0
Research Papers: Fundamental Issues and Canonical Flows

Velocity and Momentum Decay Characteristics of a Submerged Viscoplastic Jet

[+] Author and Article Information
Khaled J. Hammad

Mem. ASME
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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Chhabra, R. P., and Richardson, J. F., 2008, Non-Newtonian Flow and Applied Rheology, Second Edition: Engineering Applications, Butterworth-Heinemann, London.
Landfried, D. T., Jana, A., and Kimber, M. L., 2012, “Characterization of the Behavior of Confined Laminar Round Jets,” ASME Paper No. FEDSM2012-72257.
Milanovic, I. M., and Hammad, K. J., 2010, “PIV Study of the Near-Field Region of a Turbulent Round Jet,” ASME Paper No. FEDSM-ICNMM2010-31139.
Bird, R. B., Dai, G. C., and Yarusso, B. J., 1983, “The Rheology and Flow of Viscoplastic Materials,” Rev. Chem. Eng., 1(1), pp. 1–70.
Ellwood, K. R. J., Georgiou, G. C., Papanastasiou, T. C., and Wilkes, J.O., 1990, “Laminar Jets of Bingham Plastic Liquids,” J. Rheol., 34, pp. 787–812. [CrossRef]
Papanastasiou, T. C., 1987, “Flow of Materials With Yield,” J. Rheol., 31(5), pp. 385–403. [CrossRef]
Shekarriz, A., Hammad, K. J., and Powell, M. R., 1997, “Evaluation of Scaling Correlations for Mobilization of Double-Shell Tank Waste,” Report No. PNNL-11737.
Gauglitz, P. A., Wells, B. E., Bamberger, J. A., Fort, J. A., Chun, J., and Jenks, J. J., 2010, “The Role of Cohesive Particle Interactions on Solids Uniformity and Mobilization During Jet Mixing: Testing Recommendations,” Report No. PNNL-19245.
Serth, R. W., and Mayaguez, P. R., 1972, “The Axisymmetric Free Laminar Jet of a Power-Law Fluid,” ZAMP, 23, pp. 131–138. [CrossRef]
Mitwally, E. M., 1978, “Solutions of Laminar Jet Flow Problems for Non-Newtonian Power-Law Fluids,” ASME J. Fluids Eng., 100(3), pp. 363–366. [CrossRef]
Kumar, K. R., Rankin, G. W., and Sridhar, K., 1984, “Laminar Length of a Non-Newtonian Fluid Jet,” J. Non-Newtonian Fluid Mech., 15, pp. 13–27. [CrossRef]
Jordan, C., Rankin, G. W., and Sridhar, K., 1992, “A Study of Submerged Pseudoplastic Laminar Jets,” J. Non-Newtonian Fluid Mech., 41, pp. 323–337. [CrossRef]
Shekarriz, A., and Hammad, K. J., 1997, “Submerged Jet Flows of Newtonian and Pseudoplastic Non-Newtonian Fluids,” Album of Visualization, 14, pp. 23–24.
Jafri, I. H., and Vradis, G.C., 1998, “The Evolution of Laminar Jets of Herschel-Bulkley Fluids,” Int. J. Heat Mass Transfer, 41, pp. 3575–3588. [CrossRef]
Hammad, K. J., 2000, “Effect of Hydrodynamic Conditions on Heat Transfer in a Complex Viscoplastic Flow Field,” Int. J. Heat Mass Transfer, 43(6), pp. 945–962. [CrossRef]
Vradis, G. C., and Hammad, K. J., 1998, “Strongly Coupled Block-Implicit Solution Technique for Non-Newtonian Convective Heat Transfer Problems,” Numer. Heat Transfer, Part B, 33, pp. 79–97. [CrossRef]
Hammad, K. J., 2012, “Depth of Penetration of a Submerged Viscoplastic Non-Newtonian Jet,” ASME Paper No. FEDSM2012-72456.
Hammad, K. J., Ötügen, M. V., Vradis, G. C., and Arik, E. B., 1999, “Laminar Flow of a Nonlinear Viscoplastic Fluid Through an Axisymmetric Sudden Expansion,” ASME J. Fluids Eng., 121(2), pp. 488–496. [CrossRef]
Hammad, K. J., Vradis, G. C., and Ötügen, M. V., 2001, “Laminar Flow of a Herschel-Bulkley Fluid Over an Axisymmetric Sudden Expansion,” ASME J. Fluids Eng., 123(3), pp. 588–594. [CrossRef]
Mitsoulis, E., and Huilgol, R. R., 2004, “Entry flows of Bingham Plastics in Expansions,” J. Non-Newtonian Fluid Mech., 142, pp. 207–217. [CrossRef]
Wang, C. H., and Ho, J. R., 2008, “Lattice Boltzmann Modeling of Bingham Plastics,” Physica A, 387(19–20), pp. 4740–4748. [CrossRef]
Sánchez–Sanza, M., Rosalesb, M., and Sánchezb, A. L., 2010, “The Hydrogen Laminar Jet,” Int. J. Hydrogen Energy, 35(8), pp. 3919–3927. [CrossRef]
Hammad, K. J., and Shekarriz, A., 1998, “Turbulence in Confined Axisymmetric Jets of Newtonian and Non-Newtonian Fluids,” Proceedings of the ASME 1998 Fluids Engineering Summer Meeting, Paper No. FEDSM98-5272.

Figures

Grahic Jump Location
Fig. 1

Shear stress versus shear rate for Bingham and Newtonian fluids

Grahic Jump Location
Fig. 2

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

Grahic Jump Location
Fig. 3

Computational domain and boundary conditions for a top-hat jet

Grahic Jump Location
Fig. 4

Inflow velocity profiles for top-hat and pipe jets

Grahic Jump Location
Fig. 5

Schematic of the grid design

Grahic Jump Location
Fig. 6

Analytical and numerical fully developed velocity profiles in a pipe

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
Fig. 8

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

Grahic Jump Location
Fig. 9

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

Grahic Jump Location
Fig. 10

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 12

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

Grahic Jump Location
Fig. 13

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

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In