Review of drag coefficients on gas – liquid tower: the drag coefficient independent and dependent on bubble diameter in bubble column experiment

Document Type: Review Article

Author

Department of chemical Engineering, University of Sistan and Baluchestan, Zahedan, Iran

Abstract

Drag coefficient independent on bubble diameter is required to ease design sieve trays or bubble column, through simulation of computational fluid dynamic. In this paper, the drag coefficients, independent or dependent on the diameter, are reviewed for gas-liquid system. A number of drag coefficients are used for Computational Fluid Dynamics (CFD). Different forces are entered to the liquid-bubble separation surface in diverse directions. Forces are investigated with mathematical proving for Newtonian fluids and Eulerian coordinate. Finally, the external force as a new force, enter to the drag coefficient equations. Drag coefficient is included force coefficient. Drag force is entered in momentum equations. Drag coefficient is used in two-phase systems which bubbles and liquid are activated as dispersed and continuous phase, respectively. Bubbles and liquid are in contact with each other in separation surface on bubble. Drag force is created slip on separation surface. The drag coefficients are investigated depended on the size and configuration of bubbles. The drag coefficient of Krishna et al is used dependent on bubble diameter. Schiller - Nauman model drag coefficient is estimated with 9% error and dependence on bubble diameter. In this article, the modern drag coefficients are studied independent on the diameter and shape of the bubble. The Drag coefficients are resulted theoretical, mathematical and experimental independent and dependent of diameter bubble. The new Drag coefficient is presented dependent on surface tension and diameter of the tower hole with 6.3 of error approximately.

Graphical Abstract

Review of drag coefficients on gas – liquid tower: the drag coefficient independent and dependent on bubble diameter in bubble column experiment

Keywords


[1] R. Rahimi, S. Hajghani, Investigation of Heat Transfer Parameters of a Bundle of Heaters in a Simple Bubble Column Reactor Using CFD Method, Chemical and Petroleum Engineering 49 (2015) 31-49.
[2] Allen, M. S., 1900. Philos. Mag, 50.pp. 323-338, 519-534.
[3] Langmuir, I., and Blodgett, K. B., 1948 C.S. Army Air Force Tech. Rep. No. 5418.
 
 
 
[4] Dalla, Ville, J.M. 1948 Micrometrics, Pitman Publishing Co. New York.  
[5] Gilbert, M. Davies, L., and Altman, D.,1955 Jet  Propul,. 25, pp. 26-30.
[6] Moore. D. W., J. 1963 Fluid Mech. 16. Pp. 161 -176. [7]       Kurten.H., Raasch, J., and Rumpf, H., Chem - Ing - Tech. 38. (1966). pp. 941-948.
[8] Abraham. F. F.1970 Phys.Fluids. 13. Pp. 2194-2195.
[9] Clift, R, and Gauvin, W. H., 1970 Proc. Chenleca 70, 1, pp. 14 28.
[10]         Tanaka, Z., and Iinoya, K., J. 1970 Chem. Eng. Jpn, 3. pp. 261-262.
[11]         Ihme, F. Schmidt - Traub, H., and Brauer, H. 1972. Chern- Ing - Teclt, 44. , pp. 306 - 313.
[12]         Brauer, H., and Mewes, D., 1972 Chem,-Ing.-Tech. 44. pp. 865-868.
 
 
[13]         White, F.M. 1974. Viscous fluid flow, McGraw-Hill, New York .
[14]         D. Ma, G.J., Ahmadi, A thermo dynamical formulation for dispersed turbulent flows, 1:  basic theory, Int. J. Multiphase Flow 16 (1990) 323–340.
[15]         S. Grevskott, B.H. Sannaes, M.P. Dudkovic, K.W. Hjarbo, H.F. Svendsen, Liquid circulation, bubble size distributions and solids movement in two and three-phase bubble columns, Chem. Eng. Sci 51 (1996) 1703–1713.
[16]         K. Tsuchiya, A. Furumoto, L.S.  Fan, J., Zhang, Suspension viscosity and bubble size velocity in liquid–solid fluidized beds, Chem. Eng. Sci 52 (1997) 3053–3066.
[17]         G.L., Lane, M.P., Schwarz, G.M., Evans, Modelling of the interaction between gas and liquid in stirred vessels. In: Proceedings of 10th European Conference on Mixing, Delft, The Netherlands (2000) 197-204.
[18]         A. Tomiyama, I. Kataoka, I. Zˇun, T. Sakaguchi, Drag coefficients of single bubbles under normal and micro gravity conditions, JSME Int. J. 42  (1998) 472 – 479.
[19]         Tomiyama, A. drag lift and virtual mass forces acting on a single bubble, Third International Symposium on Two-Phase Flow Modeling and experimentation, 2004.
[20]         B. Hameed. A.N. Mahooda, A,O Campbell, RB. Thorpe sharif, Heat transfer measurement in a three-phase direct-contact condenser under flooding conditions, applied Thermal Engineering 95 (2016) 106–114.
[21]         L.A., Schiller, Z.Naumaan, A drag coefficient correlation Ver Dtsch, Ing. 77. (1935) 138.  
[22]         M.  Ishii, N. Zuber, Drag coefficient and relative velocity in bubbly, droplet or particulate flows, AIChE J. 25. (1979) 843–855.
[23]         Krishna, Van Baten, J., Ellenberger, A.P., Higler, and Taylor, CFD Simulations of Sieve Tray Hydrodynamics, Chemical Engineering Research and Design. 77. (1999) 639–646.
[24]         D.L., Bennett, R. Agrawal, and P.J., Cook, New pressure drop correlation for sieve tray distillation columns, AIChE J, 29, (1983) 434 - 442.
[25]         D. Noriler, H.F., Meier, A.A.C. Wolf, Barros , M.R. Maciel, Thermal  fluid dynamics analysis of gas–liquid flow on a distillation sieve tray, Chemical Engineering Journal, Volume 136, (2008) 133–143.
[26]         L.  Zhang, Ch  Yang,.And Z. Sh. Mao, Numerical simulation of a bubble rising in shear-thinning fluids, Journal of Non-Newtonian Fluid Mechanics, 165. (2015) 555–567.
[27]         R. Byron Bird, Warren E. Stewart ,Edwin N. Lightfoot, Transport Phenomena, John Wiley & Sons, Inc, Second Edition. 1924. pp. 80-90.
[28]         A. Brucato, F., Grisafi, G., Montante, Particle drag coefficient in turbulent fluids. Chemical Engineering Science 53, (1998) 3295 - 3314.
[29]         J.R Grace, T. Wairegi, T.H., Nguyen, Shapes and velocities of single drops and bubbles moving freely through immiscible liquids, Trans. Inst. Chem. Eng 54  (1976) 167–173.
[30]         Fengling Yang , Shenjie Zhou , Xiaohui An , Gas–liquid hydrodynamics in a vessel stirred by   dual dislocated-blade Rushton impellers, Chinese Journal of Chemical Engineering 23 (2015) 1746 -1754. 
[31]         Ning Yang, Zongying Wu, Jianhua Chen, Yuhua Wang, Jinghai Li, Multi-scale analysis of gas-liquid interaction and CFD simulation of gas–liquid flow in bubble columns, Chemical Engineering Science  66  (2011) 3212–3222.
[32]         C. E., Lapple, Particle Dynamics. Eng. Res. Lab.  E.I .1951, DuPont de Nemours and Co.Wilmington. Delawarc.
[33]         J. M., Kendall. reported by Kiichemann. D. J., FIuid Mech. 21, 1965 pp. 1 - 20.
[34]         Halliday, Resnick, Fundamentals of Physics, Tenth Edition, WILy 2014 pp. 114-115.
[35]         W.L., Habermn sad, R.K. Morton, Armed Servic'es Technical Information gency AD 19377, Navy a Department The David W. Taylor, W. Taylor Model Basin 1953 pp.1- 48.
[36]         B R., Munson, D. F. Young, T. H., Okiishi,  W. W., Huebsch, Fundamentals of Fluid Mechanics, John Wiley & Sons, Inc. Seventh Edition, USA, 2015 pp. 677-679.
[37]         H. D., Mendelson, AIChE J., 13., 250.1967. 
[38]         J. F., Davidson, and B. G. Shuler,.Trans. I. Inst, Chem. Eng, lond, 38. 144. 1960.
[39]         R. E., Treybal, MASS-TRANSFER OPERATION, Third Edition, International Edition. pp. 136-216. 1981.
[40]         R., Clift, J. R., Grace, M. E., Weber, Bubbles, Drops, and Particles, Journal of Academic Press. New York 10003. 1978 pp. 3-14.
[41]         D., Law. F.  Battaglia, T.J., Heindel, Model validation for lowand high superficial gas velocity bubble column flows, Chemical Engineering Scince 63 (2008). 4605–4616.
[42]         M.V.  Tabib, S.A.  Roy, J.B. Joshi, CFD simulation of bubble column an analysis of interphase forces and turbulence models, Chemical Engineering 139 (2008) 589 – 614.
[43]         W, Van krevelen, and P, J, Hoftijzer: Chemical Engineering, prog, 46(1)  (1950). 9.
[44]         C,C., Maneri; and H, D Mendelson: AIChE, J., 14, 295 (1968).