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Direct numerical simulation of turbulent heat transfer across a sheared wind-driven gas–liquid interface

  • Ryoichi Kurose (a1), Naohisa Takagaki (a1), Atsushi Kimura (a1) and Satoru Komori (a1)

Turbulent heat transfer across a sheared wind-driven gas–liquid interface is investigated by means of a direct numerical simulation of gas–liquid two-phase turbulent flows under non-breaking wave conditions. The wind-driven wavy gas–liquid interface is captured using the arbitrary Lagrangian–Eulerian method with boundary-fitted coordinates on moving grids, and the temperature fields on both the gas and liquid sides, and the humidity field on the gas side are solved. The results show that although the distributions of the total, latent, sensible and radiative heat fluxes at the gas–liquid interface exhibit streak features such that low-heat-flux regions correspond to both low-streamwise-velocity regions on the gas side and high-streamwise-velocity regions on the liquid side, the similarity between the heat-flux streak and velocity streak on the gas side is more significant than that on the liquid side. This means that, under the condition of a fully developed wind-driven turbulent field on both the gas and liquid sides, the heat transfer across the sheared wind-driven gas–liquid interface is strongly affected by the turbulent eddies on the gas side, rather than by the turbulent eddies and Langmuir circulations on the liquid side. This trend is quite different from that of the mass transfer (i.e. $\text{CO}_{2}$ gas). This is because the resistance to heat transfer is normally lower than the resistance to mass transfer on the liquid side, and therefore the heat transfer is controlled by the turbulent eddies on the gas side. It is also verified that the predicted total heat, latent heat, sensible heat and enthalpy transfer coefficients agree well with previously measured values in both laboratory and field experiments. To estimate the heat transfer coefficients on both the gas and liquid sides, the surface divergence could be a useful parameter, even when Langmuir circulations exist.

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Assaf, G., Gerard, R. & Gordon, A. L. 1971 Some mechanisms of oceanic mixing revealed in aerial photographs. J. Geophys. Res. 76, 65506572.
Banerjee, S., Lakehal, D. & Fulgosi, M. 2004 Surface divergence models for scalar exchange between turbulent streams. Intl J. Multiphase Flow 30, 963977.
Bird, R. B., Stewart, W. E. & Lightfoot, E. N. 1960 Transport Phenomena. Wiley.
Craik, A. D. D. & Leibovich, R. 1976 A rational model for Langmuir circulations. J. Fluid Mech. 73, 401426.
DeCosmo, J., Katsaros, K. B., Smith, S. D., Anderson, R. J., Oost, W. A., Bumke, K. & Chadwick, H. 1996 Air–sea exchange of water vapor and sensible heat: the humidity exchange over the sea (HEXOS) results. J. Geophys. Res. Oceans 101 (C5), 1200112016.
Donelan, M. A. 1990 Air–sea interaction. In The Sea, Ocean Engineering Science (ed. LeMehaute, B. & Hanes, D. M.), vol. 9, pp. 239292. Wiley.
Drennan, W. M., Zhang, J. A., French, J. R., Mccormick, C. & Black, P. G. 2007 Turbulent fluxes in the hurricane boundary layer. Part II: Latent heat fluxes. J. Atmos. Sci. 64, 11031115.
Emanuel, K. A. 1986 An air–sea interaction theory for tropical cyclones. Part I: Steady-state maintenance. J. Atmos. Sci. 43, 585604.
Francey, R. J. & Garratt, J. R. 1978 Eddy flux measurements over the ocean and related transfer coefficients. Boundary-Layer Meteorol. 14, 153166.
Friehe, C. A. & Schmitt, K. F. 1976 Parameterization of air–sea interface fluxes of sensible heat and moisture by the bulk aerodynamic formulas. J. Phys. Oceanogr. 6, 801809.
Fulgosi, M., Lakehal, D., Banerjee, S. & De Angelis, V. 2003 Direct numerical simulation of turbulence in a sheared air–water flow with a deformable interface. J. Fluid Mech. 482, 319345.
Garratt, J. R. & Hyson, P. 1975 Vertical fluxes of momentum, sensible heat and water vapour during the air mass transformation experiment (AMTEX) 1974. J. Met. Soc. Japan 53, 149160.
Guo, X. & Shen, L. 2014 Numerical study of the effect of surface wave on turbulence underneath. Part 2. Eulerian and Lagrangian properties of turbulence kinetic energy. J. Fluid Mech. 744, 250272.
Harlow, F. H. & Welch, J. E. 1965 Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8, 21822189.
Hasse, L., Grunewald, M., Wucknitz, J., Dunckel, M. & Schriever, D. 1978 Profile derived turbulent fluxes in the surface layer under disturbed and undisturbed conditions during GATE. Meteor-Forschungsergebnisse B 13, 2440.
Huang, N. E. 1979 On surface drift currents in the ocean. J. Fluid Mech. 91 (1), 191208.
Ichiye, T. 1967 Upper ocean boundary-layer flow determined by dye diffusion. Phys. Fluids Suppl. 10, S270S277.
Iwano, K.2014 Study on momentum, heat and mass transfer across the wind-sheared air–water interface at extremely high wind speeds. PhD thesis, Kyoto University (in Japanese).
Jahne, B. & Haußecker, H. 1998 Air–water gas exchange. Annu. Rev. Fluid Mech. 30, 443468.
Johnson, H. K., Hojstrup, J., Vested, H. J. & Larsen, S. E. 1998 On the dependence of sea surface roughness on wind waves. J. Phys. Oceanogr. 28, 17021716.
Jones, I. S. F. & Toba, Y.(Eds) 2001 Wind Stress over The Ocean. p. 307. Cambridge University Press.
Kermani, A., Khakpour, H. R., Shen, L. & Igusa, T. 2011 Statics of surface renewal of passive scalar in free-surface turbulence. J. Fluid Mech. 678, 379416.
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741773.
Komori, S., Kurose, R., Iwano, K., Ukai, T. & Suzuki, N. 2010 Direct numerical simulation of wind-driven turbulence and scalar transfer at sheared gas–liquid interfaces. J. Turbul. 11, 120.
Komori, S., Kurose, R., Takagaki, N., Ohtsubo, S., Iwano, K., Handa, K. & Shimada, S. 2011 Sensible and latent heat transfer across the air–water interface wind-driven turbulence. In Gas Transfer at Water Surfaces 2010 (ed. Komori, S., McGillis, W. & Kurose, K.), pp. 7889. Kyoto University Press.
Komori, S., Nagaosa, R. & Murakami, Y. 1993b Turbulence structure and mass transfer across a sheared air–water interface in wind-driven turbulence. J. Fluid Mech. 249, 161183.
Komori, S., Nagaosa, R., Murakami, Y., Chiba, S., Ishii, K. & Kuwahara, K. 1993a Direct numerical simulation of three-dimensional open-channel flow with zero-shear gas–liquid interface. Phys. Fluids A5, 115125.
Kunugi, T. 1997 Direct numerical algorithm for multiphase flow with free surfaces and interfaces. Trans. JSME B 63 (609), 15761584.
Lakehal, D., Fulgosi, M. & Yadigaroglu, G. 2008a Turbulence and heat exchange in condensing vapor–liquid flow. Phys. Fluids 20, 065101.
Lakehal, D., Fulgosi, M. & Yadigaroglu, G. 2008b Direct numerical simulation of condensing stratified flow. Trans. ASME J. Heat Transfer 130, 021501.
Lakehal, D., Fulgosi, M., Yadigaroglu, G. & Banerjee, S. 2003 Direct numerical simulation of turbulent heat transfer across a mobile, sheared gas–liquid interface. Trans. ASME J. Heat Transfer 125, 11291139.
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Langmuir, I. 1938 Surface motion of water induced by wind. Science 87, 119123.
Large, G. W. & Pond, S. 1982 Sensible and latent heat flux measurements over the ocean. J. Phys. Oceanogr. 12, 464481.
Leibovich, S. 1983 The form and dynamics of Langmuir circulations. Annu. Rev. Fluid Mech. 15, 391427.
Leibovich, S. & Paolucci, S. 1981 The instability of the ocean to Langmuir circulations. J. Fluid Mech. 102, 141167.
Lewis, W. K. & Whitman, W. G. 1924 Principles of gas absorption. Ind. Engng Chem. 16, 12151220.
Lin, M.-Y., Moeng, C.-H., Tsai, W.-T., Sullivan, P. P. & Belcher, S. E. 2008 Direct numerical simulation of wind-wave generation processes. J. Fluid Mech. 616, 130.
McCready, M. J., Vassilliadou, E. & Hanratty, T. J. 1986 Computer simulation of turbulent mass transfer at a mobile interface. AIChE J. 32, 11081115.
Melville, W. K., Shear, R. & Veron, F. 1998 Laboratory measurements of the generation and evolution of Langmuir circulations. J. Fluid Mech. 364, 3158.
Mitsuyasu, H. & Nakayama, R. 1969 Measurements of waves and wind at Hakata Bay. Rep. Res. Inst. Appl. Mech. 33, 3366.
Munz, C. & Roberts, P. V. 1984 The ratio of gas phase to liquid phase mass transfer coefficients in gas–liquid contacting processes. In Gas Transfer at Water Surfaces (ed. Brutsaert, W. & Jirka, G. H.), pp. 3546. Reidal.
Ocampo-Torres, F. J., Donelan, M. A., Merzi, N. & Jia, A. 1994 Laboratory measurements of mass transfer of carbon dioxide and water vapour for smooth and rough flow conditions. Tellus 46B, 1632.
Pedreros, R., Dardier, G., Dupuis, H., Graber, H. C., Drennan, W. M., Weill, A. & Nacass, P. 2003 Momentum and heat fluxes via the eddy correlation method on the R/V L’Atalante and an ASIS buoy. J. Geophys. Res. Oceans 108 (C11), 3339.
Richter, D. H. & Stern, D. P. 2014 Evidence of spray-mediated air–sea enthalpy flux within tropical cyclones. Geophys. Res. Lett. 41, 29973003.
Schnieders, J., Garbe, S., Peirson, W. L., Smith, G. B. & Zappa, C. J. 2013 Analyzing the footprints of near surface aqueous turbulence: an image processing-based approach. J. Geophys. Res. Oceans 118, 12721286.
Smith, C. R. & Metzler, S. P. 1983 The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer. J. Fluid Mech. 129, 2754.
Sullivan, P. P., McWilliams, J. C. & Moeng, C.-H. 2000 Simulation of turbulent flow over idealized water waves. J. Fluid Mech. 404, 4785.
Takagaki, N.2009 Effects of rainfall on mass transfer across the air–water interface. PhD thesis, Kyoto University (in Japanese).
Takagaki, N., Komori, S. & Suzuki, N. 2016 Estimation of friction velocity from the wind-wave spectrum at extremely high wind speeds. IOP Conf. Series: Earth and Environmental Science 35 (1), 012009.
Takagaki, N., Komori, S., Suzuki, N., Iwano, K., Kuramoto, T., Shimada, S., Kurose, R. & Takahashi, K. 2012 Strong correlation between the drag coefficient and the shape of the wind sea spectrum over a broad range of wind. Geophys. Res. Lett. 39, L23604.
Takagaki, N., Kurose, R., Tsujimoto, Y., Komori, S. & Takahashi, K. 2015 Effects of turbulent eddies and Langmuir circulations on scalar transfer in a sheared wind-driven liquid flow. Phys. Fluids 27, 016603.
Tetens, O. 1930 Über einige meteorologiche Begriffe. Z. Geophys. 6, 297309.
Thorpe, S. A. 2004 Langmuir circulation. Annu. Rev. Fluid Mech. 36, 5579.
Toba, Y. 1972 Local balance in the air–sea boundary processes. Part I: On the growth processes of wind waves. J. Oceanogr. 28, 109121.
Tsai, W. T., Chen, S. M., Lu, G. H. & Garbe, C. S. 2013 Characteristics of interfacial signatures on a wind-driven gravity–capillary wave. J. Geophys. Res. Oceans 118, 17151735.
Turney, D. E. & Banerjee, S. 2013 Air–water gas transfer and near-surface motions. J. Fluid Mech. 733, 588624.
Yamamoto, Y., Kunugi, T., Satake, S. & Serizawa, A. 2004 Turbulent structures and heat transfer across the air–liquid interface in the wind-driven turbulent flow. Trans. JSME B 70 (692), 10061012.
Zappa, C. J., Asher, W. E. & Jessup, A. T. 2004 Microbreaking and the enhancement of air–water transfer velocity. J. Geophys. Res. 109, C08S16.
Zhang, J. A, Black, P. G., French, J. R. & Drennan, W. M. 2008 First direct measurements of enthalpy flux in the hurricane boundary layer: the CBLAST results. Geophys. Res. Lett. 35, L14813.
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