## THERMAL SCIENCE

International Scientific Journal

### RAYEILGH NUMBER EFFECT ON THE TURBULENT HEAT TRANSFER WITHIN A PARALLELEPIPED CAVITY

**ABSTRACT**

This purpose is about a three dimensional study of natural convection within cavities. This problem is receiving more and more research interest due to its practical applications in the engineering and the astrophysical research The turbulent natural convection of air in an enclosed tall cavity with high aspect ratio (AR=H/W=28.6) is examined numerically. Two cases of differential temperature have been considered between the lateral cavity plates corresponding, respectively, to the low and high Rayleigh numbers: Ra=8.6×105 and Ra=1.43×106 [1]. For these two cases, the flow is characterized by a turbulent low Reynolds number. This led us to improve the flow characteristics using two one point closure low-Reynolds number turbulence models: RNG k-e model and SST k-w model, derived from standard k-e model and standard k-w model, respectively. Both turbulence models have provided an excellent agreement with the experimental data. In order to choose the best model, the average Nusselt number is compared to the experiment and other numerical results. The vorticity components surfaces confirm that the flow can be considered two-dimensional with stretched vortex in the cavity core. Finally, a correlation between Nusselt number and Rayleigh number is obtained to predict the heat transfer characteristics.

**KEYWORDS**

PAPER SUBMITTED: 2011-02-01

PAPER REVISED: 2011-05-29

PAPER ACCEPTED: 2011-10-08

**THERMAL SCIENCE** YEAR

**2011**, VOLUME

**15**, ISSUE

**Supplement 2**, PAGES [S341 - S356]

- Aksouh. M., Mataoui, A., Seghouani, N., and Haddad, Z., Assessment of Performance of Low Reynolds turbulence models in predicting natural convection. ECCOMAS, Fifth European Conference on Computational Fluid Dynamics, Lisbon, Portugal, 14-17 June 2010.
- Peng, S., Davidson, L., Large eddy simulation for turbulent buoyant flow in a contained cavity. Int. J. Heat Mass Transfer, 22 (2001), pp. 323-331.
- Tian, Y.S., and Karayiannis, T.G., Low turbulence natural convection in an air filled square cavity. Part I: the thermal and fluid flow fields. Intr. Comm. in Heat and Mass Transfer, 43 (2000), pp.849-866.
- Salat, J., et al, Experimental and numerical investigation of turbulent natural convection in a large air-filled cavity, International Journal of Heat and Fluid Flow, 25 (2004), pp.824-832.
- Gustaven, A. Thue, J. V., Numerical simulation of natural convection in three-dimensional cavities with a high vertical aspect ratio and low horizontal aspect ratio. Journal of Building Physics, 30 (2007), pp.217-240.
- Yang, H., Zhu, Z., Numerical study of three-dimensional turbulent natural convection in a differentially heated air-filled tall cavity. Intr. Comm. in Heat and Mass Transfer, 35 (2008), pp.606-612.
- Pons, M., Transition from single to multi-cell natural convection of air in cavities with aspect ratio of 20: A thermodynamic approach. Int. J. of Thermodynamics, 11 (2008), 2, pp.71-79.
- Aich, W., Hajri, I., Omri, A., Numerical Analysis of Natural Convection in a Prismatic Enclosure. Journal Thermal and science, 15 (2011), 2, pp.437-446.
- Betts, P.L., Bokhari, I.H., Experiments on natural convection in an enclosed tall cavity. Intr. J. of Heat and fluid flow, 21 (2000), pp.675-683.
- Hsieh, K.J., Lien, F.S., Numerical modelling of buoyancy-driven turbulent flows in enclosures, Intr. J. of Heat and fluid flow, 25 (2004) pp.659-670.
- Aksouh, M., Mataoui, A., Numerical study of the turbulent natural convection in an enclosed tall cavity for the high and low Rayleigh number, ACOMEN Advanced Computational Methods in Engineering, , Liege, Belgium, 26-28 May 2008.
- Yakhot, V. and S. A. Orszag, S.A., Renormalization Group Analysis of turbulence, Journal of scientific Computing, 1 (1986), pp.3-51.
- Menter, F.R., Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal, 32 (1994), 8, pp.1598-1605.
- Cuypers, Y, Maurel, A., Petitjeans, P., Characterization of a Turbulent Vortex Using Phase Averaged PIV Data, Progress in Turbulence II , ed. by M. Oberlack et al., Springer Proceedings in Physics, 109 (2007), pp.65-70.
- Dafa'Alla, A.A., Betts, P.L., Experimental study of turbulent natural convection in a tall air cavity. Exp Heat Transfer, 9 (1996), pp.165-194
- Incropera, F.P., et al., Fundamental of heat and mass transfer, (sixth edition), WILEY Edition, 2007.
- MacGregor, R. K., Emery, A. P., Free convection through vertical plane layers: moderate and high Prandtl number fluids, ASME J. Heat Transfer, 91 (1969), pp.391-403.
- Ouriemi, M., Vasseur, P., Bahloul, A., Natural convection of a binary mixture confined in a slightly inclined tall enclosure, Intr. J. of Heat and Mass Transfer, 32 (2005), pp.770-778
- Xaman, J. et al, Numerical study of heat transfer by laminar and turbulent natural convection in tall cavities of façade elements, Energy and buildings, 37 (2005), 787-794.
- Elsherbiny, S.M., Raithby, G.D. and Hollands, K.G.T., Heat transfer by natural convection across vertical and inclined air layers, Trans. ASME J. Heat Transf., 104 (1982), pp.96-102.
- Wilcox, D. C., Turbulence Modelling for CFD, DCW Industries Inc, La Canada, CA, 1994. Patankar, S. V., Numerical heat transfer and fluid flow, Series in Computational methods in mechanics and thermal sciences, Hemisphere Publishing Corp. & Mc Graw Hill, 1981.
- El Gharbi et al, An improved near-wall treatment for turbulent channel flows, Inter J of Compu. Fluid Dynamics, 25 (2001), 1, pp.41-46.
- Ampofo, F., Karayiannis, T.G., Experimental benchmark data for turbulent natural convection in an air filled square cavity, Intr. J. of Heat and Mass Transfer, 46 (2003), pp.3551-3572.
- Bennacer, R., et al., Generalisation of two-layer turbulent model for passive cooling in a channel, Tokyo JSME, 11th International Conference on Nuclear Engineer, Tokyo, Japan, 20-23 April 2003, No. 03-209.
- Foias, C. et al., Navier-Stokes equations and turbulence, Book Cambridge University Press, UK, 2004.
- Kemenov, K.A., New Two-Scale Decomposition Approach for Large-Eddy Simulation of Turbulent Flows, PhD Thesis, School of Aerospace Engineering Georgia Institute of Technology, Atlanta, USA, 2006.
- Aounallah, A., et al., Numerical investigation of turbulent natural convection in an inclined square cavity with a hot wavy wall, Intr. J. of Heat and Mass Transfer, 50(2007), pp.1683-1693.
- Lien, F.S., Leschziner, M.A., Computational modelling of a transitional 3D turbine-cascade flow using a modified low-Re k-e model and a multi-block scheme. Inter. J. of Comp. Fluid Dynamics, 12 (1999), pp.1-15.
- Henkes, R. A. W. M., Vander Flugt, F. F., Hoogendoorn, C. J., Natural Convection Flow in a Square Cavity Calculated with Low-Reynolds-Number Turbulence Models. Intr. J. of Heat and Mass Transfer, 34 (1991), pp.1543-1557