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Thermophysical properties for natural convection

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Old   November 7, 2013, 12:44
Default Thermophysical properties for natural convection
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Frank
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Hi Openfoam users,

I'm running simulations related to natural convection in enclosures and comparing the results with empirical correlations. The fluid is air. For this I need help to set correctly the thermophysical properties of the fluid

Info about the simulations:
OF version: 2.2.x
Solver: buoyantSimpleFoam
Geometry: concentric tubes
Thermophysical properties

Code:
   thermoType
{
    type            heRhoThermo;
    mixture         pureMixture;
    transport       const;
    thermo          hConst;
    equationOfState perfectGas;
    specie          specie;
    energy          sensibleEnthalpy;
}
Physics:
Depending on the dimensions of the tubes and the temperature difference, heat transport can be either by convection or conduction.

Empirical correlation for natural convection in concentric tubes (from book "Heat Transfer; A Practical Approach. Yunus Cengel)

This correlation looks like an equation for conduction with an "effective conductivity".

\dot{Q}=\frac{2\pi \cdot k_{eff}}{ln(D_{o}/D_{i})}

When heat transport is by conduction, the value of keff is the conductivity of air. When heat transport is by convection, the effective conductivity is calculated with the following equations

\frac{k_{eff}}{k}=0.386(\frac{Pr}{0.861+Pr})^{0.25}(F_{cyl}\cdot Ra_{L})^{0.25}

F_{cyl}= \frac{[ln(D_{o}/D_{i})]^{4}}{L_{c}^{3}(D_{i}^{-3/5}+D_{o}^{-3/5})^{5}}

All properties are evaluated at average temperature of the tubes.

Simulations:
I've been simulating several cases with different diameters and temperature difference between the tubes. What I've seen is a good agreement between the simulation and the empirical correlation but depending if it is convection or conduction, the values of the thermophysical properties have to be different. To evaluate the heat transport I use the utility wallHeatFlux

For convection there is good agreement with constant values for Pr, Cp and mu

Code:
      thermodynamics
    {
        Cp              1000;
        Hf              0;
    }
    transport
    {
        mu              1.8e-05;
        Pr              0.7;
    }
but if given the temperature difference (or geometry) heat tranport is by conduction, it is considerably underestimated. In case of conduction, if I set the thermophysical properties at average temperature, I get good results, but setting thermophysical properties at average temperature in case of convection gives results considerably overestimated.

for example if the inner tube is at 573 K and the outer tube at 300 K, I set the values as following (evaluated at 435 K)


Code:
      thermodynamics
    {
        Cp              1016;
        Hf              0;
    }
    transport
    {
        mu              2.42e-05;
        Pr              0.701;
    }
I get good results for conduction, but this means I need to know beforehand if heat transport is either by convection or conduction to get reliable results.

It is clear to me the relation between Pr, mu and Cp to calculate the conductivity of the fluid. In case of conduction, using the empirical correlation with a constant conductivity value the results are the same.

After this validation I'll run similar simulations but for other geometries where I do not have empirical correlations to know beforehand if heat transport is by convection/conduction, so I would appreciate any advice to consider both cases setting only once the values for thermophysical properties.

Regards!

ps: I'm validating is a similar way natural convection from a tube. Up to know the results of the simulation understimate heat transport compare to an empirical correlation. If somebody has an advice for this, I would really appreciate it!
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