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.

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.

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.

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 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.

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.

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 From a Stratified Two-Phase Region Through Branches on a Curved Surface

2005 ◽  
Vol 128 (4) ◽  
pp. 717-725 ◽  
Author(s):  
A. F. Andaleeb ◽  
I. Hassan ◽  
W. Saleh ◽  
T. Ahmad
Keyword(s):  
Froude Number ◽  
Phase Region ◽  
Data Sets ◽  
Critical Height ◽  
Two Phase ◽  
Gas Entrainment ◽  
Physical Limit ◽  
Predicted Values ◽  
Branch Size ◽  
Feeder Configuration

The present investigation is focused on the onset phenomena from a stratified two-phase region through a single branch located on a semi-circular wall, resembling a circular reservoir of a CANDU header-feeder configuration. Two different models have been developed, over the whole range of branch Froude number, to predict the critical height at the onset of gas-entrainment. The results showed that there is both a maximum and a minimum physical limit of prediction, which depends on the branch size and configuration. Also, at a distinct range of Froude numbers within the physical limits, the predicted values of both models collaborated to the same values. The critical height corresponding to the onset of gas entrainment was found to be a function of the branch orientation and Froude number. Three different experimental data sets at branch orientation angles of zero, 45, and 90 degrees were used to validate the present models. A good concurrence was illustrated between the experimental and theoretical values.

Experimental Investigation on the Onset of Gas Entrainment from a Stratified Two-Phase Region Through Multiple Branches Mounted on a Curved Surface

2006 ◽  
Vol 128 (4) ◽  
pp. 726-733 ◽  
Author(s):  
Tariq Ahmad ◽  
Ibrahim Hassan
Keyword(s):  
Experimental Data ◽  
Experimental Investigation ◽  
Froude Number ◽  
Hydraulic Resistance ◽  
Numerical Models ◽  
Phase Region ◽  
Critical Height ◽  
Two Phase ◽  
Gas Entrainment ◽  
Wide Range

An experimental investigation has been carried out to simulate the onset of gas entrainment phenomenon from a stratified region through branches located on a semicircular wall configuration, in close dimensional resemblance with a Canada Deuterium and Uranium (CANDU) header-feeder system. New experimental data for the onset of gas entrainment was developed during single and multiple discharge from an air/water stratified region over a wide range of Froude numbers (0 to 100), in order to thoroughly understand the onset of gas entrainment phenomenon. It was found that the critical height at the onset of gas entrainment (single or simultaneous) was a function of the corresponding Froude number of each branch, the vertical distance between the centerlines of the branches (for multiple discharge), the hydraulic resistance of the discharging lines, as well as the orientation of the branches and their diameter with respect to the main header. Concerning multiple discharge comparisons, at intermediate Fr values (1<Fr<10) the data deviates, however at higher Fr values (>10) there is convergence. The present data are necessary in validating future analytical and numerical models of the onset of gas entrainment for a curved geometry, particularly at low Froude numbers.

The admissibility domain of rarefaction shock waves in the near-critical vapour–liquid equilibrium region of pure typical fluids

2016 ◽  
Vol 795 ◽  
pp. 241-261 ◽  
Author(s):  
Nawin R. Nannan ◽  
Corrado Sirianni ◽  
Tiemo Mathijssen ◽  
Alberto Guardone ◽  
Piero Colonna
Keyword(s):  
Shock Waves ◽  
Critical Point ◽  
Compressible Flows ◽  
Three Dimensional ◽  
Fundamental Equation ◽  
Phase Region ◽  
Liquid Equilibrium ◽  
Two Phase ◽  
Rarefaction Shock ◽  
Equilibrium Region

Application of the scaled fundamental equation of state of Balfour et al. (Phys. Lett. A, vol. 65, 1978, pp. 223–225) based upon universal critical exponents, demonstrates that there exists a bounded thermodynamic domain, located within the vapour–liquid equilibrium region and close to the critical point, featuring so-called negative nonlinearity. As a consequence, rarefaction shock waves with phase transition are physically admissible in a limited two-phase region in the close proximity of the liquid–vapour critical point. The boundaries of the admissibility region of rarefaction shock waves are identified from first-principle conservation laws governing compressible flows, complemented with the scaled fundamental equations. The exemplary substances considered here are methane, ethylene and carbon dioxide. Nonetheless, the results are arguably valid in the near-critical state of any common fluid, namely any fluid whose molecular interactions are governed by short-range forces conforming to three-dimensional Ising-like systems, including, e.g. water. Computed results yield experimentally feasible admissible rarefaction shock waves generating a drop in pressure from 1 to 6 bar and pre-shock Mach numbers exceeding 1.5.

Co-Current Gas-Liquid Smooth-Stratified Flow in a Horizontal Reduced T-Junction Including Wavy and Slug Regime Transition Boundaries

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
Robert C. Bowden ◽  
Ibrahim G. Hassan
Keyword(s):  
Single Phase ◽  
Inlet Pipe ◽  
Critical Height ◽  
Two Phase ◽  
Gas Entrainment ◽  
Inlet Length ◽  
Phase Liquid ◽  
The Relationship ◽  
Stratified Regime ◽  
Good Agreement

Experiments were performed in a horizontal reduced T-junction using a branch diameter of 6.35 mm and an inlet pipe diameter of 50.8 mm. The inlet length was 1.8 m and three branch orientations were tested at 0, 45, and 90 degrees down from the horizontal. Water and air, operating at 206 kPa, were used to provide an adiabatic two-phase environment. Both fluids flowed co-currently within the inlet towards the branch in the smooth-stratified regime. Results demonstrate the relationship between the interface height and the inlet and branch two-phase quantities, including the inlet superficial liquid and gas velocities, and branch two-phase mass flow rate and quality. In certain instances transitions to wavy-stratified or slug regimes were observed and these limits are quantified for each branch orientation. Flow visualization was used to identify the initiation of two-phase flow in the branch, including the onsets of gas and liquid entrainment. The critical height at the onset of gas entrainment was quantified as a function of the single phase liquid branch Froude number for the 45 and 90 degree branches, respectively. The branch quality results were scaled using the critical height and showed good agreement with selected models.

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