Drag reduction characteristics and flow field analysis of textured surface

A textured surface with a micro-groove structure exerts a distinct characteristic on drag reduction behavior. The fluid dynamic models of four textured surfaces are constructed in various profile geometries. Computational fluid dynamics is used to study the friction factors and drag reduction properties with various flow speeds on the textured surfaces. The friction coefficient varieties in the interface between the fluid and the textured surface are examined according to the simulation of the four geometries with V-shaped, saw tooth, rectangular, and semi-circular sections. The drag reduction efficiencies decrease with the increase in water velocity while it is less than a certain value. Moreover, the simulation results of the velocity, shear stress, energy, and turbulence effect on the V-shaped groove surface are presented in comparison with those of the smooth surface to illustrate the drag reduction mechanism. The results indicate that the peaks of the V-shaped grooves inhibit the lateral movement of the turbulent flow and generate the secondary vortex, which plays a key role in the impeding momentum exchange, thereby decreasing turbulent bursting intensity and reducing shear stress in the near-wall flow field. The kinetic energy and turbulence analysis shows that the vortex in the near-wall flow field on the textured surface is more stable compared to that on the smooth surface.


Introduction
The micro-structures fabricated on a mechanical surface show very practical value because of their special functions, such as drag reduction and anti-icing, dustproof, and self-cleaning abilities, among others [1,2]. One may intuitively expect that the smallest skin friction can be obtained on a very smooth surface. However, studies on shark skin and its inspired microstructured surfaces show that the textured surface performs better on drag reduction [3]. The drag reduction phenomenon was discovered by Toms in 1948 [4]. The textured surfaces, which are longitudinally fabricated with micro-grooves with the mean flow direction effectively reduce drag. Although micro-grooves increase the surface area, experiments showed results of dramatic reduction in flow drag when compared with a smooth surface. Rohr and Andersen observed an equivalent drag reduction performance of a riblet made by the 3M Company. Their results showed drag reduction peaks between 6% and 9% at dimensionless units for a groove height h + = 12 [5]. Neumann studied a V-shaped groove surface attached to a cylinder and obtained 13% drag reduction rate in a water tunnel experiment [6]. The riblets could hamper the near wall momentum exchange and delay the development of initial turbulent structures.
Further development of this technology needs a deep understanding of the drag reduction mechanism on the textured surface. NASA has investigated the riblet effects since the 1970s. Walsh [7] first studied the turbulent drag reduction features of the microgrooves on the surface. Bechert et al. [8] investigated the 166 Friction 4(2): 165-175 (2016) riblet geometries with respect to a potential reduction in friction. Accordingly, the ratio of the riblet to the riblet width is the determinant factor. In the aspect of a drag reduction experiment, Gruneberger and Hage [9] and Teo and Khoo [10] examined the momentum exchange of turbulent flow in the near wall region. They found that the fierce momentum could reduce the drag reduction performance. The rough surface flow swept over the grooves. Moreover, the contact area was reduced in comparison with the smooth surface flow, thereby improving the tribological performance [11]. The turbulent characteristics on the textured surface were also investigated in terms of a semi-circular riblet surface [12]. The latest experiments were performed by Aljallis et al. to test the performance of superhydrophobic coated aluminum plates [13]. Most of the stream vortices, which frequently interacted with the riblet tips, were considered to stay above the riblets in the case of drag decrease. The riblet tips impeded the spanwise movement of the streamwise vortices and induced a secondary vortex. Moreover, the velocity fluctuations and turbulent kinetic energy near the riblet surface were lower than those over the smooth surface. Many attempts have been made to investigate the fluid drag mechanisms on the bioinspired structured surface. However, the entirety of the phenomena is not yet fully explained [14].
The secondary vortex is considered to weaken the low-speed fluid ejection from the near-wall region, which consequently impedes the momentum exchange and turbulent bursting intensity. It can also hinder the down-sweeping movement from the high-speed to the low-speed region with a consequent shear stress reduction on the solid wall, thereby stabilizing a lowspeed streak in the valley [15,16]. However, the drag reduction mechanisms are not fully understood in terms of velocity, stress, and energy characteristics.
The drag reduction characteristics of the textured surface are presented in this article in terms of the profile geometries and friction coefficient. The background and state-of-the-art research are first critically reviewed. The modeling and computational conditions are illustrated in Section 2. The fluid dynamic model (FDM) is built based on grid optimization, boundary setting, and turbulence model applications. The friction coefficients are researched and analyzed in Section 3.
The drag reduction mechanism is presented with a detailed analysis on the flow field in Section 4. Conclusions are then drawn in light of the section types and drag reduction mechanism.
2 Modeling on the metal textured surface

Geometrical parameters of the micro-groove structure
The simulation models of the textured surfaces with four typical sections (i.e., V-shaped, saw tooth, rectangular, and semi-circular) are built. The feature dimension of all the models is 30 μm (Fig. 1). The computational domain models are built in the commercial preprocessor, Gambit, and solved in the software package, Fluent. The FDM of the four kinds of groove surfaces is proposed in this section. The simulation accuracy is decided by the grid quality. The mesh generation with a fine grid has been adopted in the computational domain near the smooth and groove surfaces because the present study most focuses on the turbulence structure of the top and bottom surfaces. Accordingly, the mesh size gradually increases to the center section. Unstructured triangular grids are applied to the computational domains of the 3D geometrical models to achieve good grid quality (Fig. 2). The Gambit-size function is used to calculate the mesh structure size and capture the flow characteristics during the meshing process. The grid optimization, boundary setting, and turbulence effect are then set to keep the reliable accuracy of the water flow simulation. The size function can let the grids changing from small to big order in the direction of the up-bottom surfaces to the flow  center. The groove calculation region is set as 0.24 mm × 0.43 mm. This kind of meshing method can balance the simulation precision and computational efficiency. The meshed model is checked and adapted to obtain the convergence and consistence results and to affirm that the mesh density cannot affect the calculation results.

Boundary conditions and computational parameters
As regards the turbulent simulation in the research, the Reynolds stress model (RSM), with its strict consideration of vortex flow and complex surface, can be suitable for the modeling process. Therefore, the model adopts the RSM for the simulation. The boundary conditions in the model are illustrated in Fig. 3, with the V-shaped groove surface as an example. The simulation model can be assumed as one part of the limitless flow field. Therefore, the computational domain can be set as the periodic boundary in the two sides. The top side of the computational domain is the smooth surface, while the bottom side acts as the textured surface. Both the top and bottom sides are set as slip-free "wall" sides. The boundary condition settings in the other three types of textured surfaces are the same with the V-shaped groove surface. A coordinate system is set in the model shown in Fig. 3 to conveniently denote the various directions. The X direction represents the transverse direction. The Y direction is the vertical direction of the textured surface. The front and end sides of the Z direction are the velocity inlet and outflow side, respectively. The drag reduction rate is presented in Eq. (1) as follows: where C f-smooth and C f-groove are the simulation values of the friction coefficient for the smooth and textured surfaces, respectively; η is the drag reduction rate of the simulated surface. The flow velocity can be chosen in the range of 38-55 m/s, which is thought to cause less error in the simulation. According to NASA's research, the dimensionless units for groove spacing (s + ) and height (h + ) are chosen as s + < 30 and h + < 25, respectively in the simulation that follows. The fluid motion needs to satisfy the continuity and Navier-Stokes Equations, as shown in Eqs. (2) and (3) as follows: In the present research, the minimum time step is 8 × 10 −7 s. The iterations are 25 in the unit time step, which can ensure that the residual error of parameters is less than 1 × 10 −5 . Tables 1-4 (Appendix A) show all the initial simulation parameters.

Analysis results of the friction coefficients and drag reduction rate
The friction coefficients from the simulation and Prandtl's boundary layer theoretical equation [17] are compared in the simulation of the V-shaped groove textured surface to validate the Renault stress model. The variation curves of the friction coefficient on the smooth and groove surfaces with fluid speed are shown in Fig. 4 to present the textured surface drag reduction. The figure shows that the friction coefficient calculated from the simulation linearly decreases with the speed increase. Furthermore, the friction coefficient of the textured surface is smaller than that of the smooth surface, which presents good drag reduction characteristics in the fluid speed range in the simulation. About 25.17% of the maximum drag reduction rate is obtained in this model. The micro-morphology drag reduction can generally be 8%-12%. More than 20% of the drag reduction rate can be achieved on the hydrophobic surface [18]. From our research, it has been proven that the investigated textured surface can present super-hydrophobicity [19]. The drag reduction effect in the simulation can be validated by some results from other researchers under certain conditions [20−22]. The literature review shows that the maximum drag reduction rate of more than 20% is possible for the hydrophobic, even super-hydrophobic surface. However, the results have a close dependence on the simulation and experiment conditions. The simulation model adopts the no-slip boundary condition. Hence, the drag reduction rate obtained here is mainly determined by the section shape and parameter of the textured surfaces. Figure 5 shows the simulation results of the other three textured and smooth surfaces. The simulated friction coefficient curve of the rectangular groove is  similar to that of the V-shaped groove. However, some fluctuations have been observed on the saw tooth and semi-circular groove surfaces. The drag coefficient from the simulation is a little bit larger than the empirical value. The mesh close to the textured and smooth surfaces cannot be refined because of the limitation in the computing ability and efficiency, which leads to the omission of a tiny flow field variation. Furthermore, the ideal simulation conditions and general algorithm may cause the resultant error. This result may help choose the good speed condition for better drag reduction.
The drag reduction rates in the four types of textured surface are presented in Fig. 6 to compare the drag reduction characteristics. The drag reduction efficiency is arranged from high to low order as follows: saw tooth groove, V-shaped groove, rectangular groove, and semi-circular groove. No overlap of the drag reduction rate curves in the speed range of simulation has been observed, which can provide guidance for the textured surface application. This result is approximately consistent with that of Henoch [23].

Fluid velocity on the textured and smooth surfaces
The main factor affecting the surface shear stress is the momentum exchange properties in the turbulent layer close to the flow field wall. An analysis on the flow field of solid wall is necessary for an illustrative purpose of the drag reduction mechanism. The fluid velocities of the V-shaped groove and smooth surfaces are simulated under a fluid velocity of 47 m/s to minimize the simulation error after many tentative simulations. Figure 7 presents the cloud picture of the velocities of the V-shaped groove and smooth surfaces. Figure 7(a) shows that the speed of the solid-fluid interface of the V-shaped groove surface is zero on the slip-free "wall" side. Figure 7(b) also illustrates  that the speed of the solid-fluid interface on the top smooth surface is zero. The velocity gradient of the V-shaped groove surface in the near-wall region is obviously lower than that in the smooth surface. Furthermore, the V-shaped groove surface has a wider bandwidth of the low-speed streak. In other words, the low-speed streak in the near-wall flow field can decrease the direct influence of the high-speed flow in the upper layer on the solid wall, thereby decreasing the flow resistance. Figure 8 shows the variation curves of the mean velocity gradient and the transverse (X direction) velocity on the V-shaped groove and the smooth surfaces. The velocity variation close to the wall on the textured surface is slightly slower than that on the smooth surface. The result is consistent with the velocity gradient mechanism shown in Fig. 7. The lower shear stress can be achieved under this condition. Furthermore, the maximum value of the X direction velocity on the textured surface is significantly less than that on the smooth surface in view of the left and right sides of Fig. 8(b). This result indicates that the groove can inhibit the lateral movement of the turbulent flow, thereby stabilizing the near-wall flow field. In light of the velocity variations, the fundamental drag reduction mechanism on the micro-grooved surface is that the flow resistance along the flow direction is lower than that on the lateral direction. Figure 9 shows the velocity simulation of the V-shaped groove surface on the X and Y directions. Noticeably, the two deflecting secondary vortex flows occur in opposite directions ( Fig. 9(a)). Figure 9(b) shows the low-speed elliptical flow field in the groove valley. In other words, the micro-structure on textured surface can inhibit the ascending movement from the bottom surface, which consequently impedes the momentum exchange. The simulations in the Z direction velocity also present the general result that the smallest velocity generally appears near the solid surface. The possibility of turbulent bursting is also decreased in this condition. Moreover, the vortex results can prevent the down-sweeping movement from the upper high-speed flow and keep the relative stability of the low-speed flow in the near-wall flow field. The results agree with the hypothesis of the secondary vortex functions [11,24]. Figure 10 shows the shear stress on the textured and smooth surfaces. The picture of the textured surface illustrates a dramatic shear stress reduction in the valleys. In contrast with the smooth surface, the shear stress is high on the peaks of the V-shaped groove. The peaks play a key role in limiting the lateral fluid movement. Therefore, seeing such a high shear stress on the peak is reasonable. However, the calculation shows that the average shear stress on the whole textured surface is less than that on the smooth surface. More areas of the textured surface are distributed in the low shear stress region. The average shear stress in the interface may affect the surface friction and drag behavior.

Shear stress on the textured and smooth surfaces
Generally, the shear stress should be similar in different positions on the smooth surface. Noticeably, an unequal stress exists in the center of Fig. 10(b). The flow field variation may induce the stress fluctuation in different positions. The side wall was designed for the periodic boundary condition. The meshing error in the model may contribute to the difference. The model height was kept large enough to avoid the size effect and the effects on the flow field. The unequal stress cannot be eliminated from the simulation. However, the model and the grid were checked and optimized to assure that the results can be convergent and identical throughout the simulation.

Energy on the textured and smooth surfaces
The kinetic energy in the near-wall flow field was also analyzed to interpret the drag reduction effect. The differences in the turbulent kinetic energy can be noted in the cloud pictures in Fig. 11. The V-shaped groove surface presented a wider width of the lowenergy streak, which meant that the near-wall region of the V-shaped groove surface is more stable than the smooth surface. A semi-circular, low-energy region was also observed on the groove peak, which was an interesting phenomenon showing that sharp peaks can affect the local flow movement. Some regions of lower kinetic energy were found in the textured surface valleys, which was consistent with the preceding velocity variation. The maximum value of the turbulent dissipation rate calculated from the grooved surface was 0.4 m 2 /s 2 , which was ~25% lower than that from the smooth surface (i.e., 0.525 m 2 /s 2 ). In other words, there is less momentum exchange and relatively stable flow in the near-wall flow field of the textured surface.

Turbulence effect on the textured and smooth surfaces
The dissipation behavior caused by turbulent bursting in the turbulent boundary layer was the direct reason for energy consumption, which was also a key factor for flow resistance. Therefore, the turbulent, mean swirl, transverse swirl intensities, and Reynolds stress on the textured and smooth surfaces were all measured to investigate the influence of turbulence on drag reduction. The turbulent intensity is usually defined as the ratio of the average velocity to the pulse velocity. It is low-intensity turbulence when the turbulent intensity is lower than or equal to 1%. The high-intensity turbulence is the status of the turbulent intensity higher than 10%. Figure 12(a) shows that the maximum turbulent intensity on the textured surface is 1.1%, which is lower than that on the smooth surface (i.e., 1.25%). The decreased turbulent intensity can be beneficial for the drag reduction of the textured surface. This turbulence effect on the super-hydrophobic surface can be validated by reference [21]. Moreover, the value was consistent with the experiment and simulation results of previous researchers [10,25]. Figure 12(b) shows the variations of the mean swirl intensity. In the figure, the peak value of the mean swirl intensity on the textured surface was 5.25 × 10 6 1/s, which was also lower than that on the smooth surface (i.e., 6.75 × 10 6 1/s). The flow resistance in the textured surface has been down by nearly 22.2%, which was close to the results obtained by Huo et al. [22]. The reason lies in the combination of the microscale surface morphology and hydrophobicity results in a shear-free interface, which reduced the friction resistance and led to the mean swirl intensity decline. The good hydrophobic characteristics were proven from the previous investigation, which can establish the bases for achieving a high drag reduction rate [19]. The results for the Reynolds stress and transverse swirl were analyzed to be less than those on the smooth surface, which meant that the vortex in the near-wall field on the textured surface was more stable. This may decrease the negative effect of turbulent dissipation and shear stress on drag reduction. The stable flow can be beneficial to the drag reduction of the textured surface.

Conclusions
Four different simulation models of the textured surfaces are presented and analyzed in terms of the drag reduction properties in the fluid field. The drag reduction mechanism is also investigated from the aspect of fluid velocity, shear stress, turbulent kinetic energy, and turbulence effect by taking the V-shaped groove surface as a research object. The following conclusions can be drawn based on this study: 1. The drag reduction efficiencies vary among all the types of textured surfaces simulated, which means that the profile geometries are quite important for optimizing the structural parameters in terms of good drag reduction. The micro-grooves reduce the transverse fluctuation, momentum exchange shear stress, and energy fluctuation. They also stabilize the near-wall flow field. The simulation results show that the V-shaped groove textured surface could obtain the maximum friction coefficient.
2. The maximum value of the X direction velocity on the textured surface is significantly less than that on the smooth surface. A low-speed elliptical flow field in the groove valley can be found. The lowspeed streaks in the near-wall flow field can decrease the direct influence of the upper layer, high-speed flow on the solid wall. The lower shear stress and energy occur in the valley.
3. High shear stress and low-energy, semi-circular regions, which can limit the lateral fluid movement, are found on the V-shaped groove peak. The maximum turbulent and mean swirl intensities on the textured surface are lower than those on the smooth surface, thereby forming a relatively stable flow field. 4. The secondary vortex is systematically revealed on the textured surface. The effect mechanism on the drag reduction is analyzed and proven in the aspect of fluid velocity, energy, and turbulence effect. The vortex can increase the low speed flow stability in the near-wall flow field. This effect can contribute to the drag reduction characteristics on the textured surface.