本文以晶格波茲曼法探討攪拌槽內一等溫高溫葉片在攪拌槽內運轉之流場與熱傳，討論雷諾數與葉片參數以及葉片運動方式對攪拌槽外壁之熱傳特性的影響。基於不可壓縮流體之假設，本研究適當的設定轉速以確保流場的適用性。研究結果顯示，具等溫外壁面之熱傳效益隨著葉片之運動方式而產生差異。
在本文中以三種葉片運動模式模擬流場行為：
(一)等角速度旋轉：葉片以固定速率繞著中心點旋轉的運動。
(二)區間擺動：葉片以固定振幅對於中心點的擺動運動。
(三)擺動旋轉：葉片以相異振幅對於中心點的擺動並加入進程角度使其達到擺動與旋轉的運動。
首先在相同水力直徑與雷諾數下比較不同葉片長寬比對於熱傳效益的影響，其結果為在相同水力直徑與雷諾數下改變葉片設計參數對於等角速度旋轉之熱傳效益並無差異。此乃因不同的葉片設計下，固定雷諾數所產生不同角速度，進而造成相同的熱傳效益；而在區間擺動時，固定水力直徑與雷諾數下，葉片的最大半徑若越長，則熱傳效益越佳。主因為在區間擺動時，當振幅達到最大限度，流體會因葉片阻擋而產生迴流區，進而達到混合效果。在葉片等角速度旋轉、區間擺動、擺動旋轉於相同葉片尺寸與雷諾數比較下，區間擺動與擺動旋轉之熱傳效益將大於等角速度旋轉，而區間擺動與擺動旋轉之比較又因擺動旋轉有眾多設計參數可變更，故可藉由改變擺動之振幅與前進速率比而獲得較佳熱傳效益。

In this study, the Lattice Boltzmann method is applied to simulate the effect of flow field and convection heat transfer of the low-temperature isothermal stirred tank within a moving high-temperature impeller, which is moving by difference patterns, i.e., constant angular speed, oscillating and oscillating rotation. It reveals that oscillating rotation could perform better heat transfer effect with a suitable ratio between the oscillate amplitude and rotation speed.

Alexander, F. J., Chen, S. and Stering, J. D., 1993, “Lattice Boltzmann thermohydrodynamics”, Phys. Rev. E, Vol. 47, pp. R2249-2252.

Bhatnagar, P. L., Gross, E. P. and Krook, M., 1954, “A model for collision processes in gases. Ⅰ. Small amplitude processes in charged and nrutral one-component systems”, Phys. Rev., Vol. 94(3), pp. 511-525.

Bouzidi, M., Firdaouss, M. and Lallemand, P. J., 2001, “Momentum transfer of a Boltzmann-lattice fluid with boundaries”, Phys. Fluids, Vol. 13(11), pp. 3452-3459.

Chen, S. and Martinez, D., 1996, “On boundary condition in lattice Boltzmann methods”, Phys. Fluids, Vol. 8(9), pp. 2527-2536.

Chen, S. and Doolen, G. D., 1998, “Lattice Boltzmann Model for fluid flows”, Annu. Rev. Fluid Mech., Vol. 30, pp. 329-364.

Chen, C. K., Chang, S. C. and Sun, S. Y., 2007, “Lattice Boltzmann Method Simulation of Channel Flow with Square Pillars inside by the Field Synergy Principle”, CMES, Vol. 22(3), pp. 203-215.

Chang, S. C., Hsu, Y. S. and Chen, C. L., 2011, “Lattice Boltzmann simulation of fluid flows with fractal geometry: An unknown-index algorithm”, J. CSME, Vol. 32(6), pp.523~531.

Grunau, D., Chen, S. and Eggert, K., 1993, “A lattice Boltzmann model for multiphase fluid flows”, Phys. Fluids A, Vol. 5(10), pp.2557-2562.

Guo, Z. and Zhao, T. S., 2002, “Lattice Boltzmann model for incompressible flows through porous media”, Phys. Rev. E, Vol. 66, pp. 036304.

Higuera, F. J. and Jimenez, J., 1989, “Boltzmann approach to lattice gas simulations”, Europhys. Lett., Vol. 9(7), pp. 663-668.

Higuera, F. J., Succi, S. and Benzi, R., 1989, “Lattice gas dynamics with enhanced collisions”, Europhys. Lett., Vol. 9(4), pp. 345-349.

He, X. and Luo, L.-S., 1997, “Lattice Boltzmann model for the incompressible Navier-Stokes equation”, J. Stat. Phys., Vol. 88(3/4), pp. 927-944.

He, X., Chen, S. and Doolen, G. D., 1998, “A novel thermal model for the lattice Boltzmann in incompressible limit”, J. Comput. Phys., Vol.146, pp. 282-300.

Inamuro, T., Yoshino, M. and Ogino, F., 1995, “A non-slip condition for lattice Boltzmann simulattion”, Physics of Fluids, Vol 7(12),pp. 2928-2930.

Lim, C. Y., Shu, C., Niu, X. D. and Chew, Y. T., 2002, “Application of lattice Boltzmann model to simulate microchannel flows”, Physics of Fluids, Vol. 14(7), pp. 2299-2308.

Lallemand, P. and Luo, L. S., 2003, “Lattice Boltzmann method for moving boundaries”, J. Comput. Phys., Vol.184, pp. 406-421.

McNamara, G. R. and Zanetti, G., 1988, “Use of the Boltzmann equation to simulate lattice-gas automata”, Physical Review Letters, Vol. 61(20), pp. 2332-2335.

Mettu, S., Verma, N. and Chhabra R. P., 2006, “Momentum and heat transfer from an asymmetrically confined circular cylinder in a plane channel”, Heat Mass Transfer, Vol. 42, pp. 1037-1048.

Maier, R. S., Bernard R. S. and Grunau, D. W., 1996, “Boundary conditions for the lattice Boltzmann method,” Phys. Fluids, Vol. 8, 1788-1801.

Noble, D. R., Chen, S. and Georgiadis, J. G.., 1995, “A consistent hydrodynamic boundary condition for the lattice Boltzmann method”,Phys. Fluids, Vol. 7(1), pp. 203-209.

Peng, Y., Shu, C. and Chew Y. T., 2003, “Simplified thermal lattice Boltzmann model for incompressible thermal flows”, Phys. Rev. E, Vol. 68, pp.026701.

Qian, Y. H., d’Humieres, D. and Lallemand, P.,1992, “Lattice BGK models for Navier-Stokes equation”, Europhy. Lett., Vol. 17(6), pp. 479-484.

Shan, X., 1997, “Simulation of Rayleigh-Benard convection using a lattice Boltzmann method”, Phys. Rev. E, Vol. 55, pp. 2780-2788.

Succi, S., Vergassola, M. and Benzi, R. , 2001, “Lattice Boltzmann scheme for two-dimensional magnetohydrodynamics, Phys. Rev. A, Vol. 43(8), pp. 4521-4524.

Ziegler, D. P., 1993 , “Boundary conditions for lattice Boltzmann simulation”, J. Stat. Phys., Vol. 71, pp. 1171-1177.

Hou, S. L., 1995, "SIMULATION OF CAVITY FLOW BY THE LATTICE BOLTZMANN METHOD." Journal of Computational Physics Vol. 118(2), 329-347.
Zou, Q. and He, X., 1997, “On pressure and velocity boundary conditions for the lattice Boltzmann BGK model”, Phys. Fluids, Vol. 9(6), pp.1591-1598.

Shin, Y. C., 2009, “Periodic Fluid Flow and Heat Transfer in a Square Cavity Due to an Insulated or Isothermal Rotating Cylinder.” Journal of Heat Transfer, Vol. 131(11), pp.111701.

何雅玲,王勇,李慶,“格子Boltzmann方法的理論及應用”,科學出版社, 2011

郭照立,鄭楚光,“格子Boltzmann方法的原理及應用”,科學出版社, 2010