scholarly journals Experimental Investigations of Free-Surface Aeration in the Developing Flow of Two-Dimensional Water Jets

1998 ◽  
Vol 120 (4) ◽  
pp. 738-744 ◽  
Author(s):  
T. Brattberg ◽  
H. Chanson ◽  
L. Toombes
Keyword(s):  
Free Surface ◽  
Flow Region ◽  
Air Entrainment ◽  
Experimental Investigations ◽  
Two Dimensional ◽  
Air Bubble ◽  
Surface Aeration ◽  
Water Jets ◽  
Developing Flow ◽  
Air Diffusion

Turbulent water jets discharging into the atmosphere are often characterized by a substantial amount of free-surface aeration. The effects can be detrimental or beneficial. In any case, the knowledge of the air entrainment mechanisms is essential for an optimum design. New experimental data are presented in the developing flow region of two-dimensional water jets discharging into air. The results indicate that the air diffusion takes place rapidly downstream of the nozzle and it is nearly independent of the momentum transfer process. Further, the distribution of air bubble frequency may be related to the air content distribution by a parabolic relationship.

scholarly journals Air Entrainment in the Developing Flow Region of Plunging Jets—Part 1: Theoretical Development

1997 ◽  
Vol 119 (3) ◽  
pp. 597-602 ◽  
Author(s):  
P. D. Cummings ◽  
H. Chanson
Keyword(s):  
Flow Region ◽  
Air Entrainment ◽  
Theoretical Development ◽  
Liquid Jets ◽  
Two Dimensional ◽  
Air Bubble ◽  
Developing Flow ◽  
Jet Impact ◽  
Plunging Jets ◽  
Advective Diffusion

Air-water bubbly flows are encountered in many engineering applications. One type of air-water shear flows is the developing flow region of a plunging jet. The mechanisms of air entrainment by plunging liquid jets are discussed in the light of new experimental evidence. Then the air bubble diffusion is analyzed analytically in the near-flow field of both circular and two-dimensional plunging jets. The theoretical developments are compared with existing circular plunging jet data and new experiments performed with a two-dimensional vertical supported jet. The study highlights two mechanisms of air entrainment at the plunge point depending upon the jet impact velocity and results suggest that the dispersion of air bubbles within the shear layer is primarily an advective diffusion process.

scholarly journals Experimental investigations of air entrainment in transition and skimming flows down a stepped chute

2002 ◽  
Vol 29 (1) ◽  
pp. 145-156 ◽  
Author(s):  
H Chanson ◽  
L Toombes
Keyword(s):  
Free Surface ◽  
Water Flow ◽  
Air Entrainment ◽  
Stepped Spillway ◽  
Transition Flow ◽  
Flow Properties ◽  
Flow Measurements ◽  
Surface Aeration ◽  
Stepped Chute ◽  
Uniform Equilibrium

Stepped spillways have been used for about 3500 years. The last few decades have seen the development of new construction materials, design techniques, and applications, for example, embankment overtopping protection systems. Although it is commonly acknowledged that free-surface aeration is significant in stepped chutes, experimental data are scarce, often limited to very steep slopes (α ~ 50°). This paper presents an experimental study conducted in a large-size stepped chute (α = 22°, h = 0.1 m, W = 1 m). Observations demonstrate the existence of a transition flow pattern for intermediate flow rates between nappe and skimming flows. Detailed air–water flow measurements were conducted in both transition and skimming flows, immediately downstream of the inception point of free-surface aeration where uniform equilibrium flow conditions were not achieved. In skimming flows, a complete characterization is developed for the distributions of void fraction, bubble count rate, and velocity, and flow resistance data are compared with other studies. Transition flows exhibit significantly different air–water flow properties. They are highly aerated, requiring the design of comparatively high chute sidewalls.Key words: stepped spillway, air entrainment, two-phase flow properties, skimming flow, transition flow.

scholarly journals Two-Dimensional Supercavitating Plate Oscillating Under a Free Surface

1965 ◽  
Vol 9 (02) ◽  
pp. 40-55
Author(s):  
C. S. Song
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Potential Flow ◽  
Flow Region ◽  
Integral Form ◽  
Cavitation Number ◽  
Two Dimensional ◽  
First Order ◽  
Upper Half Plane ◽  
Order Quantities

The problem of a supercavitating flat plate at zero and nonzero cavitation numberoscillating under a free surface is analyzed by a linearized method using the accelerationpotential. The analysis is based on the concept of small velocity perturbations where in all second-order quantities are neglected. The flow is assumed two-dimensional, irrotational, incompressible, and gravitation-free. The potential-flow region is mapped on to an upper half-plane and the solution is expressed in an integral form using Cheng andRott's method. Special attention is given to the effect of approximate wake boundary conditions on the computed force and moment. It was estimated that the effect is of secondorder when the cavitation number is a first-order small quantity.

scholarly journals Three-Dimensional Aerators: Characteristics of the Air Bubbles

Water ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 1430
Author(s):  
Shuai Li ◽  
Jianmin Zhang ◽  
Xiaoqing Chen ◽  
Jiangang Chen
Keyword(s):  
Three Dimensional ◽  
Flow Region ◽  
Air Entrainment ◽  
Chord Length ◽  
Air Concentration ◽  
Bubble Frequency ◽  
Cross Sectional ◽  
Frequency Distributions ◽  
Air Bubble ◽  
Flow Features

Three-dimensional aerators are often used in hydraulic structures to prevent cavitation damage via enhanced air entrainment. However, the mechanisms of aeration and bubble dispersion along the developing shear flow region on such aerators remain unclear. A double-tip conductivity probe is employed in present experimental study to investigate the air concentration, bubble count rate, and bubble size downstream of a three-dimensional aerator involving various approach-flow features and geometric parameters. The results show that the cross-sectional distribution of the air bubble frequency is in accordance with the Gaussian distribution, and the relationship between the air concentration and bubble frequency obeys a quasi-parabolic law. The air bubble frequency reaches an apex at an air concentration (C) of approximately 50% and decreases to zero as C = 0% and C = 100%. The relative location of the air-bubble frequency apex is 0.210, 0.326 and 0.283 times the thickness of the layers at the upper, lower and side nappes, respectively. The air bubble chord length decreases gradually from the air water interface to the core area. The air concentration increases exponentially with the bubble chord length. The air bubble frequency distributions can be fit well using a “modified” gamma distribution function.

A Condition for an Air Entrainment by Breaking the Surface Waves at the Free Surface

2005 ◽  
Author(s):  
Ho-Yun Nam ◽  
Jong-Man Kim ◽  
Byoung-Hae Choi ◽  
Jong-Hyeun Choi
Keyword(s):  
Free Surface ◽  
Surface Wave ◽  
Water Flow Rate ◽  
Air Entrainment ◽  
Vessel Diameter ◽  
Test Facility ◽  
Critical Conditions ◽  
Air Bubble ◽  
Water Test ◽  
Entrained Air

An experimental study has been carried out to measure the critical conditions for the inception of an air entrainment by breaking the surface wave at the free surface in the water test facility. The experimental parameters are the vessel diameter, the nozzle diameter, the mean water-level and the water flow rate. More than 400 experimental data which show whether the air is entrained or not at a given experimental condition are obtained, and an experimental correlation that describes the air entrainment condition is developed. The correlation is described by the ratio between the diameter and height of the vessel, the ratio between the diameter of the nozzle and the height of the vessel, the modified Froude number and a modified Weber number. In this experiment two cases of air entrainment are observed. One case is that the air entrainment occurred due to the destruction of the surface wave from the center, and the other case is due to the crash of the water wave to the vessel wall. Theses two cases occur irregularly and the entrained air bubble distributes uniformly in the water.

On some problems of similarity flow of fluid with a free surface

1969 ◽  
Vol 36 (4) ◽  
pp. 805-829 ◽  
Author(s):  
Z. N. Dobrovol'skaya
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Singular Integral Equation ◽  
Incompressible Fluid ◽  
Singular Integral ◽  
Classical Problem ◽  
Flow Region ◽  
Hydrodynamic Characteristics ◽  
Two Dimensional ◽  
Free Surfaces

The paper presents the method of solving a class of two-dimensional problems of the similarity flow of an incompressible fluid with a free surface. The fluid is assumed to be non-viscous and weightless. We consider two-dimensional irrotational similarity flows with dimensionless hydrodynamic characteristics depending only on the ratios x/v0t, y/v0t, where x, y are Cartesian co-ordinates, t is time and v0 is a constant of the velocity dimension.The proposed method is based upon using the function introduced by Wagner (1932) and can be applied to the problems where the flow region is bounded by free surfaces and uniformly moving (or fixed) rectilinear impermeable boundaries. Introduction of Wagner's function makes it possible to reduce each of the problems under consideration to a non-linear singular integral equation for the real function.The method is illustrated by solving the classical problem of the uniform symmetrical entry of a wedge into a half-plane of a fluid.

scholarly journals Air Entrainment in the Developing Flow Region of Plunging Jets—Part 2: Experimental

1997 ◽  
Vol 119 (3) ◽  
pp. 603-608 ◽  
Author(s):  
P. D. Cummings ◽  
H. Chanson
Keyword(s):  
Shear Layer ◽  
Flow Region ◽  
Air Entrainment ◽  
Chord Length ◽  
Strong Interactions ◽  
Air Bubbles ◽  
Air Concentration ◽  
Air Bubble ◽  
Wide Range ◽  
Bubble Sizes

When a water jet impinges a pool of water at rest, air bubbles may be entrained and carried away below the pool free surface: this process is called plunging jet entrainment. The study presents new experimental data obtained with a vertical supported jet. Distributions of air concentration and mean air-water velocity, and bubble chord length distributions measured in the developing shear layer are presented. The results indicate that the distributions of void fraction follow closely analytical solution of the diffusion equation. Further, the momentum shear layer and the air bubble diffusion layer do not coincide. Chord length data show a wide range of air bubble sizes and overall the experimental results suggest strong interactions between the entrained air bubbles and the momentum transfer mechanisms.

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

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