# Influence of the geometry on the two- and three-dimensional dynamics of the flow in a 180 degree sharp bend

• Lintao Zhang

Student thesis: Doctoral ThesisDoctor of Philosophy

### Abstract

In this thesis, I numerically simulate the ﬂow past a 180◦ sharp bend. The main objective of this research is to characterize the inﬂuences of the bend geometry on the ﬂow regimes when Reynolds number (Re) is varied. Reynolds number and the opening ratio (β) (the deﬁnition of β is deﬁned in section 4.1.1) of the bend are the control parameters which are varied to perform the parametric study. For the ﬁrst part of our research, I focus on the ﬂow past a twodimensional 180◦ sharp bend. An extensive parametric study on the transitions of the ﬂow regimes by varying the values of Re and β is performed. The values of Re and β are in the ranges of (0...2500] and [0.1...10], respectively. As Reynolds number is increased, I ﬁnd a laminar ﬂow, then a ﬂow with a ﬁrst recirculation attached the inside boundary, then a ﬂow with a second recirculation attached to the top boundary. The onset of the unsteadiness occurs through instability of the main stream and the vortex shedding starts from the inside boundary. For β < 0.3, the ﬂow is characterised by the dynamics of the jet ﬂow near the very narrow turning part. For β ≥ 0.3, the ﬂow exhibits strong similarities with the ﬂow behind an obstacle placed in a channel. For the second part of our work, I focus on the ﬂow past a threedimensional 180◦ sharp bend. Simulations with periodic conditions are performed for selected Re and β in order to determine the validity of the 2D assumptions. The results show that two-dimensional dynamics can predict the features of three-dimensional ﬂow in steady ﬂow regimes, even for unsteady ﬂow regimes to some extent. Simulations on the more realistic situations of a three-dimensional bend with walls are carried out as well. The results show that ﬂow is symmetric to the center of the bend at low Re along spanwise direction. As Re increases, the inﬂuences of Dean ﬂow on the mainstream ﬂow are obvious. Near-wall quasi-symmetric shedding is presented in unsteady ﬂow regimes as well. The unsteadiness is ﬁrst originated from the shear layer between the ﬁrst recirculation and the Dean ﬂow region.
Date of Award Apr 2013 English Coventry University Alban Potherat (Supervisor)

### Keywords

• Fluid mechanics
• Bend geometry
• Flow

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