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研究生： 蘇柏豪
Su, Po-Hao
論文名稱： 應用田口法於 γ型史特靈引擎之設計參數優化研究
Optimization of some important parameters of a gamma-type Stirling engine with Taguchi method
指導教授： 陳文立
Chen, Wen-Lih
學位類別： 碩士
Master
系所名稱： 工學院 - 航空太空工程學系
Department of Aeronautics & Astronautics
論文出版年： 2022
畢業學年度： 110
語文別： 中文
論文頁數： 75
中文關鍵詞： CFD模擬 、田口優化法 、γ- type史特靈引擎
外文關鍵詞： gamma type Stirling engine, CFD, Taguchi method
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    • 摘要
    論文題目:應用田口法於 γ型史特靈引擎之設計參數優化研究
    研究生:蘇柏豪
    指導教授:陳文立
    此論文中分別選取三項不同的模擬輸出結果進行田口優化法的計算，其中包含引擎熱效率、移動再生器之再生效率以及引擎輸出功，而選定的引擎設計參數有四項，包含再生孔洞總面積對底板面積比、底板孔洞配置數量、引擎冷熱端溫差及引擎轉速，而其四項設計參數皆有三種設計水準，再生孔洞總面積對底板面積比設計水準為14%、17%、20%，底板孔洞配置數量設計水準為75個、105個、140個，引擎冷熱端溫差設計水準為200K、300K、400K，引擎轉速設計水準為60rpm、180rpm、300rpm，文中包含了數值模擬的設置條件、各項輸出結果搭配數值模擬結果的計算方式、田口法分析方式及驗證方法以及田口分析結果。田口法的分析結果表明，輸出功最佳化之值為129.86(W)，最佳化參數配置為面積比20%、孔洞數75個、溫差400K、引擎轉速300rpm，影響程度為:引擎轉速 > 引擎冷熱端溫差 > 再生孔洞總面積對底板面積比 > 底板孔洞配置數量；熱效率最佳化之值為51.25 % ，最佳化參數配置為面積比20%、孔洞數75個、溫差400K、引擎轉速60rpm，影響程度為: 引擎冷熱端溫差 > 再生孔洞總面積對底板面積比 > 引擎轉速 > 底板孔洞配置數量；再生效率最佳化之值為67.63 % ，最佳化參數配置為面積比20%、孔洞數75個、溫差400K、引擎轉速60rpm，影響程度為: 引擎冷熱端溫差 > 引擎轉速 > 再生孔洞總面積對底板面積比引擎 > 底板孔洞配置數量。本篇論文結合田口優化法和計算流體力學，大幅度減少研究成本的同時，也能看出不同的設計參數對引擎內部熱傳、流場狀況及溫度分布的影響，不只完成模型最佳化也捕捉到各參數影響輸出結果的趨勢，對於模型最佳化和引擎參數分析的研究此篇論文很有參考價值。

    關鍵字:CFD模擬、田口優化法、γ- type史特靈引擎

    SUMMARY
    In this study, Taguchi Method and CFD (Computational Fluid Dynamic) have been applied to a gamma type Stirling engine to understand the effects posed by several operational and geometrical parameters on engine performance and to find the optimal combinations of some important parameters. Here, thermal efficiency, regenerate efficiency and power are selected as the indicators of Taguchi Method. The optimum composition of four parameters, number of holes, area ratio, temperature difference and rotational speed, of the Stirling engine was obtained using a Taguchi's L9 orthogonal array design. CFD simulations are conducted using L9 orthogonal array with three different levels of input parameters. The ranges for each parameter were: number of holes (75-140) , area ratio (14–20%), temperature difference (200-400K) and rotational speed (60-300rpm). Finally, the analysis of results is done using “Larger-the-better” standard for the signal-to-noise ratio (SNR). The results suggest that the optimal combination of design parameters setting are: number of holes 75, area ratio 20%, temperature difference 400K and rotational speed 300rpm for power; and number of holes 75, area ratio 20%, temperature difference 400K and rotational speed 60rpm for both thermal efficiency and regenerate efficiency.

    Keywords : gamma type Stirling engine, CFD, Taguchi method

    目錄 摘要............................................................................................. I 致謝............................................................................................. X 目錄............................................................................................. XI 圖目錄......................................................................................... XV 表目錄......................................................................................... XVII 符號說明..................................................................................... XVIII 第一章 緒論................................................................................ 1 1-1文獻回顧............................................................................. 3 1-2研究動機與目的................................................................. 7 1-3論文架構............................................................................. 9 第二章 基礎理論........................................................................ 10 2-1史特靈循環(Stirling cycle)................................................. 10 2-2 γ- type史特靈引擎工作原理............................................. 13 2-3史特靈引擎熱力循環及再生器......................................... 15 2-4自製 γ- type史特靈引擎.......................................................... 17 2-5自製 γ- type史特靈引擎熱力循環.......................................... 20 第三章 模擬設置和數學模型........................................................... 22 3-1模擬假設(流體和多孔區)....................................................... 22 3-2模型前處理............................................................................... 23 3-2.1 自製引擎之幾何模型........................................................... 24 3-2.2 氣體幾何模型建立................................................................ 26 3-2.3 模型網格分割....................................................................... 27 3-2.4 網格移動機制....................................................................... 29 3-2.5 數學模型及自定義場函數.................................................... 30 第四章 田口法應用和配置.............................................................. 33 4-1田口法介紹與架構.................................................................... 33 4-1.1 田口法介紹.......................................................................... 33 4-1.2 田口法架構與步驟.............................................................. 34 4-2因子和水準設置........................................................................ 35 4-3田口直交表設計........................................................................ 36 4-4 S/N值分析及公式..................................................................... 37 第五章 結果與分析........................................................................... 41 5-1模擬條件及驗證........................................................................ 41 5-1.1 Baseline幾何參數條件及模型建立.................................... 41 5-1.2 Baseline初始條件及邊界條件............................................ 43 5-1.3模型獨立性測試及絕熱條件驗證....................................... 44 5-1.4 Baseline物理現象分析........................................................ 46 5-2因子選定依據及其對應直交表................................................ 49 5-3最佳化目標值計算及S/N值轉換............................................ 52 5-3.1輸出功計算及其S/N值轉換............................................... 53 5-3.1-1輸出功計算...................................................................... 53 5-3.1-2輸出功S/N值轉換.......................................................... 55 5-3.2熱效率計算及其S/N值分析............................................... 56 5-3.2-1熱效率計算...................................................................... 56 5-3.2-2熱效率S/N值分析......................................................... 58 5-3.3再生效率計算及S/N值轉換.............................................. 59 5-3.3-1再生效率計算................................................................. 59 5-3.3-2再生效率S/N值轉換..................................................... 61 5-4最佳化模型參數討論............................................................... 62 5-4.1最佳輸出功參數討論.......................................................... 62 5-4.2最佳熱效率參數討論.......................................................... 64 5-4.3最佳再生效率參數討論...................................................... 66 5-5最佳化配置結果驗證............................................................... 67 5-6總結與討論............................................................................... 70 第六章 未來工作及展望................................................................... 72 參考資料............................................................................................ 73 圖目錄 圖(2-1-1)理想史特靈循環................................................................ 11 圖(2-1-2)配置再生器之理想史特靈循環........................................ 12 圖(2-3-1)理想及實際史特靈循環圖................................................ 15 圖(2-3-2)配置再生器之實際史特靈循環........................................ 16 圖(2-4-1)自製γ- type史特靈引擎.................................................... 19 圖(2-5-1)自製史特靈引擎之循環圖................................................. 21 圖(3-2.1-1)自製史特靈引擎各項參數.............................................. 24 圖(3-2.1-2)自製史特靈引擎之立體模型.......................................... 25 圖(3-2.2-1)再生器薄殼模型(圖左)、多孔再生材模擬區塊(圖右) 26 圖(3-2.2-2)五分之一模擬模型.......................................................... 26 圖(3-2.3-1)體網格配置圖.................................................................. 28 圖(4-1.2-1)田口法流程圖.................................................................. 34 圖(4-3-1) L9田口直交表................................................................... 36 圖(5-1.1-1)五分之一移氣器底板正視圖.......................................... 41 圖(5-1.1-2)Baseline模擬模型(圖左)、立體網格圖(圖右)............. 42 圖(5-1.2-1) Baseline模型邊界條件設置圖...................................... 43 圖(5-1.3-1) Baseline網格獨立測試結果.......................................... 45 圖(5-1.3-1) Baseline時間獨立測試結果.......................................... 45 圖(5-1.4-1)引擎內溫度分布圖視角一(左圖)、視角二(右圖)........ 47 圖(5-1.4-2)引擎氣體流速圖(圖左)、底板熱傳圖(圖右)................ 48 圖(5-2-1)底板與其再生孔洞面積比14%參數配置圖.................... 51 圖(5-2-2)底板與其再生孔洞面積比20%參數配置圖.................... 51 圖(5-2-3)底板與其再生孔洞面積比17%參數配置圖.................... 51 圖(5-3.1-1) Case 4之P-V圖及其擷取數據點................................ 54 圖(5-3.2-1)氣體各邊界總熱傳圖...................................................... 57 圖(5-3.3-1)再生器冷熱端溫度及溫差圖.......................................... 60 圖(5-4-1)輸出功最佳化分析圖......................................................... 63 圖(5-4-2)熱效率最佳化分析圖......................................................... 65 圖(5-4-3)無因次化之輸入熱、輸出功成長輸出圖......................... 65 圖(5-4-4)再生效率最佳化分析圖..................................................... 66 圖(5-5-1)最佳化輸出功PV圖......................................................... 68 圖(5-5-2) 最佳化輸出功邊界熱傳圖................................................ 68 圖(5-5-3) 最佳化輸出功再生器冷熱端溫度及溫差圖.................... 69 表目錄 表(4-4-1) S/N值轉換表.................................................................... 39 表(4-4-2) S/N值分析表.................................................................... 40 表(5-2-1)引擎設計因子及水準......................................................... 50 表(5-2-2)最佳化模擬參數設置圖..................................................... 50 表(5-3.1-1)輸出功S/N轉換表......................................................... 55 表(5-3.2-1)熱效率S/N轉換表......................................................... 58 表(5-3.3-1)再生效率S/N轉換表..................................................... 61

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