Numerical simulation of effect of bionic V-riblet non-smooth surface on tire anti-hydroplaning

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1 DOI: /s Numerical simulation of effect of bionic V-riblet non-smooth surface on tire anti-hydroplaning ZHOU Hai-chao( 周海超 ), WANG Guo-lin( 王国林 ), YANG Jian( 杨建 ), XUE Kai-xin( 薛开鑫 ) School of Automotive and Traffic Engineering, Jiangsu University, Zhenjiang , China Central South University Press and Springer-Verlag Berlin Heidelberg 2015 Abstract: Inspired by the idea that bionic non-smooth surfaces (BNSS) can reduce fluid adhesion and resistance, and the effect of bionic V-riblet non-smooth structure arranged in tire tread pattern grooves surface on anti-hydroplaning performance was investigated by using computational fluid dynamics (CFD). The physical model of the object (model of V-riblet surface distribution, hydroplaning model) and SST k ω turbulence model were established for numerical analysis of tire hydroplaning. With the help of a orthogonal table L 16 (4 5 ), the parameters of V-riblet structure design compared to the smooth structure were analyzed, and obtained the priority level of the experimental factors as well as the best combination within the scope of the experiment. The simulation results show that V-riblet structure can reduce water flow resistance by disturbing the eddy movement in boundary layers. Then, the preferred type of V-riblet non-smooth structure was arranged on the bottom of tire grooves for hydroplaning performance analysis. The results show that bionic V-riblet non-smooth structure can effectively increase hydroplaning velocity and improve tire anti-hydroplaning performance. Bionic design of tire tread pattern grooves is a good way to promote anti-hydroplaning performance without increasing additional groove space, so that tire grip performance and roll noise are avoided due to grooves space enlargement. Key words: tire; anti-hydroplaning; bionic non-smooth surfaces (BNSS); numerical simulation 1 Introduction Safe operation on wet road is one of the major concerns of pavement engineers and researchers. It was reported that approximately 20% of all road traffic accidents occur under wet weather conditions and most of the traffic accidents are related to tire performance [1]. When vehicle maneuver at a certain speed on a wet road, once the vertical effort generated by the hydrodynamic pressure resulted from the contact area exceeds the weight of the tire, the contact between tire and road is destroyed by a fluid film and hydroplaning is formed [2 3]. Driving under such conditions is hazardous. As the only part that vehicle interacts with the road surface, tire tread determines the comprehensive performance of tire, such as noise, wear, and hydroplaning. So, it is critically important to improve tire anti-hydroplaning performance. Therefore, experimental work and theoretical analysis have brought in some innovations, such as pavement grooving, which permits at least partial elimination of hydroplaning. Based on experimental investigations and virtual of photos, researchers use glass plate to present visual images of tire contact shape in water [4]. Unfortunately, this kind of experimental method requires tire manufacture and test set-up, which is more time consuming and costly. For analytical theory, there are still some complicated problems in analysis of hydroplaning phenomenon. For example, the fluid flow system is non-linear and there is no accurate mathematical model for tire surface deformation. Consequently, attempting to formulate a description of tire hydroplaning is impossible. The rapid developments of computer and numerical simulation technology provide necessary technical support for analyzing tire anti-hydroplaning. AKSENOV et al [5] presented a three-dimensional simulation of the interaction between tire and free surface flow by virtual of computational fluid dynamics (CFD) technology, but the deformation of tire surface was ignored and the computational domain remained fixed in time in his work. GROGGER and WEISS [6] pointed out that deformed tire had significant influence on hydrodynamic pressure at higher vehicular speeds. By simulating on several patterned tires and compared the resulting contact forces [7], it was shown that the structure parameters of Foundation item: Project( ) supported by the National Natural Science Foundation of China; Project( ) supported by the Jiangsu University Advanced Talents Initial Funding, China; Project(QC201303) supported by the Open Fund of Automotive Engineering Key Laboratory, China; Project(2014M551509) supported by the China Postdoctoral Science Foundation Received date: ; Accepted date: Corresponding author: ZHOU Hai-chao, PhD, Lecturer; Tel: ; hczhou@ujs.edu.cn

2 3901 of tread pattern determines hydroplaning performance. Normally, increasing void in tread pattern grooves can provide additional space to absorb rainwater and increase force to cut water film. This method indeed increases the tire anit-hydroplaning performance, but, it comes with at a cost of other performance factors, as improving one may degrade the other performance factors. WISE et al [8] discovered that 1% improvement in hydroplaning long realized by increasing grooves void will lead to 0.6% reduction in handing, 0.4% increase in rolling resistance, 2.3% deduction in rolling noise and so on. From research on the surface characteristics of nature animals, biologists found that some animals have formed special surface structures with the ability of drag reduction, among which non-smoothness is the most common characteristic. NASA Research Center spearheaded the study on the surface structure of shark skin in the 1970s, and found that the sharks skin surface has micro-groove structure distributed all over the body that can reduce the resistance of the shark s high-speed underwater swimming. Then, bionic principles was presented and applied in engineering domain [9 10]. Great achievements for bionic applications have come out. For example, the frictional force of bionic dimple structure can be reduced by as much as 7% to 10% in laboratory experiments; bionic riblet structure can reduce 1% to 2% drag force even in actual airplane flight test [11 13]. Inspired by the bionic design, a new method is proposed in this work, which applies bionic V-riblet nonsmooth surface to reduce tire pattern grooves water flow resistance in the footprint, and increase flow rate to improve hydroplaning velocity. Firstly, the hydroplaning velocity of the circumferential grooves tire was simulated with the FLUENT software. Then, the hydroplaning velocity was compared with coupled Eulerian-Lagrangian (CEL) techniques and experimental data from OKANO et al [14] in order to illustrate hydroplaning model computing efficiency and validity. Thirdly, with the help of a orthogonal table L 16 (4 5 ), the parameters of V-riblet structure design compared to the smooth structure were analyzed, and obtained the priority level of the experimental factors as well as the best combination within the scope of the experiment. Finally, arranging the optimized V-riblet non-smooth structure on the bottom of the circumferential grooves, CFD technology is used to predict tire anti-hydroplaning performance. The present work shows that the tire pattern grooves bionic design by non-smooth structures can improve tire antihydroplaning performance. 2 Computational details The traditional simulations of tire hydroplaning focus on the CEL method which can acquire tire deformation and lift force correctly. However, the water movement cannot be investigated in detail due to the arithmetic deficiency. Meanwhile, the calculation costs too much time. The CFD technique can smoothly solve the coupling problem and successfully deal with flow problems, and the free interface between air and water can be tracked by the volume of fluid (VOF) model. 2.1 Tire model The structures of tire pattern grooves decide the tire drainage capability. The deformation of tire tread under load affects the drainage space. To analyze the water flow field in grooves in the tire-ground contact, the shape of the deformed tire and the contact pressures under normal load and pressure must be known. The finite element model (FEM) of a tire (205/50R 16) was established, and the tire deformation was acquired with the wheel load of 4 kn and the inflation pressure of 200 kpa. The tire was not supposed to rotate, so no centrifugal load was applied. With that assumption, the tire static contact pressure is simulated. The results are shown in Fig. 1, and the method of tire print experiment was provided in Ref. [15]. The design of the circumferential grooves is in accordance with the testing tire, in which the breadth and the depth are 8 mm and 9 mm, respectively. Fig. 1 Tire footprint and contact-deformation of under normal load and pressure 2.2 Hydroplaning computational domain definition When hydroplaning occurs, both water and air flow from the tire-pavement contact area. First, establish a fluid model which contains both water film and air flow. And then, create the geometric outer contour of the tire after rolling deformation, and remove the rolling tire model during the fluid calculation. Simulation results may vary by 5% 10% with the computation domain size. The domain size with height 50 mm, length in front of tire 300 mm and behind 600 mm, width 350 mm is considered from previous studies [16]. Figure 2 shows the computational domain, which is meshed by multiblock grid technique. The computational domain is discretized into five-sided structure mesh hydrides with unstructured tetrahedral mesh. The mesh in the front of the contact area and within the tread groove was refined,

3 3902 to ensure there are at least eight discrete units in a single tread grooves. The whole grid is made up of cells and nodes. The simulation is done by using half of the flow direction of tire model, and the water and air is z-direction. Fig. 2 Computational model and boundary conditions 2.3 VOF model In multi-phase flow, the identifiable class of material is a phase that has a particular inertial response to and interaction with the flow and the potential held in which it is immersed. The proposed model is essentially a free surface flow with moving boundary. Generally, there are three approaches to solve this difficulty and compute free surface flows, namely: 1) surface fitting method, 2) surface capturing method, and 3) surface tracking method. Schematic representations of these methods are given in Fig. 3. The major advantages and drawbacks of these three methods were discussed by ZHAO et al [17]. VOF method, which keeps and updates the field of volume fraction of one fluid in each cell instead of surface height, could be utilized to solve the advection equation of the volume fraction and predict the fluid interface accurately. In VOF model, fluids are not considered to be penetrating. For each additional phase in the model, a variable (volume fraction of the phase) is introduced in the computational cell. In every control volume, the volume of all phases must sum to unity. Alternatively, variables and properties of a given cell are purely representative of one phase or a mixture phase, depending on the volume fraction values. The volume fraction equation in the cell is denoted by α q, then α q =0, the cell is empty (of the q-th fluid); α q =1, the cell is full (of the q-th phase); 0<α q <1, the cell contains an interface between the q-th fluid and one or more other fluids. Based on the local value of α q, the appropriate properties and variables will be assigned to each control volume within the domain. The continuity equation, for particular fluid s volume fraction, is then solved, followed by the momentum equation. The primary phase volume fraction can be computed based on the constraint shown in Eqs. (1) (3). After the momentum equation is solved throughout the domain, the resulting velocity field and other quantities are shared among the phases, and thus tracking of the interface (volume fraction of each fluid) between phases is done. q t n q1 v 0 (1) q 1 (2) q T ( v) ( vv) p [ ( v v )] g F t (3) where v is velocity vector; g is gravitation force vector; t is time; F is the force vector due to external source. For additional scalars, such as turbulence quantities, a single set of transport equations is solved and the quantities are shared by the phases throughout the field. The density ρ and the molecular viscosity μ in the equations are dependent on the volume fractions of all phases: q q (4) q q (5) 2.4 Control equation and turbulence model At present, for turbulence simulation analysis, there are mainly three turbulence control equations, namely, direct numerical simulation (DNS), large eddy Fig. 3 Surface fitting (a), surface capturing (b) and surface tracking (c) methods

4 3903 simulation (LES) and Reynolds-averaged numerical simulation (RANS). In the three turbulent numerical simulation algorithms, Reynolds-averaged numerical simulation method can really reflect the swirl distribution within the boundary layer and other micro-flow information, including the merit of low computational and high efficiency, thus the Reynolds-averaged numerical simulation (RANS) is adopted in this work. Equation (6) is the continuity equation and Eq. (7) is the Reynolds-averaged Navier-Stokes equation. ( ui ) 0 x i ( uiu j ) p x x j x ij j i x j u u i j 2 ui ij u j ui 3 xi where ρ and μ are the fluid density and the coefficient of the molecular viscosity, respectively; u i is the mean velocity components; x i is the Cartesian coordinates; p is the static pressure; δ ij is the Kronecker delta. SST k ω model [18] is chosen for the reason of consolidating the advantages of high Reynolds number model and the low Reynolds number model, utilizing mixed function to achieve gradual transition from standard model within the boundary layer to high Reynolds number model outside the boundary layer, and making the transition from the near-wall region to the full development region more perfect along with the higher calculation accuracy. Equation (8) is the turbulent kinetic energy equation, and Eq. (9) is the turbulence dissipation rate equation: ( ) ( ui ) Γ k G ~ Y S (8) t x i x j x j ( ) ( u i) Γ w Gw Y D S t x i x j x j (9) where G ~ is the generation of turbulence kinetic energy due to the mean velocity gradients; G w is the generation of w; Γ κ and Γ ω are the effective diffusivities of k and ω, respectively; Y κ and Y ω are the dissipations of k and ω; D ω is the cross-diffusion term; S κ and S ω are source terms. Pressure-implicit with splitting of operators (PISO) is grounded on higher degree of approximate relation between the corrections for pressure and velocity. This work combines PISO algorithm with an implicit and second-order accurate scheme to get the time-advanced solution, which can greatly decrease iteration numbers required for convergence. (6) (7) 2.5 Boundary conditions The hydroplaning phenomenon on a locked tire sliding on a flooded smooth pavement is modeled in this work. For an observer in stationary frame of reference, the hydroplaning phenomena can be viewed as a moving tire at speed U sliding along a smooth pavement flooded with water. Alternatively, in a moving wheel frame of reference, the hydroplaning phenomena can be viewed as a jet with a layer of air and a layer of water, entering on tire surface and pavement surface also moving at a speed of U towards the tire surface. The hydroplaning model has been modeled in a moving frame of reference in this work. Figure 2 demonstrates the boundary conditions of the computational domain. As for a two-phase flow, the inlet has two similar types of boundary conditions for water and air. The lower part of 10 mm height stands for water and the rest stands for air, and both water and air inlet velocity are 80 km/h. The outlet condition is defined as one atmospheric pressure. The friction produced by the fixed wall and the deflection of tread pattern grooves generated by flowing water force is neglected. The longitudinal plane in the center of the tire forms the symmetry plane. 3 Hydroplaning results and discussions Figure 4 shows the interfacial velocities and void fractions on the ground, where the deep grey part represents water flow. It can be seen that flow separates and wave forms at the front of tire and water drains from the tire tread grooves, which is consistent with the reality. Hydroplaning is assumed to occur when the total fluid hydrodynamic force acting on the tire is equal to the wheel load. The hydrodynamic force is found by the integration of the total pressure over the projected tire surface in the y-direction. This work also simulates tire hydroplaning with Abaqus software by using traditional coupled Eulerian-Lagrangian (CEL) method [19]. The results of the two methods are highly compatible (Fig. 5). During the calculating process, the traditional CEL simulation needs 96 h on an eight-core and 32 GB memory computer, whereas the CFD simulation only needs 36 h on a double core and 4 GB memory computer. Apparently, CFD is more efficient in simulating tire hydroplaning. The main reason for different computing efficiency is that CEL method contains Lagrangian elements and requires more exact grid quality. Thus, compared with CFD, CEL method takes up larger computer resource and needs much more time. OKANO and KOISHI [14] conducted an experiment about tire hydroplaning, as shown in Fig. 6. In the experiment, tires with different tread patterns were

5 3904 Fig. 4 Free surface of water in tire hydroplaning process: (a) t=0.005 s; (b) t=0.01 s; (c) t=0.015 s; (d) t=0.04 s Fig. 5 Comparison of hydrodynamic force resulted from CEL and CFD assembled to the same car, and then the car run on a proving ground at certain acceleration. A high-speed photography was used to shoot the whole process. One of their tires (the middle tire) is the same with tire used in this work. From the experiment results, it is noted that tire hydroplaning occurs when vehicle moving at about 82 km/h. Comparison between experiment and simulation results shows that hydroplaning critical velocity obtained from this work is in reasonable agreement with experiment results. Just from the comparison among CFD, CEL, and experiment results, it is proved that CFD is high efficiency and accurate method for predicting hydroplaning speed. 4 Numerical investigations about tire hydroplaning of bionic non-smooth surfaces The physical model, governing equation, computational domain, and boundary conditions are the same with the hydroplaning model mentioned above except that bionic V-riblet surface is arranged on tire pattern grooves surfaces. Fig. 6 Relationships among slip ratio, velocity and tread pattern obtained by experiment 4.1 Mesh of computational domain Computational domain of tread groove is shown in Fig. 7. Based on the size of longitudinal groove of this tire, the model size of bottom groove is 7.5 mm along the x direction, 30 mm along the y direction, and the depth of groove is 8 mm. Importing the model as shown in Fig. 3 to Hypermesh software, the method of combining hexahedral and tetrahedral grid is used to mesh the grid,

6 3905 and the grid is refined close to the region of the surface. The viscous sub-layer of the boundary layer is probably for 0 y + 5, therefore the dimensionless number of first grid close to the surface must be controlled within y + 5. The grid thickness of the first layer close to the wall surface can be obtained from y 1/ 4 1/ 2 kp y (10) C where y + is dimensionless distance to the wall surface; μ is the dynamic viscosity of the fluid; C μ is an empirical constant often taken as 0.09; k p is the turbulent kinetic energy of the first node [10]. In addition, when using the SST k ω model, the number of grids within the boundary layer is at least 15. The equation of boundary layer thickness is δ=0.34re 0.2, where L is the characteristic length and Re is the Reynolds number. After repeated attempts, the final grid size of first layer is 0.01 mm whose growth rate is 1.2 and the maximum grid size of the computational domain is 0.2 mm. Figure 8 shows the meshes in the region near non-smooth surface. 4.2 Analysis of orthogonal experiment To facilitate the analysis of drag reduction effect of V-riblet non-smooth structure, drag reduction rate is defined as Cf Cf Q (11) C f where positive Q indicates the reduction of the resistance and negative Q indicates the increase of the resistance; C f is the wall drag coefficient of original smooth model; C f is the wall drag coefficient of V-riblet non-smooth model. The formula of C f is C f =F/(ρV 2 A/2), where F is the wall resistance; A is the projection area perpendicular to the flow direction; ρ is the density of water; V is the flow velocity of water. In order to explore the influence of V-riblet non-smooth structure on tire grooves water resistance, using orthogonal experiment method, the height of V-riblet, the degree of vertex angle, the spacing between the adjacent V-riblet and the number of riblet are taken as the experimental factors named A, B, C, D, respectively. Table 1 shows the factors and levels of the orthogonal experiment. Table 1 Factors and levels of orthogonal experiment B(degree of C(spacing Level A(height of D(number vertex between rank V-riblet/mm) of riblets) angle/( )) adjacent/mm) Fig. 7 Design of V-riblet and mesh of single tire pattern groove: (a) Design of V-riblet in grooves; (b) Model of single groove Fig. 8 Sketch map of meshes on V-riblet non-smooth surface According to the experiment arrangement of Table 2, simulation analysis is conducted and the results are included in the table. Wherein, k i (i=1, 2, 3, 4) is the average value of the ratio of reduced resistance, reflecting the effects of the value of the same factor on the ratio of reduced resistance; R is range, indicating changes in the factors affecting the level of the ratio of reduced resistance. The greater the range is, the greater the impact that the selected factors on the ratio of reduced resistance. From the results in Table 2, the height of V-riblet structure has a largest effect on wall drag reduction, followed by the degree of vertex angle of V-riblet structure, then the spacing between the adjacent V-riblet, finally the number of the V-riblet. 4.3 Analysis of resistance reduction Wall-shear stress analysis Figures 9 and 10 show the comparison chart of wall-shear stress between the smooth surface and the V-riblet non-smooth surface with Q=14.7. As illustrated

7 3906 Table 2 Programs and results of orthogonal experiment Empty Drag reduction Test number A B C D column rate, Q/% k k k k R(range) Primary and A>C>B>D secondary order Superior level A 3 B 1 C 1 D 4 Superior A3 B1 C1 D4 combination area s digressive distribution of small shear stress. Thus, the V-riblet structure can reduce the average wall-shear stress of the surface as well as the water resistance flowing through the tire pattern grooves. Fig. 9 Wall-shear stress of smooth surface Fig. 10 Wall-shear stress of V-riblet surface in Fig. 9 and Fig. 10, the wall-shear stresses are almost the same at the inlet initial. However, when moving along the flow direction, the wall-shear stress of V-riblet structure is significantly less than that of smooth surface, especially the region arranged with V-riblet whose wall-shear stress obviously decreased. Figure 11 shows the comparison chart of shear stress of a characteristic plane in y-direction, which is perpendicular to the flow direction. The wall-shear stress of smooth surface keeps 2000 Pa, and the farther away from the surface the smaller the shear stress is. For V-riblet surface, the maximum shear stress appears in the vicinity of apex; and the closer to the V-riblet bottom, the smaller the shear stress is. V-riblet structure changes the distribution of the shear stress, because it can transform the large shear stress of smooth surface evenly distributed into a small area s large shear stress of the apex and the most Fig. 11 Comparison of wall shear stress of characteristic plane in y-direction Velocity field analysis Figure 12 shows the comparison chart of velocity of a characteristic plane in the flow z-direction between the smooth surface and V-riblet surface. As shown in Fig. 12, the flow field between the smooth surface and the V-riblet surface is quite different. The velocity of the

8 3907 velocity gradient of the V-riblet surface significantly decreases because of the low velocity fluid inside the V-riblet. In other words, V-riblet surface is equivalent to increasing the thickness of the boundary layer. As a result, the frictional resistance is reduced and the water can flow through the tire grooves more easily. 5 V-riblet tire hydroplaning prediction Fig. 12 Comparison of velocity of characteristic plane in z-direction: (a) Velocity distribution of smooth model; (b) Velocity distribution of V-riblet surface smooth surface within the boundary layer reaches the mainstream velocity in a short distance, which means a thinner boundary layer and a more intense variation of velocity compared to the V-riblet surface, while the The optimized V-riblet structure through orthogonal experiment is arranged on the bottom of tire pattern grooves and comparison is made with the original smooth structure after the CFD analysis of tire hydroplaning. Considering the symmetry of the model, half of the grounding region area is used for analysis. Figure 13 shows the half tire hydroplaning model arranged with V-riblet non-smooth structure. A method of combining structured grid and unstructured grid is adopted to mesh, and the turbulence model, boundary conditions and other settings are the same with single grooves analysis. Figure 14 shows the tread dynamic pressure of the two models. As illustrated, the tread dynamic pressure arranged with V-riblet structure has a decrease compared to the original model. The tread dynamic pressure of the original model is kpa, and the tread dynamic pressure of the V-riblet model is kpa. Based on the formula of dynamic pressure p=0.5ρv 2, where V is the velocity of water, ρ is the density of water, p is the dynamic pressure, a improvement of 1.2 km/h hydroplaning speed can be calculated by using the V-riblet non-smooth structure grooves. Fig. 13 Mesh of tire hydroplaning model

9 3908 References Fig. 14 Tread dynamic pressure of original model and V-riblet model: (a) Original tire hydroplaning model; (b) V-riblet tire hydroplaning model 6 Conclusions 1) The arrangement of V-riblet non-smooth surface on the bottom of tire pattern grooves has an impact on reducing the water resistance flowing through the grooves as well as improving the grooves drainage capacity. The height of V-riblet, the degree of V-riblet, the spacing between the adjacent V-riblet and the number of V-riblet all have influence on the drag reduction effect. However, the height of V-riblet has most notably impact on the drag reduction. 2) V-riblet non-smooth surface can reduce the wallshear stress and decrease the velocity gradient perpendicular to the flow direction along with the frictional resistance of the surface. The tread dynamic pressure can decrease when driving on the water surface by the method of arranging the V-riblet structure on the bottom of tire pattern grooves. As a consequence, the tire anti-hydroplaning performance is improved. 3) Compared with the traditional method which improve tire anti-hydroplaning performance by virtual of increasing grooves void, BNSS can improve the tire anti-hydroplaning performance without increasing additional space in grooves. This greatly appeases the contradiction between tire hydroplaning and noise. [1] MURAD M M, ABAZA K A. Pavement friction in a program to reduce wet weather traffic accidents at the network level [J]. Transportation Research Record: Journal of the Transportation Research Board, 2006, 1949: [2] HORNE W B, DREHER R C. Phenomena of pneumatic tire hydroplaning [M]. USA: National Aeronautics and Space Administration, 1963: [3] VINCENT S, SARTHOU A, CALTAGIRONE J P, SONILHAC F, FEVRIER P, MIGNOT C, PIANET G. Augmented Lagrangian and penalty methods for the simulation of two-phase flows interacting with moving solids: Application to hydroplaning flows interacting with real tire tread patterns [J]. Journal of Computational Physics, 2011, 230(4): [4] SUZUKI T, FUJIKAWA T. Improvement of hydroplaning performance based on water flow around tires [J]. SAE Paper, [5] AKSENOV A, DYADKIN A, GUDZOVSKY A. Numerical simulation of car tire aquaplaning [C]// ECCOMAS Computational Fluid Dynamics Conference. France, 1996: [6] GROGGER H, WEISS M. Calculation of the hydroplaning of a deformable smooth-shaped and longitudinally-grooved tire [J]. Tire Science and Technology, 1997, 25(4): [7] CHO J R, LEE H W, SOHN J S, KIM G J, WOO J S. Numerical investigation of hydroplaning characteristics of three-dimensional patterned tire [J]. European Journal of Mechanics-A/Solids, 2006, 25(6): [8] WIES B, ROEGER B, MUNDL R. Influence of pattern void on hydroplaning and related target conflicts [J]. Tire Science and Technology, 2009, 37(3): [9] REN Lu-quan, LIANG Yun-hong. Coupling bionics [M]. Beijing: Science Press, (in Chinese) [10] WANG Guo-lin, ZHOU Hai-chao, YANG Jian, LIANG Chen, JIN Liang. Study on the influence of bionic non-smooth surface on water flow in antiskid tire tread pattern [J]. Journal of Donghua University: English Edition, 2013, 30(4): [11] ZHOU Chang-hai. Coupling bionics for functions surface of drag and noise reduction based on pigeon body surface [D]. Jilin: Jilin University, (in Chinese) [12] FISH F E, BATTLE J M. Hydrodynamic design of the humpback whale flipper [J]. Journal of Morphology, 1995, 225(1): [13] WALSH M J. Riblets as a viscosity drag reduction technique [J]. AIAA Journal, 1983, 21(4): [14] OKANO T, KOISHI M. Hydroplaning Simulation Using MSC.Dytran [C]// The 3rd European LS-DYNA Users Conference. France, [15] LIANG Chen, WANG Guo-lin, AN Deng-feng, MA Yin-wei. Tread wear and footprint geometrical characters of truck bus radial tires [J]. Chinese Journal of Mechanical Engineering, 2013, 26(3): [16] ISAM J, ALI R, VINCENT E. Tire tread pattern analysis for ultimate performance of hydroplaning. computational fluid and solid mechanics proceedings [C]// First MIT Conference on Computational Fluid and Solid Mechanics. USA, [17] ZHAO Y, TAN H H, ZHANG B. A high-resolution characteristicsbased implicit dual time-stepping VOF method for free surface flow simulation on unstructured grids [J]. Journal of Computational Physics, 2002, 183(1): [18] ZHAO Gang, LI Fang, DU Jun-wei. Optimization design of bionic jet surface and mechanism analysis of drag reduction [J]. Journal of Central South University: Science and Technology, 2014, 45(5): (in Chinese) [19] WANG Guo-lin, CHEN Hai-yong. Simulation analysis of hydroplaning characteristics of radial tire [J]. Journal of System Simulation, 2012, 24(8): (in Chinese) (Edited by YANG Hua)