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
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:
" 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
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-
= 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!!