Some aspects of bifurcation structure of laminar flow in curved ducts

Abstract

A bifurcation study is made of laminar flow in curved ducts. The problem is formulated in a curvilinear coordinate system, and the governing equations, after orthogonal mapping is applied, are solved numerically by an iterative finite-difference method. Many computer runs were made with various duct cross-sections ranging from a circle to a square, to learn the transition of bifurcation structure with this change in cross-section and to reconcile the differences between them. In addition, a simpler technique is proposed to generate symmetric four-cell solutions in a circular pipe and a means is put forward to stabilize four-vortex structures in a complete cross-section.

Bifurcation and stability analysis of laminar flow in curved ducts

“…Machane [20] proved mathematically the existence andfor a small range of Dean numbers-the uniqueness of weak solutions of the Dean problem and supplied extensions of the bifurcation diagrams provided by Winters [6]. Later the morphological understanding was broadened by Bara et al [8], Chen and Jan [21], Finlay and Nandakumar [22], Hatzikonstantinou and Sakalis [23], Ishigaki [24], Tiwari et al [25] and Kao [26]. Comparative studies have been done by Jayanti and Hewitt [27], Lee and Baek [28] or Yang and Wang [29].…”

Numerical study of non-isothermal flow with convective heat transfer in a curved rectangular duct

“…Studies of the flow through a curved duct have been made, experimentally or numerically, for various shapes of the cross section. For example, for a circle (Dennis and Ng [1], Yang and Keller [2], Yanase et al [3]), a semi-circle (Nandakumar and Masliyah [4]), an oval (Kao [5]) and a rectangle (Ligrani and Niver [6], Yanase and Nishiyama [7], Thangam and Hur [8] and Finlay and Nandakumar [9]). An extensive treatment of the bifurcation structure of the flow through a curved duct of rectangular cross section was presented by Winters [10] and Yanase et al [11].…”

Centrifugal Instability with Convective Heat Transfer Through a Tightly Coiled Square Duct

“…However, an important circumstance of the flow through a curved duct is the bifurcation of the flow because various types of steady solutions are existed for the presence of centrifugal force which is affected by the curvature of the duct. It has already seen that many authors have been presented the bifurcation structure both numerically and experimentally for various types of duct such as helically coiled ducts [3,6], rectangular ducts [7] and oval [8]. Wang et al [9] performed both bifurcation and stability for coiled ducts, where the same phenomena was studied by Yamamoto et al [10] for helical tube.…”