臺灣博碩士論文加值系統

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 ii
Abstract iii
Content v
List of Figure viii
List of Table xiii
Nomenclature xiv
Chapter 1 Introduction 1
1-1 Background and Literature Review 1
1-2 Setup of Fluid Jet Polishing and Literature Review 3
1-2-1 Experimental Setup of Fluid Jet Polishing 3
1-2-2 Literature Review 5
1-3 Objective of Thesis 7
1-4 Thesis Outline 8
Chapter 2 Flow over Surfaces with Different Geometry 9
2-1 Flow Impinges Normally on the Planar Surface 9
2-1-1 Description of the Problem 9
2-1-2 Governing Equations 10
2-1-3 Numerical Method 13
2-2 Flow Impinges Normally on a Circular Surface 17
2-2-1 Description of the Problem 17
2-2-2 Governing Equations for the Problem 18
2-2-3 Numerical Method for the Problem 30
2-2-4 Connection of Inner and Outer Solution 43
Chapter 3 Equation of Particle Motion and Erosion Model 45
3-1 Equation of Motion of a Particle 45
3-2 Numerical Method for Particle Tracking 50
3-3 Model for Estimation of Material Removal 52
Chapter 4 Results 55
4-1 Background Flow Model 55
4-1-1 Normal Stagnation Flow over Planar Surface 55
4-1-2 Normal Stagnation Flow over Circular Surface 58
4-2 Particle Motion in Fluid Flow 76
4-2-1 Stagnation Flow Normally Impinges on the Planar Surface 76
4-2-2 Stagnation Flow Impinges Normally on the Circular Surface 94
4-3 Estimation of Erosion of Surface of Material 112
Chapter 5 Conclusion & Future Aspects 119
5-1 Conclusion 119
5-2 Future Aspects 121
Reference 124

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