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Research Papers: Techniques and Procedures

Numerical Study of Circular Hydraulic Jump Using Volume-of-Fluid Method

[+] Author and Article Information
Mohammad Passandideh-Fard

Department of Mechanical Engineering, Ferdowsi University of Mashhad, Azadi Square, 9177948944 Mashhad, Iranmpfard@um.ac.ir

Ali Reza Teymourtash

Department of Mechanical Engineering, Ferdowsi University of Mashhad, Azadi Square, 9177948944 Mashhad, Iranteymourtash@um.ac.ir

Mohammad Khavari

Department of Mechanical Engineering, Ferdowsi University of Mashhad, Azadi Square, 9177948944 Mashhad, Iranmohammad.khavari@yahoo.com

J. Fluids Eng 133(1), 011401 (Jan 28, 2011) (11 pages) doi:10.1115/1.4003307 History: Received May 08, 2010; Revised December 11, 2010; Published January 28, 2011; Online January 28, 2011

When a vertical liquid jet impacts on a solid and horizontal surface, the liquid starts spreading radially on the surface, until a sudden increase in the fluid height occurs and a circular hydraulic jump (CHJ), easily seen in the kitchen sink, is formed. In this study, the formation of CHJ is numerically simulated by solving the flow governing equations, continuity and momentum equations, along with an equation to track the free surface advection using the volume-of-fluid (VOF) method and Youngs’ algorithm. The numerical model is found to be capable of simulating the jump formation and its different types. Extensive comparisons are performed between the model results and those of the available experiments and modified Watson’s theory. The model is shown to accurately predict the jump location and its behavior. Also a parametric study for the effects of different parameters including volumetric flow rate, downstream height, viscosity and gravity on the jump radius, and its characteristics is carried out. Compared with previous works on CHJ available in the literature, employing the VOF method considering the surface tension effects and performing a full parametric study and a complete comparison with experiments and theory are new in this paper. The simulations are performed for two different liquids, water and ethylene glycol, where it is found that the jump is more stable and its location is less sensitive to the downstream height for the more viscous liquid (ethylene glycol). When the downstream height is increased, the radius of the circular hydraulic jump reduces up to a certain limit after which there would be no stable jump. If the gravity is decreased, the radius of the jump and the length of the transition zone will both increase. The radius of the jump in microgravity conditions is less sensitive to the downstream height than it is in normal gravity.

Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 7

The evolution of a circular hydraulic jump formation (for tap water as the working fluid, a flow rate of Q=30 ml/s, a jet radius of 5 mm, and a downstream height of H∞=2 mm)

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Figure 8

The 3D view of simulation of the CHJ with a qualitative comparison with experiments (45)

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Figure 9

Comparison of the jump radius from numerical model and experiments (Errico (13))

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Figure 10

Variation of jump radius with (a) downstream height and (b) volumetric flow rate

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Figure 11

The variation of circular hydraulic jump radius with viscosity for two different flow rates

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Figure 12

The variation of jump radius with gravity in a nondimensional form

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Figure 13

Comparison between the effect of downstream height on jump radius in normal and microgravity conditions

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Figure 14

Comparison between the effect of volumetric flow rate on jump radius in normal and microgravity conditions

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Figure 15

Circular hydraulic jump in low and normal gravity conditions for four different flow rates

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Figure 16

3D views of circular hydraulic jump in low and normal gravity conditions

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Figure 17

Comparison of variation of jump radius with flow rate between water and ethylene glycol

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Figure 18

The effect of downstream height on jump radius for ethylene glycol for different flow rates

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Figure 19

Comparison of variation of jump radius with downstream height between water and ethylene glycol

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Figure 20

A 3D view of circular hydraulic jump for ethylene glycol

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Figure 21

Different types of circular hydraulic jump obtained from the model: (a) jump with no vortex (H∞=1.5 mm), (b) type I jump (with wall vortex) (H∞=2.5 mm), and (c) type IIa jump (with both wall vortex and surface roller) (H∞=5 mm)

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Figure 22

A 2D and 3D view of the simulation of a double jump

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Figure 23

Comparison of the numerical results with those of the experiments (17) and Watson's theory

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Figure 6

A mesh study on the CHJ by simulating the jump for different CPR values (for tap water as the working fluid, a flow rate of Q=30 ml/s, a jet radius of 5 mm, and a downstream height of H∞=2 mm)

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Figure 5

The computational domain for simulating the CHJ (top) and a magnified view of the uniform grid used for simulation (bottom)

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Figure 4

The flow initial setup along with the specifications of the boundary conditions, the obstacle, and the fluid layer

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Figure 3

Schematics of different types of circular hydraulic jump as introduced by Bush (18)

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Figure 2

The general structure of circular hydraulic jump

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Figure 1

The circular hydraulic jump (45)

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