# Caradonna-Tung rotor in hover

A simulation of rotor in hover is considered. The rotor has two untwisted, untapered, rectangular blades with a NACA0012 airfoil. The rotor radius is $$R=1.143$$m and the aspect ratio is $$AR=6$$. The rotor has a collective pitch of $$\theta=8$$deg, and is rotating at $$\omega=1250$$rpm, corresponding to a tip Mach number of $$M\_{tip}=0.439$$. A structured mesh with 40 panels in the chordwise and 20 panels in the spanwise direction (for each blade) is used. The mesh is scaled so that the chord of the rotor blades $$c\_{ref}$$equals 1 and the span $$b\_{ref}$$equals 6. The resulting rotational velocity is then adjusted to $$\omega=24.9364$$rad/s. The results are obtained with an azimuthal step of $$\Delta\phi\approx7.14$$deg ($$\Delta t=5\times10^{-3}$$s) for 10 revolutions. From $$t=0$$s to $$t=0.1$$s the rotational velocity is increased gradually from $$\omega=1.2468$$rad/s to $$\omega=24.9364$$rad/s. The gradual increase of the rotational velocity allows the wake to develop without numerical instabilities. The image below shows the pressure coefficient distribution and the developed wake.

![](/files/-Mgv32yVA-YZBJrtKZnV)

The animation below shows the development of the wake.

{% embed url="<https://youtu.be/k0aoCdwtnq4>" %}
Caradonna-Tung rotor wake development
{% endembed %}

The images below show the pressure coefficient at $$r/R=0.68$$ and $$r/R=0.96$$. The experimental results from Caradonna and Tung \[1] are shown for comparison.

<img src="/files/-Mh5A2x8qrpv12cabT4b" alt="" data-size="original"><img src="/files/-Mh5A2x9CgBn4O8EW24l" alt="" data-size="original">&#x20;

Overall, good agreement between the simulation and the experimental results is observed.

## Files

{% file src="/files/YkqFDxmHJBmYDW6U6qcX" %}

## References

\[1] Caradonna, F.X. and Tung, C., "Experimental and Analytical Studies of a Model Helicopter Rotor in Hover", NASA Technical Memorandum 81232, 1981


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