# Shark Skin—An Inspiration for the Development of a Novel and Simple Biomimetic Turbulent Drag Reduction Topology

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

^{+}, h

^{+}, etc.) and shapes of different riblets, the flow field, and the yaw angle (γ) on turbulent drag reduction have become the focus of research, since excellent performance and significant development prospects have been scientifically demonstrated by many experimental and numerical studies. In a classic experiment, Bechert et al. investigated drag reduction using a plastic model surface of compliant shark scales with riblets [3]. The surface consisted of 800 individual movable scales, allowing different angles of flow attack to be simulated. The achievable wall shear stress reduction was 3%. Lee and Lee [4] reported various effects of a non-smooth surface with different sizes of circular concavities on near-wall turbulence (reduced drag when s

^{+}= 25.2 and increased drag when s

^{+}= 40.6). Djenidi and Antonia [5] applied laser Doppler anemometry to investigate flow over surfaces with V-shaped riblets and found that the riblets could decrease and increase drag when s

^{+}= 25 and s

^{+}= 75, respectively. The linear relationship between drag reduction and the non-dimensional parameter of the rectangular riblet in pipe flow was proven by Rapp [6] in 2006. With well-designed experiments in an oil tank, Bechert et al. [1] investigated the drag reduction performance of different riblet shapes, including triangular, trapezium, and blade-shaped riblets. The results showed that blade-shaped riblets, which reduced turbulent shear stress by 9.9% compared to smooth surfaces when h = 0.5 s, had the best drag reduction performance. Wang et al. [7] experimented with four different types of riblets and found excellent drag reduction performance, with the maximum reduction being 26%. Comparative studies by Cong et al. [8] on drag reduction and turbulent flow over triangular, scalloped, and blade-shaped riblets showed that the drag of these three bionic non-smooth surfaces was smaller than that of smooth surfaces, with blade-shaped riblets producing the greatest drag reduction and scalloped riblets producing the second greatest. Researchers including Choi [9], Debisschop and Nieuwstadt [10], Wang et al. [11], and Cong and Feng [12] have researched the effect of the pressure gradient of the flow field on drag reduction, but no general agreement has yet been reached. There have also been elaborate investigations of the differences between longitudinal and transverse non-smooth surfaces. Paolo et al. [13] employed numerical methods to study the general aspects of flows over transverse and longitudinal regular sinusoidal, triangular, and parabolic riblets. Fukagata [14] experimentally found that drag decreased over longitudinal wavy surfaces.

^{+}= 8~23 and the maximum drag reduction was gained when s

^{+}= 11~15. Nevertheless, some researchers pointed out that the riblets with rounded peaks that Nitschke used did not produce the greatest effects in reducing turbulent drag on flat plates in the developing external flows. Chen and Leung [16] performed a series of experiments with three different types of ribletted surface and proved that all three longitudinal surfaces achieved drag reduction in internal turbulent flow. In a comparative experiment, Reidy and Anderson [17] applied sharply peaked, symmetrical, triangular riblets manufactured by 3M Company to both flat plates and the inside of a six-inch pipe. The results showed that the drag reduction in internal turbulent flow was three times that in external turbulent flow. Enyutin et al. [18] studied fully developed turbulent air flow in a pipe with different types of riblets and reported a maximum drag reduction of 5~6%. In that experiment, the authors again proved that surfaces with triangular riblets showed better drag reduction performance than ribletted surfaces with rounded peaks. Shiki et al. [19] made further progress in this direction. These authors analyzed the velocity profile, static pressure, and flow rate of triangular riblets of different shapes and sizes in a fully developed turbulent pipe flow. The pipe was 492 mm in interior diameter and 4000 mm in length, with Reynolds number flows between 3.0 × 10

^{5}and 8.0 × 10

^{5}, and the maximum drag reduction gained was 8% at approximately h

^{+}= 11.4. The authors thereby deduced the optimum geometrical shape and size of riblets for turbulent drag reduction in pipes.

^{4}and Re = 7 × 10

^{4}, these authors observed some phenomena, such as airfoils with different thicknesses and camber caused LSB (either short or long) to form, resulting in variations in aerodynamic force with time. Taking LFM as the research object on Clark-Y airfoils was the first and pioneering research by Koca et al. [32]. In their study, the objective was to determine flow phenomena in detail and the authors investigated the effects of LFM mounted on the leading edge over the suction surface of a Clark-Y airfoil. The results showed that a more stable airfoil aerodynamic performance, which produced less vibration and less noise, could be obtained by means of flow-induced passive oscillation with LFM at the local surface of the airfoil, thereby increasing turbine blade stability.

## 2. Materials and Methods

_{SMOOTH}= dr.

^{+}≈ 1 according to previous experience and the requirements of LES [39]. Second, mesh coarsening away from the pipe wall helps to reduce the overall number of cells. Third, streamwise and spanwise meshing should be uniformly distributed. Fourth, the cell size should be small enough to capture the coherent structure and other flow features. Last, but not least, the meshing of the non-smooth pipe with riblets and the smooth pipe should be basically the same. An appropriate time step strongly influences accuracy and time expenditure. According to the suggestion by Wu and Moin [40], the time step should be relatively small at the beginning of the calculation to eliminate the “priming effect” caused by an initial velocity field that does not fit with reality. The time step can be appropriately increased after a period of calculation time. In the first 500 iterations, the maximum axial CFL component was fixed at a small value of 0.05 and the corresponding time step Δt was approximately 0.0002. This was to allow the start-up effect associated with the imposed unrealistic initial velocity field to diminish. After the first 500 iterations, the computational time step was fixed at Δt = 0.01 and the maximum allowed axial CFL component was set at 1.0.

## 3. Results and Discussion

#### 3.1. Evolution of a Coherent Structure near the Wall

#### 3.2. Turbulent Drag

^{+}= 18.9737). We can state that the optimum drag reduction s

^{+}was not less than 18.9737, but we could determine the exact value. With reference to formerly published research, we next studied the turbulent drag of the two biomimetic topologies using riblets C1 and C2, in comparison with the results shown in Table 4. The ribletted pipes studied in the present work showed excellent drag reduction performance. Riblet C2, designed from the bionic perspective, evidenced the best drag reduction performance in this research.

#### 3.3. Thickness of Viscous Sublayer

_{w}is the wall shear stress, and ρ is the density of the fluid.

#### 3.4. Analysis of Turbulent Flow Field

#### 3.4.1. Velocity Profiles

#### 3.4.2. Velocity Fluctuation

#### 3.4.3. Streamwise Vorticity Distribution

#### 3.4.4. Reynolds Shear Stress

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

U | Mean streamwise velocity |

τ_{w} | Wall shear stress |

u^{*} | Friction velocity |

U^{+} | Non-dimensional mean streamwise velocity |

${s}^{+}=su\ast /\nu $ | Non-dimensional riblet spacing |

${h}^{+}=hu\ast /\nu $ | Non-dimensional riblet height |

γ | Angle between the flow direction and riblets |

C_{s} | Smagorinsky constant |

D | External diameter of non-smooth pipe |

A | Cross-sectional area of non-smooth pipe |

$\mathrm{DR}=\frac{F-{F}_{RIBLET}}{F}\times 100\%$ | Drag reduction efficiency |

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**Figure 1.**Schematic demonstration of streamwise vortex interaction with ribletted surface via viscous effects [34].

**Figure 2.**Schematic of mean velocity profiles and effective protrusion heights for flow in both the longitudinal protrusion direction, h

_{pl}, and cross-flow direction, h

_{pc}[1].

**Figure 6.**Evolution of coherent structure near the pipe wall. Figure 6 was obtained by monitoring the streamwise velocity of the same cross-section in four consecutive flow periods (

**a**–

**d**).

**Figure 7.**Diagrams of (

**a**) coherent structure parallel to streamwise direction and detailed views of (

**b**) ellipse 1 and (

**c**) ellipse 2.

**Figure 9.**Contour of velocity at flow cross-section for (

**a**) smooth pipe and (

**b**) non-smooth pipe with riblet C1.

**Figure 10.**Contours of velocity near the surface of $\frac{r}{R}=0.03$ for (

**a**) smooth pipe and (

**b**) non-smooth pipe with riblet C1.

**Figure 12.**Contours of RMS of velocity magnitude at vertical flow cross-section for (

**a**) smooth pipe and (

**b**) non-smooth pipe with riblet C1.

**Figure 13.**Contours of velocity fluctuations near surface of $\frac{r}{R}=0.03$ for (

**a**) smooth pipe and (

**b**) non-smooth pipe with riblet C1.

s | h | s_{1} | s_{2} | h_{2} | D | dr | L | |
---|---|---|---|---|---|---|---|---|

riblet C1 (mm) | 0.1524 | 0.1524 | —— | 0.0762 | 0.0762 | 12.7 | 12.5718 | 63.5 |

riblet C2 (mm) | 0.1524 | 0.1524 | 0.0381 | 0.0762 | 0.0762 | 12.7 | 12.6039 | 63.5 |

Riblet Form | Flow Rate of the Whole Pipe | Flow Rate of the Quarter of Pipe | A (mm^{2}) | d_{r} (mm) | ρ (kg/m^{3}) | $\overline{\mathit{u}}\text{}(\mathbf{m}/\mathbf{s})$ | ν (m^{2}/s) | Re |
---|---|---|---|---|---|---|---|---|

riblet C1 | 0.4 kg/s | 0.1 kg/s | 124.1323 | 12.5718 | 1000 | 3.2224 | 10^{−6} | ≈40,459 |

riblet C2 | 0.4 kg/s | 0.1 kg/s | 124.7670 | 12.6039 | 1000 | 3.2060 | 10^{−6} | ≈40,459 |

Re = 10,115 | Re = 40,459 | |||||
---|---|---|---|---|---|---|

Smooth | Riblet C1 | Riblet C2 | Smooth | Riblet C1 | Riblet C2 | |

s^{+} | 0 | 6.9601 | 6.9601 | 0 | 18.9737 | 18.9737 |

s_{1}^{+} | 0 | 0 | 1.74 | 0 | 0 | 4.7434 |

s_{2}^{+} | 0 | 3.4801 | 3.4801 | 0 | 9.4869 | 9.4869 |

Turbulent drag | 0.0013 | 0.0011 | 0.001061 | 0.0107 | 0.0086 | 0.008327 |

% DR | — | 15.3846 | 18.3462 | — | 19.6262 | 21.4475 |

Ref. | Shape of Riblet | Domains | % DR |
---|---|---|---|

[1] | Longitudinal blade-shaped ribs with slits | Oil channel experiment | 9.9 at fully developed turbulent state |

[2] | Fins | Flat plate flow experiment | 7.3 at fully developed turbulent state |

[3] | Individual movable scales | Surface flow experiment | 3 at fully developed turbulent state |

[7] | Trapezoidal riblet | Flat plate flow experiment | 26 at Re = 31406 |

[15] | Longitudinal grooves | Tubes flow experiment | 3 at moderate Re |

[18] | Triangular riblet | Pipe flow experiment | 6 at Re = 3.0 × 10^{5} − 4.0 × 10^{5} |

[19] | Isosceles-shaped V-groove riblet | Pipe flow experiment | 8 at Re = 3.0 × 10^{5} − 8.0 × 10^{5} |

[42] | Real shark skin | Water tunnel experiment | 13.63 at fully developed turbulent state |

[43] | Blade-shaped riblet | Channel flow simulation | 9 at Re = 210 |

Present | Riblet C1 | Pipe flow simulation | 19.63 at Re = 40,459 |

Present | Riblet C2 | Pipe flow simulation | 21.45 at Re = 40,459 |

Re = 10,115 | Re = 40,459 | |||||
---|---|---|---|---|---|---|

Smooth | Riblet C1 | Riblet C2 | Smooth | Riblet C1 | Riblet C2 | |

Thickness of viscous layer | 1.0948 × 10^{−4} | 1.749 × 10^{−4} | 1.8426 × 10^{−4} | 3.84 × 10^{−5} | 6.4253 × 10^{−5} | 7.157 × 10^{−5} |

Increment (%) | — | 59.755 | 68.303 | — | 67.417 | 83.278 |

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**MDPI and ACS Style**

Fan, S.; Han, X.; Tang, Y.; Wang, Y.; Kong, X.
Shark Skin—An Inspiration for the Development of a Novel and Simple Biomimetic Turbulent Drag Reduction Topology. *Sustainability* **2022**, *14*, 16662.
https://doi.org/10.3390/su142416662

**AMA Style**

Fan S, Han X, Tang Y, Wang Y, Kong X.
Shark Skin—An Inspiration for the Development of a Novel and Simple Biomimetic Turbulent Drag Reduction Topology. *Sustainability*. 2022; 14(24):16662.
https://doi.org/10.3390/su142416662

**Chicago/Turabian Style**

Fan, Shaotao, Xiangxi Han, Youhong Tang, Yiwen Wang, and Xiangshao Kong.
2022. "Shark Skin—An Inspiration for the Development of a Novel and Simple Biomimetic Turbulent Drag Reduction Topology" *Sustainability* 14, no. 24: 16662.
https://doi.org/10.3390/su142416662