Sensitivity study on interfacial closure laws in two-fluid bubbly flow simulations

AIChE Journal

Volumn 49, Issue 7, 2003, Pages 1621-1636

  Oey, R S ^a   Mudde, R F ^a   Van den Akker, H E A ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

BUBBLE COLUMNS; DRAG; FLOW OF FLUIDS; PHASE INTERFACES;

INTERFACIAL CLOSURE LAWS;

BUBBLES (IN FLUIDS);

BUBBLE COLUMN; BUBBLY FLOW; DIFFUSION; MATHEMATICAL MODELING; TURBULENCE;

ACCURACY; ARTICLE; DIFFUSION; FLUID FLOW; MATHEMATICAL MODEL; MOLECULAR DYNAMICS; SIMULATION; TURBULENT FLOW;

EID: 0037810644     PISSN: 00011541     EISSN: None     Source Type: Journal    
DOI: 10.1002/aic.690490703     Document Type: Article

References (51)

1. Auton, T. R., "The Lift Force on a Spherical Body in Rotational Flow," J. Fluid Mech., 183, 199 (1987).
2. Becker, S., A. Sokolichin, and G. Eigenberger, "Gas-Liquid Flow in Bubble Columns and Loop Reactors: II. Comparison of Detailed Experiments and Flow Simulations," Chem. Eng. Sci., 49, 5747 (1994).
3. Bel F'dhila, R., and O. Simonin, "Eulerian Predictions of a Turbulent Bubbly Flow Downstream a Sudden Pipe Expansion," Sixth Workshop on Two-Phase Flow Predictions, Erlangen, Germany, M. Sommerfeld, ed., 264 (1992).
4. Bunner, B., and G. Tryggvason, "Direct Numerical Simulations of Dispersed Flows," Proc. of the 9th Workshop on Two-Phase Flow Predictions, Merseburg, Germany, Apr. 13-16 (1999).
5. Celik, I., and Y.-Z. Wang, "Numerical Simulation of Circulation in Gas-Liquid Column Reactors: Isothermal, Bubbly, Laminar Flow," Int. J. Multiphase Flow, 20, 1053 (1994).
6. Delhaye, J., "Jump Conditions and Entropy Sources in Two-Phase Systems," Int. J. Multiphase Flow, 1, 395 (1974).
7. Delnoij, E., F. A. Lammers, J. A. M. Kuipers, and W. P. van Swaij, "Dynamic Simulation of Dispersed Gas-Liquid Two-Phase Flow Using a Discrete Bubble Model," Chem. Eng. Sci., 52, 1429 (1997).
8. Drew, D. A., "Mathematical Modelling of Two-Phase Flow," Ann. Rev. Fluid Mech., 15, 261 (1983).
9. Drew, D. A., and R. T. Lahey, Jr., "The Virtual Mass and Lift Force on a Sphere in a Rotating and Straining Inviscid Flow," Int. J. Multiphase Flow, 13(1), 113 (1989).
10. Drew, D. A., and R. T. Lahey, Jr., "Some Supplemental Analysis Concerning the Virtual Mass and Lift Force on a Sphere in a Rotating and Straining Flow," Int. J. Multiphase Flow, 16(6), 1127 (1990).
11. Drew, D. A. and S. L. Passman, Theory of Multicomponent Fluids, Springer-Verlag, Appl. Math. Sci., New York 135 (1999).
12. Dudukovic, M. P., F. Larachi, and P. L. Mills, "Multiphase Reactors - Revisited," Chem. Eng. Sci., 54, 1975 (1999).
13. Elgobashi, S., and T. Abou-Arab, "A Two-Equation Turbulence Model for Two-Phase Flows," Physics of Fluids, 26, 931 (1983).
14. Ferziger, J. H., and M. Peric, Computational Methods for Fluid Dynamics, 3rd revised ed., Springer-Verlag, Berlin and New York (2002).
15. Geurst, J. A., "Virtual Mass in Two-Phase Bubbly Flow," Physica, 129A, 233 (1985).
16. Gosman, A. D., R. I. Issa, C. Lekakou, M. K. Looney, and S. Politis, "Multidimensional Modelling of Turbulent Two-Phase Flows in Stirred Vessels," AIChE J., 38, 1946 (1992).
17. Grevskott, S., B. H. Sannaes, M. P. Dudukovic, K. W. Hjarbo, and H. F. Svendsen, "Liquid Circulation, Bubble Size Distribution and Solids Movement in Two- and Three-Phase Bubble Columns," Chem. Eng. Sci., 51, 1703 (1996).
18. Harten, A., "High Resolution Schemes for Hyperbolic Conservation Laws," J. Comput. Phys., 49, 357 (1983).
19. Hirsch, C., Numerical Computation of Internal and External Flows, Volume 2, Wiley, Chichester, U.K. (1990).
20. Hussaini, M. Y., B. Van Leer, and J. Van Rosendaele, Upwind and High-Resolution Schemes, Springer-Verlag, New York (1997).
21. Hinze, O. J., Turbulence, McGraw-Hill, New York (1975).
22. Issa, R. I., and P. Oliveira, "Modelling of Turbulent Dispersion in Two-Phase Flow Jets," Engineering Turbulence Modelling and Experiment 2, Florence, Italy. W. Rodi and F. Martelli, eds., Elsevier, 947, (1993).
23. Jakobsen, H. A., B. H. Sanns, S. Grevskott, and H. F. Svendsen, "Modelling of Vertical Bubble-Driven Flows," Ind. Eng. Chem. Res., 36, 4052 (1997).
24. Jakobsen, H. A., "Phase Distribution Phenomena in Two-Phase Bubble Column Reactors," Chem. Eng. Sci., 56, 1049 (2001).
25. Kaasschieter, E. F., "Preconditioned Conjugate Gradients for Solving Singular Systems," J. of Comput. Appl. Math., 24, 265 (1988).
26. Krishna, R., M. I. Urseanu, J. M. van Baten, and J. Ellenberger, "Rise Velocity of a Swarm of Large Gas Bubbles in Liquids," Chem. Eng. Sci., 54, 171 (1999).
27. Lathouwers, D., "Modelling and Simulation of Turbulent Bubbly Flow," PhD Thesis, Delft University of Technology (1999).
28. Mudde, R. F., D. J. Lee, J. Reese, and L.-S. Fan, "The Role of Coherent Structures on the Reynolds Stresses in Two-Dimensional Bubble Columns," AIChE J., 43, 913 (1997).
29. Mudde, R. F., and O. Simonin, "Two- and Three-Dimensional Simulations of a Bubble Plume Using a Two-Fluid Model," Chem. Eng. Sci., 54, 5061 (1999).
30. Oey, R. S., R. F. Mudde, L. M. Portela, and H. E. A. van den Akker, "Simulation of a Slurry Airlift Using a Two-Fluid Model," Chem. Eng. Sci., 56, 673 (2001).
31. Patankar, S. V., "Numerical Heat Transfer and Fluid Flow," Hemisphere Publ. Corp., McGraw-Hill, New York (1980).
32. Pan, Y., M. P. Dudukovic, and M. Chang, "Numerical Investigation of Gas-Driven Flow in 2-D Bubble Columns," AIChE J., 46, 434 (2000).
33. Pfeger, D., S. Gomes, N. Gilbert, and H.-G. Wagner, "Hydrodynamic Simulations of Laboratory Scale; Fundamental Studies of the Eulerian-Eulerian Modelling Approach," Chem. Eng. Sci., 54, 5091 (1999).
34. Pfleger, D., and S. Becker, "Modelling and Simulation of the Dynamic Flow Behavior in a Bubble Column," Chem. Eng. Sci., 56 1737 (2001).
35. Ranade, V. V., "Modelling of Turbulent Flow in a Bubble Column Reactor," Chem. Eng. Res. Des., 75, 14 (1997).
36. Ranade, V. V., and R. P. Utikar, "Dynamics of Gas-Liquid Flows in Bubble Column Reactors," Chem. Eng. Sci., 54, 5237 (1999).
37. Saad, Y., "Analysis of Augmented Krylov Subspace Methods," SIAM J. Matrix Anal. Appl., 18(2), 435 (1997).
38. Saad, Y., and M. H. Schultz, "A Generalized Minimum Residual Algorithm for Solving Nonsymmetric Linear Systems," SIAM J. Sci. Stat. Comput. 7, 856 (1986).
39. Sankaranarayanan, K., and S. Sundaresan, "Lift Force in Bubbly Suspensions," Chem. Eng. Sci., 57, 3521 (2002).
40. Sokolichin, A., and G. Eigenberger, "Gas-Liquid Flow in Bubble Columns and Loop Reactors: Part I. Detailed Modelling and Numerical Simulation," Chem. Eng. Sci., 49, 5735 (1994).
41. Sokolichin, A., and G. Eigenberger, "Applicability of the Standard k-ε Turbulence Model to the Dynamic Simulation of Bubble Columns: Part I. Detailed Numerical Simulations," Chem. Eng. Sci., 54, 2273 (1999).
42. Tchen, C. M., "Mean Value and Correlation Problems Connected with the Motion of Small Particles Suspended in a Turbulent Fluid," PhD Thesis, Delft University of Technology (1947).
43. Tennekes, H., and J. L. Lumley, A First Course in Turbulence, MIT Press, Cambridge, MA (1942).
44. Van Leer, B., "Towards the Ultimate Difference Scheme I. The Quest for Monotonicity," Lect. Notes Phys., 18, 164 (1973).
45. Van Leer, B., "Towards the Ultimate Difference Scheme II. Monotonicity and Conservation Combined in a Second Order Scheme," J. Comput. Phys., 14, 361 (1974).
46. Viollet, P. L., and O. Simonin, "Modelling Dispersed Two-Phase Flows: Closure, Validation and Software Development," Appl. Mech. Rev., 47 (6 part 2), S80 (1994).
47. Wells, M. R., and D. E. Stock, "The Effect of Crossing Trajectories on the Dispersion of Particles in a Turbulent Flow," J. Fluid Mech., 136, 31 (1983).
48. Wen, Y. C., and Y. H. Yu, Mechanics of Fluidization, Chem. Eng. Prog. Symp. Ser., 62, 100 (1966).
49. Zhang, D. Z., and A. Prosperetti, "Momentum and Energy Equations for Dispersed Two-Phase Flows and Their Closure for Dilute Suspensions," Int. J. Multiphase Flow, 23, 425 (1997).
50. Zijlema, M., "Computational Modelling of Turbulent Flows in General Domains," PhD Thesis, Delft University of Technology (1996a).
51. Zijlema, M., "On the Construction of a Third-Order Accurate Monotone Convection Scheme with Application to Turbulent Flows in General Domains," Int. J. Numer. Meth., 22, 619 (1996b).