**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31097

##### Investigation of Buoyant Parameters of k-ε Turbulence Model in Gravity Stratified Flows

**Authors:**
A. Majid Bahari,
Kourosh Hejazi

**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

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1055930

**References:**

[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╬äApproximation 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.