Turbulence Aspects of Mass Transfer in the Thin Interfacial Region of the Concentration Boundary Layer in Gas–Liquid Systems

Turbulence Aspects of Mass Transfer in the Thin Interfacial Region of the Concentration Boundary Layer in Gas–Liquid Systems

Harry Edmar Schulz | Francisco Antonio Loyola Lavin | Bruno Batista Gonçalves 

School of Engineering at São Carlos, University of São Paulo, Brazil

Faculty of Engineering, University of Magallanes, Chile

University Centre of Patos de Minas, Brazil

Page: 
186-197
|
DOI: 
https://doi.org/10.2495/CMEM-V6-N1-186-197
Received: 
N/A
| |
Accepted: 
N/A
| | Citation

OPEN ACCESS

Abstract: 

The quantification of overall mass transfers in gas–liquid systems depends on the spatial evolution of the relevant variables close to the interface of the two phases. When turbulence is present (in the present study the turbulence is considered in the liquid phase), the methods of treating the problem consider the differential form of the momentum and mass conservation equations. The continuous hypothesis that underlies these equations in principle allows verifying the limiting trends very close to the interface. Because the theoretical concepts of turbulence are defined using statistical tools, the mentioned verification depends on the intrinsic definitions used in the statistical approach. In this study the turbulent mass transfer parameters are calculated for the thin region close to the interface based on the tool of random square waves (RSW). Theoretical results are obtained and analyzed in the context of existing experimental data and conceptual discussions of the literature, using a constant ‘reduction function’, a parameter defined in this methodology. The results of the present analysis show that the RSW method allows obtaining functional trends, as well as indicate the adequacy of using a variable reduction function to better represent reality.

Keywords: 

concentration fluctuations, gas-liquid interfaces, RSW, turbulence statistics

  References

[1] Brumley, B.H. & Jirka, G.H., Near-surface turbulence in a grid-stirred tank. Journal of Fluid Mechanics, 183, pp. 236–263, 1987. https://doi.org/10.1017/s0022112087002623

[2] Hunt, J.C.R., Turbulent structure and turbulent diffusion near gas-liquid interfaces.

Proceedings of the Gas Transfer at Water Surfaces Conference, pp. 67–82, 1984.

[3] Janzen, J.G., Jirka, G.H. & Schulz, H.E., Details of air-water gas transfer: experiments with precision – in Portuguese. Proceedings of the 16th Brazilian Conference on Water Resources (XVI Simpósio Brasileiro de Recursos Hídricos), pp. 1–17, 2005.

[4] Janzen, J.G., Schulz, H.E. & Jirka, G.H., Details of air-water gas transfer – in Portuguese. Brazilian Journal of Water Resources, 11(4), pp. 153–161, 2006. https://doi.org/10.21168/rbrh.v11n4.p153-161

[5] Herlina, Gas transfer at the air-water interface in a turbulent flow environment. Dissertation Series of the Institute for Hydromechanics of the University of Karlsruhe, Monograph 2005/4, 2005.

[6] Janzen, J.G., Gas transfer near the air-water interface in oscillating-grid tanks and proprieties of isotropic turbulent flows – in Portuguese. Dissertation at the School of Engineering at São Carlos of the University of São Paulo, 2006.

[7] Janzen, J.G., Herlina, H., Jirka, G.H., Schulz, H.E. & Gulliver, J.S., Estimation of  mas transfer velocity based on measured turbulence parameters. American Institute of Chemical Engineers Journal, 56(8), pp. 2005–2017, 2010. https://doi.org/10.1002/aic.12123

[8] Janzen, J.G., Schulz, H.E. & Jirka, G.H., Turbulent gas flux measurements near the air-water interface in an oscillating-grid tank. Proceedings of the 2010 Gas Transfer at Water Surfaces Conference, pp. 65–77, 2011.

[9] Herzog, A.G., Imaging of water-sided gas-concentration fields at a wind-driven, wavy air-water interface. Dissertation at the Faculties for the Natural Sciences and for Mathematics Institute of the Ruperto-Carola University of Heidelberg, Heidelberg, Germany, 2010.

[10] Friedl, F., Investigating the transfer of oxygen at the wavy air-water interface under wind-induced turbulence. Dissertation at the Faculties for the Natural Sciences and   for Mathematics Institute of the Ruperto-Carola University of Heidelberg, Heidelberg, Germany, 2013.

[11] Krah, N., Visualization of air and water-sided concentration profiles in laboratory gas exchange experiments. Dissertation at the Faculties for the Natural Sciences and for Mathematics Institute of the Ruperto-Carola University of Heidelberg, Heidelberg,  Germany, 2014.

[12] Schulz, H.E., Lopes Jr., G.B., Simões, A.L.A. & Lobosco, R.J., One-dimensional turbulent transfer using random square waves – scalar/velocity and velocity/velocity interactions (Chapter 1). Schulz, H.E., Simões, A.L.A. & Lobosco, R.J., (eds), Hydrodynamics: Advanced Topics, InTech, Rijeka, pp. 3–34, 2011.

[13] Schulz, H.E., Simões, A.L.A. & Janzen, J.G., Statistical approximations in gas-liquid mass transfer. Proceedings of the 2010 Gas Transfer at Water Surfaces Conference, pp. 208–221, 2011.

[14] Schulz, H.E. & Janzen, J.G., Concentration fields near air-water interfaces during interfacial mass-transport: oxygen transport and random square wave analysis. Brazilian Journal of Chemical Engineering, 26(3), pp. 527–536, 2009. https://doi.org/10.1590/s0104-66322009000300008

[15] Gonçalves, B.B., Detailing the one-dimensional solution for the RSW method considering a constant reduction function applied to the turbulent interfacial scalar transport – text in Portuguese. Dissertation at the School of Engineering at São Carlos of the University of São Paulo, 2014.

[16] Schulz, H.E. & Gonçalves, B.B., Solutions of scalar mean profiles close to gas-liquid interfaces under turbulent free slip motion. Proceedings of the Eight Conference on Computational Methods in Multiphase Flow, pp. 33–44, 2015, available at: https:// www.researchgate.net/publication/312171886_Errata_to_-_Solutions_of_scalar_ mean_profiles_close_to_gas-liquid_interfaces_under_turbulent_free_slip_motion_-

[17] Gonçalves, B.B. & Schulz, H.E., One-dimensional turbulent mass transfer at air-water interfaces: details of discontinuities of derivatives using the RSW method. Proceedings of the Seventh Conference on Computational Methods in Multiphase Flow, pp. 365– 376, 2013.

[18] Falkenroth, A., Visualization of oxygen concentration profiles in the aqueous boundary layer. Dissertation at the Faculties for the Natural Sciences and for Mathematics Institute of the Ruperto-Carola University of Heidelberg, Heidelberg, Germany, 2007.

[19] Atmane, M.A. & George, J., Gas transfer cross a zero-shear surface: a local approach. Proceedings of the Gas Transfer at Water Surfaces Conference, Geophysical Monograph 127, pp. 255–259, 2002.

[20] Chu, C.R. & Jirka, G.H., Turbulent gas flux measurements below the air-water interface of a grid-stirred tank. International Journal of Heat and Mass Transfer, 35(8), pp. 1957–1968, 1992. https://doi.org/10.1016/0017-9310(92)90198-2