# NACA4412 wing

A rectangular wing of aspect ratio $$AR=6$$ with a NACA4412 airfoil is considered. Experiments of such wing were performed by R.M. Pinkerton \[1] at different angles of attack. A structured mesh consisting of 1680 elements is used. The mesh is scaled so that the chord of the wing is $$c\_{ref}=1$$m and the span $$b\_{ref}=6$$m. The freestream velocity is set to $$|\mathbf{V}\_{ref}|=1$$m/s. The image below shows the pressure coefficient distribution.

![](https://81269019-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MV8htLPXN-_fWc_anY_%2F-Mh5BaGYlgZt9nFGCrqh%2F-Mh5CHx_ASQfTlxhayB2%2Fnaca4412_wing_cp.png?alt=media\&token=e9bb7ab9-a3da-4265-ab3b-ef92766adda8)

The image below shows the pressure coefficient at $$y/b=0$$ for angle of attack $$\alpha=0$$deg. The experimental results from Pinkerton \[1] are shown for comparison.

<img src="https://81269019-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-MV8htLPXN-_fWc_anY_%2Fuploads%2FBiPHZX1sOE9v9cIaXs52%2Fnaca4412_spanwise_cp.png?alt=media&#x26;token=224ef3a9-cfc2-482e-82b2-f849e4339494" alt="" data-size="original">&#x20;

Good agreement between the simulation and the experimental results is observed.

## Vortex particle wake

The image below compares a doublet wake and a vortex particle wake. The freestream velocity is  $$|\mathbf{V}\_{ref}|=1$$m/s and the angle of attack is 0 deg. The Rosenhead-Moore and the Gaussian kernels were used to regularize the vortex particles.

<figure><img src="https://81269019-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-MV8htLPXN-_fWc_anY_%2Fuploads%2FUb81HXKrH7aWTWFYuSlx%2Fnaca4412_wing_wake_comparison.png?alt=media&#x26;token=2e0293f7-04ed-437d-a54e-90c515271851" alt=""><figcaption></figcaption></figure>

<figure><img src="https://81269019-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-MV8htLPXN-_fWc_anY_%2Fuploads%2FFtr2qWSboLmCTRx94cys%2Fnaca4412_wing_CLCD_comparison.png?alt=media&#x26;token=30627760-c949-403a-8a61-5f48697249b2" alt=""><figcaption></figcaption></figure>

As observed from the integrated loads the CL and CD compare favourably between the doublet and the vortex particle wake. The solution is not sensitive to the choice of a regularization kernel.

## Files

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## References

\[1] Pinkerton, R. M. "Calculated and measured pressure distributions over the midspan section of the N.A.C.A 4412 airfoil", 1936
