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Research Papers: Techniques and Procedures

New Two-Fluid Model Near-Wall Averaging and Consistent Matching for Turbulent Bubbly Flows

[+] Author and Article Information
Avinash Vaidheeswaran

School of Nuclear Engineering,
Purdue University,
West Lafayette, IN 47906
e-mail: avaidhee@purdue.edu

Deoras Prabhudharwadkar

GE Global Research,
Bangalore 560066, India
e-mail: dprabhud@gmail.com

Paul Guilbert

ANSYS UK Ltd,
Abingdon OX14 4RW, Oxon, UK
e-mail: paul.guilbert@ansys.com

John R. Buchanan, Jr.

Bechtel Marine Propulsion Corporation,
Bettis Laboratory,
West Mifflin, PA 15122
e-mail: jack.buchanan@unnpp.gov

Martin Lopez de Bertodano

School of Nuclear Engineering,
Purdue University,
400 Central Drive,
West Lafayette, IN 47906
e-mail: bertodan@purdue.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 15, 2016; final manuscript received July 11, 2016; published online September 14, 2016. Assoc. Editor: Samuel Paolucci.

J. Fluids Eng 139(1), 011302 (Sep 14, 2016) (11 pages) Paper No: FE-16-1170; doi: 10.1115/1.4034327 History: Received March 15, 2016; Revised July 11, 2016

A new two-fluid model averaging in the near-wall region is proposed to ensure consistent matching of the two-phase k–ε turbulence model with the two-phase logarithmic law of the wall (Marie J. L., Moursali, E., and Tran-Cong, S., 1997, “Similarity Law and Turbulence Intensity Profiles in a Bubbly Boundary Layer,” Int. J. Multiphase Flow, 23(2), pp. 227–247). The void fraction distribution obtained with the averaging procedure is seen to conform to the two-phase wall function approach which is based on a double step function void fraction distribution. In particular, the proposed averaging technique is shown to achieve grid convergence in the near-wall region, which could not be obtained otherwise. Computational fluid dynamics (CFD) results with the proposed technique are in good agreement with experiments on upward bubbly flows over a flat plate, and upward and downward flows in pipes. An additional advantage of the proposed technique is that it replaces the wall force model, which has a significant degree of uncertainty in turbulent flow modeling, with a simpler geometric constraint.

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References

Launder, B. E. , and Spalding, D. B. , 1974, “ The Numerical Computation of Turbulent Flows,” Comput. Methods Appl. Mech. Eng., 3(2), pp. 269–289. [CrossRef]
Marie, J. L. , Moursali, E. , and Tran-Cong, S. , 1997, “ Similarity Law and Turbulence Intensity Profiles in a Bubbly Boundary Layer,” Int. J. Multiphase Flow, 23(2), pp. 227–247. [CrossRef]
Drew, D. A. , and Lahey, R. T., Jr. , 1981, “ Phase Distribution Mechanisms in Turbulent Two-Phase Flow in Channels of Arbitrary Cross Section,” ASME J. Fluids Eng., 103(4), pp. 583–589. [CrossRef]
Lance, M. , and Lopez de Bertodano, M. , 1994, “ Phase Distribution Phenomena and Wall Effects in Bubbly Two-Phase Flows,” Multiphase Sci. Technol., 8(1), pp. 69–123. [CrossRef]
Lopez de Bertodano, M. , Lahey, R. T., Jr. , and Jones, O. C. , 1994, “ Development of a k-epsilon Model for Bubbly Two-Phase Flow,” ASME J. Fluids Eng., 116(1), pp. 128–134. [CrossRef]
Tomiyama, A. , 1998, “ Struggle With Computational Bubble Dynamics,” Multiphase Sci. Technol., 10(4), pp. 369–405. [CrossRef]
Lucas, D. , Krepper, E. , and Prasser, H.-M. , 2001, “ Prediction of Radial Gas Profiles in Vertical Pipe Flow on the Basis of Bubble Size Distribution,” Int. J. Therm. Sci., 40(3), pp. 217–225. [CrossRef]
Cheung, S. C. P. , Yeoh, G. H. , and Tu, J. Y. , 2008, “ Population Balance Modeling of Bubbly Flows Considering the Hydrodynamics and Thermomechanical Processes,” AIChE J., 54(7), pp. 1689–1710. [CrossRef]
Das, A. K. , and Das, P. K. , 2010, “ Modelling Bubbly Flow and Its Transitions in Vertical Annuli Using Population Balance Technique,” Int. J. Heat Fluid Flow, 31(1), pp. 101–114. [CrossRef]
Rzehak, R. , and Krepper, E. , 2013, “ Closure Models for Turbulent Bubbly Flows: A CFD Study,” Nucl. Eng. Des., 265, pp. 701–711. [CrossRef]
Rzehak, R. , Krepper, E. , Liao, Y. , Ziegenhein, T. , Kriebitzsch, S. , and Lucas, D. , 2015, “ Baseline Model for the Simulation of Bubbly Flows,” Chem. Eng. Technol., 38(11), pp. 1972–1978. [CrossRef]
Nakoryakov, V. E. , Kashinsky, O. N. , Randin, V. V. , and Timkin, L. S. , 1996, “ Gas–Liquid Bubbly Flow in Vertical Pipes,” ASME J. Fluids Eng., 118(2), pp. 377–382. [CrossRef]
Troshko, A. A. , and Hassan, Y. , 2001, “ A Two-Equation Turbulence Model of Turbulent Bubbly Flows,” Int. J. Multiphase Flows, 27(11), pp. 1965–2000. [CrossRef]
Aliseda, A. , and Lasheras, J. C. , 2006, “ Effect of Buoyancy on the Dynamics of a Turbulent Boundary Layer Laden With Microbubbles,” J. Fluid Mech., 559, pp. 307–334. [CrossRef]
Sad Chemloul, N. , and Benrabah, O. , 2008, “ Measurement of Velocities in Two-Phase Flow by Laser Velocimetery: Interaction Between Solid Particles' Motion and Turbulence,” ASME J. Fluids Eng., 130(7), p. 071301. [CrossRef]
Antal, S. P. , Lahey, R. T. , and Flaherty, J. E. , 1991, “ Analysis of Phase Distribution in Fully Developed Laminar Bubbly Two-Phase Flow,” Int. J. Multiphase Flow, 17(5), pp. 635–652. [CrossRef]
Hosokawa, S. , Tomiyama, A. , Misaki, S. , and Hamada, T. , 2002, “ Lateral Migration of Single Bubbles Due to the Presence of Wall,” ASME Paper No. FEDSM2002-31148.
Frank, T. , Shi, J. M. , and Burns, A. D. , 2004, “ Validation of Eulerian Multiphase Flow Models for Nuclear Safety Applications,” Third International Symposium on Two-Phase Flow Modeling and Experimentation, Pisa, Italy, Sept. 22–24.
Felton, K. , and Loth, E. , 2001, “ Spherical Bubble Motion in a Turbulent Boundary Layer,” Phys. Fluids, 13(9), pp. 2564–2577. [CrossRef]
Zaruba, A. , Lucas, D. , Prasser, H.-M. , and Hohne, T. , 2007, “ Bubble-Wall Interactions in a Vertical Gas–Liquid Flow: Bouncing, Sliding, and Bubble Deformations,” Chem. Eng. Sci., 62(6), pp. 1591–1605. [CrossRef]
Tran-Cong, S. , Marie, J. L. , and Perkins, R. J. , 2008, “ Bubble Migration in a Turbulent Boundary Layer,” Int. J. Multiphase Flow, 34(8), pp. 786–807. [CrossRef]
Larrateguy, A. E. , Drew, D. A. , and Lahey, R. T., Jr ., 2002, “ A Particle Center-Averaged Two-Fluid Model for Wall-Bounded Bubbly Flows,” ASME Paper No. FEDSM2002-31212.
Moraga, F. J. , Larreteguy, A. E. , Drew, D. A. , and Lahey, R. T., Jr. , 2006, “ A Center-Averaged Two-Fluid Model for Wall-Bounded Bubbly Flows,” Comput. Fluids, 35(4), pp. 429–461. [CrossRef]
Nakoryakov, V. E. , Kashinsky, O. N. , Kozmenko, B. K. , and Gorelik, R. S. , 1986, “ Study of Upward Bubbly Flow at Low Liquid Velocities,” Izv. Sib. Otdel. Akad. Nauk SSSR, 16, pp. 15–20.
Serizawa, A. , Kataoka, I. , and Michiyoshi, I. , 1986, “ Phase Distribution in Bubbly Flow, Data Set No. 24,” The Second International Workshop on Two-Phase Flow Fundamentals, Troy, NY.
Wang, S. K. , Lee, S. J. , Jones, O. C., Jr. , and Lahey, R. T., Jr. , 1987, “ 3-D Turbulence Structure and Phase Distribution Measurements in Bubbly Two-Phase Flows,” Int. J. Multiphase Flow, 13(3), pp. 327–343. [CrossRef]
Ishii, M. , 1975, Thermo-Fluid Dynamic Theory of Two-Phase Flow, Eyrolles, Paris, France.
Drew, D. A. , and Passman, S. L. , 1998, Theory of Multicomponent Fluids, Springer-Verlag, New York.
Ishii, M. , and Zuber, N. , 1979, “ Drag Coefficient and Relative Velocity in Bubbly, Droplet or Particulate Flows,” AIChE, 25(5), pp. 843–855. [CrossRef]
Auton, T. R. , 1987, “ The Lift Force on a Spherical Body in a Rotational Flow,” J. Fluid Mech., 183, pp. 199–218. [CrossRef]
Prabhudharwadkar, D. M. , Bailey, C. A. , Lopez de Bertodano, M. A. , and Buchanan, J. R., Jr. , 2009, “ Two-Fluid CFD Model of Adiabatic Air-Water Upward Bubbly Flow Through a Vertical Pipe With a One-Group Interfacial Area Transport Equation,” ASME Paper No. FEDSM2009-78306.
Frank, T. H. , Zwart, P. J. , Krepper, E. , Prasser, H.-M. , and Lucas, D. , 2008, “ Validation of CFD Models for Mono- and Poludisperse Air-Water Two-Phase Flows in Pipes,” Nucl. Eng. Des., 238(3), pp. 647–659. [CrossRef]
Lopez de Bertodano, M. , 1992, “ Turbulent Bubbly Two-Phase Flow in a Triangular Duct,” Ph.D. dissertation, Rensselaer Polytechnic Institute, Troy, NY.
Sato, Y. , Sadatomi, M. , and Sekoguchi, K. , 1981, “ Momentum and Heat Transfer in Two-Phase Bubble Flow,” Int. J. Multiphase Flow, 7(2), pp. 167–177. [CrossRef]
Prandtl, L. , 1925, “ A Report on Testing for Built-Up Turbulence,” ZAMM J. Appl. Math. Mech., 5, pp. 136–139.
Tennekes, H. , 1965, “ Similarity Laws for Turbulent Boundary Layers With Suction or Injection,” J. Fluid Mech., 21(04), pp. 689–703. [CrossRef]
Lopez de Bertodano, M. , Lahey, R. T., Jr. , and Jones, O. C. , 1994, “ Phase Distribution in Bubbly Two-Phase Flow in Vertical Ducts,” Int. J. Multiphase Flow, 20(5), pp. 805–818. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Convergence of (a) α2 and (b) u1 distributions with standard TFM—Nakoryakov et al. [24]

Grahic Jump Location
Fig. 2

Computational domain and boundary conditions—Marie et al. [2]

Grahic Jump Location
Fig. 3

Prediction of (a) α2 and (b) u1 with standard TFM—Marie et al. [2]

Grahic Jump Location
Fig. 4

Computational domain and boundary conditions—Serizawa et al. [25]

Grahic Jump Location
Fig. 5

Prediction of (a) α2 and (b) u1 with standard TFM—Serizawa et al. [25]

Grahic Jump Location
Fig. 6

(a) Double-step function approximation and (b) velocity profiles with modified scaling for different peak void fractions—Marie et al. [2]

Grahic Jump Location
Fig. 7

(a) Geometry of a spherical bubble in the near-wall region and (b) void fraction approximation for near-wall averaging using data—Marie et al. [2]

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Fig. 8

Comparison of averaged and reconstructed void fraction profiles—Nakoryakov et al. [24]

Grahic Jump Location
Fig. 9

(a) Convergence of void fraction and (b) liquid velocity profiles with new near-wall averaged TFM—Nakoryakov et al. [24]

Grahic Jump Location
Fig. 10

(a) Convergence of void fraction and (b) liquid velocity profiles with new near-wall averaged TFM—Marie et al. [2]

Grahic Jump Location
Fig. 11

(a) Dimensionless velocity profile using standard scaling and (b) modified scaling with new near-wall averaged TFM—Marie et al. [2]

Grahic Jump Location
Fig. 12

(a) Convergence of void fraction and (b) liquid velocity distributions for jg = 0.077 m/s and jf = 1.36 m/s with new near-wall averaged TFM—Serizawa et al. [25]

Grahic Jump Location
Fig. 13

(a) Convergence of void fraction liquid velocity and (b) distributions for jg = 0.086 m/s and jf = 1.72 m/s with new near-wall averaged TFM—Serizawa et al. [25]

Grahic Jump Location
Fig. 14

(a) Computational domain and boundary conditions and (b) comparison of α2 distributions for jg = 0.1 m/s and jf = 0.94 m/s—Wang et al. [26]

Grahic Jump Location
Fig. 15

(a) Convergence of α2 and (b) u1 distributions for jg = 0.1 m/s and jf = 0.94 m/s—Wang et al. [26]

Grahic Jump Location
Fig. 16

(a) Convergence of α2 and (b) u1 distributions for jg = 0.1 m/s and jf = 0.71 m/s—Wang et al. [26]

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