本文利用數值方法探討往復振盪圓柱對渠道內加熱塊之暫態流場結構及熱傳特性的影響。在數值計算方面，本研究採用Arbitrary Lagrangian-Eulerian（ALE）座標描述系統，配合葛拉金有限元素法(Galerkin finite element method)，以處理流體與固體介面間相互影響的問題。

　　本文研究參數為雷諾數(Re=800~8000 )、 無因次振盪頻率(F=0.1~0.4)和無因次振幅(L=0.05~0.4)。由數值計算結果得知，流場受到圓柱進行往復式的振盪運動牽引的效應，使管道內的流體呈現上下振盪的現象，引導流體向壁面衝擊，擾亂在圓柱後方的流場，提高熱傳效率。此外，當圓柱振盪的頻率接近流場的渦流剝離頻率(vortex shedding frequency)時，會與管道內的流體產生共振的現象，此現象能夠增加流體的擾動，擾亂管道內的流場以及溫度場，產生較佳的熱傳增益，在本文的研究範圍中可得到最佳的無因次圓柱振盪頻率和振幅分別為0.21和0.1。結果顯示當圓柱的振盪頻率在鎖住(lock-in)區時，被加熱塊的熱傳增益有明顯的提升。

　In this study, numerical simulations has been carried out to investigate the influence of transient flow field structures, and heat transfer characteristics of heated blocks in the channel with a transversely oscillating cylinder are also examined. To solve the interaction problems between liquid and solid interface in the simulations, a Galerkin finite element formulation with Arbitrary Lagrangian-Eulerian method (ALE) is adopted.

　The main parameters in the study are Reynolds number (Re=800~8000),dimensionless oscillating frequency (F=0.1~0.4), dimensionless amplitudes (L=0.05~0.4). The results of numerical simulation show that the oscillating cylinder induces the flow vibration. This phenomenon would disturb the flow and thermal fields in the channel flow, and the heat transfer rate in the channel would be enhanced. Furthermore, the resonance effect of channel flow and oscillating cylinder can be observed, as the oscillating frequency of the cylinder approach to the vortex shedding frequency. Due to the phenomenon of resonance in the channel flow, the heat transfer rate is enhanced more remarkably. In the studied range, the results show that the optimum dimensionless cylinder oscillating frequency and dimensionless amplitude value are 0.21 and 0.1. The results show that the heat transfer from heated blocks is enhanced as the oscillating frequency of the cylinder is in lock-in region.

參考文獻
[1]A.E. Bergles, “Survey and Evaluation of Techniques to Augment Convective Heat and Mass Transfer,” Heat and Mass Transfer, vol.1, pp.331-424, 1969.

[2]A.E. Bergles, “Recent Development in Convective Heat-transfer Augmentation,”Applied Mechanics Reviews, vol.26, pp.675-682, 1973.

[3]E. M. Sparrow, J. E. Nithammer and A. Chaboki, “Heat Transfer and Pressure Drop Characteristics of Arrays of Rectangular Modules Encountered in Equipment,”International Journal of Heat and Mass Transfer, vol.25, pp. 961-973, 1982.

[4]G. Bergeles and N. Athanassiadis, “The Flow Pass a Surface-Mounted Obstacle,”J. Fluids Eng. Trans. ASME, vol. 105, pp. 461-463, 1983.

[5]N.K. Ghaddar, M. Magen, B.B. Mikic, A.T. Patera, “Numerical Investigation of Incompressible Flow in Grooved Channels. I. Stability and self-sustained oscillations,” Journal of Fluid Mechanics, vol. 163, pp. 99-127, 1986

[6]N.K. Ghaddar, M. Magen, B.B. Mikic, A.T. Patera, “Numerical Investigation of Incompressible Flow in Grooved Channels. II. Resonance and oscillatory heat transfer enhancement,” Journal of Fluid Mechanics, vol. 168, pp. 541-567, 1986

[7]T. M. Liou, Y. Chang, D. W. Hwang, “Experimental and Computational Study of Turbulent Flows in a Channel with Two Pairs of Turbulence Promoters in Tandem,” J. Fluids Eng. Trans. ASME, vol. 112, pp. 302-310, 1990.

[8]T. M. Liou, W. B. Wang, Y. J. Chang, “Holographic Interferometry Study of Spatially Periodic Heat Transfer in a Channel with Ribs Detached From one Wall,” Transactions of the ASME, vol. 117, pp. 199, 1995.

[9]J. J. Hwang, T. M. Liou, “Heat Transfer in a Rectangular Channel with Perforated Turbulence Promoters Using Holographic Interferometry Measurement,” International Journal of Heat and Mass Transfer, vol.38, pp. 3197-3207, 1995.

[10]C. H. Amon., B. B. Mikic, “Numerical Prediction of Convective Heat Transfer in Self-Sustained Oscillatory Flows,” Journal of Thermophysics & Heat Transfer, vol. 4(2), pp.239-246, 1990.

[11]D. Majumdar, C. H. Amon, “Heat and Momentum Transport in Self-Sustained Oscillatory Viscous Flows,” Journal of Heat Transfer-Transactions of the ASME, vol. 114(4), pp.866-873, 1992.

[12]T. A. Myrum, S. Acharya, S. Inamdar, and A. Mehrotra, “Vortex Generator Induced Heat Transfer Augmentation Past a Rib in a Heated Duct Air Flow,” Journal of Heat Transfer, vol. 114, pp. 280-284, 1992.

[13]T. A. Myrum, X. Qiu, and S. Acharya, “Heat Transfer Enhancement in Ribbed Duct Using Vortex Generators, International Journal of Heat and Mass Transfer,” vol. 36, pp. 3497-3508, 1993.

[14]H. H. Lin and Y. H. Hung, “Transient Forced Convection Heat Transfer in a Vertical Rib-Heated Channel Using a Turbulence Promoter,” International Journal of Heat and Mass Transfer vol.36(6), pp. 1553-1571, 1993.

[15]T. Fusegi, “Numerical Study of Turbulent Forced Convection in a Periodically Ribbed Channel with Oscillatory Throughflow,” International Journal of Numerical Methods in Fluids, vol.23, pp.1223-1233, 1996.

[16]Y. M. Chen and K. C. Wang, “Experimental Study on the Forced Convective Flow in a Channel with Heated Blocks on Tandem,” Experimental Thermal and Fluid Science, Vol. 16, pp.286-298, 1997.

[17]J. J. Hwang, “Heat Transfer-Friction Characteristic Comparison in Rectangular Ducts with Slit and Solid Ribs Mounted on one Wall,” Journal of Heat Transfer Trans. ASME, vol.120, pp. 709-716, 1998.

[18]H. W. Wu and S. W. Perng, “Effect of an Oblique Plate on the Heat Transfer Enhancement of Mixed Convection Over Heated Blocks in a Horizontal Channel,” International Journal of Heat and Mass Transfer, vol. 42, pp. 1217-1235, 1999.

[19]Y. Iida, T. Tsuyuki, T. Mashima, T. Takashima, and K. Okuyama, “Augmentation of Boiling Heat Transfer from Horizontal Cylinder to Liquid by Movable Particles,” Kagaku Kogaku Ronbunshu, vol.26, pp.575-580, 2000.

[20]C. Herman, E. Kang, “Heat Transfer Enhancement in a Grooved Channel with Curved Vanes,” International Journal of Heat and Mass Transfer, vol. 45, pp. 3741-3757, 2002.

[21]W.F. Noh, “A Time-dependent Two-Space-Dimensional Coupled Eulerian-Lagrangian Code”, Methods in Computational Physics, vol.3, p.117, B. Alder, S.Fernbach and M. Rotenberg, Academic Press, New York, 1964.

[22]C.W. Hirt, A.A. Amsden, and H.K. Cooks, “An Arbitrary Lagrangian–Eulerian Computing Method for all Flow Speeds,” Journal of Computational Physics, vol.14, pp.227-253, 1974.

[23]T.J.R. Hughes, W.K. Liu, and T.K. Zimmermann, “Lagrangian- Eulerian Finite Element Formulation for Incompressible Viscous Flows,” Computer Methods in Applied Mechanics and Engineering, vol.29, pp.329-349, 1981.

[24]J. Donea, S. Giuliani, and J.P. Halleux, “An Arbitrary Lagrangian- Eulerian Finite Element Method for Transient Dynamic Fluid Structure Interactions,” Computer Methods in Applied Mechanics and Engineering, vol.33, pp.689-723, 1982.

[25]A. Huerta and W.K. Liu, “Viscous Flow Structure Interaction,” Journal of Pressure Vessel Technology, vol.110, pp.15-21, 1988.

[26]T. Nomura and T.J.R. Hughes, “An Arbitrary Lagrangian-Eulerian Finite Element Methods for Interaction of Fluid and a Rigid Body,” Computer Methods in Applied Mechanics and Engineering , vol.95, pp.115-138, 1992.

[27]T. Nomura, “Finite Element Analysis of Vortex-induced Vibrations of Bluff Cylinders,” Journal of Wind Engineering and Industrial Aerodynamics, vol.46, pp.587.594, 1993.

[28]A. Masud and T.J.R. Hughes, “A Space-Time Galerkin/least- Squares Finite Element Formulation of the Navier-Stokes Equation for Moving Domain Problems,” Computer Methods in Applied Mechanics and Engineering, vol.146, pp.91-126, 1997.

[29]C. Gau, J.M. Wu, C.Y. Liang, “Heat Transfer Enhancement and Vortex Flow Structure Over a Heated Cylinder Oscillating in the Crossflow Direction,” Journal of Heat Transfer, vol.121 pp. 789-795, 1999.

[30]W.S.Fu and B.H.Tong, “Numerical Investigation of Heat Transfer Characteristics of the Heated Blocks in the Channel with a Transversely Oscillating Cylinder,” Journal of Heat Transfer, vol.47,pp341-351,2004

[31]R. K. Shah and A. L. London, “Laminar Flow Forced Convection in Ducts, ” Academic Press, 1978.

[32]B.E.Launder and D.B.Spalding, “The Numerical Computation of Turbulent Flow, ” Computer Method in Applied Mechanics and Engineering, Vol.3, pp.269-289, 1972

[33]C.L.Jayatilleke, “The influence of Prandtl Number and Surface Roughness on the Resistance of the Laminar Sublayer to Momentum Heat Transfer and Fluid Flow, ” Prog.Heat Mass Transfer, Vol.1, pp.193-329,1969