热线探针对数校准方法研究及改进

开展了可压缩流体中热线探针校准方法的研究,以满足其在各种速度测量场合的使用需求。研究了对数校准数学模型,发现校准系数求解过程中存在矩阵奇异性过强的问题,导致在速度小扰动条件下方程求解稳定性差。对对数校准数学模型进行了参数无量纲化及添加正向偏置的改进,建立了无量纲化对数校准数学模型。在马赫数为0.3~0.5,引射压力为150~300 k Pa范围内进行了校准实验,利用对数校准数学模型对实验数据进行拟合,拟合优度为0.997 61,拟合速度平均偏差为1.378 m/s,校准系数求解过程中系数矩阵条件数为1.595×108,矩阵奇异性过强,加入速度小扰动(1 m/s)后,拟合优度为0.379 74,拟合速度平均偏差为43.81 m/s,方程求解稳定性差。利用无量纲化对数校准数学模型对实验数据进行拟合,拟合优度为0.998 95,拟合速度平均偏差为1.203 m/s,校准系数求解过程中系数矩阵条件数为3.655×102,且无量纲化方法不受速度小扰动影响。对流体速度进行不确定度分析,速度平均不确定度为3.168 m/s,无量纲化拟合速度平均偏差明显小于速度平均不确定度。实验结果证明了无量纲化对数校准数学模型应用于可压缩流体热线探针校准的可行性。

Research and improvement on logarithmic calibration method of hot-wire probe

Research on calibration method of hot-wire probe in compressible fluid is carried out to meet usage requirements of various velocity measurements. The logarithmic calibration mathematical model is stud-ied and it is discovered that there is a problem of matrix singularity in the process of solving calibration coeffi-cients,which results in poor stability in solving linear equations with a small velocity perturbation. The mathe-matical model is improved by nondimensionalizing the parameters and adding a positive offset to build a dimen-sionless logarithmic calibration mathematical model. Calibration experiments are conducted with Mach number varying from 0. 3 to 0. 5 and ejection pressure varying from 150 kPa to 300 kPa. When using the original loga-rithmic calibration mathematical model,the results of data fitting show that correlation coefficient is 0. 99761 and deviation of fitting velocity in average is 1. 378 m/s. Condition number of coefficient matrix in the process of solving calibration coefficients is 1. 595 × 108 ,which means that the matrix has a strong singularity. After introducing a small velocity perturbation (1 m/s),correlation coefficient becomes 0. 37974 and deviation of fitting velocity in average becomes 43. 81 m/s,which shows instability in solving linear equations. When using the dimensionless logarithmic calibration mathematical model,the results of data fitting show that correlation coefficient is 0. 99895 and deviation of fitting velocity in average is 1. 203 m/s. Condition number of coeffi-cient matrix in the process of solving calibration coefficients is 3. 655 × 102 ,which indicates a weak singulari-ty,and the improved mathematical model is not affected by a small velocity perturbation due to selection of di-mensionless method. Uncertainty of fluid velocity is analyzed and velocity uncertainty in average is 3. 168 m/s, which is obviously greater than the deviation of fitting velocity in average. The experimental results verify the feasibility of application of the dimensionless logarithmic calibration mathematical model to hot-wire probe cali-bration in compressible fluid.