Design and analysis of micro-nano scale nested-grooved surface structure for drag reduction based on ‘Vortex-Driven Design’

Highlights

• Secondary vortex structure is the key factor to drag reduction of grooved surface.

• ‘Vortex-Driven Design’ is proposed to guide the design of grooved surface.

• The conventional grooved surface structure is improved.

• Micro-nano nested-grooved surface structure is better in drag reduction.

• A geometric optimization of nested-grooved surface structure is conducted.

Abstract

Bioinspired grooved surface structure design has been widely used as an efficient passive flow control method in drag reduction. The total drag of plate with grooved surface structure can be decomposed into friction and pressure drag. In this paper, the relationship between them and the distribution of vortex structure in flow field has been analyzed for obtaining the drag reduction mechanism of grooved surface structure. The concept of ‘Vortex-Driven Design’ is proposed to improve the performance of conventional periodic single-level grooved surface structure. A design scheme of micro-nano scale nested-grooved surface structure with better drag reduction performance is given. The authors conduct numerical simulation of rectangular nested-grooved surface structure in laminar flow considering rarefaction based on Lattice Boltzmann Method at high Knudsen number. The results show that the nested-grooved surface structure induces higher complexity in the secondary vortex structure, and that the changes of vorticity distribution and flow characteristics drive the changes of velocity distribution and shear stress in the grooved surface. Compared with conventional grooved surface structure, the average friction drag of the surface is further reduced. Two geometric optimization cases of the conventional grooved surface and nested-grooved surface are realized by Genetic Algorithm, showing that the maximum drag reduction rate of the optimal nested-grooved surface can reach 18.76% while that of the optimal conventional grooved surface only reaches 13.61%. Based on ‘Vortex-Driven Design’, an innovative material improvement method for drag reduction is proposed as a new direction for subsequent research on microstructure in terms of drag reduction and energy conservation.

Introduction

In recent years, drag reduction has attracted more and more attention for its significance in energy conservation and emission limitation [1]. In aircraft industry, drag reduction is an effective means to improve aircraft performance. Generally speaking, total drag can be decomposed into two types: pressure drag and friction drag. The friction drag can account for nearly 50% of total drag of a large air freighter during cruise [2], and the ratio is even larger for smaller civil aircraft [3]. Besides, if the aerodynamic layout of a civil aircraft is determined, the reduction of pressure drag is relatively limited [4], which makes it necessary to reduce friction drag for aircraft design.

Passive flow control methods are widely used to improve the drag properties, usually through the passive manipulation of near-wall turbulence through changes in flow boundary conditions, without additional equipment or energy consumption, e.g. vortex generator [5], [6], anisotropic porous wall [7], [8], grooves [9], [10], et al. In the perspective of bionics, passive flow control using grooved surface is known as an effective method to reduce friction drag, the idea of which is originated from the study of textured denticles in shark’s skins. Walsh  [11], [12] believed that the textured surface on shark’s skins effectively protects the low-velocity flow in boundary layer, thus reducing friction drag. Luo et al. [13] investigated manufacturing sharkskin morphologies of different shape and conducted a hydrodynamic drag reduction experiment, showing that drag can be reduced by more than 12% compared with the smooth skin. These textured surface structures modify the near-wall flow in the sharks’ skin to control friction drag.

In recent years, various shapes of grooved surface structure have been investigated in laminar flows [14], [15], [16], [17]. Researches on the mechanism of friction drag showed that the ordered and directional vortex structure is induced through grooved surface structure, which is different from traditional isotropic turbulence. Low-velocity vortices (“secondary vortices”, thereafter) [18] that stay in the groove rotating, cause local flow blockage. On one hand, this forms an almost stagnant fluid buffer and may even lead to local flow and shear stress reversal, i.e. ‘thrust’ [19]. On the other hand, the high-friction area on the wall retreats as the vortices rising up [20]. Therefore, the friction drag caused by the interaction between flow and surface can be reduced.

With the development of computational fluid dynamics, more and more numerical simulation methods are applied to the study of drag reduction via grooved surface structure. Friedmann [21] optimized the grooves of microscale by finite element method (FEM) in Couette flow, and the drag reduction reached 2%–6% compared with smooth plate. Bacher and Smith [18] employed the momentum integral formula of boundary layer and found low-velocity streak structure above the texture surface by the means of flow visualization. Dasciel et al. [22] studied the sub-laminar drag effect of groove at subcritical Reynolds numbers by finite volume method (FVM). Shabnam Raayai-Ardakani [23] used the finite volume method with the SIMPLE (Semi Implicit Method for Pressure Linked Equations) algorithm to simulate the periodic arranged fold texture and discussed the effect on the evolution of laminar boundary layer flow. Benedetto et al. [24] carried out RANS CFD simulations on an advanced turbo-prop, which shows that the adoption of texture provides an important contribution to drag reduction. Choi et al. [25] studied the drag reduction effect of textured surface in channel flow field by direct numerical simulation (DNS). The results showed that the vorticity fluctuation and Reynolds stress decrease with the increase of the size of microstructure. According to the LES results of Klumpp [26], the texture is effective for drag reduction of three-dimensional turbulent structure. Considering the effect of sweep angle, Zhang et al. [27] carried out an implicit large eddy simulation (LES) on channel flow and an infinite swept wing with or without texture.

In this paper, we study the micro-nano scale grooved surface structure, which is similar to the super-hydrophobic surface with excellent drag reduction performance [28], [29] in theory. In this scale, the continuous medium assumption is broken when rarefaction is considered. Therefore, particle-based methods such as Molecular Dynamics (MD) and Direct Simulation Monte Carlo (DSMC) are widely used to simulate the flow under rarefaction. However, these methods such as Molecular Dynamics (MD) are typically computationally expensive. Therefore, Lattice Boltzmann Method (LBM), as a mesoscopic numerical method between the macroscopic method and the microscopic method, has been widely used in recent years. H.F. Tan et al. [30] concluded that the microstructure which has appropriate size to induce the secondary vortices can reduce the wall shear stress by LBM. In 2017, Daeian et al. [20] used the Lattice Boltzmann multi-phase model to investigate the effect of microstructure on the wall’s pressure drop in the channel. Yusuke Kuwata et al. [31] conducted numerical calculations by the D3Q27 Multiple-Relaxation-Time Lattice Boltzmann Method (MRT-LBM) to discuss the dynamical effects of rough wall turbulence, including velocity dispersion and turbulence on friction drag coefficient. In 2019, Asadzadeh et al. [32] studied drag reduction effect of a series of rectangular microgrooves in the plate created by LBM and verified the correctness of this method to simulate the flow field in microscale.

Up to now, most researches focus on the design of single-level periodic groove structure. However, this structure can only be adjusted in single dimension, which makes it difficult to achieve an excepted drag reduction effect when the groove size is not appropriate. According to García Mayoral and Jiménez [33], viscous regime was broken down for large riblets with the appearance of quasi-two-dimensional spanwise vortices, resulting in drag increase. As is shown in Fig. 1, the design of the nested-grooved surface structure adds the second-level groove to conventional groove, which realizes the dimension expansion in geometry and improve the drag properties of large microstructure. The design of nested-grooved surface was inspired by the development of micro-nano materials: multi-level roughness increases the super-hydrophobicity of materials compared to single-level roughness  [34]. Jo et al. [35] fabricated water-repellent hybrid structural surfaces by synthesizing superhydrophobic nanowires on micro-scale denticle structure. In our previous work, Tao et al. [36] conducted wind tunnel tests on airfoil with multi-level micro-nano coating. The tests showed that the coating could move backward the boundary layer transition position and expand the infiltration area of laminar flow, thus effectively reducing drag of airfoil. The experiments also proved that the drag reduction performance of multi-level structure is better than that of single-level structure.

This paper is organized as follows. In Section 2, the method of numerical simulation is introduced and the accuracy of the simulation is verified. In Section 3, the concept of ‘Vortex-Driven Design’ is proposed and nested-grooved surface structure is designed on the basis of Model A and Model B. In Section 4, we conduct two geometric optimizations of the rectangular conventional grooved surface structure and nested-grooved surface structure. Finally, in Section 5, some conclusions are drawn according to the results and analysis.