# Aerodynamics Analysis of Speed Skating Helmets: Investigation by CFD Simulations
## 6 Results and Discussions  
### Skater's Flow Topology  
Figure 8a illustrates zero streamwise velocity regions around the skater without helmet. The size and shape of the recirculation regions can be visualized, in particular downstream the upper left leg, the lower right leg, the occipital and the ears.  
Pressure coefficient \(C_{p}\) iso-surface is shown in Figure 8b, in order to visualize the suction generated by the head. In black, positive pressure (\(C_{p}=0.55\)) is visualized to identify the stagnation regions in front of the head, the shoulders and the legs. The negative pressure (\(C_{p}=-0.3\)) is color-coded by the streamwise velocity component to allow differentiating the natural acceleration of the flow around a curved surface (in red) and the boundary layer separation (blue-green-yellow). Large suction appears downstream the occipital, ears, upper left leg, lower right leg and left sole. It has to be noted that a large low pressure stream emerges from the head, as a consequence of the boundary layer separation at the upper head side.  
Besides, the flow topology in the wake of the skater is discussed in the form of spatial distribution of streamwise velocity (Figure 9) and vorticity with velocity field vectors. The vertical plane was located at \(x\sim 0.85\) distance downstream from the lower back of the model. The lateral asymmetry of both velocity and vorticity fields originate from the asymmetric posture of the mannequin. The streamwise velocity contour exhibits four main regions of relevant velocity deficit (Figure 9a). The first two are located behind the upper left leg (\(z\sim 0.5\) m & \(y\sim-0.125\) m) and the left foot (\(z\sim 0.25\) m & \(y\sim-0.125\) m), featuring a minimum velocity of \(v_{x}/U_{\infty}\sim 0.6\). The first one has a larger area, as the frontal area of the upper left leg is significantly larger. The remaining two regions characterized by velocity deficit are located behind the head (\(z\sim 1\) m & \(y\sim 0\) m) and the lower right leg (\(z\sim 0.4\) m & \(y\sim 0.125\) m) and feature a velocity of \(v_{x}/U_{\infty}\sim 0.8\). The velocity is higher in these last regions as the corresponding body segments are located more upstream from the evaluated vertical plane. A dominant region of strong downwash downstream of the upper left leg (\(z\sim 0.5\) m & \(y\sim-0.125\) m) is identified in Figure 9b, with a peak vertical velocity of \(v_{z}/U_{\infty}\sim-0.4\). The absolute value is higher than the one observed in cycling (\(v_{z}/U_{\infty}\sim-0.17\) at \(x\sim 0.8\) from the bike saddle) [33]. This downwash occurs in the middle of a counter rotating streamwise vortex pair that is characteristic also for the flow across a cyclist [34]. Moreover, it has to be noted that a weaker counter-rotating vortex pair is originated behind the head (\(z\sim 1\) m & \(y\sim 0\) m), indicating a weak upwash trend.  
Figure 8: Flow topology around a skater without helmet, **(a)**zero velocity iso-surface schematic in blue colour and **(b)**\(C_{p}\) iso-surface schematics, in black positive \(C_{p}=0.55\) and in blue–red rainbow negative \(C_{p}=-0.3\). Negative pressure coefficient iso-surface was coloured with streamwise velocity \(v_{x}/U_{\infty}\).