A new type of microstructure inspired by the cross section of barchan dunes was proposed to reduce windage, which was considered as a passive drag reduction technology in aerospace manufacturing field. Computational fluid dynamics method was carried out to discuss the effect of the microstructure on the skin friction reduction under high velocity flow condition. Different microstructure heights were employed to survey the reduction of drag. The results illustrated that the appearance of microstructure led to a generation of pressure drag in non-smooth model (with microstructures inspired by cross section of barchan dune) in contrast to smooth model. However, the microstructure significantly increased the thickness of the low-speed fluid by 11.4% in the near-wall flow field, causing the low-speed fluid to rise and decreasing the velocity gradient near the wall, thereby reducing viscous resistance. In addition, high-speed fluid flowed above the microstructure units instead of along the inner side of the units due to the influence of micro-vortex, resulting in a reduction of friction near the surface. Furthermore, micro-vortex was considered to be the significant internal factor to achieve turbulent drag reduction since it could not only reduce the viscous resistance by promoting the fluid flow above the microstructure but also provide a reverse thrust force. The understanding of the mechanism of drag reduction provides theoretical guidance for further fabrication of drag reduction coatings using renewable materials.

In recent years, the proportion of air transport in the transportation industry is becoming larger with the development of economy. Due to the severe challenges posed by climate change, modern aviation technology developments are driven by the requirement of energy conservation and environmental protection. The need for greatly reduced greenhouse gases such as carbon dioxide and nitrogen oxides, will establish a new criterion in aeronautical material design. It is worth noting that emissions can be significantly reduced by curtailing fuel consumption, which can be achieved by reducing the drag generated during flight. Therefore, it is important to reduce skin friction, a major element of the overall drag, for the purpose of fuel consumption during flight. It has been reported that almost half of total drag is due to the viscous drag, which is directly related to the friction drag of the aircraft [

As a typical type of passive drag reduction methods, bionic non-smooth surface methods have been raised in early 1970s [

However, traditional riblet structures inspired by shark skin are more suitable for hydrodynamic drag reduction than aerodynamic drag reduction, owing to the limitations of shark’s living environment [

Although structures inspired by cross section of barchan dunes exhibit excellent drag reduction in the aerodynamic field, nevertheless, previous researches are mainly limited to the drag variations caused by large-size (millimeter range) structure under the condition of low-speed air flow. Obviously, uncertainties still exist in extrapolating outcomes from low speed to high speed, High-Reynolds-number flows. Moreover, the interactions between inner and outer wall mechanisms and the role of the structural scale in the increasing speed have not yet been reported in detail. In this work, the effectiveness of micro-structure inspired by cross section of barchan dune on drag reduction performance was studied using computational fluid dynamics (CFD) methods under high-speed flow condition. Pressure distribution and velocity analysis were mainly used to characterize the variation of flow field. Furthermore, the drag reduction mechanism was also analyzed to provide theoretical guidance for the design and optimization of microstructures in aeronautical applications, thereby providing technical support for further fabrication of drag reduction coatings using renewable materials.

The microstructure units are based on the nature barchan dunes, which are shaped by blowing in the same direction [

A typical model of the barchan dune is constructed as a simple geometric shape consisting of the symmetrical windward side and slip face, as presented in

To investigate the drag reduction effect by the geometrical parameters of microstructure, the height of microstructure (H) and the angle of repose (α) were introduced, which represented the main parameters of the microstructure unit.

A rectangle field was adopted as the computational domain with a length of 400 mm. To avoid the interaction between the top and bottom wall of the calculation model, the height of the rectangle field was defined to be 250 mm. In addition, microstructure with total length of 80 mm was arranged at the middle of the underside of the computational domain. Furthermore, two flat regions were placed in the front and back of the microstructure region with identical length of 60 mm. These regions were created to ensure a steady flow field when the fluid flowed through the microstructure. In view of the compressible flow condition, extra 100 mm lengths were reserved at the inlet and outlet boundary respectively, increasing the precision of the calculation results as shown in

For the same geometric structure, the physical model can be changed when the geometric parameter of structure transforms significantly. Thus, it is essential to reconsider the continuity of the physical model due to the fact that the size of structure unit reaches the micron scale. The mean molecular free path of air is 69 nm [

Considering applications in aviation field, the flow velocity (_{∞}) was defined as 250 km/h. The calculation equation of the Reynolds number of a plate is shown below:_{∞} is the fluid flowing velocity, and ν is the coefficient of kinematic viscosity.

The coefficient of kinematic viscosity of air is 1.4607 × 10^{−5} m^{2}/s. The corresponding Re_{L} is 9.50 × 10^{5}, revealing a turbulent state in flow field. The velocity distribution of the inlet part and the front of structure area is inset in _{L}) and the allowable roughness values (k_{adm}) at different speeds need to be determined by following equations:

Realizing the influence of microstructure on boundary layer fluid is an important method to reduce drag. Therefore, the height of microstructure unit should be smaller than the thickness of the turbulent boundary layer, which is calculated to 4.72 mm. In addition, when the height of the microstructure is less than the allowable roughness value, the structure demonstrates a few disturbances to the flow field, which can be considered as a smooth surface. According to the flow velocity used in this work, the allowable roughness value was defined as 21.65 μm. Moreover, the dimensionless roughness k^{+} was described as following:

where _{*} is characteristic length. Therein,

According to the flow velocity, the corresponding _{*} is 4.36 × 10^{−6}. When the height of the structure is set as 30 μm, the corresponding ^{+} ^{+}

The calculation model was analyzed by both incompressible and compressible model. N–S equations were employed as governing equations, simultaneously, the RANS method was introduced to approach the equations and calculate the physical quantity in flow field. Previous researches indicated that the realizable

The equations for turbulent kinetic energy

For ideal gas, the turbulent viscosity coefficient is expressed as following:

The enhanced wall treatment, which was suitable for complex flow in a high-Reynolds-number turbulence model, was used for the near-wall treatment. More specific parameters of above equations can be referred to previous literatures [

To verify the reliability of realizable _{f}) was used as an evidence for judgement, which was expressed as

Turbulent model | Simulation C_{f} |
Theoretical C_{f} |
Relative error |
---|---|---|---|

S-A | 5.6985 × 10^{−3} |
4.7167 × 10^{−3} |
20.90% |

K-e-realizable | 4.7483 × 10^{−3} |
0.74% | |

K-e-standard | 5.1433 × 10^{−3} |
9.12% | |

K-e-RNG | 5.1004 × 10^{−3} |
8.21% | |

K-w-standard | 5.5990 × 10^{−3} |
18.79% | |

K-w-SST | 5.6745 × 10^{−3} |
20.39% | |

RSM-L | 5.0061 × 10^{−3} |
6.21% | |

RSM-Q | 5.2229 × 10^{−3} |
10.81% | |

RSM-L-R | 6.2184 × 10^{−3} |
31.93% |

Fluent 19.2 was used for numerical simulation. The TOP and BOTTOM regions were defined as symmetry boundary in order to prevent sidewall interference. The detail condition was set as follows:

Moreover, PLATE and STRUCTURE regions were set as stationary walls. Since the fluid is incompressible, the wall temperature is set to a default value of 300 K and the effect of temperature on density is ignored. The no-slip boundary condition was set as follows:

For incompressible flow, the INLET and OUTLET were defined as velocity inlet boundary and pressure outlet boundary, respectively. The inlet velocity was set as follows:

Moreover, the flow is assumed to be fully developed, and the pressure outlet boundary was set as follows:

The grid of the calculation model was established by ICEM 19.2. Inflation layers were adopted on the downside of the computational domain in order to satisfy the computation requirement near the wall. The number of inflation layers was defined as 10, and the growth rate was set as 1.2, as shown in

where τ_{ω} is the wall shear stress, ρ is the fluid density of 1.225, _{∞} is the fluid flowing velocity, _{τ} is the velocity calculated by the wall shear stress, ^{+} is a non-dimensional parameter that expresses the distance to the wall and μ is the dynamic viscosity. Therefore, the initial height was defined as 1 × 10^{−6} mm, which guarantees ^{+} about 1.

To implement the verification of grid independence, the inlet velocity is defined as 250 km/h (Re = 9.50 × 10^{5}), and the skin friction coefficient of the plate is calculated under five grids with different densities, as shown in

The pressure-based solver was selected for incompressible flow condition. A second-order upwind format with higher precision was employed to analyses the dissociation of the momentum, turbulent kinetic energy, and turbulent dissipation rate. The SIMPLEC algorithm was adopted to facilitate a rapid convergence of the calculation under stable conditions. A Green-Gauss node based discrete format was used for the gradient of spatial discretization. All the residual values for determining convergence were set to be less than 10^{−6}. The stability of the import and export flows was also monitored to further ensure the veracity of convergence.

Different flow velocities were selected for simulation calculation and theoretical skin friction coefficient values were compared with simulation results in order to further verify the accuracy of the calculation model. As depicted in ^{−3} to 4.106 × 10^{−3} with the increase of flow velocity. Otherwise, simulation results demonstrate the same tendency with theoretical values. The maximum relative error between the simulation and theoretical results is 6.99%, indicating the reliability of calculation model used in this work. Moreover, the accuracy of the computation was also validated by comparing turbulent flow characteristics over the microstructure surface with previous research results [

Drag reduction ratio (R_{D}) is usually used to evaluate drag reduction performance of non-smooth surfaces. The drag reduction rate is calculated using the following equation:_{non-smooth}_{smooth}

A series of microstructures with different height were adopted to explore the variation of drag reduction under a certain flow velocity of 250 km/h. In contrast, a smooth model was calculated in the same condition. The detailed data of drag variation is listed in

Height (μm) | Drag of non-smooth model (N) | Viscous drag of non-smooth model |
Pressure drag of non-smooth model (N) | Drag of smooth model (N) | R_{D} |
---|---|---|---|---|---|

40 | 2.87 | 1.94 | 0.93 | 2.98 | 3.54 |

50 | 2.85 | 1.88 | 0.97 | 4.23 | |

60 | 2.88 | 1.81 | 1.07 | 3.36 | |

70 | 2.90 | 1.79 | 1.10 | 2.70 | |

80 | 2.94 | 1.74 | 1.19 | 1.28 | |

90 | 3.00 | 1.71 | 1.28 | 0.67 | |

100 | 3.05 | 1.67 | 1.38 | −2.34 | |

120 | 3.20 | 1.62 | 1.57 | −7.51 | |

140 | 3.33 | 1.57 | 1.76 | 11.90 |

In order to further investigate the influence of microstructures on the pressure distribution, three positions were selected to observe at 160 mm (initial of structure), 200 mm (middle of structure) and 240 mm (terminal of structure) from the entrance, respectively. Local details are presented and enlarged in the upper right corner, as shown in

For purpose of surveying the influence of the microstructure on the velocity distribution in the flow field, the smooth and non-smooth models are calculated for comparison, as shown in

A velocity vector graph of the flow field along the middle of microstructures area is extracted in

Moreover, the low-speed micro-vortexes are formed within the microstructure units, and each micro-vortex has an extremely similar shape. It is clear that the rotation direction of the bottom of the micro-vortex is opposite to the fluid direction giving rise to the negative velocity in local area, as observed in the enlarged area in

To quantitatively analyze the influence of the microstructure on the horizontal velocity distribution of the flow field, a straight line perpendicular to the bottom surface is selected from the middle position of microstructures region where the flow field is relatively stable and can better reveal the effect of structure on flow field distribution. Meanwhile, the horizontal velocity values along the same line are also extracted. For comparison, the smooth model is also analyzed under the same conditions. As presented in ^{+}) in the two models is revealed. In particular, the low-speed region marked by the blue dotted frame is enlarged and displayed in the upper left corner. In order to show the velocity distribution at the boundary layer clearly, the velocity data in partial high-speed areas are hidden, on account of the extreme similarity of velocity values among the two models.

It can be seen that the existence of the microstructure changes the velocity profile at the bottom of the boundary layer. Comparing with the velocity curve of the smooth model, the curve of the non-smooth model is shifted to the left. This indicates that the appearance of microstructure significantly reduces flow velocity near the wall, thereby reducing the viscous resistance. Simultaneously, as observed in the enlarged area, the velocity profile diagram shows that the velocity of the non-smooth model is much smaller than that of the smooth model under the height of microstructure unit. It means that the microstructure retains a large amount of low-speed fluid, increasing the thickness of the low-velocity fluid and reducing the viscous resistance. This is consistent with the results of the velocity clouds. In addition, due to the appearance of micro-vortexes within the microstructures, reverse velocity even appears near the wall, as shown in the enlarged area. The reverse fluid in the microstructure provides an extra opposing thrust, which contributes to drag reduction. This also validates the analysis of the velocity vector diagram. Moreover, when the Y^{+} is higher than 160, the velocity profile curves under the two models show a high degree of consistency, which proves once again that the microstructure only changes the flow field at the bottom of the boundary layer without causing interference to the external flow field.

The wall friction resistance is closely related to the wall shear stress. The direction along fluid flow is defined as the X direction. The wall shear stress of the front, the end and the middle of the microstructure area in X direction is illustrated in

In addition, the wall shear stress of the microstructure is smaller than that of the smooth surface in a large number of regions, which is displayed by the black dotted line. Moreover, the wall shear stress value in the local area is even less than 0, resulting in the appearance of a reverse friction which can be called “viscous thrust”.

Despite of the pressure drag, it is believed that the decrease of viscous resistance still plays a major role in the change of total drag.

A bionic microstructure inspired by the shape of cross section of barchan dune has been proposed in this study. A series of tests were employed to reveal the influence of microstructure on the drag reduction under high flow velocity condition. Numerical simulation results indicated that the microstructure with a height of 50 μm had a significant effect on drag reduction, with a maximum value of 4.23% at a flow speed of 250 km/h.

In contrast to smooth model, the non-smooth model demonstrated an obvious pressure drag caused by microstructures. However, the microstructure significantly increased the thickness of the low-speed fluid by 11.4% in the near-wall flow field, causing the low-speed fluid to rise and decreasing the velocity gradient near the wall, thereby reducing viscous resistance. In addition, high-speed fluid flowed above the microstructure units instead of along the inner side of the units due to the influence of micro-vortex, leading to a reduction of friction near the surface. Furthermore, the existence of micro-vortexes could be considered to be the significant internal factor to achieve turbulent drag reduction since it could not only reduce the viscous resistance by promoting the fluid flow above the microstructure but also provide a reverse thrust force. The understanding of the mechanism of drag reduction provides theoretical guidance for further preparation of drag reduction coatings using renewable materials.