臺灣博碩士論文加值系統

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.

摘 要‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧I
英文摘要‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧II
目 錄‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧III
表目錄‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧VII
圖目錄‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧VIII
符號說明‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧XIII
第一章緒論‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧1
1-1研究動機與背景‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧1
1-2大渦漩數值模擬之概述‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧3
1-3數值方法之概述‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧5
1-3-1 處理對流項方法之概述‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 6
1-3-2 處理暫態項方法之概述‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 7
1-3-3 解線性方程式系統方法之概述‧‧‧‧‧‧‧‧‧‧‧‧ 8
1-4本論文探討之主題及方法‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧9
第二章紊流流場及熱傳現象之數學模式 ‧‧‧‧‧‧‧‧‧‧‧‧10
2-1 基本假設 ‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧10
2-2 統御方程式 ‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧10
2-3 次尺度模式(subgrid-scale model)‧‧‧‧‧‧‧‧‧‧‧‧‧16
2-4 邊界條件‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 20
2-4-1 牆函數‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 20
2-4-2 紊流及熱傳邊界條件‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 21
2-5 初始條件‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 22
2-6 氣體之熱力性質‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 23
第三章數值方法‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 25
3-1 通式之離散方程式推導‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 25
3-2 全交錯格點系統‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 29
3-3 動量離散方程式之推導‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 29
3-4 速度修正方程式之推導‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 30
3-5 壓力修正方程式之推導‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 32
3-6 對流項之處理‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 33
3-6-1 邊界條件之數值處理‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 33
3-6-2 ELUD法在非均勻格點上的推導‧‧‧‧‧‧‧‧‧‧‧ 36
3-7 時間暫態項之處理‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 41
3-8 線性方程式系統之解法之處理‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 42
3-8-1 共軛梯度法(conjugate gradient method)‧‧‧‧‧‧‧‧ 42
3-8-2 預設法(preconditioning)‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 44
3-8-3 Incomplete Cholesky conjugate gradient method (ICCG)‧‧ 45
3-8-4 Incomplete LU bi-conjugate gradient stabilized method (ILUBICGSTAB) ‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 46
第四章結果與討論‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 48
4-1各種次尺度模式(subgrid-scale model)之比較‧‧‧‧‧‧‧‧‧ 48
4-1-1 網格獨立與時間間距獨立‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 50
4-1-2 平板型活塞引擎燃燒室內不同SGS模式之比較‧‧‧‧‧ 52
4-1-3 平板型活塞引擎燃燒室內紊流流場與溫度場之分析‧‧‧ 53
4-1-4 深碟型活塞引擎燃燒室內不同SGS模式之比較‧‧‧‧‧ 54
4-1-5 深碟型活塞引擎燃燒室內紊流流場之分析‧‧‧‧‧‧‧ 56
4-1-6 深碟型活塞引擎燃燒室內漩渦衰減現象之探討‧‧‧‧‧ 57
4-1-7 次尺度SGS模式之分析‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 58
4-2引擎參數對燃燒室內紊流流場及壁面熱傳之影響與效應‧‧‧ 59
4-2-1 活塞擠壓面積百分比對燃燒室內紊流流場及壁面熱傳之影響‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 62
4-2-2 引擎轉速對燃燒室內紊流流場及壁面熱傳之影響‧‧‧‧ 67
4-2-3 初始整體漩渦比對燃燒室內紊流流場及壁面熱傳之影響 70
4-2-4 壓縮比對燃燒室內紊流流場及壁面熱傳之影響‧‧‧‧‧ 71
第五章結論與建議‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 74
5-1 綜合結論‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 74
5-2 未來研究方向之建議‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 75
參考文獻‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 77

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