Monday, September 17, 2007
My Papers about Multiphase Flow
[1]“Effect of Fiber Length Distribution on Gas Holdup in a Cocurrent Gas-Liquid-Fiber Bubble Column,” Chemical Engineering Science, 62, 2006, pp. 1408-1417.
An experimental investigation is reported on the effect of fiber length distribution on gas holdup in a cocurrent air–water–fiber bubblecolumn. Different combinations of 1 and 3mm Rayon fibers are used to simulate different fiber length distributions. At a constant totalfiber mass fraction, gas holdup generally decreases with increasing mass fraction of the 3mm Rayon fiber while other conditions remainconstant. Crowding factors estimated using four different methods (Nc = Nc,A, Nc , Nc,L, and Nc,M) and the parameters Nc,L^0.8*Nf^0.2 andNc,M^0.8*Nf^0.2 are tested on their performance to quantify the overall effects of fiber mass fraction and fiber length and its distribution on gasholdup. Nc,L^0.8Nf^0.2 and Nc,M^0.8*Nf^0.2 provide the best characterization of the fiber effects on gas holdup in the cocurrent air–water–fiberbubble column. The crowding factor estimated using the model-based average fiber length (Nc,M) also provides a good characterization andis better than the other crowding factor definitions.
[2]“Estimation of Gas Holdup via Pressure Difference Measurements in a Cocurrent Bubble Column,” International Journal of Multiphase Flow, 32, 2006, pp. 850-863.
Estimating gas holdup via pressure difference measurements is a simple and low-cost non-invasive technique to study gasholdup in bubble columns. It is usually used in a manner where the wall shear stress effect is neglected, termed Method II inthis paper. In cocurrent bubble columns, when the liquid velocity is high or the fluid is highly viscous, wall shear stress maybe significant and Method II may result in substantial error. Directly including the wall shear stress term in the determinationof gas holdup (Method I) requires knowledge of two-phase wall shear stress models and usually requires the solution ofnon-linear equations. A new gas holdup estimation method (Method III) via differential pressure measurements for cocurrentbubble columns is proposed in this paper. This method considers the wall shear stress influences on gas holdup valueswithout calculating the wall shear stress. A detailed analysis shows that Method III always results in a smaller gas holduperror than Method II, and in many cases, the error is significantly smaller than that of Method II. The applicability ofMethod III in measuring gas holdup in a cocurrent air–water–fiber bubble column is examined. Analysis based on experimentaldata shows that with Method III, accurate gas holdup measurements can be obtained, while measurement error issignificant when Method II is used for some operational conditions.
[3] “A Gas Holdup Model for Cocurrent Air-Water-Fiber Bubble Columns,” Chemical Engineering Science, 61, 2006, 3299-3312.
A gas holdup model is developed for cocurrent air–water–fiber bubble column flows using the drift–flux model. The model coefficients areestimated using a nonlinear least square method and systematically acquired experimental data. The model correlates gas holdup with superficialgas and liquid velocity, and fiber type and mass fraction. The model reproduces most experimental data within ±10% error and all but 3 ofthe 3839 experimental data points within ±15% error. It also accurately predicts air–water bubble column gas holdup data; these data werenot used in estimating the model coefficients. The physical implications of the model coefficients are also discussed.
[4]“Quantifying the Fibre Effect on Gas Holdup in a Cocurrent Air-Water-Fibre Bubble Column,” The Canadian Journal of Chemical Engineering, 84, 2006, pp. 198-208.
Fibre type and mass fraction have signifi cant effects on gas holdup in gas-liquid-fi bre bubble columns. An experimental study is introduced toidentify a parameter that simultaneously characterizes the fi bre type and mass fraction effects on gas holdup in gas-liquid-fi bre bubble columns.This parameter satisfi es the following condition: when this parameter is constant, the gas holdup trend in different fi bre suspensions is generallysimilar at most operating conditions. A method is proposed to identify a characterization parameter by combining the crowding factor and fi brenumber density. The identifi ed parameter is Ic=1n(Nc^0.8*Nf^0.2). This parameter can be used to model gas holdup in gas-liquid-fi bre bubble columnsand quantitatively compare the fi bre effects in different fi bre suspensions.
[5] “Similitude Analysis for Gas-Liquid-Fiber Flows in Cocurrent Bubble Columns,” 2nd Joint U.S.-European Fluids Engineering Summer Meeting, July 17-20, 2006, Miami, FL, USA.
Gas-liquid-fiber systems are different from conventional gas-liquid-solid systems in that the solid material (i.e., fiber) is flexible, has a large aspect ratio, and forms flocs or networks when its mass fraction is above a critical value. With its wide application to the pulp and paper industry, it is important to investigate the hydrodynamics of gas-liquid-fiber systems. In this paper, 19 parameters that influence gas holdup in gas-liquid-fiber bubble columns are critically examined and then a dimensional analysis based on the Buckingham Pi Theorem is used to derive the dimensionless parameters governing gas-liquid-fiber bubble column hydrodynamics. Seven dimensionless parameters that are related to the fiber effects on gas holdup are further analyzed, and a single dimensionless parameter combining these dimensionless parameters is derived based on a force analysis and experimental results. This dimensionless parameter is shown to be sufficient to quantify the influence of fiber on gas holdup in gas-liquid-fiber cocurrent bubble columns. It also reduces the number of parameters needed in correlating experimental gas holdup data in gas-liquid-fiber bubble columns.
[6] “Gas-Liquid-Fiber Flow in a Cocurrent Bubble Column,” AIChE Journal, 51, 2005, pp. 2665-2674.
Effects of superficial gas velocity (Ul <= 10 cm/s), superficial liquid velocity (Ug <= 10cm/s), and fiber mass fraction (0 <= C <= 2%) on gas holdup and flow regime transitionare studied experimentally in well-mixed water-cellulose fiber suspensions in a cocurrentbubble column. Experimental results show that gas holdup decreases with increasingsuperficial liquid velocity when fiber mass fraction and superficial gas velocity areconstant. Gas holdup is not significantly affected by fiber mass fraction in the range of C<= 0.4%, but decreases with increasing fiber mass fraction in the range of 0.4% < C <1.5%. The mechanisms behind the influences of superficial liquid velocity and fiber massfraction on gas holdup in a gas-liquid-fiber bubble column are analyzed. The effects of gasdistribution methods are also explained by comparison to previous results. The axial gasholdup distribution is shown to be a complex function of superficial gas and liquidvelocities and fiber mass fraction. The drift-flux model is used to identify the flow regimetransitions at different operating conditions. Three distinct flow regimes are observedwhen C < 0.4%, but only two are identified when 0.6% < C < 1.5%. The superficial gasvelocities at which the flow transitions from one regime to another are not significantlyaffected by Ul, and only slightly decrease with increasing C.
[7] “Effect of Fiber Type on Gas Holdup in a Cocurrent Air-Water-Fiber Bubble Column,” Chemical Engineering Journal, 111, 2005, pp. 21-30.
An experimental investigation of the effect of fiber type on gas holdup in a cocurrent air–water–fiber bubble column is presented. Threetypes of cellulose fibers (i.e., hardwood, softwood, and bleached chemithermomechanical pulp (BCTMP)) and three different lengths of Rayon fibers are used in the investigation. The results indicate fiber type has a significant influence on the gas holdup in the air–water–fiberbubble column. Mechanisms by which fibers influence gas holdup in gas–liquid–fiber bubble columns are summarized and used to explainthe experimental results. Fiber physical properties, including fiber length, coarseness, and flexibility are proposed to be the main factorsresponsible for the fiber type effects on gas holdup.
[8] “Time-Dependent Gas Holdup Variation in an Air-Water Bubble Column,” Chemical Engineering Science, 59, 2004, pp. 623-632.
Time-dependent gas holdup variation in a two-phase bubble column is reported with air and tap water as the working 1uids. Theresults indicate that time-dependent gas holdup is closely related to the water, whose quality is unsteady and changes, not only during thetwo-phase 1ow, but also during idle periods. The significance and characteristics of the time-dependent gas holdup variation are in1uencedby the bubble column operation mode (cocurrent or semi-batch), the sparger orientation, the superficial gas velocity, and the superficial liquid velocity. It is proposed that a volatile substance (VS), which exists in the water in very small concentrations and inhibits bubblecoalescence, evaporates during column operation and results in a time-dependent gas holdup. The in1uence of bubble column operationmode, sparger orientation, superficial gas velocity, and superficial liquid velocity on the time-dependent gas holdup variation are explainedbased on their effects on bubble size, bubble contacting frequency and mixing intensity. This work reveals that regular tap water maycause significant reproducibility problems in experimental studies of air–water two-phase 1ows.
An experimental investigation is reported on the effect of fiber length distribution on gas holdup in a cocurrent air–water–fiber bubblecolumn. Different combinations of 1 and 3mm Rayon fibers are used to simulate different fiber length distributions. At a constant totalfiber mass fraction, gas holdup generally decreases with increasing mass fraction of the 3mm Rayon fiber while other conditions remainconstant. Crowding factors estimated using four different methods (Nc = Nc,A, Nc , Nc,L, and Nc,M) and the parameters Nc,L^0.8*Nf^0.2 andNc,M^0.8*Nf^0.2 are tested on their performance to quantify the overall effects of fiber mass fraction and fiber length and its distribution on gasholdup. Nc,L^0.8Nf^0.2 and Nc,M^0.8*Nf^0.2 provide the best characterization of the fiber effects on gas holdup in the cocurrent air–water–fiberbubble column. The crowding factor estimated using the model-based average fiber length (Nc,M) also provides a good characterization andis better than the other crowding factor definitions.
[2]“Estimation of Gas Holdup via Pressure Difference Measurements in a Cocurrent Bubble Column,” International Journal of Multiphase Flow, 32, 2006, pp. 850-863.
Estimating gas holdup via pressure difference measurements is a simple and low-cost non-invasive technique to study gasholdup in bubble columns. It is usually used in a manner where the wall shear stress effect is neglected, termed Method II inthis paper. In cocurrent bubble columns, when the liquid velocity is high or the fluid is highly viscous, wall shear stress maybe significant and Method II may result in substantial error. Directly including the wall shear stress term in the determinationof gas holdup (Method I) requires knowledge of two-phase wall shear stress models and usually requires the solution ofnon-linear equations. A new gas holdup estimation method (Method III) via differential pressure measurements for cocurrentbubble columns is proposed in this paper. This method considers the wall shear stress influences on gas holdup valueswithout calculating the wall shear stress. A detailed analysis shows that Method III always results in a smaller gas holduperror than Method II, and in many cases, the error is significantly smaller than that of Method II. The applicability ofMethod III in measuring gas holdup in a cocurrent air–water–fiber bubble column is examined. Analysis based on experimentaldata shows that with Method III, accurate gas holdup measurements can be obtained, while measurement error issignificant when Method II is used for some operational conditions.
[3] “A Gas Holdup Model for Cocurrent Air-Water-Fiber Bubble Columns,” Chemical Engineering Science, 61, 2006, 3299-3312.
A gas holdup model is developed for cocurrent air–water–fiber bubble column flows using the drift–flux model. The model coefficients areestimated using a nonlinear least square method and systematically acquired experimental data. The model correlates gas holdup with superficialgas and liquid velocity, and fiber type and mass fraction. The model reproduces most experimental data within ±10% error and all but 3 ofthe 3839 experimental data points within ±15% error. It also accurately predicts air–water bubble column gas holdup data; these data werenot used in estimating the model coefficients. The physical implications of the model coefficients are also discussed.
[4]“Quantifying the Fibre Effect on Gas Holdup in a Cocurrent Air-Water-Fibre Bubble Column,” The Canadian Journal of Chemical Engineering, 84, 2006, pp. 198-208.
Fibre type and mass fraction have signifi cant effects on gas holdup in gas-liquid-fi bre bubble columns. An experimental study is introduced toidentify a parameter that simultaneously characterizes the fi bre type and mass fraction effects on gas holdup in gas-liquid-fi bre bubble columns.This parameter satisfi es the following condition: when this parameter is constant, the gas holdup trend in different fi bre suspensions is generallysimilar at most operating conditions. A method is proposed to identify a characterization parameter by combining the crowding factor and fi brenumber density. The identifi ed parameter is Ic=1n(Nc^0.8*Nf^0.2). This parameter can be used to model gas holdup in gas-liquid-fi bre bubble columnsand quantitatively compare the fi bre effects in different fi bre suspensions.
[5] “Similitude Analysis for Gas-Liquid-Fiber Flows in Cocurrent Bubble Columns,” 2nd Joint U.S.-European Fluids Engineering Summer Meeting, July 17-20, 2006, Miami, FL, USA.
Gas-liquid-fiber systems are different from conventional gas-liquid-solid systems in that the solid material (i.e., fiber) is flexible, has a large aspect ratio, and forms flocs or networks when its mass fraction is above a critical value. With its wide application to the pulp and paper industry, it is important to investigate the hydrodynamics of gas-liquid-fiber systems. In this paper, 19 parameters that influence gas holdup in gas-liquid-fiber bubble columns are critically examined and then a dimensional analysis based on the Buckingham Pi Theorem is used to derive the dimensionless parameters governing gas-liquid-fiber bubble column hydrodynamics. Seven dimensionless parameters that are related to the fiber effects on gas holdup are further analyzed, and a single dimensionless parameter combining these dimensionless parameters is derived based on a force analysis and experimental results. This dimensionless parameter is shown to be sufficient to quantify the influence of fiber on gas holdup in gas-liquid-fiber cocurrent bubble columns. It also reduces the number of parameters needed in correlating experimental gas holdup data in gas-liquid-fiber bubble columns.
[6] “Gas-Liquid-Fiber Flow in a Cocurrent Bubble Column,” AIChE Journal, 51, 2005, pp. 2665-2674.
Effects of superficial gas velocity (Ul <= 10 cm/s), superficial liquid velocity (Ug <= 10cm/s), and fiber mass fraction (0 <= C <= 2%) on gas holdup and flow regime transitionare studied experimentally in well-mixed water-cellulose fiber suspensions in a cocurrentbubble column. Experimental results show that gas holdup decreases with increasingsuperficial liquid velocity when fiber mass fraction and superficial gas velocity areconstant. Gas holdup is not significantly affected by fiber mass fraction in the range of C<= 0.4%, but decreases with increasing fiber mass fraction in the range of 0.4% < C <1.5%. The mechanisms behind the influences of superficial liquid velocity and fiber massfraction on gas holdup in a gas-liquid-fiber bubble column are analyzed. The effects of gasdistribution methods are also explained by comparison to previous results. The axial gasholdup distribution is shown to be a complex function of superficial gas and liquidvelocities and fiber mass fraction. The drift-flux model is used to identify the flow regimetransitions at different operating conditions. Three distinct flow regimes are observedwhen C < 0.4%, but only two are identified when 0.6% < C < 1.5%. The superficial gasvelocities at which the flow transitions from one regime to another are not significantlyaffected by Ul, and only slightly decrease with increasing C.
[7] “Effect of Fiber Type on Gas Holdup in a Cocurrent Air-Water-Fiber Bubble Column,” Chemical Engineering Journal, 111, 2005, pp. 21-30.
An experimental investigation of the effect of fiber type on gas holdup in a cocurrent air–water–fiber bubble column is presented. Threetypes of cellulose fibers (i.e., hardwood, softwood, and bleached chemithermomechanical pulp (BCTMP)) and three different lengths of Rayon fibers are used in the investigation. The results indicate fiber type has a significant influence on the gas holdup in the air–water–fiberbubble column. Mechanisms by which fibers influence gas holdup in gas–liquid–fiber bubble columns are summarized and used to explainthe experimental results. Fiber physical properties, including fiber length, coarseness, and flexibility are proposed to be the main factorsresponsible for the fiber type effects on gas holdup.
[8] “Time-Dependent Gas Holdup Variation in an Air-Water Bubble Column,” Chemical Engineering Science, 59, 2004, pp. 623-632.
Time-dependent gas holdup variation in a two-phase bubble column is reported with air and tap water as the working 1uids. Theresults indicate that time-dependent gas holdup is closely related to the water, whose quality is unsteady and changes, not only during thetwo-phase 1ow, but also during idle periods. The significance and characteristics of the time-dependent gas holdup variation are in1uencedby the bubble column operation mode (cocurrent or semi-batch), the sparger orientation, the superficial gas velocity, and the superficial liquid velocity. It is proposed that a volatile substance (VS), which exists in the water in very small concentrations and inhibits bubblecoalescence, evaporates during column operation and results in a time-dependent gas holdup. The in1uence of bubble column operationmode, sparger orientation, superficial gas velocity, and superficial liquid velocity on the time-dependent gas holdup variation are explainedbased on their effects on bubble size, bubble contacting frequency and mixing intensity. This work reveals that regular tap water maycause significant reproducibility problems in experimental studies of air–water two-phase 1ows.
# posted by sidewatcher @ 9:14 PM 
