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Influence of slip velocity in a two-phase bubbly jet

Published online by Cambridge University Press:  25 January 2022

Hyunduk Seo Open the ORCID record for Hyunduk Seo [Opens in a new window] ,
Goran Marjanovic ,
S. Balachandar Open the ORCID record for S. Balachandar [Opens in a new window]  and
Kyung Chun Kim Open the ORCID record for Kyung Chun Kim [Opens in a new window]
Hyunduk Seo
Affiliation:
School of Mechanical Engineering, Pusan National University, Busan 46241, Republic of Korea
Goran Marjanovic
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA
S. Balachandar
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA
Kyung Chun Kim*
Affiliation:
School of Mechanical Engineering, Pusan National University, Busan 46241, Republic of Korea
*
†Email address for correspondence: kckim@pusan.ac.kr
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Abstract

The effect of the slip velocity in a bubbly jet ($Re = 3000$, initial void $\textrm {fraction} = 1.1\,\%$) is studied with various bubble slip ratios (0.07–2.1 times the inlet velocity, 0.01–0.31 m s$^{-1}$ in dimension). The governing equations, which are the conservation of mass, momentum and volume fraction, are solved by direct numerical simulations. A set of ordinary differential equations was derived by using a conventional one-dimensional integral framework on jets and by expressing the slip velocity using an exponential function. The one-dimensional analysis of bubbly jets successfully predicted the jet velocity radius, centreline velocity and the gas spread rate downstream of the bubbly jet. Second- and third-order statistics were also analysed to better understand the turbulent characteristics of the bubbly jet. A high slip ratio results in a rigid, narrower bubbly jet core region, where the turbulent kinetic energy is conserved along the centreline but does not diffuse towards the ambient region. The narrow, circular region around the core at high slip ratios decreased the turbulent kinetic energy. In the rigid bubbly jet core, turbulent diffusion of the gas phase is suppressed and has low correlations with the velocity fluctuations. Turbulence characteristics such as turbulence stress were compared with single-phase jet and plume results from existing literature. The magnitude of the turbulence characteristics at the lowest slip ratio is comparable with what is found in the literature, but there is a rapid transition from slip ratios of $0.14$ to $0.7$. Furthermore, the turbulent kinetic energy budget was analysed for each case. The production term had the largest contribution, and its magnitude was almost five times the buoyancy production downstream. High slip ratio cases show a positive peak of pressure strain and turbulent diffusion along the centreline.

JFM classification

Multiphase and Particle-laden Flows: Gas/liquid flow Wakes/Jets: Buoyant jets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 935 , 25 March 2022 , A4
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Akiki, G., Moore, W.C. & Balachandar, S. 2017 Pairwise-interaction extended point-particle model for particle-laden flows. J. Comput. Phys. 351, 329–357.CrossRefGoogle Scholar
Alméras, E., Plais, C., Euzenat, F., Risso, F., Roig, V. & Augier, F. 2016 Scalar mixing in bubbly flows: experimental investigation and diffusivity modelling. Chem. Engng Sci. 140, 114–122.CrossRefGoogle Scholar
Asaeda, T. & Imberger, J. 1993 Structure of bubble plumes in linearly stratified environments. J. Fluid Mech. 249, 35–57.CrossRefGoogle Scholar
Becker, H.A. & Massaro, T.A. 1968 Vortex evolution in a round jet. J. Fluid Mech. 31 (3), 435–448.CrossRefGoogle Scholar
Boersma, B.J., Brethouwer, G. & Nieuwstadt, F.T.M. 1998 A numerical investigation on the effect of the inflow conditions on the self-similar region of a round jet. Phys. Fluids 10 (4), 899–909.CrossRefGoogle Scholar
Bryant, D.B., Seol, D.G. & Socolofsky, S.A. 2009 Quantification of turbulence properties in bubble plumes using vortex identification methods. Phys. Fluids 21 (7), 075101.CrossRefGoogle Scholar
Buscaglia, G.C., Bombardelli, F.A. & García, M.H. 2003 Numerical modeling of large-scale bubble plumes accounting for mass transfer effects. Intl J. Multiphase Flow 28 (11), 1763–1785.CrossRefGoogle Scholar
Chen, C.J. & Nikitopoulos, C.P. 1979 On the near field characteristics of axisymmetric turbulent buoyant jets in a uniform environment. Intl J. Heat Mass Transfer 22 (2), 245–255.CrossRefGoogle Scholar
Combest, D.P., Ramachandran, P.A. & Dudukovic, M.P. 2011 On the gradient diffusion hypothesis and passive scalar transport in turbulent flows. Ind. Engng Chem. Res. 50 (15), 8817–8823.CrossRefGoogle Scholar
Darisse, A., Lemay, J. & Benaïssa, A. 2015 Budgets of turbulent kinetic energy, Reynolds stresses, variance of temperature fluctuations and turbulent heat fluxes in a round jet. J. Fluid Mech. 774, 95–142.CrossRefGoogle Scholar
Ditmars, J.D. & Cederwall, K. 1974 Analysis of air-bubble plumes. In Proceedings of the 14th Conference on Coastal Engineering, Copenhagen, Denmark, pp. 2209–2226. ASCE.CrossRefGoogle Scholar
Du Cluzeau, A., Bois, G. & Toutant, A. 2019 Analysis and modelling of Reynolds stresses in turbulent bubbly up-flows from direct numerical simulations. J. Fluid Mech. 866, 132–168.CrossRefGoogle Scholar
El Khoury, G.K., Schlatter, P., Noorani, A., Fischer, P.F., Brethouwer, G. & Johansson, A.V. 2013 Direct numerical simulation of turbulent pipe flow at moderately high Reynolds numbers. Flow Turbul. Combust. 91 (3), 475–495.CrossRefGoogle Scholar
Evans, J.T. 1955 Pneumatic and similar breakwaters. Proc. R. Soc. Lond. A 231 (1187), 457–466.Google Scholar
Fabregat, A., Dewar, W.K., Ozgokmen, T.M., Poje, A.C. & Wienders, N. 2015 Numerical simulations of turbulent thermal, bubble and hybrid plumes. Ocean Model. 90, 16–28.CrossRefGoogle Scholar
Fabregat, A., Poje, A.C., Özgökmen, T.M. & Dewar, W.K. 2016 Dynamics of multiphase turbulent plumes with hybrid buoyancy sources in stratified environments. Phys. Fluids 28 (9), 095109.CrossRefGoogle Scholar
Ferdman, E., Ötügen, M.V. & Kim, S. 2000 Effect of initial velocity profile on the development of round jets. J. Propul. Power 16 (4), 676–686.CrossRefGoogle Scholar
Fiscehr, H.B., List, E.J., Koh, R.C.Y., Imberger, J. & Brooks, N.H. 1979 Chapter 9. Turbulent jets and plumes. In Mixing in Inland and Coastal Waters (ed. H.B. Fischer, E. John List, R.C.Y. Koh, J. Imberger & N.H. Brooks), pp. 315–389. Academic Press.CrossRefGoogle Scholar
Fischer, P.F., Lottes, J.W. & Kerkemeier, S.G. 2008 NEK5000 solver. http://nek5000.mcs.anl.gov.Google Scholar
Fraga, B. & Stoesser, T. 2016 Influence of bubble size, diffuser width, and flow rate on the integral behavior of bubble plumes. J. Geophys. Res. 121, 3887–3904.CrossRefGoogle Scholar
George, W.K. 1989 The self-preservation of turbulent flows an its relation to initial conditions and coherent structures. In Advances in Turbulence, pp. 39–73. CRC Press.Google Scholar
Henderson-Sellers, B. 1983 The zone of flow establishment for plumes with significant buoyancy. Appl. Math. Model. 7 (6), 395–398.CrossRefGoogle Scholar
Ince, S. 1964 A guide to the design of air bubblers for melting ice. In Proceedings of the 9th Conference on Coastal Engineering, Lisbon, pp. 600–610. ASCE.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Jobehdar, M.H., Siddiqui, K., Gadallah, A.H. & Chishty, W.A. 2016 Bubble formation process from a novel nozzle design in liquid cross-flow. Intl J. Heat Fluid Flow 61, 599–609.CrossRefGoogle Scholar
Kobus, H. 1968 Analysis of the flow induced by air-bubble systems. Proceedings of the 11th Conference on Coastal Engineering, London, pp. 1016–1031. ASCE.CrossRefGoogle Scholar
Lai, C.C.K. & Socolofsky, S.A. 2019 The turbulent kinetic energy budget in a bubble plume. J. Fluid Mech. 865, 993–1041.CrossRefGoogle Scholar
Lima Neto, I.E. 2015 Self-similarity of vertical bubbly jets. Braz. J. Chem. Engng 32 (2), 475–487.CrossRefGoogle Scholar
Lima Neto, I.E., Zhu, D.Z. & Rajaratnam, N. 2008 Bubbly jets in stagnant water. Intl J. Multiphase Flow 34 (12), 1130–1141.CrossRefGoogle Scholar
List, E.J. 1982 Turbulent jets and plumes. Annu. Rev. Fluid Mech. 14 (1), 189–212.CrossRefGoogle Scholar
Mcdougall, T.J. 1978 Bubble plumes in stratified environments. J. Fluid Mech. 85 (Apr), 655–672.CrossRefGoogle Scholar
Milgram, J.H. 1983 Mean flow in round bubble plumes. J. Fluid Mech. 133, 345–376.CrossRefGoogle Scholar
Morton, B.R., Taylor, G. & Turner, J.S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234 (1196), 1–23.Google Scholar
Nguyen, V.T., Bae, B.U., Euh, D.J., Song, C.H. & Yun, B.J. 2012 The effect of bubble-induced turbulence on the interfacial area transport in gas-liquid two-phase flow. J. Comput. Multiphase Flows 4 (3), 327–340.CrossRefGoogle Scholar
Panchapakesan, N.R. & Lumley, J.L. 1993 Turbulence measurements in axisymmetric jets of air and helium. Part 2. Helium Jet. J. Fluid Mech. 246, 225–247.CrossRefGoogle Scholar
Papanicolaou, P.N. & List, E.J. 1988 Investigations of round vertical turbulent buoyant jets. J. Fluid Mech. 195, 341–391.CrossRefGoogle Scholar
Priestley, C.H.B. & Ball, F.K. 1955 Continuous convection from an isolated source of heat. Q. J. R. Meteorol. Soc. 81 (348), 144–157.CrossRefGoogle Scholar
Reddy, R.K., Sathe, M.J., Joshi, J.B., Nandakumar, K. & Evans, G.M. 2013 Recent developments in experimental (PIV) and numerical (DNS) investigation of solid-liquid fluidized beds. Chem. Engng Sci. 92, 1–12.CrossRefGoogle Scholar
Reichardt, T., Tryggvason, G. & Sommerfeld, M. 2017 Effect of velocity fluctuations on the rise of buoyant bubbles. Comput. Fluids 150, 8–30.CrossRefGoogle Scholar
Rodi, W. 1975 A new method of analysing hot-wire signals in highly turbulent flow, and its evaluation in a round jet. DISA Inf. 17, 9–18.Google Scholar
Salehipour, H., Peltier, W.R. & Mashayek, A. 2015 Turbulent diapycnal mixing in stratified shear flows: the influence of Prandtl number on mixing efficiency and transition at High Reynolds number. J. Fluid Mech. 773, 178–223.CrossRefGoogle Scholar
Santarelli, C., Roussel, J. & Fröhlich, J. 2016 Budget analysis of the turbulent kinetic energy for bubbly flow in a vertical channel. Chem. Engng Sci. 141, 46–62.CrossRefGoogle Scholar
Sarikurt, F.S. & Hassan, Y.A. 2017 Large eddy simulations of erosion of a stratified layer by a buoyant jet. Intl J. Heat Mass Transfer 112, 354–365.CrossRefGoogle Scholar
Schmidt, W. 1941 Turbulent propagation of a stream of heated air. Z. Angew. Math. Mech. 21, 265–278.CrossRefGoogle Scholar
Seo, H. & Kim, K.C. 2021 Experimental study on flow and turbulence characteristics of bubbly jet with low void fraction. Intl J. Multiphase Flow 142, 103738.CrossRefGoogle Scholar
Seol, D.-G., Bhaumik, T., Bergmann, C. & Socolofsky, S.A. 2007 Particle image velocimetry measurements of the mean flow characteristics in a bubble plume. J. Engng Mech. 133 (6), 665–676.Google Scholar
Shabbir, A. & George, W.K. 1994 Experiments on a round turbulent buoyant plume. J. Fluid Mech. 275, 1–32.CrossRefGoogle Scholar
Shah, Y.T., Kelkar, B.G., Godbole, S.P. & Deckwer, W.-D. 1982 Design parameters estimations for bubble column reactors. AIChE J. 28 (3), 353–379.CrossRefGoogle Scholar
Simiano, M. & Lakehal, D. 2012 Turbulent exchange mechanisms in bubble plumes. Intl J. Multiphase Flow 47, 141–149.CrossRefGoogle Scholar
Socolofsky, S.A. & Adams, E.E. 2005 Role of slip velocity in the behavior of stratified multiphase plumes. J. Hydraul. Engng 131 (4), 273–282.CrossRefGoogle Scholar
Sokolichin, A., Eigenberger, G. & Lapin, A. 2004 Simulation of buoyancy driven bubbly flow: established simplifications and open questions. AIChE J. 50 (1), 24–45.CrossRefGoogle Scholar
Sun, T.Y. & Faeth, G.M. 1986 Structure of turbulent bubbly jets – II. Phase property profiles. Intl J. Multiphase Flow 12 (1), 115–126.CrossRefGoogle Scholar
Tammisola, O. & Juniper, M.P. 2016 Coherent structures in a swirl injector at $Re= 4800$ by nonlinear simulations and linear global modes. J. Fluid Mech. 792, 620–657.CrossRefGoogle Scholar
Taub, G.N., Lee, H., Balachandar, S. & Sherif, S.A. 2013 A direct numerical simulation study of higher order statistics in a turbulent round jet. Phys. Fluids 25 (11).CrossRefGoogle Scholar
Taub, G.N., Lee, H., Balachandar, S. & Sherif, S.A. 2015 An examination of the high-order statistics of developing jets, lazy and forced plumes at various axial distances from their source. J. Turbul. 16 (10), 950–978.CrossRefGoogle Scholar
Taylor, G.I. 1955 The action of a surface current used as a breakwater. Proc. R. Soc. Lond. A 231 (1187), 466–478.Google Scholar
Terasaka, K., Hirabayashi, A., Nishino, T., Fujioka, S. & Kobayashi, D. 2011 Development of microbubble aerator for waste water treatment using aerobic activated sludge. Chem. Engng Sci. 66 (14), 3172–3179.CrossRefGoogle Scholar
Tominaga, Y. & Stathopoulos, T. 2007 Turbulent Schmidt numbers for CFD analysis with various types of flowfield. Atmos. Environ. 41 (37), 8091–8099.CrossRefGoogle Scholar
Wang, B., Lai, C.C.K. & Socolofsky, S.A. 2019 Mean velocity, spreading and entrainment characteristics of weak bubble plumes in unstratified and stationary water. J. Fluid Mech. 874, 102–130.CrossRefGoogle Scholar
Wang, H.W. & Law, A.W.K. 2002 Second-order integral model for a round turbulent buoyant jet. J. Fluid Mech. 459, 397–428.CrossRefGoogle Scholar
Wu, F., Luo, K. & Fan, J. 2016 DNS of a turbulent flow past two fully resolved aligned spherical particles. Adv. Powder Technol. 27 (4), 1149–1161.CrossRefGoogle Scholar
Wüest, A., Brooks, N.H. & Imboden, D.M. 1992 Bubble plume modeling for lake restoration. Water Resour. Res. 28 (12), 3235–3250.CrossRefGoogle Scholar
Wygnanski, I. & Fiedler, H. 1969 Some measurements in the self-preserving jet. J. Fluid Mech. 38 (3), 577–612.CrossRefGoogle Scholar
Yang, D., Chen, B.C., Socolofsky, S.A., Chamecki, M. & Meneveau, C. 2016 Large-eddy simulation and parameterization of buoyant plume dynamics in stratified flow. J. Fluid Mech. 794, 798–833.CrossRefGoogle Scholar
Zhang, J.P., Grace, J.R., Epstein, N. & Lim, K.S. 1997 Flow regime identification in gas-liquid flow and three-phase fluidized beds. Chem. Engng Sci. 52 (21–22), 3979–3992.CrossRefGoogle Scholar