A preliminary study on calibration-free hot-wire anemometry method
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摘要: 本文通过实验方法研究了直径5 μm圆柱与来流之间的对流换热规律。实验结果表明：传热努塞尔数经温度修正后与雷诺数的0.45次方成线性关系。根据该关系，本文提出了一种免标定的热线风速测量方法。该方法的核心是利用恒温热线风速仪记录热线探头产生的热量，并根据来流气温等参数直接计算风速。与现有热线测量技术相比，该方法对来流温度变化不敏感，且可实现免标定直接测量，使用便利性得到了提升。利用本文提出的新方法对均匀来流、湍流边界层、钝体绕流等流动进行验证实验，发现测量结果与真实值存在4% ～ 23%的偏差。这些差异可能与探头大小、冷态电阻测量、导线电阻和接口接触电阻等多种因素相关。因此，本文提出的免标定热线风速测量方法具有发展潜力，但仍有一些技术细节需要解决。Abstract: The study aimed to investigate convective heat transfer from a heated circular cylinder with a diameter of 5 microns and a length-to-diameter ratio of approximately 200 or more using experimental methods. A new relationship between the Nusselt number and the Reynolds number was proposed. The results obtained from this study and those reported in the literature were fitted linearly to a curve. This curve served as the basis for proposing a novel hot-wire velocity measurement technique. In this method, velocities are directly calculated from the voltage outputs of the anemometer without requiring calibration. However, validation measurements indicated that there were errors of up to 23% between the measured and actual values. These errors may be due to measurement uncertainties in the probe's length, cold resistance measurement, the resistance of the lead wire, and connectors.
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图 3 探头在不同风速及过热比条件下的桥顶电压输出和无量纲换热强度
Figure 3. Comparisons of system output voltages and Nusselt numbers for different velocities and overheat ratios
图 4 Nu（实验1～3获得的、对应Re0.45 = 1.4）随热膜与来流平均温度Tm变化规律图
Figure 4. Distribution of the Nusselt number interpolated from marked data points in fig. 3
图 6 边界层平均速度、脉动速度的估测值与真实值对比
Figure 6. Comparisons between the estimated and true values for themean and fluctuating velocity in a turbulent boundary layer
图 7 近壁点（y = 1 mm）瞬时速度、脉动速度功率谱密度的估测值与真实值对比（实验5结果）
Figure 7. Instantaneous velocities and velocity spectrum from the turbulent boundary layer measurements （experiment 5）, measured at a position 1 mm from the wall
图 8 钝体尾流（实验6）的一段瞬时速度和脉动速度功率谱密度分布
Figure 8. Instantaneous velocities and velocity spectrum from the wake flow measurements (experiment 6)
表 1 实验参数列表
Table 1. List of experiments in this work
实验组别 探头 过热比 风速/(m·s−1) 流动情况 1 #1 1.4 0 ～ 18.0 均匀来流 2 #1 1.6 0 ～ 18.0 均匀来流 3 #1 1.8 0 ～ 18.0 均匀来流 4 #2 1.6 0 ～ 18.0 均匀来流 5 #2 1.6 14.7 湍流边界层 6 #1 1.6 14.7 钝体尾流 
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表 2 实验参数及线性拟合结果
Table 2. Parameters for each test and results of the linear fitting
数据来源 过热比 钨丝长度/mm 室温/oC a b 探头1 1.4 0.98 23.0 0.994 1.274 探头1 1.6 0.98 23.0 1.021 1.258 探头1 1.8 0.98 23.0 1.001 1.190 探头2 1.6 1.50 23.0 0.950 0.904 Morrison[7] 1.6 2.00 0.906 0.834 Morrison[7] 1.8 2.00 0.950 0.807 Morrison[7] 2.2 2.00 0.952 0.876 Koch[14] 1.5 1.15 20.7 0.962 0.782 Koch[14] 1.7 1.15 20.7 0.920 0.844 Koch[14] 1.9 1.15 20.7 0.894 0.854 George[8] 1.5 24.5 1.178 0.953 George[8] 1.5 47.5 1.255 1.006 平均 0.999 0.965
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