高浮慣比混合對流之熱傳效益提升

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，在入口處區因應浮力效應區分固體壁面區、強制對流區、開放區域，可使高溫壁面處產生相對較高的速度。若無固體壁面，高速的區域較靠近管中央，熱傳效果較差；而增大入口固體壁面範圍，速度越集中高溫壁面，使熱傳效果上升；當固體壁面達到一定程度，會產生渦流使流場混亂，維持部份熱傳效果；當開口比過小時，受黏性效應影響，開放區域流速下降，再無法提升熱傳效果。提高中央強制對流入口速度使浮慣比下降，流場受浮力效應影響越低，流場較趨於等速；浮慣比越大，速度相對較高區域集中在高溫壁面。

An investigation of heat transfer in a three-dimensional straight rectangular pipe 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, due to buoyancy effect, inlet boundary condition is distinguish between forced convection areas, a solid wall areas and open areas, and it allows high-temperature wall at a relatively high speed. If there is no solid wall at the entrance, high-speed region takes place in the middle of the tube, and the heat transfer is less effective. Then, increasing the entrance of solid wall range, the high speed is more close to the high-temperature wall, so that the effect of heat transfer increases. When the solid wall region increases to some extent, there is vortex making flow the field chaotic. Those effects maintains part of the heat transfer effect. When the open proportion is too small, the open area flow rate decreases, and it can’t enhance the effect of heat transfer, because of the viscous effects. With the increasing of the central forced convection area inlet velocity, Richardson number is smaller, and the flow field affected is lower by the buoyancy. Then, flow field tend to be a more constant speed field. Contrarily, when Richardson number is bigger, the relatively high speed is more close to the high temperature wall.