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 噴射顆粒流拋光為一用於進行材料表面粗糙度處理之新興技術。其工作原理為使用帶有切削顆粒之高速噴射流衝擊工件表面以進行材料之移除。噴射流工作壓力、入射角度，以及切削顆粒與工件之材料特性與幾何形狀將會影響此技術之材料移除效率。本論文嘗試去建立噴射顆粒流垂直入射於平面及二維半圓曲面之分析方法。背景流場之數學模型將先被求得。在衝擊流入射於平面的問題之中，流動即為Navier-Stokes 方程式求之解；至於正向入射於圓曲面的問題，可以分成遠離邊界與近邊界兩部分。遠場流動使用Method of Fundamental Solutions來修正平面停滯位勢流場，並搭配Levenberg-Marquardt方法以求算流場。接著考慮流體黏滯性靠近邊界之影響，以有限差分法來求解曲線坐標邊界層方程式，來求得流體在邊界附近之流場速度分布。根據流場的條件，提出單向耦合(one-way coupling)做為流固耦合的假設，Basset-Boussinesq-Oseen (B.B.O.) 方程式為顆粒運動之統御方程式，再搭配4階 Runge-Kutta法，可求得顆粒在流場中運動。最後再搭配單顆粒於表面之碰撞模型,以估計顆粒與表面做一次碰撞後的材料移除量。由結果可知，因為幾何形狀的關係，噴射流在圓形表面會發生流動分離；另外，對顆粒於流場中的運動而言，若顆粒慣性愈大，在流場中運動的歷時及距離會愈短，並且接觸邊界時於材料表面的衝擊力會愈大；反之，若顆粒質量愈小，將提供較小的表面衝擊力；如果顆粒之質量過小，其將不具有移除材料的能力。另外，在相同的顆粒質量下，若背景流場強度愈強，將使得顆粒於表面的衝擊力加大，因此可預期材料移除量也會較多。
 Fluid Jet Polishing is an innovative technique that is used to finish the roughness of surface of material. Its main working mechanism is using a high-speed fluid jet carried with abrasive particles to incident on the surface so that surface of material can be removed due to the collision between the particles and the surface. Pressure of working fluid, incident angle of jet and material properties and geometry of abrasive particles and work piece to be finished will affect the efficiency of material removal of this technique. This thesis is aimed to establish an analysis method for fluid jet polishing hitting normally on the planar surface and on the two-dimensional circular curve surface. Mathematical models of background flow with different cases are first inspected and established. For the cases hitting on the planar surface, solutions of fluid motion are from the Navier-Stokes equations; as for the solid boundary is circular surface, we can treat flow field as two regions: flow field far from the surface and near the surface. For the far field, solution can be obtained through modifying the inviscid normal stagnation flow over planar surface with method of fundamental solutions and using Levenberg-Marquardt method for assistance; near the boundary viscous effect of fluid should be taken into consideration, solving the boundary-layer equation with the assistance of the finite difference method.According to flow condition, one-way coupling assumption for solid-liquid two phase coupling is proposed; Basset- Boussinesq -Oseen (B.B.O.) equation is served as the governing equation of motion of a particle in the flow field; using 4th order Runge-Kutta method such that information of temporal variation of a particle in the flow field can be found. At last, through the erosion model of particle on the surface, the material removal can be estimated due to one collision between particle and surface. According to the results, when flow normally impinges on the circular surface, flow separation will occur due to the geometry of surface; in addition to the motion of abrasive particles in the flow field, the larger the inertia of an abrasive particle, the elapsed time and traveling distance is shorter; while the inertia of particle is smaller, impact force on the particle is smaller, however, if particle is too small, surface erosion will not occur. On the other hand, for the higher value of strength of background flow, under the condition that particle size is identical, impact force from a particle will become greater such that larger material removal is expected.
 Content誌謝 i中文摘要 iiAbstract iiiContent vList of Figure viiiList of Table xiiiNomenclature xivChapter 1 Introduction 11-1 Background and Literature Review 11-2 Setup of Fluid Jet Polishing and Literature Review 31-2-1 Experimental Setup of Fluid Jet Polishing 31-2-2 Literature Review 51-3 Objective of Thesis 71-4 Thesis Outline 8Chapter 2 Flow over Surfaces with Different Geometry 92-1 Flow Impinges Normally on the Planar Surface 92-1-1 Description of the Problem 92-1-2 Governing Equations 102-1-3 Numerical Method 132-2 Flow Impinges Normally on a Circular Surface 172-2-1 Description of the Problem 172-2-2 Governing Equations for the Problem 182-2-3 Numerical Method for the Problem 302-2-4 Connection of Inner and Outer Solution 43Chapter 3 Equation of Particle Motion and Erosion Model 453-1 Equation of Motion of a Particle 453-2 Numerical Method for Particle Tracking 503-3 Model for Estimation of Material Removal 52Chapter 4 Results 554-1 Background Flow Model 554-1-1 Normal Stagnation Flow over Planar Surface 554-1-2 Normal Stagnation Flow over Circular Surface 584-2 Particle Motion in Fluid Flow 764-2-1 Stagnation Flow Normally Impinges on the Planar Surface 764-2-2 Stagnation Flow Impinges Normally on the Circular Surface 944-3 Estimation of Erosion of Surface of Material 112Chapter 5 Conclusion & Future Aspects 1195-1 Conclusion 1195-2 Future Aspects 121Reference 124
 [1] S. M. Booij, "Fluid jet polishing- possibilities and limitations of a New Fabrication Technique", Ph.D. Dissertation, Delft U. Technol. Press, 22 September, 2003.[2] Van Brug, Hedser, et al., "Optical Fabrication in the Optics Research Group", 2000.[3] Z. R. Yu, C. H. Kuo, C. C. Chen, W. Y. Hsu, D. P. Tsai , "Study of air-driving fluid jet polishing", Proc. SPIE 8126, 812611, 2011.[4] O. W. Fahnle , H. van Brug, and H. J. Frankena, “Fluid jet polishing of optical surfaces“, Appl. Opt.37, 6771- 6773, 1998.[5] H. Fang, P. J. Guo, and J. C. Yu, "Optimization of the material removal in fluid jet polishing", Opt. Eng. 45, 053401, 2006.[6] Li, Zhaoze, et al. "Optimization and application of influence function in abrasive jet polishing", Applied optics 49.15: 2947-2953, 2010.[7] J. G. A. Bitter, "A study of erosion phenomena Part I", Wear 6.1, 5-21, 1963.[8] J. G. A. Bitter, "A study of erosion phenomena Part II", Wear 6.3, 169-190, 1963.[9] F. M., White, "Viscous Fluid Flow 3e", Tata McGraw-Hill Education, 1974.[10] L. F. Shampine, J. Kierzenka and M. W. Reichelt, "Solving boundary value problems for ordinary differential equations in MATLAB with bvp4c", tutorial notes, (2000).[11] F. L. Yang, C. T. Wu, and D. L. Young, "On the calculation of two-dimensional added mass coefficients by the Taylor theorem and the method of fundamental Solutions", Journal of Mechanics, 28.01: 107-112, 2012.[12] H. Schlichting, "Boundary-layer theory", Vol. 539. New York: McGraw-Hill, 1968.[13] A. Ranganathan, "The Levenberg-Marquardt algorithm", tutorial on LM Algorithm, 2004.[14] R. L. Panton, "Incompressible flow", John Wiley & Sons, 2006.[15] Maxey, Martin R., and James J. Riley. "Equation of motion for a small rigid sphere in a non-uniform flow", Physics of fluids 26, 883, 1983.[16] http://en.wikipedia.org/wiki/Archimedes_number[17] Bombardelli, Fabian A., Andrea E. Gonzalez, and Yarko I. Nino, "Computation of the particle Basset Force with a Fractional-derivative Approach", Journal of Hydraulic Engineering 134.10: 1513-1520, 2008.[18] Data sheet for N-BK7, Schott Glass Company, 2012.[19]J.C.Goldsby,"Basic Elastic Properties Predictions of Cubic Cerium Oxide Using First-Principles Methods",Journal of Ceramics,2012,2013.[20] http://www.efunda.com/units/hardness/convert_hardness.cfm?HD=HV&Cat=Steel
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 1 穩態乾顆粒流於粗糙傾斜槽中流變特性之直接與間接量測 2 以拉格朗日結構變化探討滾筒中穩態顆粒流之動態行為 3 社群網路分身攻擊之偵測 4 我國銀髮族數位學習探討－以南瀛網路社區大學為例 5 分析精神分裂症及癌症之基因網路：發掘潛在抑癌效果之路徑及藥物 6 臺灣西南海域重力流引發海底地質災害事件之研究 7 以末端氨基的小分子作為氧化鋅奈米柱表面修飾劑在有機/無機混合太陽能電池中的效果 8 利用基因群層級之存活分析方法鑑定肺癌之穩定預後基因標記 9 糖尿病共同照護對病患之糖化血色素、健康信念與健康行為之影響 10 中剪跨鋼纖維混凝土梁剪力強度預測研究 11 都會區公共運輸系統區段整合費率之研究 12 低雷諾數近牆之等速度、等加速度固體球其流體力邊界效應之即時量測 13 低黏滯性流體中二正向靠近球體受力之理論推導 14 多條件耦合之半監督式學習於中文知識擷取之研究 15 使用機器學習方法預測程序執行時間

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