flow field reconstruction method and application for turbine blade cascade based on experimental data assimilation
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摘要:
为提高平面叶栅试验效率，基于集合卡尔曼滤波原理，采用拉丁超立方抽样组装生成shear stress transport（SST）湍流模型参数、计算数据与试验数据的集合矩阵，通过K-nearest neighbors（KNN）算法对不同数据间的分辨率进行误差对齐，编写了一套适用于涡轮平面叶栅的数据同化程序，对某宽攻角涡轮平面叶栅多种工况下的流场进行了数据同化研究。通过植入3种策略的试验数据，重新适配了SST湍流模型的系数，获得了与试验数据高度吻合的同化数据。同化结果表明：在不同工况下，3种同化策略均可使数值计算结果与试验数据的相对误差降低64.7%以上。故在试验中可适当采信同化数据，调整试验方案，起到提高试验效率，降低试验成本的作用。
Abstract:To improve the efficiency of linear cascade row experiment, this study employs the principles of ensemble Kalman filtering. A Latin hypercube sampling method is used to generate a set matrix of SST turbulence model parameters, computational data, and experimental data. The KNN algorithm is applied to align the resolution errors between different datasets. A data assimilation program suitable for linear cascade rows is developed. The program is used for data assimilation analysis of the flow field under various operating conditions of a linear cascade row with a wide range of attack angles. Experimental data from three strategies are incorporated to re-calibrate the coefficients of the SST turbulence model. The assimilation results show a high degree of agreement with the experimental data. The findings indicate that, under different operating conditions, all three assimilation strategies reduce the relative error between numerical calculations and experimental data by more than 64.7%. Therefore, assimilated data can be appropriately trusted in experiments to adjust experimental plans, which helps improve experimental efficiency and reduce costs.
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图 2 叶栅几何构型及测点分布
Figure 2. Blade cascade geometrical configuration and measurement point distribution
图 5 不同工况下各参数计算结果
Figure 5. Calculation results of various parameters under different operating conditions
图 6 各参数计算结果与试验数据的相对偏差
Figure 6. Relative deviation between calculation results of various parameters and experimental data
图 7 各同化策略下不同工况的参数变化率
Figure 7. Parameter variation rates for different assimilation strategies under different operating conditions
图 9 同化前后前缘流线图
Figure 9. Streamlines at the leading edge before and after data assimilation
表 1 选取的SST模型常数、功能及默认值
Table 1. Selected SST model constants, functions, and default values
常数 功能 默认值 $ {\beta }^{*} $ 改变模型在强剪切流动中的控制能力 0.09 $ \alpha $ 控制湍流耗散的计算 0.31 $ {\alpha }_{\omega } $ 调节湍流频率方程的扩散项 0.55317 $ {\beta }_{\omega } $ 调整ω方程的精度与稳定性 0.075 $ {\alpha }_{\varepsilon } $ 调节湍流耗散方程的扩散项 0.44036 $ {\beta }_{\varepsilon } $ 调整ε方程的精度与稳定性 0.0828 
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表 2 叶栅主要设计参数
Table 2. Main design parameters of the blade cascade
参数 数值 稠度t/c 0.67 来流马赫数Ma 0.6，0.9 进口构造角/（°） 63 叶片安装角/（°） 26 轴向速度密度比 1.15
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表 3 数据同化选取的工况
Table 3. Selected operating conditions for data assimilation
攻角/（°） 马赫数 0 0.6 0 0.9 20 0.6 20 0.9 −35 0.6 −35 0.9
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表 4 高密度同化策略下不同工况的适配参数及参数变化率
Table 4. Fitted parameters and their variation rates for different operating conditions under high-density assimilation strategy
参数 工况1 工况2 工况3 工况4 工况5 工况6 默认值 $ {\beta }^{*} $ 0.100731 0.10972 0.12493 0.12156 0.13632 0.167592 0.09 $ {\beta }^{*} $变化率/% 11.923 21.914 38.813 35.066 51.466 86.213 $ \alpha $ 0.335735 0.35995 0.38224 0.42106 0.452807 0.500319 0.31 $ \alpha $变化率/% 8.302 16.114 23.305 35.826 46.067 61.393 $ {\alpha }_{\omega } $ 0.709245 0.75024 0.88999 0.85829 1.038703 1.159642 0.55317 $ {\alpha }_{\omega } $变化率/% 28.215 35.626 60.891 55.159 87.774 109.637 $ {\beta }_{\omega } $ 0.084066 0.06014 0.04511 0.051605 0.034543 0.053899 0.075 $ {\beta }_{\omega } $变化率/% 12.088 −19.807 −39.852 −31.193 −53.943 −28.135 $ {\alpha }_{\varepsilon } $ 0.527756 0.59999 0.70019 0.796681 0.991422 0.960342 0.44036 $ {\alpha }_{\varepsilon } $变化率/% 19.848 36.252 59.007 80.918 125.142 118.084 $ {\beta }_{\varepsilon } $ 0.104842 0.07016 0.09225 0.052325 0.071246 0.11187 0.0828 $ {\beta }_{\varepsilon } $变化率/% 26.620 −15.261 11.421 −36.806 −13.955 35.108
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