不同高寬比之螺旋矩型管內全展層流場研究

Laminar Flow in Healical Rectangular Ducts with Different Aspect Ratios

張永鵬(Yeon-Pun Chang) ； 蔡瑞益(Ruey-Yih Tsai) ； 黃錦文(Jiin-Wen Hwang)

《中原學報》 27卷1期 (1999/03) Pp. 41-49

https://doi.org/10.6358/JCYU.199903.0041

摘要

本文主要是利用Galerkin有限元素法解求非正交螺旋座標系之連續之Navier-Stokes 方程式，以討論不同高寬比之螺旋矩型管中於穩態、不可壓縮及全展層流狀態下，曲率及撓率對二次流變化之影響。高寬比分別以0.5、1.5、2.0及5.0為例，分析其在不同曲率、撓率及高寬比等情況下不同軸向壓力梯度時之變化現象。於曲率、撓率均低於0.025，及高寬比小於2.0而軸向壓力梯度低於-0.4x10^(5)時其二次流變化差異不大，唯高寬比對渦漩流動的影響較大，且愈大愈不規則；此外，亦導出不同高寬比之摩擦因子比（（fRe）/（fRe）(下標 s)）與迪恩參數（K）之相關方程式。

關鍵字

二次流 ； 高寬比 ； 摩擦因子比

並列摘要

In this study, the Galerkin finite element method is applied to solve the continuity and Navier-Stokes equations which are derived by non-orthogonal helical coordinate system for steady, incompressible, fully developed laminar flow in helical rectangular ducts with different aspect ratios discussing the effect of curvature and torsion towards secondary flow. The aspect ratios are 0.5, 1.5, 2.0, and 5.0, respectively. The interaction effects with different curvatures, torsions and aspect ratios under variable axial pressure gradients are presented. When curvature and torsion are smaller (Ex. ≦0.025), the aspect ratio is under 2.0, and the axial pressure gradients are low than -0.4x105, the changing differences of the secondary flow are not large. In other words, the aspect ratio has greater effect to the vortex flow, and the larger it is, the more irregular it will be. Besides, we also derive the relationship equations of friction factor ratio ((fRe)/(fRe)(superscript s)) with Dean number (K) that is at different aspect ratios.

並列關鍵字

secondary flow ； aspect ratio ； friction factor ratio