Research Papers: Fundamental Issues and Canonical Flows

Velocity and Momentum Decay Characteristics of a Submerged Viscoplastic Jet

[+] 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 June 3, 2013; final manuscript received November 3, 2013; published online December 12, 2013. Assoc. Editor: Francine Battaglia.

J. Fluids Eng 136(2), 021205 (Dec 12, 2013) (8 pages) Paper No: FE-13-1354; doi: 10.1115/1.4025990 History: Received June 03, 2013; Revised November 03, 2013

Velocity and momentum decay characteristics of a submerged viscoplastic non-Newtonian jet are studied within the steady laminar flow regime. The governing mass and momentum conservation equations along with the Bingham rheological model are solved numerically using a finite-difference scheme. A parametric study is performed to reveal the influence of the initial velocity profile, flow inertia, and yield stress presence on the flow field characteristics. Two initial velocity profiles are considered, a top-hat and fully developed pipe jets. The centerline velocity decay is found to be more rapid for the pipe jet than the top-hat one when the fluid is Newtonian while the opposite trend is observed for yield stress Bingham fluids. The decay in the momentum flux of the pipe jet is always less than that of the top-hat jet. Momentum and velocity based jet depths of penetration are introduced and used to analyze the obtained flow field information for a wide range of Reynolds and yield numbers. Depths of penetration are found to linearly increase with the Reynolds number and substantially decrease with the yield number. The presence of yield stress significantly reduces the momentum and velocity penetration depths of submerged top-hat and pipe jets. Penetration depths of yield stress fluids are shown to be more than an order of magnitude smaller than the ones corresponding to Newtonian fluids.

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Fig. 1

Shear stress versus shear rate for Bingham and Newtonian fluids

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Fig. 2

Influence of a Bingham fluid rheology on the evolution of a submerged top-hat jet

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Fig. 3

Computational domain and boundary conditions for a top-hat jet

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Fig. 4

Inflow velocity profiles for top-hat and pipe jets

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Fig. 5

Schematic of the grid design

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Fig. 6

Analytical and numerical fully developed velocity profiles in a pipe

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Fig. 7

Yield number effect on effective viscosity for a top-hat jet at Re = 50

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Fig. 8

Yield number effect on effective viscosity for a pipe jet at Re = 50

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Fig. 9

Yield number effect on flow field streamlines for a top-hat jet at Re = 50

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Fig. 10

Yield number effect on flow field streamlines for a pipe jet at Re = 50

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Fig. 11

Influence of the radial extent of the computational domain, L/R, on the centerline velocity decay of a nozzle jet at Re = 100 for (a) Newtonian and (b) Bingham non-Newtonian fluids

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Fig. 12

Yield number effect on jet centerline velocity decay for (a) Re = 50, (b) Re = 100, and (c) Re = 200

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Fig. 13

Yield number effect on jet momentum decay for (a) Re = 50, (b) Re = 100, and (c) Re = 200



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