Experimental investigation of the hydrodynamics of a slipping cylinder in a viscous shallow water flow.*

In the context of atmospheric re-entry flows, viscous effects cause a thick boundary layer around the object, which plays an important role in the aerodynamics of the object. The flows encountered can be at low Reynolds number and supersonic conditions. Using the analogy between rarefied supersonic flows and viscous shallow water flows, it is possible to study the aerodynamic behaviour. This work focuses on the hydrodynamics of a cylinder in a viscous shallow water flow. Slip at the cylinder wall is synthetically added with a super-hydrophobic treatment to add slip and achieve analogy with the slip regime of rarefied flows. Different cylinder diameters and configurations of the shallow water hydraulic test bench were used to vary the Reynolds number between 10 and 500 for a Froude number of 2. A random dot pattern in the background of the flow is imaged with a high-resolution camera, which allows the reconstruction of the water free surface height by backward oriented schlieren technics. The drag coefficient is thus obtained using a momentum budget on the reconstructed heights and velocity field.