本研究主要是採用計算流體力學方法(CFD)來深入瞭解軸流壓縮機有葉頂間隙存在時的複雜三維流場現象，並由此探討葉頂間隙大小對壓縮機整體性能之影響。所採用的數值方法是以套裝軟體CFX-TASCflow為基礎，它是以有限體積法解析三維黏性雷諾平均Navier-Stokes方程式。壓縮機的模型取自與Inoue和Kuroumaru實驗相同外型的轉子及操作條件，計算的結果與Inoue和Kuroumaru所做的轉子實驗結果作驗證，結果指出本研究所用的數值方法對於葉頂間隙流場的分析有良好的準確性，並由本研究的數值結果，可細部觀察到如洩漏噴流、洩漏渦流及流道二次流等三維流場結構。在不同葉頂間隙條件下，發現葉頂間隙越大，洩漏渦流越強，能量損失越大，這與前人所發展的理論是一致的。葉頂間隙流場的細部瞭解及能量的損失機構對設計高效率及節能壓縮機是有幫助的。

The main purpose of the present study is to investigate in depth, using computational fluid dynamics (CFD) method, the complex three-dimensional flow field associate with the tip clearance of an axial compressor. The influence of tip clearance on compressor performance is discussed. The CFD method employed is based on CFX-TASCflow, which is a finite volume based method solving Reynolds averaged Navier-Stokes equations. The Compressor model under study is based on the same configuration and operating condition used in the experimental work done by Inoue and Kuroumaru. The comparison with experimental data indicates that the present calculation predicts tip clearance flow with good accuracy. It further provides good simulations of three-dimensional leakage jet flow, leakage vortex, and passage secondary vortex flow. With large tip clearance, the leakage vortex is stronger and with greater energy loss. This is consistent with the theory developed by other researchers earlier. The understanding of tip clearance loss mechanism is useful to the compressor design improvement.

[1]Ainley, D. G., and Mathieson, G. C. R., "A Method of Performance Estimation for Axial-Flow Turbine," ARC R&M 2974, 1951.
[2]Arnone, A., and Swanson, R. C., "A Navier-Stokes Solver for Turbomachinery Applications," ASME Journal of Fluid Engineering, Vol. 115, pp. 305-313, 1993.
[3]Baliga, B. R., and Patankar, S. V., "A Control Volume Finite-Element Method for Two-Dimensional Fluid Flow and Heat Transfer," Numerical Heat Transfer, Vol. 6, pp. 245-261, 1983.
[4]Basson, A., and Lakshminarayana, B., "Numerical Simulation of Tip Clearance Effects in Turbomachinery," ASME Paper 93-GT-316, 1993.
[5]Booth, T. C., Doge, P. R. and Hepworth, H. K., "Rotor-Tip Leakage: Part I – Basic Methodology," Gas Turbine Conference, Mar. 1981
[6]Booth, T. C., Doge, P. R. and Hepworth, H. K., "Rotor-Tip Leakage: Part I – Basic Methodology," ASME Journal of Engineering for Power, Vol. 104, pp. 155-161, 1982
[7]Chen, S. H., and Tsai, C. R., " The Effect of Tip Clearance Flow on Compressor Performance," AIAA Paper 98-3414, 1998.
[8]Chen, G. T., Greitzer, E. M., Tan, C. S., and Marble, F. E.," Similarity Analysis of Compressor Tip Clearance Flow Structure," ASME Journal of Turbomachinery, Vol. 113, pp. 260-271, 1991.
[9]Cohen, H., Rogers, G. F. C., and Saravanamuttoo, H. I. H., "Gas Turbine Theory," John Wiley & Sons, 1987.
[10]Denton, J. D., " Loss Mechanisms in Turbomachines," ASME Journal of Turbomachinery, Vol. 115, pp. 621-656, 1993.
[11]Eckert, B., and Schnell, E., "Axial und Radial Kompressoren," 5th ed., Spring-Verlag, 1961, p.193.
[12]Gallus, H. E., Hah, C., and Schulz, H. D., "Experimental and Numerical Investigation of Three-Dimensional Viscous Flows and Vortex Motion Inside an Annular Compressor Blade Row," ASME Journal of Turbomachinery, Vol. 113, pp. 198-206, 1991.
[13]Hah, C., "A Numerical Modeling of Endwall and Tip-Clearance Flow of an Isolated Compressor Rotor," ASME Journal of Engineering for Gas Turbine and Power, Vol. 108, No. 3, pp. 15-21, 1986.
[14]Horlock, J. H., "Axial Flow Compresor," Krierer, 1973.
[15]Inoue, M., and Kuroumaru, M., "Three-Dimensional Structure and Decay of Vortices Behind an Axial Flow Rotating Blade," ASME Journal of Engineering for Gas Turbine and power, Vol. 106, No. 3, pp. 561-569, 1984.
[16]Inoue, M., and Kuroumaru, M., and Fukuhara, M., "Behavior of Tip Leakage Flow Behind an Axial Compressor Rotor," ASME Journal of Engineering for Gas Turbine and Power, Vol. 108, No. 3, pp. 7-14, 1986.
[17]Inoue, M., and Kuroumaru, M., "Structure of Tip Clearance Flow in an Isolated Axial Compressor Rotor," ASME Journal of Turbomachinery, Vol. 111, No. 3, pp. 250-256, 1989.
[18]Kang, S., and Hirsch, C., "Three Dimensional Flow in a Linear Compressor Cascade at Design Conditions," ASME Paper No. 91-GT-114, 1991.
[19]Kang, S., and Hirsch, C., "Experimental Study on the Three-Dimensional Flow Within a Compressor Cascade With Tip Clearance: PartⅠ-Velocity and Pressure Fields," ASME Journal of Turbomachinery, Vol.115, pp.434-443, 1993.
[20]Kang, S., and Hirsch, C., "Experimental Study on the Three-Dimensional Flow Within a Compressor Cascade With Tip Clearance: PartⅡ-The Tip Leakage Vortex, " ASME Journal of Turbomachinery, Vol.115, pp.444-452, 1993.
[21]Kang, S., and Hirsch, C., "Numerical Simulation of 3D Viscous Flow in a Linear Compressor Cascade With Tip Clearance," ASME Paper 94-GT-364, 1994.
[22]Kang, S., and Hirsch, C., "Tip Leakage Flow in Liner Compressor Cascade," ASME Journal of Turbomachinery, Vol. 116, pp. 657-664, 1994.
[23]Kang, S., and Hirsch, C., "Numerical Simulation of Three-Dimensional Flow in a Linear Compressor Cascade With Tip Clearance," ASME Journal of Turbomachinery, Vol. 118, pp. 492-505, 1996.
[24]Kunz, R. F., Lakshminarayana, B., and Basson, A. H., "Investigation of Tip Clearance Phenomena in an Axial Compressor Cascade using Euler and Navier-Stokes Procedures," ASME paper 92-GT-299, 1992.
[25]Kunz, R. F., Lakshminarayana, B., and Basson, A. H., "Investigation of Tip Clearance Phenomena in an Axial Compressor Cascade Using Euler and Navier-Stokes Procedures," ASME Journal of Turbomachinery, Vol. 115, pp. 453-467, 1993.
[26]Lakshminarayana, B., "Method of Predicting the Tip Clearance Effects in Axial Flow Turbomachinery," ASME Journal of Basic Engineering, Vol.92, pp.467-480, 1970.
[27]Lakshminarayana, B., and Ravindranath, A., "Interaction of Compressor Rotor Blade Wake With Wall Boundary Layer/Vortex in the End-Wall Region," ASME Journal of Engineering for Power, Vol. 104, pp. 467-478, 1982.
[28]Lakshminarayana, B., Pouagare, M., and Davino, R., "Three-Dimensional Flow Field in the Tip Region of a Compressor Rotor Passage－ Part I : Mean Velocity Profiles and Annulus Wall Boundary Layer," ASME Journal of Engineering for Power, Vol. 104, pp. 760-771, 1982.
[29]Lakshminarayana, B., "An Assessment of Computational Fluid Dynamic Techniques in the Analysis and Design of Turbomachinery-The 1990 Freeman Scholar Lecture," ASME Journal of Fluid Engineering, Vol. 113, pp. 315-352, 1991.
[30]Launder, B. E. and Spalding, D. B., "The Numerical Computation of Turbulent Flows," Comp. Meth. Appl. Eng., Vol.3, No. 2, pp.269-289, 1974.
[31]Murthy, K. N. S., and Lakshminarayana, B., "Laser Doppler Velocimeter Measurement in the Tip Region of a Compressor Rotor," AIAA Paper 84-1602 AIAA Journal, vol. 24, p. 807-814, 1986.
[32]Patankar, S. V., "Numerical Heat Transfer," Hemisphere, Washington, D. C., 1980.
[33]Prakash, C. and Patankar, S. V. , "A Control Volume Based Finite Element Method for Solving the Navier-Stokes Equations Using Equal Order Velocity-Pressure Interpolation," Numerical Heat Transfer, Vol.8, pp.259-280, 1985.
[34]Rains, D. A., "Tip Clearance Flow in Axial Flow Compressors and Pumps," California Institute of Technology, Mech. Eng. Lab., Report 5, 1954.
[35]Raithby, G. D., "Skewed Upstream Differencing Schemes for Problems Involving Fluid Flow," Comp. Meth. Appl. Mech. Eng., Vol.9, No. 2, pp.153-164, 1976.
[36]Rhie, C. M. and Chow, W. L., "A Numerical Study of the Turbulent Flow Past an Isolated Airfoil with Trailing Edge Separation," AIAA paper 82-0998, 1982.
[37]Robert, P. D., and William, D. S., and Harris, D. W., "A Navier-Stokes Analysis of the Effect of tip Clearance on compressor Stall Margin," ASME Paper No. 95-GT-190, 1995.
[38]Schneider, G. E. and Raw, M. J., "A Skewed, Positive Influence Coefficient Upwinding Procedure for Control-Volume-Based Finite Element Convection-Diffusion Computation," Numerical Heat Transfer, Vol.8, pp.1-26, 1986.
[39]Schneider, G. E. and Raw, M. J., "Control-Volume Finite Element Method for Heat Transfer and Fluid Flow Using Collocated Variables – 1.Computational Procedure, "Numerical Heat Transfer, Vol.11, pp.363-390, 1987.
[40]Stauter, R. C., "Measurement of the Three-Dimensional Tip Region Flow Field in Axial Compressor," ASME Journal of Turbomachinery, Vol. 115, pp. 468-476, 1993.
[41]Storer, J. A., and Cumpsty, N. A., " Tip Leakage Flow in Axial Compressor," ASME Journal of Turbomachinery, Vol. 113, pp. 252-259, 1991.
[42]Van Doormaal, J. P., Turan, A. and Raithby, G. D., "Evaluation of New Techniques for the Calculation of Internal Recirculating Flows," AIAA Paper 87-0059, 1987.
[43]Vavra, M. H., "Aero-Thermodynamics and Flow in Turbomachines," Wiley, New York, 1960.
[44]Wadia, A. R., and Booth, T. C., "Rotor-Tip Leakage: Part II – Design Optimization Through Viscous Analysis and Experiment," ASME Journal of Engineering for Power, Vol. 104, pp. 162-169, 1982.
[45]Williams, A. D., "The Effect of Tip Clearance Flow in the Performance of Axial Flow Compressors," California Institute of Technology, AE Thesis, 1960.
[46]Zierke, W. C., Farrell, K. J., and Straka, W. A., "Measurements of The Tip Clearance Flow for a High Reynolds Number Axial-Flow Rotor: Part 1－Flow Visualization," ASME Paper 94-GT-453, 1994.
[47]Zierke, W. C., Farrell, K. J., and Straka, W. A., "Measurements of The Tip Clearance Flow for a High Reynolds Number Axial-Flow Rotor: Part 2－Detail Flow Measurement," ASME Paper 94-GT-454, 1994.
[48]李隆正、陳世雄、蘇聖斌、許文英, "交談式渦輪機葉片網格產生法",第三屆全國計算流體力學研討會, pp. 541-552, 1995年8月.