## 3 Results
### Fluid Dynamics Phenomena  
Despite the simple geometry of the gripper, the flow structure that develops is rather complex due to the superposition and the interactions among several elementary flows. Patterns reported here for the reference geometry were observed in most of the computations. For the sake of simplicity, the gripper's inner volume was divided into four regions (front chamber, jet, annular and terminal region), as shown in Figure 8.  
The airflow forced inside the gripper through the lateral hole impinges normally on the releasing mass wall, reaching a peak in static pressure (stagnation point). The jet velocity increases with the imposed negative pressure (\(\Delta p\)) with a maximum Mach number of 0.78 (for \(\Delta p\) = 30 kPa and \(d\) = 0.77 mm): flow is subsonic in all geometrical configurations taken into account. Due to the jet impingement on the releasing mass wall, several vortical structures arise in the region nearby the lateral hole, developing along circumferential direction and tending to disappear downstream in the annular region (see Figure 9). Figure 10 shows vortex structures development at the cross-section perpendicular to the gripper axis and passing through lateral jet axis (\(z_{2}\)) for three different gripper geome  
Figure 8: Gripper body subregions. Figure 9: Vortices around the releasing mass surface in the first part of the annular region visualized by velocity streamlines (\(d\) = 0.77 mm, \(L\) = 32.2 mm, \(D\) = 3.6 mm). tries. Vortices are symmetric with respect to the lateral jet axis, showing different shapes depending on gripper body diameter value (\(D\)). A smaller gripper body diameter indeed reduces the distance between lateral inlet and the impinging wall surface, influencing the vortices' spatial distribution and the tendency of the flow to stay attached to the cylindrical wall. Other parameters (\(d\), \(L\), \(p_{2}\)) do not have such an influence on that. Figure 10(a) shows the development of the average value of the static pressure, averaged over the cross-section, along the axis of the gripper. Immediately upstream of the jet, a negative pressure peak can be noted between the front chamber end (\(z_{1}\)) and the lateral jet axis (\(z_{2}\)) as a result of the vortex structure previously discussed (see Figure 10(b)). The flow entering the front chamber slows down until it almost stops and the pressure stabilizes at a uniform value. In the annular region, except for the first part where the flow is still affected by the vortices associated with the jet, the transverse velocity components (\(U_{x}\),\(U_{y}\)) tend to zero, while average average axial velocity component (\(U_{2}\)) increases and become dominant (see Figure 12). The flow accelerates in the axial direction: due to the pressure drop in the annulus, density falls sufficient quickly so that fluid velocity must rise to maintain a constant mass flow rate. The lower the outlet pressure value (\(p_{2}\)), the greater  
Figure 11: Pressure averaged over section \(z\) (constant), plotted against \(z/L_{tot}\) (**a**). Velocity streamlines and average pressure in front chamber and jet region (**b**). Figure 10: Vortical structures and velocity contours at plane (\(z=z_{2}\)) for different gripper body diameter values (\(D\)) (\(d\) = 0.77 mm, \(L\) = 32.2 mm, \(p_{2}\) = 90 kPa). the density fall in annular region, and as a consequence, the higher the increase of velocity in axial direction (see Figure 13). The flow at the end of the annulus region (\(z_{4}\)) detaches, creating a recirculation bubble whose length increases for lower outlet pressure. Moreover, a secondary recirculation region can be recognized close to the lateral wall due to the adverse pressure gradient occurring in the downstream region. In fact, the lowest pressure is localized just after the base of the releasing mass (see Figure 14), and a zone of diffusion is required to recover the outlet pressure.