三維波形管之熱傳分析

Abstract

本研究利用數值方法分析可壓縮流在三維垂直波形管道中的流動及熱傳機制。網格採用橢圓偏微分方程法生成。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，使程式在計算低速可壓縮流可獲得良好之收斂結果，而由於使用Preconditioning 法時加入Artificial time term 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。由於本研究為可壓縮流之模擬，不需使用Boussinesq assumption，適用於溫差高於30K 之情形，應用範圍更為廣泛。另外為提升計算速度，本文採用OpenMP 方法進行平行化運算。 本研究以振幅波長比及瑞利數為主要參數進行模擬。對於三維波形管，流體流經波峰時類似流經漸縮管，邊界層縮小，熱傳能力較好。而流經波谷時，流體在壁面處近乎停滯，熱傳效率較差。在所計算之瑞利數(104 ~ 106)和振幅波長比(0、0.1、0.2)之間流場並無出現不穩定的情形。三維波形管在自然對流時平均紐塞數隨振幅波長比增加而下降，且雖然散熱面積增加，但總熱傳量反而下降。

An investigation of heat transfer in a three-dimensional wavy duct 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. Due to the consideration of flow compressibility , Boussinesq assumption is not used. Therefore, applicable to cases with temperature difference higher than 30K.Besides, to enhance the computing efficiency, the OpenMP method is also used. In this study, amplitude-wavelength ratio and Rayleigh number is set to be primary variables. The results show that when flow passes through the crests, the boundary layer gets smaller, therefore a better heat transfer rate. And when flow passes through the troughs, fluid is almost stagnant near the walls , which leads to a poor heat transfer rate. Flow field shows no instability for Rayleigh number ranging from 104~106 and amplitude-wavelength ratio 0~0.2. In all cases studied, the averaged Nusset number is decreased as amplitude-wavelength ratio increases, and the total heat flux decreases too even though the cooling area is increased .