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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

杜钰锋, 林俊, 马护生, 等 . 热线探针对数校准方法研究及改进[J]. 北京航空航天大学学报, 2017, 43(11): 2224-2231. doi: 10.13700/j.bh.1001-5965.2017.0145
引用本文: 杜钰锋, 林俊, 马护生, 等 . 热线探针对数校准方法研究及改进[J]. 北京航空航天大学学报, 2017, 43(11): 2224-2231. doi: 10.13700/j.bh.1001-5965.2017.0145
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)
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)

热线探针对数校准方法研究及改进

doi: 10.13700/j.bh.1001-5965.2017.0145
详细信息
    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

    通讯作者:

    林俊, E-mail: lj@cardc-2.com

  • 中图分类号: V221.71

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

More Information
  • 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。

     

  • 图 1  热线探针校准风洞示意图

    Figure 1.  Schematic of hot-wire probe calibration wind tunnel

    图 2  拟合速度偏差对比

    Figure 2.  Comparison of fitting velocity deviation

    图 3  无量纲化拟合速度偏差与速度不确定度对比

    Figure 3.  Comparison of nondimensionalized fitting velocity deviation and velocity uncertainty

    表  1  热线探针校准实验数据

    Table  1.   Data of hot-wire probe calibration experiment

    pe/kPa E/V u/(m·s-1) p0/kPa T0/K Ma p/kPa T/K
    151.727 8 1.989 6 103.563 0 89.971 59 296.064 2 0.302 14 84.431 88 290.755 8
    149.573 2 2.090 3 119.608 2 92.018 07 295.797 0 0.350 92 84.537 09 288.687 0
    149.767 1 2.172 6 136.852 8 94.236 87 295.526 7 0.402 18 84.330 02 286.266 2
    150.004 1 2.232 5 152.453 6 96.477 22 295.220 4 0.448 39 84.035 05 283.808 4
    150.068 8 2.291 6 169.145 6 99.148 41 295.028 3 0.499 72 83.610 31 280.994 1
    199.366 3 1.940 0 102.981 2 82.302 70 294.631 5 0.301 66 77.267 83 289.365 2
    200.185 0 2.030 4 119.696 6 84.047 59 294.588 1 0.349 86 77.197 20 287.548 9
    200.982 3 2.106 0 136.410 3 86.201 77 294.599 5 0.401 29 77.168 82 285.407 6
    200.422 1 2.163 9 153.318 0 88.851 41 294.599 5 0.449 60 77.225 88 283.152 4
    199.905 0 2.232 4 169.811 9 91.651 86 294.626 9 0.502 26 77.238 02 280.476 1
    249.827 3 1.864 0 102.435 2 73.793 69 294.689 7 0.300 05 69.306 57 289.477 4
    250.883 1 1.956 9 119.159 4 75.452 41 294.646 2 0.350 00 69.339 75 287.599 8
    250.366 0 2.041 6 136.317 2 77.649 67 294.553 7 0.401 37 69.522 38 285.359 5
    250.796 9 2.111 3 153.334 8 79.911 57 294.466 9 0.452 31 69.465 87 282.892 0
    248.776 1 2.174 1 168.775 2 82.668 91 294.385 9 0.501 19 69.740 60 280.303 8
    300.094 5 1.786 9 104.509 8 65.306 21 294.492 1 0.306 63 61.183 71 289.056 4
    299.275 7 1.868 9 119.193 9 67.180 35 294.401 1 0.350 80 61.730 54 287.329 4
    299.124 9 1.956 9 137.085 8 69.420 70 294.350 4 0.403 32 62.081 20 285.076 1
    300.137 5 2.026 4 153.597 3 71.510 25 294.301 1 0.452 81 62.137 74 282.708 0
    299.469 6 2.080 9 169.643 2 73.987 56 294.257 7 0.501 27 62.298 86 280.177 7
    下载: 导出CSV

    表  2  数学模型校准系数

    Table  2.   Calibration coefficients of mathematical model

    校准系数 数值
    c1 4 071.75
    c2 -1 938.92
    c3 -1 650.43
    c4 -2 108.53
    c5 785.941
    c6 1 008.88
    c7 854.547
    c8 -408.857
    下载: 导出CSV

    表  3  真实速度与拟合速度偏差对比

    Table  3.   Comparison of real velocity and fitting velocity deviation

    u/(m·s-1) Δu/(m·s-1)
    103.563 0 0.492 1
    119.608 2 -0.443 8
    136.852 8 -1.867 8
    152.453 6 -2.591 2
    169.145 6 -2.016 8
    102.981 2 -0.574 5
    119.696 6 0.632 2
    136.410 3 -0.135 6
    153.318 0 -5.104 6
    169.811 9 -4.954 2
    102.435 2 0.461 4
    119.159 4 0.280 0
    136.317 2 0.713 4
    153.334 8 0.901 3
    168.775 2 2.710 0
    104.509 8 0.220 0
    119.193 9 0.162 0
    137.085 8 0.489 4
    153.597 3 0.785 0
    169.643 2 -2.030 6
    下载: 导出CSV

    表  4  数学模型校准系数和相对变化量(加入速度小扰动)

    Table  4.   Calibration coefficients of mathematical model and relative change amount (small velocity perturbation added)

    校准系数 数值 相对变化量/%
    c1 4 773.38 17.23
    c2 -2 297.34 18.49
    c3 -1 934.59 17.22
    c4 -2 427.80 15.14
    c5 931.113 18.47
    c6 1 172.13 16.18
    c7 983.852 15.13
    c8 -474.975 16.17
    下载: 导出CSV

    表  5  真实速度与拟合速度偏差对比(加入速度小扰动)

    Table  5.   Comparison of real velocity and fitting velocity deviation (small velocity perturbation added)

    u+ε/(m·s-1) Δu/(m·s-1)
    104.563 0 -25.46
    120.608 2 -33.28
    137.852 8 -43.04
    153.453 6 -53.48
    170.145 6 -63.85
    103.981 2 -33.50
    120.696 6 -39.39
    137.410 3 -46.44
    154.318 0 -57.26
    170.811 9 -64.61
    103.435 2 -27.77
    120.159 4 -33.78
    137.317 2 -41.07
    154.334 8 -49.21
    169.775 2 -56.78
    105.509 8 -27.63
    120.193 9 -33.90
    138.085 8 -40.76
    154.597 3 -47.71
    170.643 2 -57.32
    下载: 导出CSV

    表  6  数学模型校准系数(参数无量纲化)

    Table  6.   Calibration coefficients of mathematical model (parameters nondimensionalized)

    校准系数 数值
    c1 0.043 05
    c2 0.307 9
    c3 0.061 27
    c4 0.404 8
    c5 -0.200 2
    c6 -0.739 0
    c7 0.205 8
    c8 -0.221 5
    下载: 导出CSV

    表  7  真实速度与拟合速度偏差对比(参数无量纲化)

    Table  7.   Comparison of real velocity and fitting velocity deviation (parameters nondimensionalized)

    u/(m·s-1) Δu/(m·s-1)
    103.563 0 0.286 1
    119.608 2 -0.260 6
    136.852 8 -0.904 5
    152.453 6 -0.998 3
    169.145 6 1.589 7
    102.981 2 0.142 7
    119.696 6 -0.527 6
    136.410 3 -1.106 7
    153.318 0 -5.074 4
    169.811 9 -1.972 7
    102.435 2 0.352 9
    119.159 4 -0.032 5
    136.317 2 0.505 6
    153.334 8 1.292 8
    168.775 2 4.826 3
    104.509 8 -0.442 3
    119.193 9 0.180 5
    137.085 8 1.038 1
    153.597 3 1.746 4
    169.643 2 -0.783 9
    下载: 导出CSV

    表  8  真实速度与速度不确定度对比(参数无量纲化)

    Table  8.   Comparison of real velocity and velocity uncertainty (parameters nondimensionalized)

    u/(m·s-1) Uu/(m·s-1)
    103.563 0 3.652 0
    119.608 2 3.137 2
    136.852 8 2.756 6
    152.453 6 2.496 2
    169.145 6 2.261 4
    102.981 2 3.979 6
    119.696 6 3.457 8
    136.410 3 3.014 0
    153.318 0 2.716 2
    169.811 9 2.430 8
    102.435 2 4.459 6
    119.159 4 3.827 6
    136.317 2 3.339 8
    153.334 8 2.981 4
    168.775 2 2.683 0
    104.509 8 4.936 6
    119.193 9 4.280 0
    137.085 8 3.724 2
    153.597 3 3.329 0
    169.643 2 3.015 6
    下载: 导出CSV
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出版历程
  • 收稿日期:  2017-03-13
  • 录用日期:  2017-06-09
  • 刊出日期:  2017-11-20

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