In practice, it doesn’t matter what length scale is chosen, as long as the resulting turbulent viscosity ratio is within 0.1~2 for external aerodynamics of a plane, because a plane operates in a ‘clean’ inflow environment, as opposed to a car travelling in the wake of the car in front. Since you have decided to use the length of the fuselage, by all means stick with it (unless the turbulent viscosity ratio is very large). You can calculate the ratio using the formula below, or see Turbulence free-stream boundary conditions -- CFD-Wiki, the free CFD reference
where, mut/mu is turbulent viscosity ratio.
Btw, k can be calculated using
What difference would it make if you change the ratio within that range? Very likely you will see changes in Cd and Cl, but they will most likely shift upward or downward consistently. For example, if you increase the ratio, chances are all Cd values will shift up or down for approximately the same amount. The trend of these values will remain the same.
The LES Spalart-Allmaras model is detached eddy simulation suitable for transient computation, so you won’t need it.
Is this ‘turbulent viscosity ratio’ the same as the ‘Modified Turbulent Viscosity’ here?
I have seen an I (turbulent intensity) value of 0.01% used for sailplanes and a value of 0.1% used for ‘normal aircraft’. My design is somewhere between them, is the value to use for I, a sort of subjective value?
You have shown the formula for e (epsilon), is that not dissipation rate?
Modified turbulent viscosity, or nuTilda, is for the SpalartAllmaras model. Turbulent viscosity ratio, or eddy viscosity ratio, is nut/nu, or mut/mu
where
nut: kinematic turbulent/eddy viscosity of the fluid
mut: dynamic turbulent/eddy viscosity of the fluid
nu: kinematic molecular/laminar viscosity of the fluid
mu: dynamic molecular/laminar viscosity of the fluid
@jousefm SimScale only has standard-kEpsilon, kOmega, and KOmegaSST as RANS models? I don’t think many people still use kOmega, because SST is a much better option. Why is SpalartAllmaras not implemented as RANS? The standard-KE is probably occasionally used for fully developed internal flow.
I am unable to find a kinematic or dynamic ‘molecular viscosity of air’ or ‘laminar viscosity of air’ to make the ‘turbulent viscosity ratio’ calculation.
In fact, it appears to me that ‘turbulent viscosity ratio’ is dependent only on the type of fluid, so how can it ever have a range from 0.1-2? Shouldn’t I just be able to find a ‘turbulent viscosity ratio’ for air or water etc?
Sorry for being so dense, it is late/early here in Florida …
Turbulent viscosity ratio = turbulent viscosity / molecular viscosity. For incompressible flow, OpenFOAM uses the kinematic version of viscosity. In this case you have kinematic viscosity ratio (nut/nu) = kinematic turbulent viscosity / kinematic molecular viscosity = kinematic turbulent viscosity / 1.5e-5.
The kinematic turbulent viscosity (nut) is calculated by the turbulence model. With each pair of k and omege values, you will get a unique nut.
I should have explained this better. The table on Dry Air - Thermodynamic and Physical Properties contains molecular/laminar viscosity only. The molecular viscosity is a fluid property independent of the turbulence models. The turbulent viscosity is the result of turbulence modelling.
The SA 1 equation turbulence model is adapted for flows around an airfoil and as you know boussinesq approximations to not behave super accurate (whatever you define as accurate in this case), but a contracting section is a good example as the eddies loose their identity along the way. And standard k-epsilon is by definition not realizable (need a separate post to explain what that means) so one usually uses realizable k-epsilon but fully developed pipe flow for instance work pretty well with standard k-epsilon. k-omega SST does a pretty good job and there is no need for SA model, what do you think?
I exclusively use SpalartAllmaras, RealizableKE, and SST as RANS. In fact, I find SpalartAllmaras very useful for external aerodynamics with mild separation, such as a plane or a wing. I think @DaleKramer’s problem can be very well solved by SA, because I have done similar projects.
Just curious as to why you suggest calculating ut/u from the cfd_online.com formula rather than from the Spalart and Rumsey recommendation of 2e-7 * Re ?
There is a 20% difference in my case.
And by the way, I did have to change my reference length from a fuselage length of 5m to a value of 2m to stay in your suggested ut/u range of 0.1~2. My ut/u value is now 1.89 (EDIT actual value is now 1.6182, see edit 2 posts down).
The 2e-7*Re is just an estimation. The actual nut calculated at inlet should return a nut/nu = 1.888 or much closer to 1.888. I don’t think a length scale of 2 or 3 will lead to much difference in Cd or Cl. It is safe to use what you have here.
Turbulent viscosity and eddy viscosity are the same thing. However, nut = mut/rho, where nut is commonly used in incompressible flow, and mut in compressible flow.
…
is the turbulent viscosity ratio;
is air density;
is dynamic molecular viscosity of air (not kinematic).