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Influence of the geometry on the two- and three-dimensional dynamics of the flow in a 180° sharp bend
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10.1063/1.4807070
/content/aip/journal/pof2/25/5/10.1063/1.4807070
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/5/10.1063/1.4807070

Figures

Image of FIG. 1.
FIG. 1.

Key points of 180° bend duct have been studied: turning part shape (a), turning part width (b), divider thickness (c), and secondary flow recirculations (d).

Image of FIG. 2.
FIG. 2.

The geometry of 180° bend duct for the whole domain. Boundaries are labelled as follows: 1, top boundary (T); 2, inside boundary (I); 3, bottom boundary (B); 4, end wall boundary (E).

Image of FIG. 3.
FIG. 3.

Details of the meshes around turning part area.

Image of FIG. 4.
FIG. 4.

Sequence of flow regimes in the outlet part for β = 1. (a)–(c) Streamlines of steady flow. (d)–(e) Snapshot of vorticity contours taken from the unsteady flow. The outlet part is only represented up to 15 duct widths for clarity, when the simulated domain extends in fact to 30 duct widths. ω stands for the dimensionless maximum vorticity which is normalised by /.

Image of FIG. 5.
FIG. 5.

Flow regimes in outlet part of bend for β = 0.5. See legend of Fig. 4 . The outlet part is only represented up to 15 duct widths for clarity, when the simulated domain extends in fact to 30 duct widths.

Image of FIG. 6.
FIG. 6.

Flow regimes in outlet part of bend for β = 0.1. The outlet part is only represented up to 15 duct widths for clarity, when the simulated domain extends in fact to 30 duct widths.

Image of FIG. 7.
FIG. 7.

Streamlines of the steady flow at β = 0.2, showing the stages of the development of the inside recirculation within R at different values of Re.

Image of FIG. 8.
FIG. 8.

Relationship between the critical Reynolds number Re for the appearance of the inside recirculation within R, and β.

Image of FIG. 9.
FIG. 9.

Phase diagram of 180° sharp bend: flow regimes are labelled by Roman characters followed by numbers. These, respectively, stand for the outlet flow regimes and the number of merged recirculations in the turning part section. A schematic representation of each combined flow regime is given for each distinct region of the phase diagram. Error bars span the interval between numerical simulations showing the “last stable” and those showing “first unstable” one.

Image of FIG. 10.
FIG. 10.

Sketch of separation and re-attachment points defining the locations of all recirculations.

Image of FIG. 11.
FIG. 11.

Time average of separation and re-attachment points in the outlet branch of the bend vs. Re. (a) β = 2, (b) β = 1, (c) β = 0.2, and (d) β = 0.1.

Image of FIG. 12.
FIG. 12.

Variations of recirculation lengths ⟨ ⟩ (top) and ⟨ ⟩ (bottom) against their respective critical parameters for several fixed values of β.

Image of FIG. 13.
FIG. 13.

Sketch of and : just before (top) and just after (bottom) the collapse of R (top), in the sense of increasing Reynolds.

Image of FIG. 14.
FIG. 14.

Variations of the length of the steady and unsteady recirculations with β for fixed values of Re.

Image of FIG. 15.
FIG. 15.

Force direction on inside boundary: (up) and (bottom).

Image of FIG. 16.
FIG. 16.

The relationship between with Re of inside boundary.

Image of FIG. 17.
FIG. 17.

The relationship between with Re of inside boundary.

Image of FIG. 18.
FIG. 18.

The relationship between with Re of β = 1 and β = 0.5. Black and white symbols, respectively, refer to shedding in regimes IV and V.

Image of FIG. 19.
FIG. 19.

Snapshot of vorticity contours taken from unsteady flow for β = 1: (a) At Re = 1500, near the Maximum of (), the vortex street is still well defined; (b) at Re = 2000, past the Maximum of (), the interaction with the walls destroy the vortex street.

Image of FIG. 20.
FIG. 20.

The relationship between with Re of β = 0.2.

Image of FIG. 21.
FIG. 21.

Flow regimes of the turning part section of 180° sharp bend.

Image of FIG. 22.
FIG. 22.

Time average of separation and re-attachment points in the turning part area of the bend vs. Re. (a) β = 0.5, (b) β = 1, (c) β = 3, and (d) β = 5.

Image of FIG. 23.
FIG. 23.

β* vs. Re for different β.

Image of FIG. 24.
FIG. 24.

Sketch of 3D geometry.

Image of FIG. 25.
FIG. 25.

Details of the meshes for 3D geometry: (a) domain near the turning part and (b) mesh view from the end wall.

Image of FIG. 26.
FIG. 26.

Velocity streamlines (a) for Re = 400 and iso-surfaces of -vorticity [ω = 0.025ω] and (b) for Re = 2000 at β = 1.

Image of FIG. 27.
FIG. 27.

Velocity streamlines (a) for Re = 500 and iso-surfaces of -vorticity [ω = 0.027ω] and (b) for Re = 2000 at β = 5.

Image of FIG. 28.
FIG. 28.

Iso-surfaces of -vorticity for Re = 2000 at β = 1: (a) TC1 [ω = 0.025ω] and (b) TC2 [ω = 0.023ω].

Image of FIG. 29.
FIG. 29.

Velocity streamlines (a) for Re = 65 and iso-surfaces of -vorticity [ω = 0.027ω] and (b) for Re = 520 at β = 0.2.

Image of FIG. 30.
FIG. 30.

Snapshot of vorticity contours taken from the 2D simulation (a) and 3D simulation (b) for Re = 520 at β = 0.2. Even though the flow is strongly 3D, the general structure of the flow is very similar in both simulations, with in particular, a large 2D recirculation R, acting as “wheel,” which conveys smaller structures generated by the instability of the jet that wraps around it. Values of , , , and found in the 2D and 3D simulations are accordingly very close to each other.

Tables

Generic image for table
Table I.

Characteristics of different meshes and , S, and errors at Re = 100 and 800 for β = 1.

Generic image for table
Table II.

Comparison of , , and for different resolutions and domain widths at Re = 2000 for β = 1. and are expressed per width of 2. The superscript stands for relative discrepancies to the reference case (C0).

Generic image for table
Table III.

Comparison of , , , , and discrepancy between 2D and 3D simulations. Quantities from 3D simulations are expressed per unit length.

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/content/aip/journal/pof2/25/5/10.1063/1.4807070
2013-05-24
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Influence of the geometry on the two- and three-dimensional dynamics of the flow in a 180° sharp bend
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/5/10.1063/1.4807070
10.1063/1.4807070
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