利用CUDA平行計算平台探討可壓縮流在三維煙囪管道的熱傳分析

Abstract

本研究利用數值方法分析可壓縮流在三維煙囪漸縮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；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。出口設非反射性邊界條件避免可壓縮流中壓力波的干擾。 由數值計算結果得知，流體速度隨三維漸縮管道的主流方向截面積縮小而加快，使壁面中央區域熱傳效果大幅增加。但壁面與壁面間的夾角隨之減小，導致流經夾角附近(壁面兩側)的流體，因壁面摩擦阻抗增加流速降低，反而使熱傳效果急遽劣化。此外雷諾數越大，熱傳效果越好，壁面兩側三維效應現象依舊存在。而利用CUDA平台作平行化運算可使計算速度較一般四核心中央處理器加快約4.72倍，可見其顯著的效率提升。

An investigation of heat transfer in a three-dimensional chimney with consideration of the flow compressibility is studied numerically.The finite difference is adopted and the computational approaches could be divided into two parts. One is the inviscid terms The Roe scheme is utilized to deal with the flux of inviscid terms and the preconditioning matrix is added to let the scheme to be more effective for all speed filed. The other is viscous term and the central difference of second order is utilized to handle it. The temporal term is solved by LUSGS. Non-reflection conditions at the outlet is derived in order to resolve reflections induced by acoustic waves. The result shows that the convergent chimney construction can accelerate flow velocities by changing the area of cross section ,and the superior enhancement of heat transfer rates of the center of the heat wall are achieved. With the decreasing of the angle between the walls, velocities of the fluids sides by wall decrease due to the friction and the heat transfer efficiency decrease. Moreover, the heat transfer efficiency increase with increasing Reynolds number. In order to improve the efficiency of CFD program,CUDA platform is employed for paralleled program in graphic hardware and shows significantly advantage over the CPU implementation.