Research Papers: Multiphase Flows

The Effect of Initial Momentum Flux on the Circular Hydraulic Jump

[+] Author and Article Information
K. P. Vishwanath

Department of Mathematical and
Computational Sciences,
National Institute of Technology Karnataka,
Mangalore 575 025, India
e-mail: shastryvishwanath@gmail.com

Ratul Dasgupta

Department of Chemical Engineering,
Indian Institute of Technology Bombay,
Powai, Mumbai 400 076, India
e-mail: dasgupta.ratul@gmail.com

Rama Govindarajan

TIFR Centre for Interdisciplinary Sciences,
Hyderabad 500 075, India
e-mail: rama@tifrh.res.in

K. R. Sreenivas

Engineering Mechanics Unit,
Jawaharlal Nehru Centre for
Advanced Scientific Research,
Bangalore 560 064, India
e-mail: krs@jncasr.ac.in

1Corresponding authors.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received June 24, 2014; final manuscript received January 16, 2015; published online March 9, 2015. Assoc. Editor: Samuel Paolucci.

J. Fluids Eng 137(6), 061301 (Jun 01, 2015) (7 pages) Paper No: FE-14-1329; doi: 10.1115/1.4029725 History: Received June 24, 2014; Revised January 16, 2015; Online March 09, 2015

Earlier studies on the circular hydraulic jump have shown that the radial position of the hydraulic jump depends on the flow rate, gravity, and fluid viscosity. In this study, results from numerical simulations and experiments on circular hydraulic jumps are presented and through analysis, it is shown that the momentum flux is an additional controlling parameter in determining the jump location. Apart from the jump location, the variation of the film thickness with flow parameters is also obtained from experiments and numerical simulations. By including the dependence of the momentum flux and dissipation in the film along with other controlling parameters, the data on jump radius obtained from experiments and simulation (including the present study) covering a wide range of parameters reported in the literature can be collapsed on to a single curve.

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Grahic Jump Location
Fig. 1

(a) Simulation domain. (b) Film thickness profiles obtained from axisymmetric Navier–Stokes simulations for a nozzle Froude number Frn≡U/grn = 7.58. The legend indicates Ren≡Urn/ν, where U is the uniform velocity-profile at the nozzle-inlet, rn is the nozzle radius, and ν is the kinematic viscosity. The crosses are the location where the local Froude number, Fr, is unity and taken to be the radius of the jump. The simulations include the impinging jet (not shown) from which the impingement radius ri can be determined. (c) The same plot as in (b) but now for Reynolds number Ren≡Urn/ν = 400 while varying the nozzle Froude number Frn.

Grahic Jump Location
Fig. 2

Jump radius from simulation and experiments: (a) fit for the data from present numerical simulations and (b) Q versus rj scatter plots for experimental data from Refs. [3,12] and present experiments. These datasets include observations with different viscosities, varying momentum flux by varying Nozzle impingement height and nozzle diameter.

Grahic Jump Location
Fig. 3

(a) Schematic of the experimental setup for radius and film-thickness measurements and (b) image of the circular jump taken from experiments

Grahic Jump Location
Fig. 4

The hydraulic jump: (a) raw image and (b) binary image

Grahic Jump Location
Fig. 5

Variation of jump radius and film thickness. Variation of jump radius rj with volume flow rate Q for (a) different impingement heights H when the nozzle radius rn = 4.6 mm; (b) different nozzle radii rn when the impingement height H = 7 mm is fixed, and (c) variation of the film thickness with radius for different nozzle radii and impingement heights (Q = 13 ml/s is maintained constant).

Grahic Jump Location
Fig. 6

Collapse of the (rj/ri) data obtained from Eq. (6) for present experimental results and from other simulations and experimental studies reported in the literature




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