# Aerodynamic Drag Reduction on Speed Skating Helmet by Surface Structures
## 4 Results and Discussion
### Fluid Field Profile  
The pressure drags accounted for 96% of the total aerodynamic drags according to the CFD results. As a result, the pressure distribution on the helmet surface played an important role in aerodynamic drag. The pressure coefficient was defined as  
\[C_{p}=\frac{P-P_{0}}{\frac{1}{2}\rho U^{2}} \tag{7}\]  
Figure 12a-c presented the iso-surface of zero streamwise velocity around the helmet models that were colored by \(C_{p}\). The direction of local velocity of air was opposite on both side of the iso-surface, which meant that the flow separation occurred on helmet surfaces. The separation line of the original helmet model mostly kept a line; however, for the riblet helmet model and the bump helmet model, the separation lines were obviously delayed, especially on the helmet sides. For the middle region of the helmets, the riblet structure did not have noticeable influence on separation line, while the bump structure was able to delay the separation line significantly. The flow separation could lead to generation of a low pressure region, thus increasing the pressure drag. Figure 12d-f illustrated the \(C_{p}\) contour on helmet model surfaces. The distribution of \(C_{p}\) on the windward side for all simulated models was similar, and the microstructure did not influence the pressure at  
this region. Obvious differences could be found at the rear region of the helmet. For the original helmet model, the low-pressure region at the rear that caused the pressure drag was much larger than that of the riblet structured helmet or the bumped helmet. Figure 13 presented the \(C_{p}\) along the midline of the helmet. It was found that \(C_{p}\), for all CFD helmet models, had almost the same values at the frontal region, and separated with the increase in \(\theta\). This difference in pressure reflected the changes of the fluid field near the helmet surface that were caused by the surface structures. With the increase in the air flow distance on the helmet surface (the increase in \(\theta\)), the interaction between the air and the surface structure was gradually enhanced, and finally, the flow properties changed. The decrease in \(C_{p}\) was due to the conversion process of kinetic energy of fluid to pressure energy. For the original helmet model, the pressure was especially lower than the structured models at \(\theta>90^{\circ}\), which led to a higher pressure drag. It was noted that \(C_{p}\) for the original helmet model was higher than others at the end of the helmet surface, and it was revealed that less kinetic energy was lost within the flow boundary layer for the original model compared with the structured ones. On the other hand, the surface structures increased the resistance of the fluid along the surface, including frictional resistance and local pressure resistance. The local pressure separation could be observed from Figure 12b,c around the riblet structures and bumps, which was the reason for increased local pressure resistance. As mentioned above, the frictional resistance and local pressure resistance were only a tiny  
Figure 12: (**a–c**) The iso-surface of zero velocity: (**a**) original, (**b**) riblet, (**c**) bump. (**d–f**) The contour of pressure on the helmet surface: (**d**) original, (**e**) riblet, (**f**) bump. fraction of the total drag of the helmet; therefore, these phenomena had scant impact on the total drag. The pressure drag and separation position were closely related to the boundary layer of the air near the helmet surface. Figure 14 presented the dimensionless root mean square (RMS) as \(\sqrt{\overline{u^{\prime 2}}}/U\) at different positions near the surface, where \(u^{\prime}\) was the fluctuating velocity, \(U\) was the free stream velocity, and r was the distance from the surface. The RMS of fluctuation velocity could present local turbulence intensity. The fluctuating velocity for all helmet models in the vicinity of \(\theta=60^{\circ}\) had a large value far from the surface, as shown in Figure 14a.