Investigation of Buoyant Parameters of k-ε Turbulence Model in Gravity Stratified Flows
Different variants for buoyancy-affected terms in k-ε turbulence model have been utilized to predict the flow parameters more accurately, and investigate applicability of alternative k-ε turbulence buoyant closures in numerical simulation of a horizontal gravity current. The additional non-isotropic turbulent stress due to buoyancy has been considered in production term, based on Algebraic Stress Model (ASM). In order to account for turbulent scalar fluxes, general gradient diffusion hypothesis has been used along with Boussinesq gradient diffusion hypothesis with a variable turbulent Schmidt number and additional empirical constant c3ε.To simulate buoyant flow domain a 2D vertical numerical model (WISE, Width Integrated Stratified Environments), based on Reynolds- Averaged Navier-Stokes (RANS) equations, has been deployed and the model has been further developed for different k-ε turbulence closures. Results are compared against measured laboratory values of a saline gravity current to explore the efficient turbulence model.
[1] Simpson, J., "Gravity Currents in the Environment and the laboratory,"
Cambridge University Press, 1997.
[2] Wilcox, D. C., "Turbulence modeling for CFD, Third Edition,"
Birmingham Press, Inc., San Diego, California, 2006.
[3] Nicolette, V.F., Tieszen, S. R., Black, A. R., Domino, S. P., O-Hern, T.
J., "A Turbulence Model for Buoyant Flows Based on Vorticity
Generation," Sandia National Laboratory, Sandia Report, SAND2005-
6273, 2005.
[4] Mellor, G. L., Yamada, T., "Development of Turbulence Closure Model
for Geophysical Fluid Problems," Reviews of Geophysics and Space
Physics, J., vol.20, No.5, 1982, pp. 851-875.
[5] Yan Z., Holmstedt G., "A two-equation model and its application to a
buoyant diffusion flame," International Journal of Heat and Mass
Transfer, vol.42, 1999, pp. 1305-1315.
[6] Worthy, J., Sanderson, V., and Rubini, P., "A Comparison of Modified
k-╬Á Turbulence Models for Buoyant Plumes", Cranfield University
Library, Staff Publications, School of Engineering, 2001.
[7] Kun, Y., Yiping, H., Xueyi, Z., Yuliang, L., "Study on Anisotropic
Buoyant Turbulence Model," Applied Mathematic s and Mechanics J.,
vol.21, No.1, 2000, pp. 43-48.
[8] Rodi, W., "Examples of Calculation Methods for Flow and Mixing in
Stratified Fluids," Geophysical Research J., vol.92, No.C5, 1987, pp.
5305-5328.
[9] Davidson L., "Second-order Correction of the k-╬Á Model to Account for
Non-isotropic Effects due to Buoyancy," International Journal of Heat
and Mass Transfer, vol.33, 1990, pp. 2599-2608.
[10] Verdier-Bonnet, C., Angot, Ph., Fraunie, Ph., Coantic, M., "Three
Dimensional Modeling of Coastal Circulations with Different k-╬Á
Closures," Marine System J., vol.21, 1999, pp. 321-339.
[11] Annarumma, M.O., Most, J.M., Joulain, P., "On the Numerical
Modeling of Buoyant-dominated Turbulent Vertical Diffusion Flames,"
Combustion and Flame J., vol.85, 1991, pp. 403-415.
[12] Shabbir, A., Taulbee, D. B., "Evaluation of Turbulence Models for
Predicting Buoyant Flows," Heat Transfer J., vol. 112, 1990, pp. 945-
951.
[13] Daly B. J., Harlow F. H., Transport equations of turbulence, Journal of
Physics Fluids, Vol. 13, 1970, pp. 2634-649.
[14] Henkes, R.A.W.M., LeQuere, P., Three Dimensional Transition of
Natural-Convection Flows, Journal of Fluid Mechanics, vol.319, 1996,
pp. 281-303.
[15] Gerber, G. Experimental Measurement and Numerical Modeling of
Velocity, Density and Turbulence Profiles of a Gravity Current, PhD
Thesis, University of Stellenbosch, 2008.
[16] Rodi, W. "Turbulence Models and their
Applications in Hydraulics" A State of the Arts Review,
University of Karlsruhe, Germany, 1984.
[17] Nam, S., Bill, R.G., "Numerical Simulation of Thermal Plumes," Fire
Safety J., vol.21, 1993, pp. 231-256.
[18] Chorin, A.J., "Numerical Solution of the Navier-Stokes Equations,"
Mathematics of Computation J., vol.22, 1968, pp. 745-762.
[19] Temam, R., "Sur l΄Approximation de la Solution des Equation de
Navier-Stokes par la Méthode des pas Fractionnaires," Archive for
Rational Mechanics and Analysis, vol.32, 1969, pp. 135-153.
[20] Kneller, B. C., Bennet, S. J., McCaffrey, W. D., "Velocity Structure,
Turbulence and Fluid Stresses in Experimental Gravity Currents,"
Geophysical Research J., vol.104, No.C3, 1999, pp. 5381-5391.
[1] Simpson, J., "Gravity Currents in the Environment and the laboratory,"
Cambridge University Press, 1997.
[2] Wilcox, D. C., "Turbulence modeling for CFD, Third Edition,"
Birmingham Press, Inc., San Diego, California, 2006.
[3] Nicolette, V.F., Tieszen, S. R., Black, A. R., Domino, S. P., O-Hern, T.
J., "A Turbulence Model for Buoyant Flows Based on Vorticity
Generation," Sandia National Laboratory, Sandia Report, SAND2005-
6273, 2005.
[4] Mellor, G. L., Yamada, T., "Development of Turbulence Closure Model
for Geophysical Fluid Problems," Reviews of Geophysics and Space
Physics, J., vol.20, No.5, 1982, pp. 851-875.
[5] Yan Z., Holmstedt G., "A two-equation model and its application to a
buoyant diffusion flame," International Journal of Heat and Mass
Transfer, vol.42, 1999, pp. 1305-1315.
[6] Worthy, J., Sanderson, V., and Rubini, P., "A Comparison of Modified
k-╬Á Turbulence Models for Buoyant Plumes", Cranfield University
Library, Staff Publications, School of Engineering, 2001.
[7] Kun, Y., Yiping, H., Xueyi, Z., Yuliang, L., "Study on Anisotropic
Buoyant Turbulence Model," Applied Mathematic s and Mechanics J.,
vol.21, No.1, 2000, pp. 43-48.
[8] Rodi, W., "Examples of Calculation Methods for Flow and Mixing in
Stratified Fluids," Geophysical Research J., vol.92, No.C5, 1987, pp.
5305-5328.
[9] Davidson L., "Second-order Correction of the k-╬Á Model to Account for
Non-isotropic Effects due to Buoyancy," International Journal of Heat
and Mass Transfer, vol.33, 1990, pp. 2599-2608.
[10] Verdier-Bonnet, C., Angot, Ph., Fraunie, Ph., Coantic, M., "Three
Dimensional Modeling of Coastal Circulations with Different k-╬Á
Closures," Marine System J., vol.21, 1999, pp. 321-339.
[11] Annarumma, M.O., Most, J.M., Joulain, P., "On the Numerical
Modeling of Buoyant-dominated Turbulent Vertical Diffusion Flames,"
Combustion and Flame J., vol.85, 1991, pp. 403-415.
[12] Shabbir, A., Taulbee, D. B., "Evaluation of Turbulence Models for
Predicting Buoyant Flows," Heat Transfer J., vol. 112, 1990, pp. 945-
951.
[13] Daly B. J., Harlow F. H., Transport equations of turbulence, Journal of
Physics Fluids, Vol. 13, 1970, pp. 2634-649.
[14] Henkes, R.A.W.M., LeQuere, P., Three Dimensional Transition of
Natural-Convection Flows, Journal of Fluid Mechanics, vol.319, 1996,
pp. 281-303.
[15] Gerber, G. Experimental Measurement and Numerical Modeling of
Velocity, Density and Turbulence Profiles of a Gravity Current, PhD
Thesis, University of Stellenbosch, 2008.
[16] Rodi, W. "Turbulence Models and their
Applications in Hydraulics" A State of the Arts Review,
University of Karlsruhe, Germany, 1984.
[17] Nam, S., Bill, R.G., "Numerical Simulation of Thermal Plumes," Fire
Safety J., vol.21, 1993, pp. 231-256.
[18] Chorin, A.J., "Numerical Solution of the Navier-Stokes Equations,"
Mathematics of Computation J., vol.22, 1968, pp. 745-762.
[19] Temam, R., "Sur l΄Approximation de la Solution des Equation de
Navier-Stokes par la Méthode des pas Fractionnaires," Archive for
Rational Mechanics and Analysis, vol.32, 1969, pp. 135-153.
[20] Kneller, B. C., Bennet, S. J., McCaffrey, W. D., "Velocity Structure,
Turbulence and Fluid Stresses in Experimental Gravity Currents,"
Geophysical Research J., vol.104, No.C3, 1999, pp. 5381-5391.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:50967", author = "A. Majid Bahari and Kourosh Hejazi", title = "Investigation of Buoyant Parameters of k-ε Turbulence Model in Gravity Stratified Flows", abstract = "Different variants for buoyancy-affected terms in k-ε turbulence model have been utilized to predict the flow parameters more accurately, and investigate applicability of alternative k-ε turbulence buoyant closures in numerical simulation of a horizontal gravity current. The additional non-isotropic turbulent stress due to buoyancy has been considered in production term, based on Algebraic Stress Model (ASM). In order to account for turbulent scalar fluxes, general gradient diffusion hypothesis has been used along with Boussinesq gradient diffusion hypothesis with a variable turbulent Schmidt number and additional empirical constant c3ε.To simulate buoyant flow domain a 2D vertical numerical model (WISE, Width Integrated Stratified Environments), based on Reynolds- Averaged Navier-Stokes (RANS) equations, has been deployed and the model has been further developed for different k-ε turbulence closures. Results are compared against measured laboratory values of a saline gravity current to explore the efficient turbulence model.
", keywords = "Buoyant flows, Buoyant k-ε turbulence model, saline gravity current.", volume = "3", number = "7", pages = "463-8", }
