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Turbulent Schmidt and Prandtl numbers

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Old   December 27, 2020, 12:14
Default Turbulent Schmidt and Prandtl numbers
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Guillaume Beardsell
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I have a simple question regarding the conduction/diffusion terms in the energy/species transport equations, when a turbulence model is employed. In the manual, the expressions for molecular and turbulent conduction/diffusion coefficients are given. However, it is not said what the terms are in the transport equations. Do the conduction/diffusion terms use a diffusion coefficient that is the sum of the molecular and turbulent coefficients? Or is it just the turbulent coefficient being used?

I also have a other small question. The default values for turbulent Prandtl and Schmidt numbers are 0.9 and 0.78, respectively. However, since turbulence mixes all things evenly, would it be good practice to set these numbers to 1?

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Old   December 28, 2020, 10:40
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Sameera Wijeyakulasuriya
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We take the sum of molecular and turbulent conductivity and diffusivity when used in the transport equations. Typically the turbulent quantities dwarf the molecular quantities in turbulent flows, such as in-cylinder flows, gas turbine flows, etc..

The turbulent Sc and Pr numbers are found to be spatially varying in several turbulent engineering flows. The presence of walls affect these values. Hence we use the values of 0.78 and 0.9 respectively which have proved to be satisfactory for a wide range of reacting and non-reacting turbulent flows. The constants we use should be used as first approximations in your simulations and can be changed if you know that the flow you simulate warrant any different values.
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Old   March 25, 2021, 17:59
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Sibylle Walter
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Just so you know - there is always uncertainty around the Schmidt number. Usually, the default between 0.7 and 0.8 is a good start. However, if you are comparing to experimental data, you may have to tinker with that number to see how it changes your answer. Robert Baurle from NASA did a study in 2016 on a combustor (doi:10.2514/1.J055339) flowfield, varying the Schmidt number, which is a good read on the subject.

Hope that helps!
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