臺灣博碩士論文加值系統

我們將二維軸對稱火焰片(flame sheet)模型應用到層流擴散火焰(laminar diffusion flame)，此層流擴散火焰是由一同心圓的兩根管子組成，內管輸送燃料外管輸送氧氣。火焰片模型是擴散火焰模型的一種近似模型，本文對此二維軸對稱火焰片模型進行數值計算。火焰片模型的管轄方程式是使用旋度-速度型式(vorticity-velocity formulation)，它們是由徑向速度方程式、軸向速度方程式、旋度方程式、保存量(conserved scalar)方程式所共同組成。管轄方程式的相關變數包含徑向速度、軸向速度、旋度、保存量，而溫度及主要的化學分子含量可由保存量進行計算恢復。我們的目標是計算此管轄方程式的離散解，所使用的數值方法包括：以有限差分法離散偏微分方程組、以牛頓迭代法解非線性代數方程組、以BICGSTAB法解線性代數方程組、適應網目多重網格法。我們已經為此火焰片模型發展C語言程式碼，且於文內展示一些計算結果。

This thesis takes aim at the numerical calculations of the two-dimensional axisymmetric flame sheet model, which is an approximation of a diffusion flame model. The governing equations of the flame sheet model are written in vorticity-velocity formulation, consisting of the equations of the radial velocity, axial velocity, vorticity, and conserved scalar. Temperature and major chemical species can be recovered from the conserved scalar. Numerical procedure includes finite difference discretization for partial differential equations, Newton iterations for nonlinear algebraic system, BICGSTAB method for linear system, and adaptive mesh multigrid method. A code for the flame sheet model in C language has been developed, and some numerical results will be presented in this work.

CONTENTS
中文摘要 ……………………………………………………………………i
Abstract ……………………………………………………………………ii
Acknowledgements ………………………………………………………iii
Contents ……………………………………………………………………iv
List of figures …………………………………………………………v
Symbol glossary ………………………………………………………vi
Chapter 1 Introduction…………………………………………………1
1.1 Combustion Systems…………………………………………1
1.2 Diffusion Flame Model………………………………………2
1.3 Flame Sheet Model……………………………………………3
1.4 Numerical Modeling……………………………………………3
Chapter 2 The Conservation Equations for Multicomponent
Reacting System………………………………………………4
2.1 Conservation of Mass…………………………………………4
2.2 Conservation of Momentum……………………………………8
2.3 Conservation of Energy……………………………………12
Chapter 3 The Governing Equations for Laminar Diffusion
Flames…………………………………………………………15
3.1 Transform the Governing Equations to
Vorticity-Velocity Formulation…………………………15
3.2 Transform the Governing Equations to Cylindrical
Coordinates…………………………………………………17
3.3 Governing Equations in Vorticity-Velocity
Formulation……………………………………………………22
3.4 Boundary Conditions for Diffusion Flame Model………25
Chapter 4 The Governing Equations for Flame Sheet Model………28
4.1 The Governing Equations for Flame Sheet Model………28
4.2 Recover the Temperature and the Major Species
Profiles from the Conserved scalar……………………35
4.3 Boundary Conditions for Flame Sheet Model……………38
Chapter 5 Numerical Methods……………………………………………41
5.1 Finite Difference Method…………………………………41
5.2 Newton Method for Nonlinear System……………………56
5.3 Krylov Subspace Method for Linear System……………59
5.4 Adaptive Mesh Multigrid Methodology……………………60
Chapter 6 Numerical Results……………………………………………61
References ……………………………………………………………… 69

References
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