In the three cases of vertical cylinder, cavity and finite channel, the boundary layer is in the state of development whereas in the case of the infinite channel, the boundary layer has a fully developed condition. In the vertical cylinder the natural convection is the dominant phenomenon although a small air-flow enters the geometry to reduce flow recirculations. In the cases of the vertical infinite channel and cavity there exists only a pure natural convection boundary layer. In the vertical finite channel, however, the boundary layer is of mixed convection type and radiation heat transfer affects its development owing to high channel wall temperatures.

The Grashof numbers based on the cylinder height, channel width, cavity and finite channel widths are Gr=5x10¹¹, Gr=9.6x10⁵, Gr=3.9x10⁸ and Gr=9.4x10⁷, respectively.

The boundary layers are studied using two powerful numerical methods namely Direct Numerical Simulation or DNS and Large Eddy Simulation or LES. DNS is only used in the case of the vertical infinite channel. Three different sub-grid scale models are used in the case of the cavity and it is shown that the dynamic SGS model is the only model that is capable of predicting the location of the transition from laminar to turbulent flow correctly.

Mean flow parameters as well as turbulence parameters in all cases are studied and the results are compared with the existing experimental results. Comparisons are also made between the results of the vertical cylinder and experimental results obtained from a vertical flat plate.


 

1. D.G. Barhaghi and L. Davidson and R. Karlsson
   "Natural Convection Heat Transfer in a Vertical Shell and Tube", Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology, Göteborg, Sweden, Report 03/01, 2003
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2. D.G. Barhaghi and L. Davidson"
   "LES of Natural Convection Heat Transfer in a Vertical Shell and Tube", Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology, Göteborg, Sweden, Report 03/01, 2003
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3. L. Davidson, D. Cuturic and S.-H. Peng
   "DNS in a Plane vertical Channel With and Without Buoyancy", Turbulence Heat and Mass Transfer 4, pp. 401-408, K. Hanjalic, Y. Nagano and M.J. Tummers (eds.), begell house, inc., New York, Wallingford (UK), 2003.
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4. S.-H. PENG and L. DAVIDSON
   Large Eddy Simulation for Turbulent Buoyant Flow in a Confined Cavity, Int. J. Heat and Fluid, Vol. 22, pp. 323-331, 2001.
    
   
5. S.-H. PENG and L. DAVIDSON
   "On a Subgrid-Scale Heat Flux Model for Large Eddy Simulation of Turbulent Thermal Flow", Int. J. Heat and Mass Transfer, Vol. 45, pp. 1393-1405, 2002.
    
   
6. D.G. Barhaghi and L. Davidson and R. Karlsson
   Large Eddy Simulation of Natural Convection Boundary Layer on a Vertical Cylinder", Engineering Turbulence Modelling and Measurements - ETMM6, Sardinia, Italy, May 23-25, 2005.
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7. D.G. Barhaghi and L. Davidson and R. Karlsson
   Large Eddy Simulation of Natural Convection Boundary Layer on a Vertical Cylinder", Selected paper, International Journal of Heat and Fluid Flow, Vol. 27(5), pp. 811-820, 2006.
    
   
8. D.G. Barhaghi and L. Davidson
   "LES of Mixed Convection Boundary Layer Between Radiating Parallel Plates", 5th International Symposium on Turbulence, Heat and Mass Transfer", Dubrovnik, Croatia, September 25-29, 2006.
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9. D.G. Barhaghi, L. Davidson and R. Karlsson
   "Large-eddy simulation of natural convection boundary layer on a vertical cylinder", Int. Journal of Heat and Mass Transfer, Vol. 27(5), pp. 811-820, 2006.
    
   
10. D.G. Barhaghi and L. Davidson
    "LES of Mixed Convection Boundary Layer Under Influence of Radiation", Div. of Fluid Dynamics, Dept. of Applied Mechanics, Chalmers University of Technology, Göteborg, Sweden, Report 06/04, 2006
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11. D.G. Barhaghi
    "A Study of Turbulent Natural Convection Boundary Layers Using Large-Eddy Simulation", PhD thesis, Division of Fluid Dynamics, Dept. of Applied Mechanics, Chalmers University of Technology, Göteborg, Sweden, 2007.
     
    
12. D.G. Barhaghi and L. Davidson
    "Natural Convection Boundary Layer in a 5:1 Cavity", Physics of Fluids, Vol. 19, No. 125106, 2007.
     
    
13. Darioush G. Barhaghi and Lars Davidson
    "Large-eddy simulation of mixed convection-radiation heat transfer in a vertical channel", International Journal of Heat and Mass Transfer, Vol. 52, pp. 3918-3928, 2009.