| Citation: | DU Yufeng, LIN Jun, MA Husheng, et al. Research and improvement on logarithmic calibration method of hot-wire probe[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(11): 2224-2231. doi: 10.13700/j.bh.1001-5965.2017.0145(in Chinese)
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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.
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