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Research Papers: Fundamental Issues and Canonical Flows

Flow in a Curved Pipe 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

Elbit Systems—Kinetics,
P.O. Box 50,
Airport City 79100, Israel
e-mail: artyom.ramus@elbitsystems.com

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 December 3, 2014; final manuscript received July 20, 2015; published online September 10, 2015. Assoc. Editor: Mark F. Tachie.

J. Fluids Eng 138(2), 021203 (Sep 10, 2015) (11 pages) Paper No: FE-14-1722; doi: 10.1115/1.4031259 History: Received December 03, 2014; Revised July 20, 2015

This study considers a combination of two well studied flows: the flow in a curved pipe and the flow in a straight pipe with a sudden expansion. Steady laminar flow of an incompressible fluid through an axisymmetric sudden expansion followed by a curved pipe was investigated numerically. The influence of the expansion ratio and the Reynolds number on the vortex pair in the bend and on the recirculating flow caused by the sudden expansion was studied. A correlation for the length of the recirculation flow was obtained.

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Figures

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Fig. 1

Axisymmetric sudden expansion flow

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Fig. 3

Flow in a curved pipe with a sudden expansion

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Fig. 4

Axial velocity profile at the pipe exit for three outlet lengths for Re = 600 and the expansion ratio of 3

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Fig. 5

Reattachment length in axisymmetric sudden expansion flow with the expansion ratio of 2

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Fig. 6

Velocity magnitude contours in the plane of symmetry: (a) expansion ratio 1.5, Re = 200; (b) expansion ratio 4, Re = 200; (c) expansion ratio 2, Re = 50; and (d) expansion ratio 2, Re = 600

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Fig. 7

Velocity vectors in the symmetry plane for the expansion ratio of 2 and Re = 400: (a) straight pipe and (b) curved pipe

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Fig. 8

Reattachment length in sudden expansion flow in a curved and straight pipe with the expansion ratio of 2

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Fig. 9

Reattachment length for various expansion ratios: (a) inner side and (b) outer side

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Fig. 10

Velocity vectors in the 0 deg cross section of the pipe bend for the expansion ratio of 2 and Re = 400: (a) with expansion and (b) no expansion

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Fig. 11

Velocity vectors in the 22.5 deg cross section of the pipe bend for the expansion ratio of 2 and Re = 400: (a) with expansion and (b) no expansion

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Fig. 12

Velocity vectors in the 45 deg cross section of the pipe bend for the expansion ratio of 2 and Re = 400: (a) with expansion and (b) no expansion

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Fig. 13

Velocity vectors in the 67.5 deg cross section of the pipe bend for the expansion ratio of 2 and Re = 400: (a) with expansion and (b) no expansion

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Fig. 14

Velocity vectors in the 90 deg cross section of the pipe bend for the expansion ratio of 2 and Re = 400: (a) with expansion and (b) no expansion

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Fig. 15

Vorticity magnitude for the curved pipe flow with the expansion ratio of 2 and Re = 400: (a) with expansion—only values above 1000 1/s are shown; (b) no expansion—only values above 400 1/s are shown. The four circles denote (from left to right) the expansion, the start of the bend, the end of the bend, and the pipe outlet.

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Fig. 16

Directions for plotting vorticity magnitude profiles

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Fig. 17

Radial distribution of the vorticity magnitude in the direction that is perpendicular to the plane of symmetry. Expansion ratio of 2 and Re = 400: (a) the 0 deg and 11.25 deg cross sections and (b) the 22.5 deg and 45 deg cross sections.

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Fig. 18

Vorticity magnitude profile in the symmetry plane along the diameter that is parallel to the bend curvature radius. Expansion ratio of 2 and Re = 400: (a) the 0 deg and 22.5 deg cross sections and (b) the 45 deg and 67.5 deg cross sections. The direction is from the inner to the outer wall.

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Fig. 19

Vorticity magnitude profile in the symmetry plane along the diameter that is parallel to the bend curvature radius for two Reynold numbers. Expansion ratio of 2: (a) the 0 deg and 22.5 deg cross sections and (b) the 45 deg and 67.5 deg cross sections. The direction is from the inner to the outer wall.

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