以ALE移動網格法及GMRES迭代解法探討內流場中固體運動對熱傳效率及壓力變化影響之研究

Abstract

本研究利用數值方法分析大面積薄板垂直運輸下之流場，並探討氣流擾動對薄板所產生之舉昇飄浮現象。探討流場影響薄板飄浮之舉昇力須先獲得壓力分佈，且此為移動邊界問題，本研究採用Generalized Minimal Residual法(GMRES)及Arbitrary Lagrangian-Eulerian法(ALE)解此一問題。本研究先針對頂部加熱、強制流衝擊之ㄇ型渠道，在渠道內加裝固定凸塊，藉由分析流場對加熱面下游段之熱傳增益效果，作數值方法之適用性探討。結果顯示加熱面熱傳增益與渠道增壓程度有關，進而應用此數值方法計算大面積薄板垂直運輸之流場。結果顯示，以薄板及支撐架兩者之移動加速度作比較可預判薄板飄移之趨勢，而比較薄板及支撐架移動之距離則可確切判斷薄板飄浮的時機。當垂直運輸之速度愈是增加，則薄板會愈快離開支撐架而飄浮。 此外，本文採用有限元素法(FEM)，並以Pressure Convection-Diffusion(PCD)預處理法(preconditioning)針對GMRES解Navier-Stokes方程式在運算上獲得較高之收斂效率，另利用多核心電腦使用OpenMP平台，自行編撰程式執行平行運算，以減低計算時間。

This study investigates the flow field and suspension phenomena of a large thin plate being transported vertically. For analyzing the lifting forces caused by flow disturbances, pressure distributions along upper and lower surfaces of the thin plate must be acquired and for processing this moving boundary problem, both Generalized Minimal Residual method (GMRES) and Arbitrary Lagrangian-Eulerian method (ALE) are adopted. In advance, this study utilizes a top heated, reciprocating curved channel with rib installed to verify the adoptability of numerical methods mentioned, and by relationship between channel pressure distributions and increment of heated surface’s back region heat transfer rates, these numerical methods are suitable for calculating the flow field induced by large thin plate vertical transportation. The results show that by moving accelerations of supporting frames and the thin plate, a tendency of suspension can be predicted, and by displacements of moving distances, the suspension timing can be predicted exactly. Furthermore, as the transporting speed increases, more likely the thin plate will suspend. This study utilizes finite element method (FEM), also the Pressure Convection -Diffusion preconditioning method (PCD) is adopted to increase convergent efficiency of GMRES iteration, and by advantages of multi-core computer, parallelization of the program by coding OpenMP directives is utilized to lower calculating time.