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Experimental Study of Wall Shear Stress Based on Double-Layer Hot Film
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摘要: 流体壁面剪切应力是精确研究掌握流体流经固体壁面摩擦阻力的直接参量，是评估飞行器设备性能和表面摩擦分布的一个重要参数。精确测量壁面剪切应力对获取飞行器的粘性阻力、优化飞行器结构具有重要意义。针对基于双层热膜技术的壁面剪切应力测量方法的验证，设计了长管道空气流动壁面剪切应力试验平台，以验证该方法测量壁面剪切应力的准确性，同时，验证了在不同温差条件下的双层热膜传感器测量壁面剪切应力的准确性和可重复性。在ΔT = 30℃、40℃、50℃、60℃四种温差条件，测量得到的最大壁面剪切应力为1.27 Pa，壁面剪切应力测量的相对合成不确定度为0.50%，测量相对误差小于4%。
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关键词:
- 计量学 /
- 双层热膜 /
- 流体壁面剪切应力测量 /
- 长管道空气流动试验平台 /
- 试验验证 /
- 不确定度评定
Abstract: Wall shear stress is a direct parameter used to accurately study the frictional resistance of fluid flow over a solid wall and is a key factor in evaluating the performance of aircraft equipment and surface friction distribution. Accurate measurement of wall shear stress is crucial for determining the viscous resistance of aircraft and optimizing their structure. This study focuses on verifying a wall shear stress measurement method based on double-layer hot film technology. A long pipeline air flow test platform was designed to verify the accuracy of the method in measuring wall shear stress. Additionally, the stability and repeatability of the double-layer hot film sensor for measuring wall shear stress under different temperature differences were evaluated. At ΔT = 30℃, 40℃, 50℃, and 60℃, the maximum measured wall shear stress was 1.27 Pa. The relative synthetic uncertainty of the wall shear stress measurement was 0.50%, and the relative error was less than 4%. The results demonstrate the reliability of the method and its applicability for the precise measurement of wall shear stress. -
图 1 双层热膜的壁面剪切应力测试基本原理
Figure 1. Basic principle of wall shear stress measurement using a double-layer hot film
图 2 长管道壁面剪切应力测试试验台示意图
Figure 2. Schematic diagram of the long pipeline wall shear stress test platform
图 4 长圆管道双层热膜传感器布置图
Figure 4. Layout of double-layer hot film sensors in the long circular pipeline
图 8 不同温差条件下壁面剪切应力和热量的关系
Figure 8. Relationship between wall shear stress and heat transfer under different temperature differences
图 9 不同温差条件下壁面剪切应力和速度的关系
Figure 9. Relationship between wall shear stress and velocity under different temperature differences
图 10 50℃温差可重复性试验
Figure 10. Repeatability test of wall shear stress measurement at a temperature difference of 50℃
表 1 不同温差、流速下，压差、热膜传感器输出电压的测量结果
Table 1. Measurement results of pressure difference and output voltage of the hot film sensor under different temperature differences and flow velocities
温差 气流速度 0 m/s 5 m/s 10 m/s 15 m/s 20 m/s 30℃ CH-1 0.1238 − 63.1883 −282.991 −591.105 −965.371 CH-2 0.1494 −77.651 −342.969 −725.975 − 1205.04 进口流速Vin /$ {\text{m}} \cdot {{\text{s}}^{ - 1}} $ 0 4.856816 9.90277 14.87601 19.87414 CH-13 −0.806 −100.907 −473.515 −991.698 − 1643.104 CH-14 0.643 −102.486 −492.095 − 1017.240 − 1690.515 压差∆P / Pa -1.449 1.579 18.580 25.542 47.411 CH-15 / V 2.521 2.856 3.133 3.275 3.395 CH-16 / V 2.623 2.985 3.312 3.496 3.656 40℃ CH-1 1.0515 − 60.6715 −218.727 −597.207 −973.106 CH-2 0.1896 − 76.6185 −279.339 −733.083 − 1214.11 进口流速Vin /$ {\text{m}} \cdot {{\text{s}}^{ - 1}} $ 1.18522 5.099917 9.951917 14.93193 19.93038 CH-13 5.684 −94.237 −379.712 −995.760 − 1653.024 CH-14 0.712 −100.795 −395.600 − 1025.059 − 1703.907 压差∆P / Pa 4.972 6.559 15.888 29.299 50.883 CH-15 / V 2.905 3.132 3.361 3.543 3.668 CH-16 / V 2.975 3.253 3.539 3.786 3.962 50℃ CH-1 − 1.5502 − 72.3676 −294.16 −600.879 −971.36 CH-2 0.6829 − 87.4618 −352.859 −739.035 − 1210.8 进口流速Vin /$ {\text{m}} \cdot {{\text{s}}^{ - 1}} $ 0 4.961952 9.7971 15.05706 19.86541 CH-13 4.691 −110.223 −483.613 − 1006.016 − 1646.181 50℃ CH-14 −0.556 −111.138 −502.831 − 1036.128 − 1692.156 压差∆P / Pa 5.247 0.915 19.218 30.112 45.974 CH-15 / V 2.945 3.320 3.612 3.779 3.910 CH-16 / V 2.972 3.391 3.750 3.977 4.165
60℃CH-1 − 1.9744 − 77.7907 −308.475 −614.737 −988.112 CH-2 2.7022 − 92.3368 −371.033 −752.168 − 1232.9 进口流速Vin /$ {\text{m}} \cdot {{\text{s}}^{ - 1}} $ 0 4.871152 10.11488 15.01849 20.08812 CH-13 4.939 −116.847 −508.751 − 1022.936 − 1679.404 CH-14 8.610 −116.953 −517.920 − 1045.023 − 1721.269 压差∆P / Pa -3.671 0.105 9.169 22.087 41.865 CH-15 / V 3.046 3.491 3.792 3.968 4.107 CH-16 / V 3.057 3.542 3.932 4.171 4.377 
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表 2 不同温差、流速测量数据处理过程
Table 2. Data processing procedure for different temperature differences and flow velocities
温差 / ΔT 气流速度 / m/s RtW / mΩ Q / J Q / ∆T - offset（offset = 0.75Q0） τW / Pa τW-τW0 / Pa 30℃ 0 0.2057935 0.056647 0.0004720555 - 0.03622125 0.00000000 5 0.2057935 0.073365 0.0010293281 0.03947000 0.07569125 10 0.2057935 0.090312 0.0015942172 0.46450225 0.50072350 15 0.2057935 0.100599 0.0019371418 0.63854800 0.67476925 20 0.2057935 0.110023 0.0022512797 1.18527400 1.22149525 40℃ 0 0.217558 0.077016 0.0004813487 0.12430125 0.00000000 5 0.217558 0.092085 0.0008580697 0.16397300 0.03967175 10 0.217558 0.108971 0.0012802401 0.39719800 0.27289675 15 0.217558 0.12476 0.0016749460 0.73247225 0.60817100 20 0.217558 0.136577 0.0019703689 1.27206475 1.14776350 50℃ 0 0.2293225 0.081004 0.0004050185 0.13117525 0.00000000 5 0.2293225 0.105453 0.0008939960 0.02286700 - 0.10830825 10 0.2293225 0.129012 0.0013651940 0.48045050 0.34927525 15 0.2293225 0.145079 0.0016865256 0.75280600 0.62163075 20 0.2293225 0.159107 0.0019670801 1.14936075 1.01818550 60℃ 0 0.241087 0.090148 0.0003756160 - 0.09178225 0.00000000 5 0.241087 0.121007 0.0008899414 0.00263575 0.09441800 10 0.241087 0.149056 0.0013574236 0.22923075 0.32101300 15 0.241087 0.167776 0.0016694250 0.55217725 0.64395950 20 0.241087 0.184737 0.0019520966 1.04661825 1.13840050
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表 3 试验值测量不确定度评定分析表
Table 3. Evaluation and analysis table for uncertainty in the measurement of test values
参数 单位 典型值 测量误差 测量不确定度 μ kg/(ms) 1.91×10−5 ± 2.67×10−8 u(μ) = 1.54×10−8 k W/(m·K) 0.03 ± 1.80×10−5 u(k) = 1.04×10−5 ρ kg/m3 1.11 ± 8.80×10−4 u(ρ) = 5.08×10−4 cp J/(kg·k) 1006.51 ± 1.00×10−2 u(cp) = 5.77×10−3 w mm 6.12 ± 1.00×10−2 u(w) = 5.77×10−3 l mm 1.24 ± 1.00×10−2 u(l) = 5.77×10−3 E V 5.00 ± 5.00×10−4 u(E) = 2.89×10−4 Ru Ω 0.20 ± 2.00×10−4 u(Ru) = 1.15×10−4 ΔT ℃ 30/40/50/60 ± 6.00×10−2 u(ΔT) = 3.46×10−2
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