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Research Papers: Fundamental Issues and Canonical Flows

Instability of a Curved Pipe Flow With a Sudden Expansion

[+] Author and Article Information
Michael Shusser

Aeronautical Systems Department,
Rafael, P.O. Box 2250,
Haifa 3102102, Israel
e-mail: michaels@rafael.co.il

Artyom Ramus

Cleanetica,
Haluzey Taasiya 15,
Haifa Bay 2611701, Israel
e-mail: tech2@cleanetica.co.il

Oleg Gendelman

Department of Mechanical Engineering,
Technion,
Technion City, Haifa 3200003, Israel
e-mail: ovgend@technion.ac.il

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received November 11, 2015; final manuscript received July 17, 2016; published online October 18, 2016. Assoc. Editor: Samuel Paolucci.

J. Fluids Eng 139(1), 011203 (Oct 18, 2016) (10 pages) Paper No: FE-15-1818; doi: 10.1115/1.4034364 History: Received November 11, 2015; Revised July 17, 2016

Numerical calculations of laminar flow of an incompressible fluid through an axisymmetric sudden expansion followed by a curved pipe recently done by the authors discovered an early instability of this flow for a certain expansion ratio, as it becomes unsteady with periodic oscillations of the flow variables at a Reynolds number when both curved pipe flow and flow in a straight pipe with an axisymmetric sudden expansion remain stable. This study describes in detail the created oscillatory flow and suggests that the early instability of the ratio 3 flow could be caused by the higher velocity gradient near the outer wall of the bend.

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Figures

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Fig. 1

Flow in a curved pipe with a sudden expansion

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Fig. 2

Velocity magnitude profile in the symmetry plane in the 45 deg cross section (line AB in Fig. 1) for Re = 600 and the expansion ratio of 3 for the structured, unstructured, and symmetric unstructured grid. The direction is from the inner to the outer wall.

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Fig. 3

Oscillations at the center of the 90 deg cross section (point 1 in Fig. 1) for Re = 600 and the expansion ratio of 3: (a) axial y-velocity, (b) pressure, (c) secondary x- and z-velocities, and (d) limit cycle of the x- and z-velocities

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Fig. 4

Secondary x- and z-velocities in the middle of the radius in the symmetry plane in the 90 deg cross section (point 2 in Fig. 1) for Re = 600 and the expansion ratio of 3: (a) time-dependence and (b) limit cycle

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Fig. 5

Oscillations of the velocity components at the center of the 45 deg cross section (point 3 in Fig. 1) for Re = 600 and the expansion ratio of 3

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Fig. 6

Velocity magnitude contours (m/s) for Re = 600 and the expansion ratio of 3: (a) the 45 deg cross section, t = 0.91 s; (b) the 45 deg cross section, t = 0.98 s; (c) the 67.5 deg cross section, t = 0.91 s; and (d) the 90 deg cross section, t = 0.91 s

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Fig. 7

Power spectra for Re = 600 and the expansion ratio of 3: (a) the center of the 90 deg cross section (point 1 in Fig. 1), (b) the middle of the radius in the symmetry plane in the 90 deg cross section (point 2 in Fig. 1), and (c) the center of the 45 deg cross section (point 3 in Fig. 1)

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Fig. 8

Velocity vectors for the expansion ratio of 3 and Re = 600: (a) the 0 deg cross section and (b) the 22.5 deg cross section. The upper side is the inner wall, and the lower side is the outer wall of the bend.

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Fig. 9

Velocity vectors in the 45 deg cross section of the pipe bend for the expansion ratio of 3 and Re = 600: (a) t = 0.91 s and (b) t = 0.98 s. The upper side is the inner wall, and the lower side is the outer wall of the bend.

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Fig. 10

Velocity vectors in the 67.5 deg cross section of the pipe bend for the expansion ratio of 3 and Re = 600: (a) t = 0.91 s and (b) t = 0.98 s. The upper side is the inner wall, and the lower side is the outer wall of the bend.

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Fig. 11

Velocity vectors in the 90 deg cross section of the pipe bend for the expansion ratio of 3 and Re = 600: (a) t = 0.91 s and (b) t = 0.98 s. The upper side is the inner wall, and the lower side is the outer wall of the bend.

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Fig. 12

Velocity magnitude contours in the 67.5 deg cross section of the pipe bend for the expansion ratio of 3 and Re = 600 during one-half of the oscillation period. The upper side is the inner wall, and the lower side is the outer wall of the bend.

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Fig. 13

Velocity magnitude profile in the symmetry plane in the 45 deg cross section (line AB in Fig. 1) for Re = 600 and several expansion ratios. The direction is from the inner to the outer wall.

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