摘要

本文主要利用數值計算方法探討環形渦漩噴流於一圓柱擋體後之流場結構。以有限差分法求解三維時變的Navier-Stokes方程式。速度場是採用顯式Adams-Bashforth法及隱式Crank-Nicloson法的混合計算方法，使流場解答不論在時間或空間的離散上，都能獲得二階精確度；壓力場是利用投影法導出壓力的Poisson方程式，配合快速傅利葉轉換(FFT)及三對角矩陣系統直接解出；高雷諾數紊流場，是配合使用大渦紊流模式加以模擬計算。
數值計算結果龐大資料，則採用TecPlot 3D繪圖軟體加以處理，將數值計算所得到的大量資料，以圖形方式呈現，以利流況之判讀及流場特性之探討。
文中固定環形噴流之阻隔比(Di2/Do2)及突張比(De/Do)，故影響流場的主要參數為雷諾數及渦漩數，針對雷諾數100~10000，渦漩數為0~0.5之流況，進行流場之計算工作及流動特性之探討。與台大應力所沈弘俊教授多年來以切光流場顯影之實驗結果比較，初步研究結果顯示流場型態與實驗大致相符，證實本研究所發展的三維數值模式相當成功。

Abstract

A finite-difference method for the numerical simulation of the incompressible, time-dependent and three-dimensional Navier-Stokes equations in a confined annular swirling jet flow is presented. The variables of velocity are solved together with explicit Adams-Bashforth scheme and implicit Crank-Nicolson scheme, then a projection method is used to derive the pressure Poisson equation which solved by fast Fourier transform and a tridiagonal matrix system, so a second order accurate solution can be achieved in both space and time discretization. For the turbulence flow field, a Large-eddy simulation is used.
By means of the TecPlot 3D software displaying the numerical data as visual, it’s convenient for us to thrash out the flow-field.
Fixed the blockage ratio(Di2/Do2) and expansion ratio(De/Do), the Reynolds number and swirling number are the primary parameters of the flow, we discussed the Reynolds number from 100 to 10000 and swirling number from 0 to 0.5. By comparing with the Sheen et al. experiment, the results are good agreement and three dimensional numerical model was established successful indeed.

Contents
AcknowledgementⅠ
Chinese abstract ………………………………...…………...Ⅱ
English abstract Ⅲ
Contents ..……...IV
Table Lists ..……...VII
Figure Lists ..……...VIII





Chapter1 Introduction1
1-1. Introduction ...…………………………………………………………………1
1-2. Literature review2
1-2-1. Experimental analysis2
1-2-2. Theoretical analysis5
1-2-3. Numerical analysis6
1-3. Motive in this research9
1-4. Investigative method10
1-5. Contents in this work11
Chapter2 Theoretical background 12
2-1. Governing equations12
2-2. Initial and boundary conditions16
2-3. Turbulence modeling17
2-3-1. Basic assumptions of modelind17
2-3-2. Large-eddy simulation18
2-4. Controlled parameters21
Chapter3 Numerical Algorithm22
3-1. Disposition of grid system and variables of the field22
3-2. Numerical discretization and calculation23
3-3. Treatment of the pressure equation27
3-4. Computational procedures31
Chapter4 Numerical results and discussion32
4-1. Analysis of grid independence32
4-2. Relationship between the length of recirculation buble and Reynolds number 34
4-3. Regimes of laminar flow36
4-3-1. Axisymmetric and asymmetric flow patterns36
4-3-2. Illustration the flow-field on azimuthal and axial section37
4-4. Regimes of turbulence flow41
4-4-1. Analysis the Smagorinsky constant 41
4-4-2. Verification of the Large-eddy simulation 43
4-4-3. Illustration of turbulence flow-field44
4-5. Flow patterns in recirculation zone48
Chapter5 Conclusions and suggestions50
5-1. Conclusions ……50
5-2. Suggestions……52
References ……..53

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