本研究主要目的是建立一套可同時量測三分量速度之四線式熱線測速設備，並且將所需的校正程序與相關設備整合，以提升三分量熱線測速方法的實用性。四線式熱線探測頭採用Kovasznay型式配置，搭配四組恆溫型熱線測速儀來測量各熱線的有效流速值。速度分量的解算是採用蕭飛賓等人[18]於2004年提出的演算法，以有效流速值定義出方向響應及流速響應函數。經由方向校正程序，紀錄不同流向下的函數值變化，以建立方向與流速函數的查詢表。在實際測量中，即根據查詢表來推算出流速分量。為實現此方法之運用，所需設備除了熱線測速儀之外，尚需有效流速校正、方向校正、數據擷取與分析之設備。在本研究中，完成了具有二軸旋轉功能的校正設備，並且整合小型低速噴流風洞，可分別進行流速及方向校正。校正程序的控制及數據處理均由自行開發的視窗軟體來執行。三分量熱線測速之準確性經由兩階段的實驗來驗證。第一階段驗證於穩定流場中進行，比較速度分量的實際值與測量值。由結果可知，利用單一流速所建立之查詢表，在不同條件下的流速大小與方向之誤差均在可接受範圍內。第二階段驗證在低速平面噴流的不同區域進行，與十字熱線的結果比較。由實驗結果可知，流向速度之誤差極小，但橫向流速的平均值差異較大，展向流速則接近於零，符合平面噴流的特性。本研究所發展的三分量熱線測速設備，已證實可用於低速流場實驗，而且操作程序不會過於繁複，十分具有實用性。在不同流場中，流速大小、速度梯度、紊流強度等因素對於準確性的影響，則需要更進一步的研究來確認。

A three-component velocity measurement system using a four-sensor hot-wire probe is developed in the present study. The necessary calibration facilities, including a low-speed jet tunnel, an automatic 2-axis rotary platform, and a four-sensor probe of Kovasznay type, were all constructed and tested. The data-reduction scheme proposed by Hsiao et. al. [18] is adopted. The direction and speed response functions are defined based on the effective velocities of hot wires. The relations between these functions and velocity components are obtained through the direction calibration procedure, and the required look-up tables are established. The look-up tables are used to calculate the velocity components in the following experiments. In order to realize the application of this scheme, the hot-wire anemometry, calibrations facilities, data acquisition equipments and a computer are all necessary. A calibration facility has been constructed in this study. This facility consists of a two-axis rotating frame and a low-speed jet tunnel. Calibrations for flow speed and directions can be performed by this facility. The procedures of calibrations and the data reductions are operated with a Windows software. The accuracy of the 3-component hot-wire-anemometry system is evaluated in two-stage experiments. In the first stage, the experiments are performed in steady flow. The measured and the actual values are compared. Although the look-up table is established at fixed flow speed, the experimental results at various speed show that the errors are small enough. In the second stage, the four-wire probe is used to measure the velocity distributions of a low-speed plane jet flow. The experimental results are compared with the results of a cross-wire probe. The difference between the streamwise velocity components is very small, but the difference of transverse components is larger. The feasibility of this scheme has been proven. However, the influences of velocity magnitude, velocity gradients, and turbulence levels should be evaluated by additional experiments.

參考資料
[1] Kramers, H., “Heat Transfer form Spheres to Flowing Media,” Physics, vol. 12, pp.61-80, 1946.
[2] Goldstein, R. J., Fluid Mechanics Measurements, Washington, Hemisphere Pub. Cord., 1983.
[3] Lomas, C. G., Fundamentals of Hot Wire Anemometry, Cambridge, Cambridge University Press, 1986.
[4] Hintz, J. O., Turbulence, 2nd ed., McGraw-Hill, New York, 1975.
[5] Tutu, N. K. and Chevray, R, “Cross-Wire Anemometry in High Intensity Turbulence.” J. Fluid Mech., vol. 71, pp. 785-800, 1975.
[6] Culter, A. D. and Bradshaw, P., “A Crossed Hot-Wire Technique for Complex Turbulent Flows,” Exp. Fluids, vol. 12, pp. 17-22, 1991.
[7] Marasli, B, Nguyen, P, and Wallace, J. M., “A Calibration Technique for Multiple-Sensor Hot-Wire Probes and Its Application to Vorticity measurements in the Wake of a Circular Cylinder,” Exp. Fluids, vol. 15, pp.209-218, 1993.
[8] Lemonis, G. and Dracos, T., “A New Calibration and Data Reduction Method for Turbulence Measurement by Multihotwire Probes.” Exp. Fluids, vol. 18, pp. 319-328, 1995.
[9] Bruns, J. M. and Dengel, P., “A miniature Triple Hot-Wire Probe for Wall Bounded Flows,” Exp. Fluids, vol. 24, pp. 479-488, 1998.
[10] Devenport, W. J., Rife, M. C., Liapis, S. I., and Follin, G. J., “The Structure and Development of a Wing-Tip Vortex,” J. Fluid Mech., vol. 312, pp.67-106, 1996.
[11] Champagne, F. H., Sleicher, C. A., and Wehrmann, O. H., “Turbulence Measurements with Inclined Hot-Wires. Part I. Heat Transfer Experiments with Inclined Hot-Wires,” J. Fluid Mech., vol. 28, pp.153-176, 1967.
[12] Bruns, J. M. and Dengel, P., “A Miniature Triple Hot-Wire Probe for Wall Bounded Flows,” Exp. Fluids, vol.24, pp.479-488, 1998.
[13] Maciel, Y. and Gleyzes, C., “Survey of Multi-wire Probe Data Processing Techniques and Efficient Processing of Four-Wire Probe Velocity Measurements in Turbulent Flows,” Exp. Fluids, vol. 29, pp.66-78, 2000.
[14] Lavoie, P. and Pollard, A., “Uncertainty Analysis of Four-Sensor Hot-Wires and Their Data-Reduction Schemes Used in the Near Field of a Turbulent Jet,” Exp. Fluids, vol.34, pp.358-370, 2003.
[15] van Dijk, A. and Nieuwstadt, F. T. M., “The Calibration of (Multi-)Hot-Wire Probes. 2. Velocity-Calibration,” Exp. Fluids, vol.36, pp.550-564, 2004.
[16] Döbbeling K., Lenze, B., and Leuckel, W., “Computer-aided Calibration and Measurements with Quadruple Hotwire Probes,” Exp. Fluids, vol.8, pp.257-262, 1990.
[17] Wittmer, K. S., Devenport, W. J., and Zsoldos, J. S., “A Four-Sensor Hot-Wire Probe System for Three-Component Velocity Measurement,” Exp. Fluids, vol.24, pp.416-423, 1998.
[18] 江志煌、許掙強、蕭飛賓、葉泳蘭，「四線式熱線測速儀應用於低速流場之校正及資料處理方法探討」，2004中國航太學會/中華民航學會聯合學術研討會，台中，2004.
[19] Jorgensen, F. E., How to Measure Turbulence with Hot-Wire Anemometors, Dentec Dynamics, 2002.
[20] TSI, TSI Thermal Anemometry Probes, P/N 2980465 Rev. A, TSI Inc., U.S.A., 2008.