# Turbulent Drag Reduction Characteristics of Bionic Nonsmooth Surfaces with Jets
## 3 Results and Discussion
### Drag Reduction Mechanism
#### 3.4.1 Turbulent Kinetic Energy  
The drag reduction behavior was clearly related to the turbulent kinetic energy. Turbulent kinetic energy represents the fluctuation length of turbulence, which can indicate the energy exchange frequency. The larger the turbulent kinetic energy was, the greater the energy loss produced. Figure 14 shows the turbulent kinetic energy contours of three surfaces at \(\mathrm{Re}=3.44\times 10^{6}\).  
The turbulent kinetic energy intensities of the nonsmooth surface and active surface were obviously less than that of the smooth surface, especially in the nonsmooth unit cell. However, the turbulent kinetic energy intensity on the windward side of the nonsmooth surface was markedly enhanced (region C). The existence of fluid diversion was the main reason for this phenomenon. The improved active surface alleviated the problem of fluid separation and had lower turbulent kinetic energy.  
\begin{table}
\begin{tabular}{c c c} \hline
**Surface Type** & **Skin Friction (N)** & **Skin Friction Reduction Ratio (\%)** \\ \hline Smooth surface & 0.851 & - \\ Nonsmooth surface & 0.805 & 5.41\% \\ Active surface & 0.696 & 18.21\% \\ \hline \end{tabular}
\end{table}
Table 4: Drag changes of surface B.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Surface Type** & **Jet Velocity** & **Pressure Drag** & **Skin Friction** & **Total Drag** & **Drag Reduction Ratio** \\  & **(m/s)** & **(N)** & **(N)** & **(N)** & **(\%)** \\ \hline Smooth surface & - & 0.000 & 1.312 & 1.312 & - \\ Nonsmooth surface & - & 1.108 & 0.789 & 1.897 & \(-\)44.50\% \\  & 1 & 0.971 & 0.783 & 1.755 & \(-\)25.19\% \\  & 3 & 0.742 & 0.770 & 1.511 & \(-\)15.16\% \\  & 5 & 0.578 & 0.747 & 1.325 & \(-\)0.96\% \\  & 7 & 0.466 & 0.715 & 1.181 & 11.09\% \\ Nonsmooth & 9 & 0.422 & 0.672 & 1.094 & 16.63\% \\ surface with jet & 11 & 0.438 & 0.621 & 1.059 & 19.35\% \\ (active surface) & 13 & 0.501 & 0.567 & 1.067 & 18.69\% \\  & 15 & 0.605 & 0.511 & 1.116 & 14.96\% \\  & 17 & 0.743 & 0.458 & 1.201 & 8.49\% \\  & 19 & 0.913 & 0.417 & 1.329 & \(-\)1.30\% \\  & 21 & 1.088 & 0.399 & 1.488 & \(-\)13.36\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Results of numerical simulations.  
Figure 15 shows the turbulent kinetic energy in the outlet section in surface B, see Figure 4. The turbulent kinetic energy intensity of the active surface was significantly lower than that of the other surfaces. The active surface clearly affected the turbulent kinetic energy in the vicinity of the unit cell and in the downstream areas of the active surface.  
It is evident from Figure 16 that an obvious closed recirculation region in which the velocity remained very low, was formed within the unit cell, and a mainstream flowed outside this region. The rotational direction at the bottom of the recirculation was opposite to that of the mainstream, whereas the rotational direction on the top was consistent with that of the mainstream.  
The presence of low-speed recirculation was similar to a rolling bearing. The resistance of rolling friction was less than that of sliding friction under the same conditions. If the friction between the fluid and the fixed wall was defined as fluid-wall sliding friction, then the role of the rolling bearing (recirculation) was to convert the original sliding friction into fluid-fluid rolling friction. The fluid-fluid rolling friction reduced momentum exchange and turbulent kinetic energy, resulting in drag reduction. In addition, the recirculation seemed to relax the no-slip boundary condition, which  
Figure 14: Kinetic energy contour.  
Figure 15: Comparison of turbulent kinetic energy near wall (surface B).  
lead to lower momentum losses in the active surface than in the smooth surface. Thus, the rolling bearing (recirculation) was one of the mechanisms governing the observed drag reduction.