A New Criterion for the Onset of Liquid Entrainment From a Stratified Two-Phase Region Through a Small Branch

2009 ◽  
Author(s):  
Mahmoud Ahmed ◽  
Ahmed Hamza H. Ali
Keyword(s):  
Flow Instability ◽  
Vertical Wall ◽  
Phase Region ◽  
Three Dimensional Model ◽  
Critical Height ◽  
Two Phase ◽  
Local Flow ◽  
Liquid Entrainment ◽  
Small Branch ◽  
New Criterion

A new criterion has been developed to predict the onset of liquid (heavier fluid) entrainment from a stratified two-phase region through single and dual branches mounted on a vertical wall. This criterion was based on the local instability of the interface between two fluids due to the suction effect associated with the discharging of the lighter fluid. To validate the criterion, a three-dimensional model has been developed to predict the critical height at the onset of liquid entrainment. Comparisons between the theoretical critical heights with the available experimental data demonstrated a very good concurrence between the predicted and the measured values for both single and dual branches. This indicated that the onset of liquid entrainment mechanism occurs due to local flow instability of the interface analogous to Taylor instability.

Modeling of the Onset of Gas Entrainment Through a Finite-Side Branch

2003 ◽  
Vol 125 (5) ◽  
pp. 902-909 ◽  
Author(s):  
M. Ahmed ◽  
I. Hassan ◽  
N. Esmail
Keyword(s):  
Froude Number ◽  
Three Dimensional ◽  
Phase Region ◽  
Side Branch ◽  
Critical Height ◽  
Two Phase ◽  
Gas Entrainment ◽  
Branch Model ◽  
Predicted Values ◽  
New Criterion

A theoretical investigation has been conducted for the prediction of the critical height at the onset of gas entrainment during single discharge from a stratified, two-phase region through a side branch with a finite diameter. Two different models have been developed, a simplified point-sink model and a three-dimensional finite-branch model. The two models are based on a new criterion for the onset of gas entrainment. The results of the predicted critical heights at the onset of gas entrainment showed that the finite-branch model approaches the physical limits at low Froude numbers. However, as the values of the Froude number increased, the predictions of both models eventually converged to the same value. Based on the results of the models, the critical height corresponding to the onset of gas entrainment was found to be a function of Froude number and fluid densities. The results of both models are compared with available experimental data. The comparisons illustrate a very good agreement between the measured and predicted values.

Theoretical Analysis of the Onset of Gas Entrainment from a Stratified Two-Phase Region Through Two Side-Oriented Branches Mounted on a Vertical Wall

2005 ◽  
Vol 128 (1) ◽  
pp. 131-141 ◽  
Author(s):  
Mahmoud A. Ahmed
Keyword(s):  
Theoretical Analysis ◽  
Small Deviation ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Phase Region ◽  
Critical Height ◽  
Two Phase ◽  
Mass Rate ◽  
Gas Entrainment ◽  
Branch Model

A theoretical analysis has been developed to predict the critical height and the location of the onset of gas entrainment during discharge from a stratified two-phase region through two oriented-side branches mounted on a vertical wall. In this analysis, a point sink model was first developed, followed by a more accurate three-dimensional finite branch model. The models are based on a new modified criterion for the onset of gas entrainment. The theoretically predicted critical height and the location of the onset of gas entrainment are found to be a function of the mass rate of each branch (Fr1 and Fr2), the distance between the centerlines of the two branches (L∕d), and the inclination angle (θ). The effects of these variables on the predicted critical height and the onset location were investigated. Furthermore, comparison between the theoretically predicted results and the available experimental data was carried out to verify the developed models. The comparison shows that the predicted results are very close to the measured data within a deviation percentage of 12% at Fr1>10. This small deviation percentage reflects a good agreement between the measured and predicted results.

Influence of Wall Inclination Angles on the Onset of Gas Entrainment During Single and Dual Discharges From a Reservoir

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
M. Ahmed
Keyword(s):  
Froude Number ◽  
Inclination Angle ◽  
Phase Region ◽  
Critical Height ◽  
Two Phase ◽  
Gas Entrainment ◽  
Inclination Angles ◽  
Mass Flow Rates ◽  
Predicted Values ◽  
New Criterion

A theoretical analysis was carried out to predict the influences of wall inclination angles of large reservoirs on the onset of gas entrainment during single and dual discharges from a stratified two-phase region. The findings reveal that when the wall inclination angle differs from zero, along with low values of Froude number, two distinct flow regimes occur: the gas-entrainment and no gas-entrainment regimes. A new criterion has been developed to predict the critical Froude number at the transition from the gas-entrainment to the no-gas-entrainment regime. The critical Froude number is defined as a function of the wall inclination angle for a single discharge. For dual discharge, the critical Froude number is found to be dependent on the wall inclination angle, the separating distance between the centerlines of the two branches, as well as the Froude number of the second branch. Furthermore, four different flow regions are mapped, representing the flow regime, as well as the two-phase flow for each branch. These maps serve to predict the flow regions, mass flow rates, and quality during single and dual two-phase discharges. For the gas-entrainment regime, the predicted values of the critical height at the onset of gas entrainment are compared with the experimental data reported in literatures. Comparisons showed good concurrence between the measured and predicted results. Furthermore, the influence of the wall inclination angle on the flow regions, the predicted critical height, and the location of the gas entrainment are presented and discussed at different values of independent variables.

Modeling of the Onset of Gas Entrainment Through a Finite-Side Branch

2002 ◽  
Author(s):  
M. Ahmed ◽  
I. Hassan ◽  
N. Esmail
Keyword(s):  
Froude Number ◽  
Phase Region ◽  
Side Branch ◽  
Critical Height ◽  
Two Phase ◽  
Gas Entrainment ◽  
Branch Model ◽  
Single Discharge ◽  
Predicted Values ◽  
New Criterion

A theoretical investigation has been conducted for the prediction of the critical height at the onset of gas entrainment during single discharge from a stratified two-phase region through a side branch with a finite diameter. Two different models have been developed including a new criterion for the onset of gas entrainment, a simplified point-sink model and a finite-branch model. The results of the predicted critical heights at the onset of gas entrainment showed that the finite-branch model approaches the physical limits at low Froude numbers. However, as the values of the Froude number increased, the predicted values of both models eventually converged to the same value. Based on the results of the models, the critical height corresponding to the onset of gas entrainment was found to be a function of Froude number and fluid densities. The results of both models are compared with available experimental data. The comparisons illustrate a very good agreement between the measured and predicted values.

The onset of liquid entrainment from a stratified two-phase region through small branches

2014 ◽  
Vol 225 (11) ◽  
pp. 3023-3039 ◽  
Author(s):  
Mahmoud Ahmed ◽  
M. S. Youssef ◽  
Ahmed Hamza H. Ali
Keyword(s):  
Phase Region ◽  
Two Phase ◽  
Liquid Entrainment

The Onset of Gas Entrainment From a Stratified Two-Phase Region Through a Single Side-Oriented Branch

2002 ◽  
Author(s):  
M. Ahmed ◽  
K. Lenard ◽  
I. Hassan ◽  
N. Esmail
Keyword(s):  
Inclination Angle ◽  
Density Ratio ◽  
Phase Region ◽  
Data Sets ◽  
Critical Height ◽  
Two Phase ◽  
Gas Entrainment ◽  
Single Side ◽  
Inclination Angles ◽  
Predicted Values

A new theoretical investigation has been conducted for the prediction of the critical height at the onset of gas entrainment during single discharge from a stratified two-phase region through a branch installed on an inclined flat wall. Two models have been developed; a simplified point-sink model and a more-accurate finite-branch. The predicted critical height at the onset of gas entrainment was proven to be a function of Froude number (Fr) and density ratio of the interface fluids. The results of the predicted critical height at the onset of gas entrainment, at low values of Fr (<10), were found to be more accurate when using the finite-branch analysis compared to the results found using the pink-sink analysis. Whereas, with increasing Fr, the predicted values of both models converged to the same value. Furthermore, the point-sink analysis was demonstrated to be independent of wall inclination angle, while the finite-branch analysis showed a slight decrease in the value of the critical height with increasing wall inclination angle. Three different experimental data sets at wall inclination angles of zero, 45 and 90 degrees (i.e. side, inclined and bottom branches) were used in the following study for the comparisons between the experimental and theoretically predicted results. A good concurrence was illustrated between the experimental and theoretical values.

Incipience of Liquid Entrainment From a Stratified Gas-Liquid Region in Multiple Discharging Branches

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
R. C. Bowden ◽  
I. G. Hassan
Keyword(s):  
Industrial Applications ◽  
Liquid Interface ◽  
Liquid Level ◽  
Analytical Models ◽  
Liquid Region ◽  
Critical Height ◽  
Two Phase ◽  
Curvature Effects ◽  
Liquid Entrainment ◽  
Flow Quality

The onset of liquid entrainment in discharging branches, from a stratified gas-liquid region, has implications in industrial applications where safety is of concern. The onset criterion was characterized by the critical height, the vertical distance from the discharge inlet to the gas-liquid interface, and was shown to be a function of the Froude number. The critical height signified a transition in the discharging flow quality from a single phase gas to a two-phase gas-liquid mixture. The onset of liquid entrainment with multiple discharging branches, and a stratified gas-liquid region, was experimentally investigated using air and water. A test section with a semicircular cross section and three discharging branches at 0deg, 45deg, and 90deg was used. The critical height was recorded using both increasing and decreasing liquid level methods, thereby demonstrating surface tension and wetness effects. A total of eight cases were investigated for single, dual, and triple discharges, with onset occurring in the branch closest to and above the gas-liquid interface. Wall curvature effects were discussed through comparison with previous flat wall studies. Agreement between previously developed analytical models and the decreasing liquid level results was found.

Modeling of the Onset of Gas Entrainment From a Stratified Two-Phase Region Through Two Side Branches

2003 ◽  
Author(s):  
M. Ahmed ◽  
K. Lenard ◽  
I. Hassan ◽  
N. Esmail
Keyword(s):  
Phase Region ◽  
Lower Branch ◽  
Critical Height ◽  
Two Phase ◽  
Gas Entrainment ◽  
Vertical Distance ◽  
Branch Model ◽  
Vertically Aligned ◽  
Pull Through ◽  
Predicted Values

A theoretical analysis for the onset of gas pull-through (entrainment) during discharge from a stratified two-phase region through two vertically aligned side branches has been developed in this paper. Initially, a simplified point-sink model was developed; this was followed by the acquisition of a more accurate finite branch model. The predicted value of the critical height at the onset of gas entrainment was found to be a function of each branches’ corresponding Froude number (Fr1 and Fr2), as well as the ratio between the vertical distance connecting the centerlines of the two branches and the diameter of the branches (L/d). The predicted values of the critical heights were found to be consistent with the corresponding experimental data at different values of Fr1, Fr2 and L/d. From the basis of the present models, it was established that when increasing the flow through the lower branch, the critical height increased for all values of Fr1 and L/d. In addition, it was found that increasing the vertical distance between the two branches, reduced the effects of the lower branch on the determination of the critical height.

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