Study on CFD-PBM turbulence closures based on k-ε and Reynolds stress models for heterogeneous bubble column flows

Computers and Fluids

Volumn 105, Issue , 2014, Pages 91-100

  Liu, Yefei ^a   Hinrichsen, Olaf ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Bubble column; Bubble induced turbulence; CFD PBM; K model; RSM

Indexed keywords

BUBBLE COLUMN FLOW; CFD-PBM; REYNOLDS STRESS MODELS; RSM; TURBULENCE CLOSURES;

BUBBLE COLUMNS;

EID: 84907713775     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compfluid.2014.09.023     Document Type: Article

References (50)

1. Deckwer W.D. Bubble column reactors 1992, John Wiley & Sons, New York.
2. Tryggvason G., Esmaeeli A., Lu J.C., Biswas S. Direct numerical simulations of gas/liquid multiphase flows. Fluid Dyn Res 2006, 38:660-681.
3. Sokolichin A., Eigenberger G., Lapin A. Simulation of buoyancy driven bubbly flows: established simplifications and open questions. AIChE J 2004, 50:24-45.
4. Zhang D., Deen N.G., Kuipers J.A.M. Numerical simulation of the dynamic flow behavior in a bubble column: a study of closures for turbulence and interface forces. Chem Eng Sci 2006, 61:7593-7608.
5. Law D., Battaglia F., Heindel T.J. Model validation for low and high superficial gas velocity bubble column flows. Chem Eng Sci 2008, 63:4605-4616.
6. Tabib M.V., Roy S.A., Joshi J.B. CFD simulation of bubble column: an analysis of interphase forces and turbulence models. Chem Eng J 2008, 139:589-614.
7. Ekambara K., Dhotre M.T. CFD simulation of bubble column. Nucl Eng Des 2010, 240:963-969.
8. Chen P., Sanyal J., Dudukovic M.P. CFD modeling of bubble column flows: implementation of population balance. Chem Eng Sci 2004, 59:5201-5207.
9. Wang T.F., Wang J.F., Jin Y. A CFD-PBM coupled model for gas-liquid flows. AIChE J 2006, 52:125-140.
10. Bannari R., Kerdouss F., Selma B., Bannari A., Proulx P. Three-dimensional mathematical modeling of dispersed two-phase flow using class method of population balance in bubble columns. Comput Chem Eng 2008, 32:3224-3237.
11. Bhole M.R., Joshi J.B., Ramkrishna D. CFD simulation of bubble columns incorporating population balance modeling. Chem Eng Sci 2008, 63:2267-2282.
12. Ekambara K., Nandakumar K., Joshi J.B. CFD simulation of bubble column reactor using population balance. Ind Eng Chem Res 2008, 47:8505-8516.
13. Borchers O., Busch C., Sokolichin A., Eigenberger G. Applicability of the standard k-ε turbulence model to the dynamic simulation of bubble columns. Part II: Comparison of detailed experiments and flow simulations. Chem Eng Sci 1999, 54:5927-5935.
14. Mudde R.F., Simonin O. Two and three dimensional simulation of a bubble plume using a two fluid model. Chem Eng Sci 1999, 54:5061-5071.
15. Pfleger D., Gomes S., Gilbert N., Wagner H.G. Hydrodynamic simulations of laboratory scale bubble columns fundamental studies of the Eulerian-Eulerian modeling approach. Chem Eng Sci 1999, 54:5091-5099.
16. Sokolichin A., Eigenberger G. Applicability of the standard k-ε turbulence model to the dynamic simulation of bubble columns: Part I. Detailed numerical simulations. Chem Eng Sci 1999, 54:2273-2284.
17. Behzadi A., Issa R.I., Rusche H. Modeling of dispersed bubble and droplet flow at high phase fractions. Chem Eng Sci 2004, 59:759-770.
18. Selma B., Bannari R., Proulx P. A full integration of a dispersion and interface closures in the standard k-ε model of turbulence. Chem Eng Sci 2010, 65:5417-5428.
19. Cokljat D, Slack M, Vasquez SA. Reynolds-stress model for Eulerian multiphase. In: Proceedings of 4th international symposium on turbulence heat and mass Transfer; 2003. p. 1047-54.
20. Deen N.G., Solberg T., Hjertager B.H. Large eddy simulation of the gas-liquid flow in a square cross-sectioned bubble column. Chem Eng Sci 2001, 56:6341-6349.
21. Dhotre M.T., Niceno B., Smith B.L. Large eddy simulation of a bubble column using dynamic sub-grid scale model. Chem Eng J 2008, 136:337-348.
22. Niceno B., Dhotre M.T., Deen N.G. One-equation sub-grid scale (SGS) modeling for Euler-Euler large eddy simulation (EELES) of dispersed bubbly flow. Chem Eng Sci 2008, 63:3923-3931.
23. Laborde-Boutet C., Larachi F., Dromard N., Delsart O., Schweich D. CFD simulation of bubble column flows: investigations on turbulence models in RANS approach. Chem Eng Sci 2009, 64:4399-4413.
24. Jakobsen H.A., Lindborg H., Dorao C.A. Modeling of bubble column reactors: progress and limitations. Ind Eng Chem Res 2005, 44:5107-5151.
25. Marschall H., Mornhinweg R., Kossmann A., Oberhauser S., Langbein K., Hinrichsen O. Numerical simulation of dispersed gas/liquid flows in bubble columns at high phase fractions using OpenFOAM. Part II - Numerical simulations and results. Chem Eng Technol 2011, 34:1321-1327.
26. Tsuchiya K., Furumoto A., Fan L.S., Zhang J. Suspension viscosity and bubble size velocity in liquid-solid fluidized beds. Chem Eng Sci 1997, 52:3053-3066.
27. Rampure M.R., Kulkarni A.A., Ranade V.V. Hydrodynamics of bubble column reactors at high gas velocity: experiments and computational fluid dynamics (CFD) simulations. Ind Eng Chem Res 2007, 46:8431-8447.
28. Tomiyama A. Drag and lift and virtual mass forces acting on a single bubble. In: Proceedings of 3rd international symposium on two-phase flow modeling and experimentation; 2004. p. 22-4.
29. Kumar S., Ramkrishna D. On the solution of population balance equations by discretization-I. A fixed pivot technique. Chem Eng Sci 1996, 51:1311-1332.
30. Smith M., Matsoukas T. Constant-number Monte Carlo simulation of population balances. Chem Eng Sci 1998, 53:1777-1786.
31. Bove S., Solberg T., Hjertager B.H. A novel algorithm for solving population balance equations: the parallel parent and daughter classes. Deviation, analysis and testing. Chem Eng Sci 2005, 60:1449-1464.
32. Marchisio D.L., Vigil R.D., Fox R.O. Quadrature method of moments for aggregation-breakage process. J Colloid Interface Sci 2003, 258:322-334.
33. Selma B., Bannari R., Proulx P. Simulation of bubbly flows: comparison between direct quadrature method of moments (DQMOM) and method of classes (CM). Chem Eng Sci 2010, 65:1925-1941.
34. Liao Y.X., Lucas D. A literature review on mechanisms and models for the coalescence process of fluid particles. Chem Eng Sci 2010, 65:2851-2864.
35. Luo H. Coalescence, Breakup and liquid circulation in bubble column reactors. PhD thesis, The Norwegian Institute of Technology, Trondheim, Norway; 1993.
36. Wu Q., Kim S., Ishii M. One-group interfacial area transport in vertical bubbly flow. Int J Heat Mass Transfer 1998, 41:1103-1112.
37. Wang T.F., Wang J.F., Jin Y. Theoretical prediction of flow regime transition in bubble columns by the population balance model. Chem Eng Sci 2005, 60:6199-6209.
38. Luo H., Svendsen H.F. Theoretical model for drop and bubble breakup in turbulent dispersions. AIChE J 1989, 42:1225-1233.
39. Jakobsen H.A., Sannæs B.H., Grevskott S., Svendsen H.F. Modeling of vertical bubble-driven flows. Ind Eng Chem Res 1997, 36:4052-4074.
40. Sato Y., Sadatomi M., Sekoguchi K. Momentum and heat transfer in two-phase bubble flow. Int J Multiphase Flow 1981, 7:167-177.
41. Arnold G.S., Drew D., Lahey R. Derivation of constitutive equations for interfacial force and Reynolds stress for suspension of spheres using ensemble cell averaging. Chem Eng Commun 1989, 86:43-54.
42. OpenFOAM User's Guide. United Kingdom: OpenCFD Ltd.; 2010.
43. Alopaeus V., Koskinen J., Keskinen K.I. Simulation of the population balances for liquid-liquid systems in a nonideal stirred tank. Part 1: Description and qualitative validation of the model. Chem Eng Sci 1999, 54:5887-5899.
44. Oliveira J.P., Issa R.I. Numerical aspects of an algorithm for Eulerian simulation of two-phase flows. Int J Numer Meth Fluids 2003, 43:1177-1198.
45. Issa R. Solution of the implicitly discretized fluid flow equations by operator-splitting. J Comput Phys 1985, 62:40-65.
46. Rusche H. Computational fluid dynamics of dispersed two-phase flows at high phase fraction. PhD thesis, Department of mechanical Engineering, Imperial College of Science, Technology and Medicine, University of London, London, UK; 2002.
47. Sanyal J., Vasquez S., Roy S., Dudukovic M.P. Numerical simulation of gas-liquid dynamics in cylindrical bubble column reactors. Chem Eng Sci 1999, 54:5071-5083.
48. Kumar SB. Computed tomographic measurements of void fraction and modeling of the flow in bubble columns. PhD thesis, Florida Atlantic University, Florida, USA; 1994.
49. Degaleesan S. Fluid dynamic measurements and modeling of liquid mixing in bubble columns. PhD thesis, Washington University, St. Louis, Missouri, USA; 1997.
50. Launder B.E., Spalding D.B. The numerical computation of turbulent flows. Comput Method Appl Mech Eng 1974, 3:269-289.