A15013950 wrote: ↑Sun Jul 22, 2018 10:01 am

How do you calculate initial k and omega when using that turbulence model for external aerodynamics?

I will go over all the "major" variables that people may or may wish to calculate here - there are ways to skip to the ones you want, but this way will give you all that you need, I hope.

One equation for

**turbulent kinetic energy (k), in J/kg**, is:

This basically reads as "k" being equal to the time average of the velocity fluctuations in one direction squared, all divided by 2. So a rough way to calculate this would be to take your domain's inlet velocity, multiply it by your turbulence intensity (i.e. 5% = 0.05 ), and then square it. From there, you divide by 2, but since we only looked into one direction, a crude way of approximating this throughout the domain is to multiply that final result by 3; one for each axis, since there will be fluctuations in velocity in all directions.

Alternatively, you can split them out into each separate axis if you have a vector with a non-zero second or third component. If that is the case, do the same thing but use this equation below:

For Omega, its a little more involved... Assuming you know the air Pressure [Pa] and Temperature [K}, then you can use the ideal gas law equation to calculate your air density:

From there, we need to use Sutherland's Law for calculating the

**fluid dynamic viscosity of air** as it relates to temperature:

which can be written as:

, where

Taking "

" as being equal to 0.000001458 and "C" as being equal to 110.4 (these are commonly used values of dynamic viscosity of air at a specific temperature within CFD literature), you can then calculate back through to get your

**actual** at your given temperature in [ Pa . s ].

Next we need to calculate the

**turbulent length scale [m]** of the flow, which can be done crudely (yes, I am aware that the k-

model has it's own definition of the length scale utilizing the relationship between k, epsilon and

) by:

Note that

is the

**hydraulic diameter** and so depending on your shape of domain, there will be a different equation for calculating the equivalent circular section. For a rectangular domain, use this equation:

Next, we can calculate

**Epsilon [J / kg . s ]** by using the k-

specific coefficient

= 0.09 along with the turbulent length scale we just worked out and the turbulent kinetic energy (k) from before:

Next we need to calculate something called

**nuTilda which is our turbulent viscosity [ m^2 /s ]**. We can do that by

Finally, for

**Omega [J / kg . s ]**

Where "k" is the turbulent energy,

is the density,

is the molecular dynamic viscosity and

is the eddy viscosity ratio.

Hope this helps!!