# Query on Natural Convection simulation

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December 10, 2010, 06:47
Query on Natural Convection simulation
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Dynampally Pavitran
Join Date: Mar 2010
Location: India
Posts: 74
Rep Power: 8
Hello all,

I am simulating a natural convection problem in a differentially heated 2D enclosure(pls see the attachment for boundary conditions used). I am carrying out the simulations for varying Rayleigh numbers( Rayleigh number is based on the dimension of the geometry, L=H).

The rayleigh number relation used is: (g*Beta*delT*L^3)/(Kinematic viscosity*Thermal diffusivity)

All the air properties are taken at 75 C i.e at Prandtl no: 0.716
g :9.81 [m/s^2]
Beta: Thermal expansion coefficient : 2.87E-03 [1/K]
delT: temperature difference : 50 C
Kine.viscosity: 2.05E-05 [m^2/s]
Thermal diffusivity: 2.85E-05 [m^2/s]

therefore for L=H=0.02 [m] , the Ra No is: 1.92E+04

in CFX pre , I created material air with properties at 75 C and used laminar and thermal energy equations with Buoyancy ref temp of 50 C.

The convergence criteria for Momentum & continuity was 1E-4 and for energy 1E-6 with conservtion target as 0.01. Discretization scheme was high resolution with auto time scale.

The predicted nusselt number is about 100, whereas it should be around 2.5. and also the rayleigh no written in the out file is about 9E+01.

My question is:
1. why the rayleigh no. is coming different in the out file?
2. what may be the reason for overprediction of nusselt no.?
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 December 11, 2010, 06:11 #2 Super Moderator   Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 12,723 Rep Power: 99 This is a standard benchmark simulation so you should be able to get very accurate answers. If you are referring to the Rayliegh and Nusselt numbers described in the output file then you should ignore these numbers. These numbers are in the output file so you can estimate what regime the flow is in to check your physics (eg laminar vs turbulent) is correct. The calculation of these numbers is based on an arbitrary length scale (the cube root of the total volume from memory), material properties (the mass average over the entire domain) and flow velocities (again I think it is the mass average over the whole domain). This means the numbers coming out from this calculation have little to do which traditional definitions of say, Rayliegh numbers, which should involve the distance the plates are apart and the temperature of the two plates. To get accurate Rayliegh and Nusselt numbers out of your simulation you need to: 1) Define a CEL expression which uses the correct definition of Rayliegh/Nusselt number and outputs that to a monitor point, AND/OR 2) Use CFD-Post to extract the quantities required to calculate the numbers with the definition you require.

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