## 2DoF galloping of a 3D bluff body pendulum

Antoine Myskiwª, Christophe Sicotª, Yann Haffnerᵇ, Jacques Boréeª

Fluid-structure interactions between the wind and a 3D bluff body pendulum are investigated experimentally in a large scale wind tunnel at high Reynolds numbers (~$10^5$) and reduced velocities above 20. The pendulum is held by a cardan joint allowing a 2 degrees of freedom motion (2DoF, rotation in $θ$ and $φ$) as illustrated in figure 1a. The bluff body studied is a cube with different shapes of vertical edges (sharp or rounded). The pendulum dynamics is captured using a motion tracking system by cameras and pressures measurements are performed over the cube faces. Aerodynamic loads in static configuration are also measured using an aerodynamic balance.

This contribution focuses on the 2DoF galloping instability of the cube pendulum with sharp edges with as parameters the initial yaw angle $β_0$ (introduced in figure 1b) and the free-stream velocity $U_0$. The pendulum exhibits galloping instabilities with different types of motion depending on $β_0$ and $U_0$ as summarized in figure 2. Cross-flow oscillations are observed for small $β_0$, growing exponentially from rest. For larger $β_0$, a saturated elliptical motion can occur, as shown in figure 3.

A quasi-steady linear model of the pendulum dynamics is built using aerodynamic coefficients from force measurements in static configurations. Although it predicts well the cross-flow galloping, the model does not manage to predict the onset of the elliptical motion, which suggests that unsteady mechanisms play a key role in the development of this instability.

The mechanisms at stake during the self-sustained elliptical cycle are investigated from pressure measurements and an analysis of the energy transfers between the pendulum and the flow. A flow reattachment periodically moving back and forth is observed on the windward face of the cube during the self-sustained cycle. An unsteady delay in the flow reattachment dynamics at a specific phase of the cycle coincides with a strong gain of energy and seems to be responsible for sustaining the motion.

This work is supported by the ANR project "TurbCab" (ID ANR-22-CE22-0010).

<figure><img src="image_1.png" /><figcaption>Figure 1:
a) Definition of the 2DoF motion
b) Definition of the static yaw angle $β_0$ at rest</figcaption></figure>

<figure><img src="image_2.png" /><figcaption>Figure 2:
Experimental stability map of the cube pendulum in the plane ($β_0$, $U_0$) with indications on the type of motion observed ; on the green point, both cross-flow and elliptical motion can be triggered</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Figure 3:
Example of elliptical motion for $β_0$ = 15° and $U_0$=15m/s</figcaption></figure>

<footnote>ª Institut Pprime - UPR 3346, CNRS-ENSMA-Université de Poitiers, France</footnote>

<footnote>ᵇ Centre Scientifique et Technique du Bâtiment (CSTB), 44323 Nantes, France</footnote>