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2D simulation of a Transonic Airfoil at high Reynolds number

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Old   November 17, 2018, 08:21
Default 2D simulation of a Transonic Airfoil at high Reynolds number
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Hello guys,
I'm a student and I'm trying to simulate a 2D transonic airfoil (the supercritical SC(2)-0612) for my university project, using Star CCM+.
I want to obtain the C_L,C_D,C_M-Alpha curves and the final target is to design the wing of a transonic aircraft.
This airfoil represents the section of the wing characterized by the Mean Aerodynamic Chord. These are my physics conditions:

Cruise Altitude = 37000 ft
Cruise Speed = 248 m/s (Mach 0.8)
Chord lenght = 8.31 m

So the Reynolds number = 50.5 millions

At the moment, I will refer to an angle of attack of: \alpha= 0^\circ\
Simulations using Steady Time model.

I'm using a polyhedrical mesh, with prism layer. I'm using a Surface control on Leading and Trailing edges and a wake refinement too.

In order to ensure the validation of my results, I applied my mesh to simulate first the transonic airfoil RAE2822, and I refined the mesh until the solution became independent of the quality of the mesh itself. So, I compared my results with those found in the User's Guide of Star CCM+ and with the experimental data (see the Pressure Coefficient diagram).
When I was satisfied of the results, I've used the same mesh with my supercritical airfoil, the SC(2)-0612.

The first question is about the Prism Layer Thickness. In order to estimate the boundary layer thickness, I referred to this formula (for turbulent flows and flat plate(?)):

\delta= \frac{0.37 x}{Re^{1/5}}\

If "x" is the chord lenght (Is this right??), I obtain a thickness of 90 mm and I'd like to know if this is a plausible value.
In a first moment I had used a Prism Layer Thickness of 10 mm and in this case the Spalart Allmaras Residuals fall until 2x10E-3, after 9000-10000 iterations).
Instead, using 90 mm, the residuals of the Spalart Allmaras model do not fall below 10E-2, with the same iterations. However I think these results are acceptable, but which are the best ones?

10 mm: CD = 0.0460779
90 mm: CD = 0.0475477

The second question is about the steady time model. I want to simulate the flow for -10^\circ \le \alpha \le 25^\circ \. For which values of \alpha\, I have to change the model using Implicit Unsteady? Until the CL or CD are stable, can I continue using the steady model, even if the angle of attack is high?
Thanks.
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Old   November 18, 2018, 15:25
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Quote:
Originally Posted by ClAuDi0 View Post
If "x" is the chord lenght (Is this right??),
"x" is just a distance. The boundary layer will grow along the length of the airfoil, so if you want the largest it will ever be (generally) that would be the longest distance the flow moves along the boundary. In this case the chord is a decent measure of that. You should compare your results from the CFD model to this and learn how different it is than the flat-plate flow.

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Originally Posted by ClAuDi0 View Post
I obtain a thickness of 90 mm and I'd like to know if this is a plausible value.
I would probably consider that thick, but you must remember the purpose of the prism layer. They are only special cells to help resolve anisotropic gradients. Generally speaking this usually means the prism layers should be about the height of the boundary layer, but by no means is this a requirement. It is up to you to choose a meshing scheme which accurately captures gradients without a large expense.

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Originally Posted by ClAuDi0 View Post
However I think these results are acceptable, but which are the best ones?
Why do you think they are acceptable? If you can answer that shouldn't you be able to determine which is better? Also note that while there are no requirements for total prism layer height, there are requirements on the first layer height for turbulent flows. You might want to explore y+ values and convince yourself your mesh is capturing what you desire.

Quote:
Originally Posted by ClAuDi0 View Post
For which values of \alpha\, I have to change the model using Implicit Unsteady? Until the CL or CD are stable, can I continue using the steady model, even if the angle of attack is high?
Even if Cd and Cl are not entirely stable, you can get steady solutions. Unsteady cases are quite expensive, its usually worth it to run the steady ones first and see what they do, I would try that here first.
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