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Research Papers: Fundamental Issues and Canonical Flows

The Flow and Decay Behavior of a Submerged Shear-Thinning Jet With Yield Stress

[+] Author and Article Information
Khaled J. Hammad

Department of Engineering,
Central Connecticut State University,
1615 Stanley Street,
New Britain, CT 06050
e-mail: hammad@ccsu.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 19, 2015; final manuscript received February 22, 2016; published online May 19, 2016. Assoc. Editor: D. Keith Walters.

J. Fluids Eng 138(8), 081205 (May 19, 2016) (9 pages) Paper No: FE-15-1675; doi: 10.1115/1.4033027 History: Received September 19, 2015; Revised February 22, 2016

The flow and decay characteristics of submerged jets of shear-thinning fluids with yield stress are studied. Numerical solutions to the governing mass and momentum conservation equations, along with the Herschel–Bulkley rheological model, are obtained using a finite-difference scheme. A parametric study is implemented to investigate the influence of flow inertia and rheology over the following range of parameters: Reynolds number, 50 ≤ Re ≤ 200; yield number, 0 ≤ Y ≤ 1; and shear-thinning index, 0.6 ≤ n ≤ 1. A large recirculation region exists for Newtonian and shear-thinning non-Newtonian jets. However, the extent and strength of the recirculation region substantially diminish with the yield number and, to a lesser extent, when the shear-thinning index is reduced from 1 to 0.6. Increasing the yield number beyond a critical value eliminates flow recirculation. The centerline velocity and momentum decay of shear-thinning jets with yield stress, in general, increase with the yield number. Velocity- and momentum-based depths of penetration, DPU, and DPM, respectively, are introduced and presented. DPU and DPM are the downstream locations corresponding to 90% decay in the initial centerline velocity and jet momentum, respectively. A substantial decrease in DPU and DPM is observed when the shear-thinning index is reduced from 1 to 0.6 for Y = 0. The presence of yield stress significantly reduces both DPU and DPM of submerged jets. The impact of shear-thinning on the decay characteristics of the jet is more pronounced at low yield numbers.

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References

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Figures

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Fig. 1

Shear stress versus shear rate for Newtonian and non-Newtonian fluids

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Fig. 2

Evolution of Newtonian and non-Newtonian jets: (a) shear-thinning, (b) Newtonian, and (c) yield-shear-thinning

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Fig. 3

Analytical and numerical fully developed velocity profiles in a pipe

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Fig. 4

Computational domain and boundary conditions for a top-hat jet

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Fig. 5

Influence of the radial extent of the computational domain, L/R, on the centerline velocity decay for Newtonian and non-Newtonian fluids

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Fig. 6

Yield number effect on effective viscosity for Re = 50 and n = 1: (a) Y = 0.5, n = 1 and (b) Y = 1

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Fig. 7

Yield number effect on effective viscosity for Re = 100 and n = 1: (a) Y = 0.5, n = 1 and (b) Y = 1

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Fig. 8

Yield number effect on effective viscosity for Re = 50 and n = 0.6: (a) Y = 0.5, n = 0.6 and (b) Y = 1

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Fig. 9

Yield number effect on effective viscosity for Re = 100 and n = 0.6: (a) Y = 0.5, n = 0.6 and (b) Y = 1

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Fig. 10

Yield number effect on streamlines for Re = 50 and n = 1: (a) Y = 0, n = 1, (b) Y = 0.5, and (c) Y = 1

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Fig. 11

Yield number effect on streamlines for Re = 100 and n = 1: (a) Y = 0, n = 1, (b) Y = 0.5, and (c) Y = 1

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Fig. 12

Yield number effect on streamlines for Re = 50 and n = 0.6: (a) Y = 0, n = 0.6, (b) Y = 0.5, and (c) Y = 1

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Fig. 13

Yield number effect on streamlines for Re = 100 and n = 0.6: (a) Y = 0, n = 0.6, (b) Y = 0.5, and (c) Y = 1

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Fig. 14

Centerline velocity decay characteristics: (a) Re = 50, (b) Re = 100, and (c) Re = 200

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Fig. 15

Axial momentum decay characteristics: (a) Re = 50, (b)Re = 100, and (c) Re = 200

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Fig. 16

Velocity-based jet depth of penetration: (a) Y = 0, (b)Y = 0.5, and (c) Y = 1

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Fig. 17

Momentum-based jet depth of penetration: (a) Y = 0, (b) Y = 0.5, and (c) Y = 1

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