北京航空航天大学学报 ›› 2017, Vol. 43 ›› Issue (11): 2224-2231.doi: 10.13700/j.bh.1001-5965.2017.0145

• 先进测量手段 • 上一篇    下一篇

热线探针对数校准方法研究及改进

杜钰锋, 林俊, 马护生, 熊能   

  1. 中国空气动力研究与发展中心, 绵阳 621000
  • 收稿日期:2017-03-13 修回日期:2017-06-09 出版日期:2017-11-20 发布日期:2017-12-01
  • 通讯作者: 林俊 E-mail:lj@cardc-2.com
  • 作者简介:杜钰锋,男,硕士研究生。主要研究方向:流动测试技术;林俊,男,高级工程师,硕士生导师。主要研究方向:空气动力学基础与应用基础研究;马护生,男,硕士,高级工程师。主要研究方向:流动显示与测量技术;熊能,男,硕士,副研究员。主要研究方向:实验空气动力学。

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

DU Yufeng, LIN Jun, MA Husheng, XIONG Neng   

  1. China Aerodynamics Research and Development Center, Mianyang 621000, China
  • Received:2017-03-13 Revised:2017-06-09 Online:2017-11-20 Published:2017-12-01

摘要: 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 kPa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。

关键词: 热线探针, 可压缩流体, 对数, 校准, 数学模型, 无量纲化, 不确定度

Abstract: 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 studied and it is discovered that there is a problem of matrix singularity in the process of solving calibration coefficients, which results in poor stability in solving linear equations with a small velocity perturbation. The mathematical model is improved by nondimensionalizing the parameters and adding a positive offset to build a dimensionless 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 logarithmic calibration mathematical model, the results of data fitting show that correlation coefficient is 0.997 61 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 0.379 74 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 0.998 95 and deviation of fitting velocity in average is 1.203 m/s. Condition number of coefficient matrix in the process of solving calibration coefficients is 3.655×102, which indicates a weak singularity, and the improved mathematical model is not affected by a small velocity perturbation due to selection of dimensionless 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 calibration in compressible fluid.

Key words: hot-wire probe, compressible fluid, logarithm, calibration, mathematical model, nondimensionalization, uncertainty

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