高浮慣比之混合對流研究

Abstract

本研究利用數值方法分析可壓縮流在三維垂直管道中的流動及熱傳機制。流場利用有限差分法進行計算，計算方法可分為兩部分：第一部份為非黏滯性項的尤拉方程式採用Roe方法計算通量，並且加入Preconditioning矩陣，讓程式在計算低速可壓縮流可獲得良好之收斂結果，而程式因為在使用Preconditioning時，加入Artificial time term 時，已破壞了整個統御方程式，因此需使用Dual time stepping疊代使其在Artificial domain 收斂時才能進入下一個真實時階；第二部份為黏滯性項的計算，採用二階中央插分法。在時間項方面則採用LUSGS隱式法，利用LUSGS疊代以求出下一時階物理量。出口設非反射性邊界條件避免可壓縮流中壓力波的干擾。在許多應用例子中，溫差常常大於30K，因此Boussinesq assumption不適用。本文採用OpenMP方法提升運算速度。 由數值計算的結果得知，三維垂直管道之自然對流，因浮力效應往上推升，在出口端產生最大速度，雷諾數(Re=400)之熱傳效應較雷諾數(Re=100、200)之熱傳還差，主要是在出口端雷諾數(Re=100、200)所吸進的流量，大於雷諾數(Re=400)所吸進的流量，而雷諾數(Re=100)從出口端吸入的速度衝擊到出口速度，故熱傳較雷諾數(Re=200)小。雷諾數(Re=100、200)流場之迴流接近入口處，在流場中會有速度反曲點，造成流場的不穩定。

An investigation of heat transfer in a three-dimensional tapered chimney with consideration of the flow compressibility is studied numerically.The finite difference method is adopted and the computational approaches are divided into two parts. One is the Roe scheme applied for the flux of inviscid terms and the preconditioning matrix is added for the efficiency in all speed fields. The other one is the central difference method of second order utilized to solve viscous terms. The temporal term is solved by LUSGS. Non-reflection conditions at the outlet is derived in order to resolve reflections induced by acoustic waves. In many important natural convection problems, the temperature differences are often higher than 30K. Boussinesq assumption is unreasonable. Besides, the OpenMP method is also used to promote the computing efficiency. By numerical results, there is the greatest flow speed near the outlet in the three-dimensional vertical natural convection pushed upward by buoyancy effect. The enhancement of heat transfer of Reynolds number 400 is worse than the enhancement of Reynolds number 100, 200. It is mainly due to the more flow rate sucked from exterior near the outlet in the case of Reynolds number 100, 200. And the flow sucked from the exterior impacted the flow exiting the outlet in the case of Reynolds number 100. The heat transfer is worse than the case of Reynolds number 200. Besides, the flow field is unstable due to the backflow near the outlet in the case of Reynolds number 100, 200.