Differences between production term in k-epsilon!

TomWaits · May 13, 2024, 13:12

Reading about the production term for k-epsilon here:
https://www.cfd-online.com/Wiki/Stan...-epsilon_model
it is given as
$P_k=2\mu_t S_{ij}S_{ij}$

but on the NASA website here:
https://turbmodels.larc.nasa.gov/ke-chien.html
a much more complicated form is given as:
$P=\tau_{ij}\frac{du_i}{dx_j}$

where
$\tau_{ij}=\mu_t(2S_{ij}-2/3\frac{du_k}{dx_k}\delta_{ij})-2/3\rho k\delta_{ij}$

I have coded both up and get slightly different results for the production term in my k-epsilon model! Where do these two forms come from and why are they different?

Many thanks in advance,
Tom Waits

sbaffini · May 15, 2024, 07:03

Quote:

Originally Posted by TomWaits

Reading about the production term for k-epsilon here:
https://www.cfd-online.com/Wiki/Stan...-epsilon_model
it is given as
$P_k=2\mu_t S_{ij}S_{ij}$

but on the NASA website here:
https://turbmodels.larc.nasa.gov/ke-chien.html
a much more complicated form is given as:
$P=\tau_{ij}\frac{du_i}{dx_j}$

where
$\tau_{ij}=\mu_t(2S_{ij}-2/3\frac{du_k}{dx_k}\delta_{ij})-2/3\rho k\delta_{ij}$

I have coded both up and get slightly different results for the production term in my k-epsilon model! Where do these two forms come from and why are they different?

Many thanks in advance,
Tom Waits

The second one is the only correct form of the production term in k equation. The first one is, nonetheless, a very common approximation (fully correct only for soleinodal velocity fields).

The approximation is certainly more stable, that's one of the reasons it got large acceptance.

FMDenaro · May 15, 2024, 08:26

The isotropic terms could be absorbed by the “pressure”

May 13, 2024, 13:12	Differences between production term in k-epsilon!	#1
TomWaits Member Tom Waits Join Date: Aug 2018 Posts: 42 Rep Power: 7	Reading about the production term for k-epsilon here: https://www.cfd-online.com/Wiki/Stan...-epsilon_model it is given as $P_k=2\mu_t S_{ij}S_{ij}$ but on the NASA website here: https://turbmodels.larc.nasa.gov/ke-chien.html a much more complicated form is given as: $P=\tau_{ij}\frac{du_i}{dx_j}$ where $\tau_{ij}=\mu_t(2S_{ij}-2/3\frac{du_k}{dx_k}\delta_{ij})-2/3\rho k\delta_{ij}$ I have coded both up and get slightly different results for the production term in my k-epsilon model! Where do these two forms come from and why are they different? Many thanks in advance, Tom Waits

May 15, 2024, 08:26		#3
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,782 Rep Power: 71	The isotropic terms could be absorbed by the “pressure” TomWaits likes this.

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