本文係以大渦漩數值模擬（large eddy simulation，簡稱LES）來分析探討活塞凹槽之擠壓運動對往復引擎氣缸內於馬達帶動下之紊流流場與燃燒室壁面熱傳的影響。本計畫使用SIMPLE-C法則與預設式共軛梯度法（preconditioned conjugate gradient method）配合之數值方法來解統御質量加權過濾方程式（mass-weighted filtered governing equations）—連續、動量和能量方程式，進行氣缸內紊流場與壁面熱傳之探討。
本文針對在引擎壓縮、膨脹過程，探討不同壓縮比（CR=6.8、8.7及10.6）、不同的活塞擠壓面積百分比（squish area percent, SQ＝0％、46％及76％）、初始整體漩渦比（initial swirl ratio, SRo＝1.325、5.3及9.5）與引擎轉速（600 rpm 、900 rpm 及1200 rpm）對引擎氣缸燃燒室內紊流流場及壁面熱傳之影響與效應。並對氣缸內之擠壓流（squish flow）與漩渦流（swirl flow）之相互影響作進一步的分析。本文亦針對大渦漩模擬（LES）之三種次尺度(SGS)紊流模式（修正型Smagorinsky model、Van Driest wall damping model、動態次尺度模式）之比較與探討。
由模擬結果得知，本文採用之數值方法能夠成功預測壓縮及膨脹行程時，燃燒室內空氣之紊流流場與溫度場之分佈。經與前人文獻之計算值與實驗數據相比較後，本文所採用之各種次尺度(SGS)紊流模式比傳統κ-ε紊流模式預測得準確，其中又以Van Driest wall damping模式預測的最準確。增加初始整體漩渦比SRo、壓縮比CR及活塞擠壓面積百分比SQ，均可增加平均壁面熱通量，且可加速空氣之運動及促進混合。

This project applies the large eddy simulation (LES) to investigate the influence of swirl and squish motion of the piston bowl on the turbulent flow and the combustion chamber wall heat transfer in a motored engine. In this project, we use LES to model the turbulent flow field and utilize the SIMPLE-C method coupled with preconditioned conjugate gradient methods to solve the mass-weighted filtered governing equations involving continuity, momentum and energy equations. Furthermore, we will investigate the flow field and the wall heat transfer in an engine cylinder.
This study investigates the effect of various compression ratios (taken as 6.8, 8.7, and 10.6), squish area percent (taken as 0%, 46% and 76%), initial swirl ratios (taken as 1.325, 5.3, and 9.5) and engine speeds (taken as 600 rpm, 900 rpm and 1200 rpm) on the turbulent flow and wall heat transfer in the combustion chamber of a motored engine during compression and expansion strokes. Then we will analyze the interrelation between the squish flow and the swirl in the cylinder. Besides, three SGS models (modified Smagorinsky model, Van Driest wall damping model, dynamic model) for the large eddy simulation (LES) are implemented into this study to investigate the turbulent flow field and wall heat transfer in the combustion chamber of a motored engine during compression and expansion strokes.
The results show that the numerical method predicts the turbulent heat transfer in the combustion chamber of a motored engine with reasonable accuracy. Overall results were comparable with those of the conventional K-εturbulence model; on the whole, the three SGS models of LES with modified wall function method give better predictions for the local heat flux and swirl velocity than the K-εmodel in two various engine geometries respectively. From among three SGS models, the Van Driest wall damping SGS model makes the best prediction for the local heat flux and swirl velocity. Increasing the initial swirl ratio, the compression ratio and squish area percent obviously promotes the mixing of fuel and air more effectively as well as enlarges the surface heat flux of wall boundaries in the combustion chamber.

【1】 Dao, K., Uyehara, O. A. and Myers, P.S., “Heat Transfer Rates at Gas-Wall Interfaces in Motored Piston Engine,” SAE Paper 730632, 1973.
【2】 Morel, T., Wahiduzzaman, S., Tree, D. R. and Dewitt, D. P., “Effect of Speed, Load, and Location on Heat Transfer in a Diesel Engine—Measurement and Predictions,” SAE Paper 870154, 1987.
【3】 Yamada, S., Paulsen, H. and Farrel, P., “Heat Transfer Measurements in a Motored Engine,” SAE Paper 890313, 1989.
【4】 Gosman, A. D. and Johns, R. J. R., “Development of a Predictive Tools for In-Cylinder Gas Motion in Engines,” SAE Paper 780315, 1978.
【5】 Gosman, A. D., Johns, R. J. R. and Watkins, A. P., “Development of Prediction Methods for In-Cylinder Processes in Reciprocating Engines,” Combustion Modeling in Reciprocating Engines, edited by Mattavi, J. N. and Amann, C. A., Plenum Press, New York, pp.69-129, 1980.
【6】 Arcoumanis, C., Bicen, A. F. and Whitelaw, J. H., “Squish and Swirl-Squish Interaction in Motored Model Engines,” ASME Journal of Fluid Engineering, Vol.105, pp.105-112, March, 1983.
【7】 Gosman, A. D., Tsui, Y. Y. and Watkins, A. P., “Calculation of Three Dimensional Air Motion Model Engines,” SAE Paper 840229, 1984.
【8】 Kondoh, T., Fukumoto, A., Ohsawa, K. and Ohkubo, Y., “An Assessment of a Multi-Dimensional Numerical Method to Predict the Flow in Internal Combustion Engines,” SAE Paper 850500, 1985.
【9】 Itoh, T., Takagi, Y., Ishida, T., Ishikawa, S., and Ishikawa, T., ”Analysis of In-Cylinder Air Motion with LDV Measurement and Multi-Dimensional Modeling,” Proceeding of International Symposium on Diagonstics and Modeling of Combustion in Reciprocating Engines, September, Tokyo, Japan, pp.185-192, 1985.
【10】 Ikegami, M., Kidoguchi, Y. and Nishiwaki, K., “A Multi-Dimensional Model Prediction of Heat Transfer in Non-Fired Engine,” SAE Paper 860467, 1986.
【11】 Kamimoto, T., Yagita, M., Moriyoshi, Y., Kobayashi, H. and Morita, H., “Experimental Study of In-Cylinder Air Flow with a Transparent Cylinder Engine,” JSME Int. J. Series II, Vol.31, No.1, pp.150-157, 1988.
【12】 周煥銘，”引擎氣缸內擾流與層流場之數值模擬研究“，國立成功大學機械工程研究所碩士論文，1987.
【13】 吳澤松，”應用代數格點產生法模擬計算引擎汽缸內之擾流場與熱通量“，國立成功大學機械工程研究所博士論文，1990.
【14】 Chiu, Cheng Ping and Wu, Tser Son, “Study of Air Motion in Reciprocating Engine Using an Algebraic Grid Generation Technique,” Numerical Heat transfer, Part A, Vol. 17, No. 3, pp. 309-327, 1990.
【15】 Chiu, Cheng Ping and Wu, Tser Son, “Study on the Flow Fields of Irregular-Shaped Domains by an Algebraic Grid Generation Technique,” JSME International Journal, Series II, Vol. 34, No. 1, pp. 69-77, 1991.
【16】 郭英勝，”雙邊界格點產生法應用在活塞汽缸內之紊流熱傳問題研究“，國立成功大學機械工程研究所博士論文，1995.
【17】 Chiu, Cheng Ping and Kuo, Ying Sheng, “Study of Turbulent Heat Transfer in Reciprocating Engine Using an Algebraic Grid Generation Technique,” Numerical Heat transfer, Part A, Vol. 27, No. 3, pp. 255-271, 1995.
【18】 Chiu, Cheng Ping and Kuo, Ying Sheng, “Numerical Study of the Turbulent Heat Transfer in a Motroized Engine Utilizing a Two-Boundary Method Grid Generation Technique,” Numerical Heat transfer, Part A, Vol. 28, No. 2, pp. 215-230, 1995.
【19】 Chiu, Cheng Ping and Kuo, Ying Sheng, “Application of Two-Boundary Grid Generation Technique to the Calculation of Turbulent Flow inside a Piston-Cylinder System,” Journal of the Chinese Society of Mechanical Engineers, Vol. 17, No. 1, pp. 71-79, 1996.
【20】 Haworth, D. C. and Jansen, K., “Large-Eddy Simulation on Unstructured Deforming Meshes: Towards Reciprocating IC Engines,” Computers and Fluids, Vol. 29, No. 5, pp. 493-524, 2000.
【21】 Celik, I., Yavuz, I., Smirnov, A., Smith, J., Amin, E. and Gel, A., “Prediction of In-Cylinder Turbulent for IC Engines,” Combustion Science and Technology, Vol. 153, No. 1, pp. 339-368, 2000.
【22】 Saijyo, K., Nishiwaki, K. and Yoshihara, Y., “Numerical Analysis of the Auto-Ignition Process in a Premixed Charge Compression Ignition Engine,” Transactions of the Japan Society of Mechanical Enginneers, Part B, Vol. 68, No. 676, pp. 3452-3459, 2002.
【23】 Orszag, S. A. and Israeli, M., “Numerical Simulation of Viscous Incompressible Flows,” Ann. Rev. Fluid Mech., Vol. 6, pp.281-318, 1974.
【24】 Galperin, B. and Orszag, S., Large Eddy Simulation of Complex Engineering and Geophysical Flows, Cambridge University Press, Cambridge, 1993.
【25】 Smagorinsky, J., “General Circulation Experiments with Primitive Equations,” Monthly Weather Review, Vol. 91, No. 3, pp. 99-164, 1963.
【26】 Ferziger, J. H., “Higher-Level Simulation of Turbulent Flows,” Computational Methods for Turbulent, Transonic, and Viscous Flows, edited by J. A. Essers, Hemisphere Publishing Corporation, New York, pp. 93-182, 1995.
【27】 Yang, K. S. and Ferziger, J. H., “Large-Eddy Simulation of Turbulent Obstacle Flow Using a Dynamic Subgrid-Scale Model,” AIAA Journal, Vol. 31, No. 8, August, 1993.
【28】 Piomelli, U., “High Reynolds Number Calculations Using the Dynamic Subgrid Scale Stress Model,” Phys. Fluids A, Vol. 5, No. 6, pp.1484-1490, 1993.
【29】 Germano, M., Piomelli, U., Moin, P. and Cabot, W., A Dynamic Subgrid-Scale Eddy Viscosity Model, Summer Program, Center for Turbulence Research, Stanford Univ., Stanford, CA, 1990.
【30】 Moeng, C.-H., “A Large Eddy Simulation Model for the Study of Planetary Boundary Layer Turbulence,” J. Atmos. Sci., Vol. 41, No. 13, Apr., pp.2052-2062, 1984.
【31】 Patankar, S. V., Numerical Heat Transfer and Fluid Flow, Chap.5-6, pp.79-138, McGraw-Hill, New York, 1980.
【32】 Raithby, G. and Van Doormaal, I., “Enhancements of the SIMPLE Method for Predicting Incompressible Fluid Flows,” Num. Heat Trans., Vol. 7, pp. 147-163, 1984.
【33】 Leonard, B. P., “Simple High-Accuracy Resolution Program for Convective Modeling of Discontinuities,” International J. Numerical Methods in Fluids, Vol. 8, pp. 1291-1318, 1988.
【34】 Tsui, Y. Y., “A Study of Upstream Weighted High-Order Differencing for Approximation to Flow Convection,” Int. J. Num. Methods in Fluids Vol. 13, pp.167-199, 1991.
【35】 Van Doormaal, I. and Raithby, G., “Evaluation of New Techniques for Calculation of Internal Recirculating Flows,” AIAA-87-0059, 1987.
【36】 Reynilds, W. L., “The Potential and Limitations of Direct and Large Eddy Simulation,” Lecture Notes in Mathematics 357, pp. 314-343, Springer-Verlag, 1989.
【37】 Khosla, P. K. and Rubin, S. G., “Consistent Strongly Implicit Iterative Procedures for Two-Dimensional Unsteady and Three-Dimensional Space-Marching Flow Calculations,” Computers and Fluids, Vol. 15, No. 4, pp. 361-377, 1987.
【38】 Kim, J. and Moin, P., “Application of a Fractional-Step Method to Incompressible Navier-Stokes Equation,” J. Comp. Physics, Vol. 59, pp. 308-323, 1985.
【39】 Deng, G. B., Piquet, J., Queutey, P. and Visonneau, M., “A New Fully Coupled Solution of the Navier Stokes Equations,” Int. J. Num. Methods in Fluids, Vol. 19, pp. 605-639, 1994.
【40】 Kershaw, David, “The Incomplete Cholesky-Conjugate Gradient Method for the Iterative Solution of Systems of Linear Equations,” J. Comp. Phys., Vol. 26, pp. 43-65, 1978.
【41】 Van Der Vorst, H., “BI-CGSTAB: A Fast and Smoothly Converging Variant of BI-CG for the Solution of Nonsymmetric Linear System,” SIAM J. Sci. Stat. Comput., Vol. 13, No. 2, pp. 631-644, 1992.
【42】 Tu, J. Y. and Fuchs, L., “Overlapping Grids and Multigrid Methods for Three-Dimensional Unsteady Flow Calculation in IC Engines,” Int. J. Num. Methods in Fluids, Vol. 15, pp. 693-714, 1992.
【43】 Launder, B. E. and Spalding, D. B., Lectures in Mathematical Models of Turbulence, Chap. 5, pp. 90-110, Academic, London, 1972.
【44】 Moin, P., Squires, K., Cabot, W. and Lee, S., “A Dynamic Subgrid-Scale Model for Compressible Turbulence and Scalar Transport,” Phys. Fluids A, Vol. 3, pp. 2746-2757, 1991.
【45】 Verman, A. W., Geurts, B. J., Kuerten, J. G. M. and Zandbergen, P. J., “A Finite Volume Approach to Large Eddy Simulation of Compressible, Homogeneous Isotropic, Decaying Turbulence,” Int. J. Num. Methods in Fluids, Vol. 15, pp. 799-816, 1992.
【46】 Wilcox, D., Turbulence Modeling in CFD, 2nd ed., pp. 52-53, DCW Industries, Inc., Glendale, CA, 1993.
【47】 Lilly, D. K., “The Representation of Small-Scale Turbulence in Numerical Simulation Experiments,” Proc. IBM Scientific Computing Symp. Environmental Sci., pp. 195-210, 1967.
【48】 Sakamoto, S., Murakami, S. and Mochida, A., “Numerical Study on Flow Past 2D Square Cylinder by Large Eddy Simulation: Comparison between 2D and 3D Computations,” Journal of Wind Engineering and Industrial Aerodynamics, Vol. 50, pp. 61-68, 1993.
【49】 Huh, Kang Y., Chang, I-Ping and Martin, Jay. K., “A Comparison of Boundary Layer Treatments for Heat Transfer in IC Engines,” SAE Paper 900252, 1990.
【50】 Khalil, E. E., Modeling of Furnaces and Combustors, Chap. 3, pp. 13-48, Abacus Press, England, 1982.
【51】 Smith, Jason R., An Accurate Navier-Stokes Solver with an Application to Unsteady Flows, PhD thesis, West Virginia University, Morgantown West Virginia, 1996.
【52】 Agarwal, R. K., “A Third-Order Accurate Upwind Scheme for Navier-Stokes at High Reynolds Number,” AIAA Paper, 81-0112, 1981.
【53】 Reynolds, W. L., “The Potential and Limitations of Direct and Large Eddy Simulations,” in Lecture Notes in Mathematics 357, Springer-Verlag, pp. 314-343, 1989.
【54】 Hestenes, M., Conjugate Direction Methods in Optimization, Springer-Verlag, New York, 1980.
【55】 Dongarra, J. J., Leaf, G. K. and Minkoff, M., “A Preconditioned Conjugate Gradient Method for Solving a Class of Non-Symmetric Linear Systems,” Argonne National Lab Report ANL-81-71, 1981.
【56】 Sonneveld, R. and Turkel, E., “CGS, a Fast Lanczos-Type Solver for Nonsymmetric Linear Systems,” SIAM J. Stat. Comput., Vol. 10, No. 1, pp. 36-52, 1989.
【57】 Yang, J., Pierce, P., Martin, J. K. and Foster, D. E., “Heat Transfer Predictions and Experiments in a Motored Engine,” SAE Trans., Vol. 97, Section 6, pp. 1608-1622, 1988.
【58】 Ohkubo, Y., Ohtsuka, M., Kato, J., Kozuka, K. and Sugiyama, K., “Study of the In-Cylinder Flow,” (Part 1: Swirl Velocity Measurements by Back-Scattered LDV) in Japanese, 4th Joint symposium on Internal Combustion Engines, pp. 31-36, 1984.
【59】 Kuo, T. W. and Duggal, V. K., “Modeling of In-Cylinder Flow Characteristics-Effect of Engine Design Parameters,” in: T. Uzkan (Ed.), Flows in Internal Combustion Engines-II, ASME, pp. 9-17, 1984.
【60】 Wakisaka, T., Shimamoto, Y. and Isshiki, Y., “Three-Dimensional Numerical Analysis of In-Cylinder Flows in Reciprocating Engines,” SAE Paper 860464, 1986.
【61】 Lawton, B., “Effect of Compression and Expansion on Instantaneous Heat Transfer in Reciprocating Internal Combustion Engines,” Proc. Instn. Mech. Engrs., Vol. 201, No. A3, pp. 175-185, 1987.
【62】 Overbye, V. D., Bennthumn, J. E., Uyehara, O. A. and Myers, P. S., “Unsteady Heat Transfer in Engines,” SAE Trans., Vol. 69, pp. 461-494, 1961.