On the turbulent prandtl number in stably stratified turbulence by second order models
1Faculty of Science of Tunis
2Faculty of Sciences of Bizerte
Journal of Thermal Engineering 2020, Vol. 6, Issue 3, pp. 369-380; doi.org/10.18186/thermal.712584
Abstract
The aim of this work is to investigate the behavior of the Turbulent Prandtl number by second order modeling of a stably stratified homogeneous sheared turbulence. By analytic solutions, we have confirmed the asymptotic equilibrium behavior of the turbulent Prandtl number. Then two between the most second order models of turbulence; the Classic Launder-Reece-Model and the sophisticated Craft Launder model are retained. A non dimensional form of transport equations have been obtained when non dimensional parameters are introduced to substitute second order moments. A numerical integration using the fourth order Runge kutta method has been conducted for different values of the gradient Richardson number Ri. In comparison with direct numerical simulation result’s of Shih et al. the obtained results by the Craft Launder model has shown for the turbulent Prandtl number the best agreement at moderate values of gradient Richardson number 0.15 < Ri < 0.28. The classic model has shown a great default for the different values of Ri. No any concordance with retained results of DNS has been obtained by this model. We show also that prediction of this model can be improved by introducing variation and optimization of model constants.
Keywords: Prandtl Number; Stably Stratified Turbulence; Second Order Modeling
References
- Gerz, T., Shumann, U., Elghobachi, S. Direct numerical simulation of stratified homogeneous turbulent shear flow. Journal of Fluid Mechanics, 1989 ; 200, 563-594. https://doi.org/10.1017/S0022112089000765.
- Holt, S. F., Koseff, J. R., Ferziger, J. H. A numerical study of the evolution and structure of homogeneous stably stratified sheared turbulence. Journal of Fluid Mechanic, 1992; 237, 499-539. https://doi.org/10.1017/S0022112092003513.
- Shih, L. H., Koseff, J. R., Ferziger, J. H., and Rehmann, C. R. Scaling and parameterization of stratified homogeneous turbulent shear flow. Journal of Fluid Mechanics, 2000; 412, 1-20. https://doi.org/10.1017/S0022112000008405.
- Shih, L. H., Koseff, J. R., Ivey, G. N., and Ferziger, J. H. Parameterization of turbulent fluxes and scales using homogeneous sheared stably stratified turbulence simulations. Journal of Fluid Mechanics, 2005; 525, 193–214. https://doi.org/10.1017/S0022112004002587.
- Subhas, K. Venayagamoorthy and Derek, D. Stretch. On the turbulent Prandtl number in homogeneous stably stratified turbulence. Journal of Fluid Mechanics, 2010; 644, 359-369. https://doi.org/10.1017/S002211200999293X.
- Fatima MADI AROUS. Numerical simulation with a Reynolds stress turbulence model of flow and heat transfer in rectangular cavities with different aspect ratios. Journal of Thermal Science and Technology, 2016; 11(1), 1-13. doi: 10.1299/jtst.2016jtst0012.
- Abay, K., Colak, U., Yüksek, L. Computational fluid dynamics analysis of flow and combustion of a diesel engine. Journal of Thermal Engineering, 2018; 4(2), 1878-1895. doi: 10.18186/journal-of-thermal- engineering.388333.
- Bouzaiane, M., Ben Abdallah, H., and Lili, T. A study of the asymptotic behaviour of dimensionless parameters in stably stratified sheared turbulence. Journal of Turbulence, 2003; 4, N2. http://dx.doi.org/10.1088/1468-5248/4/1/002.
- Bouzaiane, M., Ben Abdallah, H., and Lili, T. A second-order modelling of a stably stratified sheared turbulence submitted to a non-vertical shear. Journal of Turbulence, 2004; 5, N33. http://dx.doi.org/10.1088/1468-5248/5/1/033. 379 Journal of Thermal Engineering, Technical Note, Vol.6, No.3, pp.369-380, April, 2020
- Thamri, N. L., Bouzaiane, M., Lili, T. A study of equilibrium states of homogeneous turbulence submitted to an inclined shear. International Journal of Computer Science Engineering, 2012; 1(2), 126-139.
- Launder, B. E. On the effects of a gravitational field on the turbulent transport of heat and momentum. Journal of Fluid Mechanics, 1975; 67, 569–581. https://doi.org/10.1017/S002211207500047X.
- Launder, B. E., Reece, G., and Rodi, W. Progress in the development of a Reynolds stress closure. Journal of Fluid Mechanic, 1975; 68, 537-576. https://doi.org/10.1017/S0022112075001814.
- Craft, T. J., Launder, B. E. A new model for the pressure/scalar-gradient correlation and its application to homogeneous and inhomogeneous free shear flows. Seventh Symposium on Turbulent Shear Flows, Stanford, California, 1989; 2, 17.1.1-17.1.6.
- Speziale, C. G., Sarkar, S., and Gatski, T. B. Modelling the pressure strain correlation of turbulence: an invariant dynamical systems approach. Journal of Fluid Mechanic, 1991; 227, 245-272. https://doi.org/10.1017/S0022112091000101.
- Younis, B. A., Speziale, C. G., Berger, S. A. Accounting for effects of a system rotation on the pressure- strain correlation. AIAA Journal, 1998; 36(9), 1746-1748. doi: 10.2514/3.14037.
- Yuji Kitamura, Akihiro Hori and Toshimasa Yagi. Flux Richardson number and turbulent Prandtl number in adeveloping stable boundary layer. Journal of the Meteorological society of Japan, 2003; 91, 655-666. doi:
- 2151/jmsj.2013-507. 380
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Naifer, S.; Bouzaiane, M. On the turbulent prandtl number in stably stratified turbulence by second order models. Journal of Thermal Engineering 2020, Vol. 6, pp. 369-380. https://doi.org/10.18186/thermal.712584
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