Heat Transfer Analysis of Impinging Flow near Entrance Region in a Serpentine Heat Exchanger

本研究探討一個蛇行管式熱交換器中氣體側前端之熱傳性能，此熱交換器由矩形截面管組合而成，氣體先與管道之側面垂直接觸，然後通過兩個狹小平行管道，最後流出熱交換器外，在進入狹小管距前，氣體會與矩形管之側面進行垂直衝擊之接觸，此研究主要探討此衝擊面處之熱傳性能。本研究首先利用有限差分法將質量平衡、Navier-Stokes與能量平衡等方程式離散成有限差分公式，格點之設計為交錯網格（staggered grid），在將所得之有限差分公式無因次化後，配合SIMPLE 演繹法進行數值分析之運算，電腦程式乃使用Fortran語言編輯。此數值分析中考慮之流體為二維層流，雷諾數(Re)為50與100兩種，流道收縮比亦分為0.25與0.5兩種，流體之普朗特數為0.7，管壁則考慮為等溫之狀態。於流場之分析結果中顯示，在較小之流道收縮比(=0.25)情形下，流體流動方向之改變會較大。於熱傳分析之結果中顯示，在相同流道收縮比之條件下，Re值增加一倍時，局部紐塞數(Nu)會增加，但平均紐塞數( )並未以等倍率增大；在Re值為50時，流道收縮比之變化對 值之影響甚小，而在Re值為100時，當流道收縮比變小時， 值會微略增加。The heat transfer performance in the front surface of a serpentine heat exchanger was investigated. The heat exchanger is composed of rectangular tubes. During operation, gas vertically contacts with the front surface of the tubes and then it passes through a narrow spacing in between two neighboring tubes. Before the gas flows into the narrow spacing, it would impinge on the lateral side of the tubes. This work focuses on the impingement heat transfer in this region. A staggered-grid finite-difference method was used to discretize the continuity, Navier-Stokes and energy equations into a set of finite difference equations. These equations were converted into a dimensionless form and then solved following the SIMPLE algorithm. The computer program was compiled using Fortran language. In the analysis, the flow was two-dimensional and laminar. Two Reynold numbers (Re=50 and 100), and two flow-field contraction ratios (0.25 and 0.5) were considered respectively. The Prandtl number was 0.7 and the wall was considered to be isothermal. The result of the fluid analysis shows that, the smaller the contraction ratio (= 0.25), the larger the change of the flow direction. The result of the heat transfer analysis shows that, at the same contraction ratio, for an increase of the Re from 50 to 100, the local Nusselt number would increase. But the average Nusselt number does not increase two-folds. At the Re of 50, the contraction ratio almost does not have any effect on the average Nusselt number. At the Re of 100, as the contraction ratio decreases, the average Nusselt number value slightly increases.摘 要.....................................................Ⅰ ABSTRACT..................................................Ⅱ 致 謝.....................................................Ⅲ 目 錄.....................................................Ⅳ 表目錄....................................................Ⅵ 圖目錄....................................................Ⅶ 符號說明..................................................Ⅹ 第一章 緒論...............................................1 1-1 前言..................................................1 1-2 文獻回顧..............................................1 1-3 研究目的..............................................6 第二章 理論分析...........................................8 2-1 計算流體力學之概述....................................8 2-2 流場內之統御方程式與邊界條件..........................9 2-2.1 統御方程式..............................9 2-2.2 邊界條件..............................10 2-3 動量方程式與連續方程式之離散過程.....................12 2-4 無因次化之統御方程式.................................19 2-5 程式中速度格點位置之表示方式.........................26 2-5.1 程式中動量方程式之表示方式.............28 2-5.2 程式中溫度方程式之表示方式.............30 2-5.3 程式中邊界方程式之表示方式.............30 2-6 SIMPLE ALGORITHM (SEMI-IMPLICIT METHOD FOR PRESSURE-LINKED EQUATION) 運算的過程...............................32 2-7 局部熱傳紐塞數.......................................33 2-8 平均熱傳紐塞數.......................................36 第三章 電腦模擬之分析....................................38 3-1 流場之網格設置.......................................38 3-2 流道收縮比對流場之影響...............................39 3-3 接近衝擊壁面處流體之溫度分佈.........................40 3-4 衝擊面上之局部紐塞數.................................42 3-5 衝擊面上之平均紐塞數.................................43 3-6 雷諾數對紐塞數之影響..................................43 3-7 流道收縮比對紐塞數之影響..............................44 第四章 結論..............................................45 參考文獻..................................................7