Research on Drag Reduction for Flexible Skin Inspired by Bionics

Abstract

Underwater vehicles typically rely on batteries or other energy sources for operation, where drag reduction can significantly lower energy consumption and extend operational endurance. Inspired by the skin structure of loaches, a flexible structure with scales and mucus pores was designed. First, numerical simulations were conducted. To accurately demonstrate the interaction between the flexible flow field and the fluid flow field and to capture the movement boundaries of the plates, a bidirectional fluid–structure interaction simulation method was used. The numerical results indicate that the flexible structure has a positive effect on drag reduction. In channel experiments, the drag reduction effects of flexible and non-flexible structures were compared. Both showed optimal drag reduction at a water flow speed of 2 m/s and mucus flow speed of 0.1 m/s. The maximum drag reduction rate for the flexible structure was 28.5%, compared to 22.8% for the non-flexible structure. This difference is attributed to the flexible structure altering the flow pattern of the near-wall boundary layer, reducing the velocity gradient of the boundary layer, and increasing its thickness. The findings of this study can provide guidance for future research on flexible surface drag reduction technologies.

1. Introduction

Underwater vehicles play a crucial role in transporting resources and underwater operations. During cruising, the surface frictional drag of the vehicle accounts for 60% to 80% of the total drag experienced by the underwater vehicle [1]. If, under constant external conditions, the frictional drag on the wall of an underwater moving object is reduced by 10%, it is possible to improve the cruising performance metrics by approximately 3.57% [2]. Therefore, to enhance cruising speed and reduce energy consumption, it is particularly important to minimize the frictional drag on the surface of the underwater vehicle [3,4].

In recent years, with advancements in experimental methods and the rapid development of numerical techniques, research on drag reduction has deepened. Researchers have made significant breakthroughs in the field of drag reduction by employing various methods such as groove drag reduction [5,6,7], hydrophobic drag reduction [8], drag reducers, and microbubble drag reduction [3,9]. However, from an engineering application perspective, there are still some limitations. For instance, the size cannot be altered, additional equipment is required, and it can only be applied to internal flows such as those in pipes. In 1960, researchers first discovered that using flexible structures with properties similar to dolphin skin could achieve drag reductions exceeding 50% [10,11]. Direct numerical simulations of flexible walls indicate that the control of flexible walls can effectively reduce the frictional drag experienced by incompressible Newtonian fluids [12]. Polydimethylsiloxane (PDMS), used as a flexible coating, has demonstrated its drag reduction capability through experiments [13]. In the field of flexible drag reduction, researchers believe that the principle behind flexible drag reduction lies in the release of surface pressure, which in turn leads to the alleviation of the boundary layer pressure gradient [14].

Fish secrete mucus on their surfaces, which prevents the attachment of impurities and organisms; plays various roles in respiration, ion and osmotic regulation, and reproduction; and effectively reduces drag [15]. Inspired by the microscopic structure of loach skin, a two-stage biomimetic drag reduction structure has been proposed. This study aims to analyze the drag reduction performance of the flexible structure using a combination of numerical simulations and experimental validation. During the numerical simulation of the flexible drag reduction structure, a bidirectional fluid–structure interaction method is employed. This involves computing the fluid and solid components separately at each time step, followed by information exchange and grid transformation at the interface between them, ultimately converging the parameters to complete the simulation process. In the experiments, a transparent, non-toxic, and stable PDMS is used to create the flexible structure, and a flow channel experimental setup is constructed to test its effectiveness in reducing drag under different water flow speeds and mucus flow rates. The drag reduction mechanism is explored through an analysis of simulation data for velocity, vortices, and surface mucus. The conclusions of this study effectively demonstrate the drag reduction characteristics of the flexible structure and lay the foundation for further research on drag reduction for underwater vehicles and other submerged objects.

2. Experiments and Methods

2.1. Biomimetic Model

Inspired by the microscopic structure of loach skin, a drag reduction method based on a scaled structure has been proposed. The geometric parameters of the model are sourced from our previous research, with a horizontal spacing of 440 μm, a longitudinal spacing of 330 μm, and a model height of 10 μm, forming a one-stage drag reduction structure [16]. Building upon this one-stage structure, a two-stage drag reduction structure is created by adding pore structures that simulate mucus secretion. To further replicate the loach skin, flexible PDMS was used to fabricate the drag reduction structure, which is non-toxic, harmless, and exhibits an ideal chemical stability. PDMS and the curing agent were obtained from Dow Corning, Midland, MI, USA. The drag reduction structure was produced through mold casting to create the flexible drag reduction components required for testing. The process begins with the fabrication of the mold corresponding to the drag reduction structure, as shown in Figure 1a. Then, PDMS is mixed in a 10:1 ratio for mold casting, with the mixture degassed in a vacuum environment and then heated at 80 °C for 8 h to produce the flexible material drag reduction structure needed for testing, measuring 15 mm × 10 mm × 5 mm, as depicted in Figure 1c. For comparison purposes, two-photon 3D printing technology was employed to fabricate non-flexible structures, using an acrylate-based photopolymer known for its rapid curing capabilities.

2.2. Modeling Design and Boundary Conditions

In this simulation analysis, dynamic mesh technology and bidirectional fluid–structure interaction (FSI) technology were employed. The overall computational process is as follows: first, the fluid domain is meshed and parameters are initialized; next, the solid domain is meshed and parameters are initialized; finally, a coupled analysis is performed through the fluid–solid interface.

The bidirectional FSI in ANSYS uses an implicit coupling algorithm, which differs from the explicit algorithms employed by other software. The implicit coupling algorithm allows for larger time steps, and the software ensures that each time step is a convergent solution through staggered iterations within the coupling time step. In contrast, explicit coupling algorithms require very small coupling time steps to ensure convergence. If the coupling time step is too large, it may not converge, and there are no staggered iterations within each coupling time step. Therefore, each coupling time step is computed only once before moving to the next coupling time step, which can lead to inaccurate unsteady results if the time step is not sufficiently small. For this reason, this study adopts the bidirectional fluid–structure interaction algorithm.

In this study, the coupling calculation employs a sequential approach where the flow field calculation is used first, and then a pressure-based transient separation solving method is used. First, the flow field governing equations are solved to obtain the loading forces on the flow field. These results are then used as input for the dynamic coupling boundary conditions, and the basic control equations for the solid part are solved to determine structural deformation or displacement. This result is subsequently used in the mesh motion equations to update the flow field mesh. The updated mesh is then used to resolve the flow field governing equations. This process is repeated until convergence is achieved. The simulation calculations are performed using ANSYS Workbench as the computational platform, with Fluent used for flow field calculations, and Mechanical used for structural calculations. Data exchange between the two is managed through System Coupling for an analysis of the bidirectional fluid–structure interaction.

The FSI computational domain is illustrated in Figure 2a. In the fluid domain at the top, the distance between the drag reduction structure model and the inlet is 5000 μm to ensure sufficient turbulence development. The distance between the model and the outlet is 3000 μm, allowing for observation of the impact of the drag reduction structure on the subsequent fluid flow. The inlet and outlet of the computational domain are set as a velocity inlet and a pressure outlet, respectively. The bottom of the fluid domain coincides with the flexible drag reduction structure model and is used as the fluid–structure interaction interface. The front and rear surfaces are both set as symmetry planes, while the top and bottom surfaces, except for the drag reduction structure area, are set as wall boundaries.

In turbulent flow, the boundary layer thickness at the location of the drag reduction structure model within the fluid computational domain can be analyzed and calculated using empirical formulas for turbulent boundary layers:

$${\mathsf{\delta }}_{\mathrm{T}}={\displaystyle \frac{0.381\mathrm{x}}{\sqrt[5]{{\mathrm{R}}_{\mathrm{ex}}}}},$$

(1)

$${\mathrm{R}}_{\mathrm{el}}={\displaystyle \frac{\mathrm{Vl}}{\mathsf{\vartheta }}},$$

(2)

In the formula, ${\mathsf{\delta }}_{\mathrm{T}}$ represents the turbulent boundary layer thickness; $\mathrm{x}$ denotes the distance from the velocity inlet to the specified location; $\mathrm{V}$ is the fluid flow velocity; $\mathsf{\vartheta }$ is the kinematic viscosity, with a value of 1.01 × 10⁻⁶m/s; and ${\mathrm{R}}_{\mathrm{el}}$ refers to the Reynolds number associated with the length of the drag reduction structure.

In this study, the fluid velocity is approximately 2 m/s. The boundary layer thickness at the drag reduction structure exceeds the height of the drag reduction structure, meeting the computational requirements. To mitigate computational errors caused by mesh quality issues in the fluid domain, local mesh refinement is introduced to the drag reduction structure. The Meshing module in Ansys Fluent 2022 R1 was utilized for mesh generation. Within the Fluent Meshing module, the Watertight Geometry workflow was selected, and a local sizing of BOI was applied with a mesh size of 50 μm. Considering the gradient height of the scale structure, which varies from 0 to 10 μm, curvature-based local sizing was incorporated with a minimum size of 2 μm, a maximum size of 4 μm, and a curvature normal angle of 10 degrees. To facilitate a reduction in the number of elements and enhance simulation efficiency, the maximum size of the overall computational domain was slightly increased. Specifically, the maximum surface mesh size was set to 0.5 mm, with a growth rate of 1.2 and a curvature normal angle of 10 degrees. The smooth-transition method was employed to generate the boundary layer mesh, with a growth rate of 1.2 and three boundary layers. The Poly-hexcore volumetric meshing method was employed, with the minimum cell length set to 2 μm and the maximum cell length set to 256 μm. We also validated the mesh independence of the flow field calculations through different mesh parameter settings, using the drag coefficient as the criterion for mesh convergence. Ultimately, 7.48 million mesh elements were selected to ensure accuracy and computational efficiency. The mesh results are shown in Figure 2b, with an enlarged view of the scaled structural section. This refinement involves finer meshing of the drag reduction structure, aiming to enhance computational accuracy while conserving computational resources. At the bottom of the drag reduction structure, flexible materials are proposed to simulate the structural deformation under drag reduction. The initialization of parameters for these flexible materials enables them to function effectively during the drag reduction process.

3. Numerical Computation

This study utilized ANSYS Workbench 2020 for the numerical simulation computations. The dimensional parameters of the solid and fluid domains were set based on computational requirements and critical Reynolds numbers. At the fluid–structure interface, mesh nodes between the fluid and solid domains corresponded one-to-one. To ensure convergence of the simulation results, the total simulation time was set to 1 s with a time step of 0.01 s. In the fluid domain settings, the fluid medium used was water at 20 °C, with the corresponding fluid density parameter set as =998.2 kg/m³ and the dynamic viscosity coefficient as =1.0 × 10⁻⁶, indicating that it is an incompressible fluid. In the solid domain settings, the simulation used the elastic material PDMS. The elastic modulus of PDMS was set to 2.66 MPa, corresponding to a common PDMS–curing agent ratio of 10:1.

Under the influence of loads, the flexible material PDMS is prone to deformation, necessitating corresponding adjustments to the mesh partitioning. In Ansys Fluent, dynamic mesh technology can be employed to handle the moving boundaries of flexible materials. This technique facilitates the simulation of boundary displacement due to the applied forces, resulting in temporal changes in mesh configurations within specific regions. It is applicable to both single-phase and multi-phase flow models. By defining the intersection between fluid and solid regions as the fluid–structure interface and implementing dynamic mesh technology, it aids in the analysis of stress distributions across fluid–structure interfaces.

In numerical simulation computations, the renormalization group (RNG) k-ε model is proposed for simulation. This model enhances the accuracy of rapid strain flow and vorticity, providing an effective viscosity differentiation method suitable for near-wall treatments. The Enhanced Wall Treatment (EWF) function is employed to handle near-wall regions, ensuring minimal errors between coarse and fine grid resolutions. The SIMPLE algorithm is used for numerical simulation computations, with the momentum equation solved using a second-order upwind scheme. At the velocity inlet boundary conditions, hydraulic diameter and turbulence intensity are computed using Equations (3) and (4) to initialize the flow field within the computational domain [17].

$$\mathrm{D}={\displaystyle \frac{2\mathrm{ab}}{\mathrm{a}+\mathrm{b}}},$$

(3)

$$\mathrm{I}=0.16{\mathrm{Re}}^{-{\displaystyle \frac{1}{8}}},$$

(4)

$$\mathrm{Re}={\displaystyle \frac{\mathsf{\rho }\mathrm{vD}}{\mathsf{\mu }}},$$

(5)

In the equation, $\mathrm{D}$ represents the hydraulic diameter, where $\mathrm{a}$ and $\mathrm{b}$ denote the length and width of the computational domain′s flow field, respectively. $\mathrm{I}$ stands for turbulence intensity, $\mathrm{Re}$ for Reynolds number, $\mathsf{\rho }$ for fluid medium density, $\mathrm{v}$ for fluid medium velocity, and $\mathsf{\mu }$ for dynamic viscosity.

At the inlet of the flow field domain, simulations are first conducted using different fluid medium velocities to explore the drag reduction capabilities of the flexible material PDMS under varying flow conditions. Figure 3a depicts the drag reduction efficiency of the one-stage drag reduction structure in different flow velocity environments. Herein, non-flexible materials refer to scenarios where the grid movement after the load force on the lamellar structure is not considered, and fluid–structure coupling calculations are not employed. In flow velocity environments ranging from 1 to 8 m/s, both scenarios exhibit a trend of the drag reduction rate initially increasing and then decreasing with increasing flow velocity. Overall, the flexible material demonstrates superior drag reduction compared to the non-flexible material, achieving a maximum drag reduction rate of 10.4% at a flow velocity of approximately 2 m/s.

The skin of loach is covered with a layer of mucus tissue, which reduces frictional resistance during swimming. The Carreau model can be used to simulate the rheological characteristics of the mucus on the loach′s body surface. Its mathematical expression is as follows [18,19]: (See

Table 1. Mucus parameters.

${\mathbf{\eta }}_{\mathbf{0}}$$\mathbf{(}\mathbf{Pa}\mathbf{·}\mathbf{s}$)	${\mathbf{\eta }}_{\mathbf{\infty }}$$\mathbf{(}\mathbf{P}\mathbf{a}\mathbf{·}\mathbf{s}$)	$\mathbf{\lambda }$$\mathbf{(}\mathbf{s}$)	$\mathbf{n}$	${\mathbf{\rho }}_{\mathbf{m}} \mathbf{\left(}\mathbf{k}\mathbf{g}\mathbf{·}{\mathbf{m}}^{\mathbf{-}\mathbf{3}}\right)$
0.3	0.0005	50	0.7	1000

)

$${\displaystyle \frac{\mathsf{\eta }-{\mathsf{\eta }}_{\infty }}{{\mathsf{\eta }}_0-{\mathsf{\eta }}_{\infty }}}={\displaystyle \frac{1}{{\left[1+{\mathsf{\lambda }\mathsf{\gamma }}^2\right]}^{\raisebox{1ex}{$\mathrm{n}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}},$$

(6)

In the equation, $\mathsf{\eta }$ represents apparent viscosity, ${\mathsf{\eta }}_0$ represents zero shear viscosity, ${\mathsf{\eta }}_{\infty }$ represents infinite shear viscosity, $\mathsf{\lambda }$ represents the time constant, $\mathsf{\gamma }$ represents shear rate, $n$ represents rate factor, and ${\mathsf{\rho }}_{\mathrm{m}}$ represents mucus density. The time constant and rate factor do not change with variations in viscosity.

In the simulation and computational analysis of the two-stage drag reduction structure, the Carreau model is utilized to simulate the flow of mucus on the drag reduction surfaces. Mucus, a polymer fluid that does not intermix with water, is modeled using the Volume of Fluid (VOF) model for numerical calculations to analyze its drag reduction mechanism in water. In the two-stage drag reduction structure, the initial water flow velocity is set to 2 m/s, which corresponds to the optimal flow velocity of the one-stage drag reduction structure. The initial flow velocity of mucus within the mucus pores is gradually increased to analyze the drag reduction effect of the two-stage structure under different mucus flow velocities. Figure 3b shows the analysis of the effect of different mucus flow velocities on the drag reduction effect of the two-stage drag reduction structure under fixed fluid flow velocity. From the figure, it is evident that when the drag reduction structure is made of flexible PDMS material, its corresponding drag reduction performance is superior to that of non-flexible materials. At a fixed fluid medium velocity, gradually increasing the initial flow velocity of mucus within the mucus pores results in a drag reduction rate of over 26% for the two-stage structure. Compared to the drag reduction effect of the one-stage structure, there is a significant improvement in the drag reduction rate.

4. Flow Channel Testing Experiment

During the experimental testing of the drag reduction structure model, an experimental setup depicted in Figure 4a was assembled, which included components such as a water pump, control valve, flow meter, flow channel pipes, and high-precision differential pressure transducers. Within the flow channel test pipes, sensors of the high-precision differential pressure transducers are positioned at the front and rear ends of the drag reduction structure model to collect differential pressure data across the sensors, which are then analyzed using a computer-based workstation. By adjusting the setting of the control valve, the flow rate of water passing over the surface of the drag reduction structure can be varied. This relationship is depicted in Equation (7):

$$\mathrm{Q}=\mathrm{V}\times \mathrm{S},$$

(7)

In the equation, $\mathrm{Q}$ represents the volumetric flow rate of water passing through in a specific time, measured in m³/s. $\mathrm{V}$ denotes the flow velocity of water in the pipeline, measured in m/s, and $\mathrm{S}$ represents the cross-sectional area of the pipeline, measured in m².

In flow channel testing experiments, it is impractical to directly measure the surface frictional resistance of the drag reduction structure model. According to the Darcy–Weisbach equation for fully developed flow in a pipe, its pressure drop form is as follows [20,21]:

$${\displaystyle \frac{\Delta \mathrm{p}}{\mathrm{l}}}=\mathrm{f}·{\displaystyle \frac{\mathsf{\rho }}{2}}·{\displaystyle \frac{{\mathsf{\vartheta }}^2}{\mathrm{d}}},$$

(8)

where $\Delta \mathrm{p}$ represents the pressure difference data between the front and rear ends of the structural model; $\mathrm{l}$ denotes the length of the pipe; $\mathrm{f}$ stands for the along-flow friction coefficient (Darcy friction factor), dimensionless; $\mathsf{\rho }$ represents the density of the fluid medium; $\mathsf{\vartheta }$ denotes the flow velocity of the fluid medium; and $\mathrm{d}$ denotes the diameter of the pipe. From Equation (8), it is evident that the pressure difference data $\Delta \mathrm{p}$ are directly proportional to the frictional resistance coefficient $\mathrm{f}$. Therefore, measuring the pressure difference data between the front and rear ends of the drag reduction structure model can be chosen as a substitute for measuring frictional resistance to assess the drag reduction effect. In flow channel pipelines, the fluid resistance is represented by the pressure difference between the front and rear points of the drag reduction structure, and the drag reduction rate is expressed by Equation (9):

$${\mathsf{\eta }}_{\mathrm{P}}={\displaystyle \frac{{\mathrm{P}}_{\mathrm{s}}-{\mathrm{P}}_{\mathrm{b}}}{{\mathrm{P}}_{\mathrm{S}}}}\times 100\%,$$

(9)

where ${\mathrm{p}}_{\mathrm{s}}$ represents the pressure difference between the front and rear ends of the smooth structure, and ${\mathrm{p}}_{\mathrm{b}}$ represents the pressure difference between the front and rear ends of the drag reduction structure.

In the experiment, the drag reduction effect of a primary one-stage drag reduction structure was tested at various water flow velocities, as shown in Figure 4b. The overall trend in the experimental results in the water channel tests closely matched the numerical simulation results. Both indicated that the drag reduction rate peaked at a water flow velocity of 2 m/s. Furthermore, the flexible drag reduction structure exhibited significantly higher drag reduction effectiveness compared to non-flexible structures. At a water flow velocity of 2 m/s, the drag reduction rate of the flexible structure under different viscous flow conditions showed a trend of initially increasing and then decreasing, ranging from 26% to 28.5%, with a peak of 28.5% observed at 0.1 m/s. In contrast, the maximum drag reduction rate achieved in the simulations at 0.1 m/s was 27.6%, slightly differing from the experimental results. This variance could be attributed to discrepancies between experimental setups and simulation environments. These experimental findings demonstrate that the structure effectively reduces fluid resistance. Through repeated flow channel experiments, we verified the stability of the drag reduction effect of this structure, as shown in Figure 4d. PDMS demonstrated consistent stability across multiple tests, comparable to the repeatability reported in various experimental studies. PDMS not only significantly reduces resistance due to its flexibility but also further diminishes frictional resistance in water due to its hydrophobic properties [5,22,23]. To highlight the significance of the results obtained in this study, a comparison with similar research in the literature was conducted. Specifically, a study that employed PDMS to mimic fish scales with uniform thickness was examined. In contrast to their approach, which achieved a drag reduction of up to 17.25% [24], the present study features scales with a progressive thickness and additional mucus pores, resulting in a substantial improvement. Our results demonstrate a drag reduction of up to 28.5%, indicating a notable advancement in the effectiveness of drag reduction techniques.

5. Drag Reduction Mechanism Analysis

In the two-stage drag reduction structure, the fluid calculation results for two different materials were analyzed. In the fluid computational domain of the two structural models, the starting point is taken as the position of the last scale model on the Y-axis center plane. A parallel line is drawn along the Z-axis from this point. Fluid velocity data along this line segment in the Z-direction are collected, resulting in the velocity gradient image shown in Figure 5a. In these structures, due to the presence of mucus pore structures, the fluid exhibits an initial flow velocity near the wall and gradually accelerates with increasing distance from the wall until it reaches the central velocity. The presence of the microscopic structure significantly reduces the thickness of the viscous sublayer and the transition layer [25]. Compared to non-flexible structures, flexible structures exhibit a slower increase in surface velocity gradient. The flexible drag reduction structure reduces the boundary layer velocity gradient and increases the boundary layer thickness by altering the flow pattern near the wall. With the fluid dynamic viscosity and contact area kept constant, the shear force and frictional resistance due to the interaction between the structure surface and the fluid medium are reduced, thereby lowering the total surface drag. Additionally, the mucus secretion on the surface of the drag reduction structure isolates the fluid medium from the structure surface, further weakening the boundary layer velocity gradient and significantly enhancing the drag reduction effect.

When the mucus flow rate was 0.1 m/s, post-processing calculations were performed on the multiphase flow model of the two-stage drag reduction structure. The phase distribution of mucus and water is shown in Figure 5b: the mucus distribution exhibits four distinct high-speed streaks. In the absence of mucus, the velocity streaks are closely spaced, resulting in their merging into two prominent high-speed streaks. Upon the introduction of mucus, the mucus distribution becomes denser in the overlapping region of the two-stage drag reduction structure, enhancing the velocity streaks in this region. Consequently, the final phase diagram reveals four distinct high-speed mucus streaks.

In addition, based on previous research, vortices are likely to form at the rear end of the scaled model and the interaction area between mucus and water. These vortices create a buffering effect on the surface of the drag reduction structure, altering the boundary layer flow pattern near the wall and converting the sliding friction at the solid–liquid interface into rolling friction between two liquid interfaces [26,27]. Furthermore, the direction of the vortex flow aligns with the direction of the fluid velocity, effectively promoting fluid motion and thereby enhancing drag reduction effect. The analysis of turbulent kinetic energy, as shown in Figure 5c, indicates that the mucous-release surface structure exhibits lower turbulence intensity. This reduction in turbulent kinetic energy contributes to decreased velocity fluctuations and reduced surface drag.

6. Conclusions

This study proposes a biomimetic loach skin structure designed to significantly reduce the hydrodynamic drag on underwater vehicles. Initially, a one-stage drag reduction structure was developed based on the morphology of loach skin, consisting solely of scales. This was followed by a two-stage drag reduction structure that includes both scales and mucus pores. Flexible drag reduction structures were fabricated using PDMS, and non-flexible drag reduction structures were prepared for comparison. To explore the optimal drag reduction effect, numerical simulations and flow channel experiments were conducted, considering the impacts of water flow velocity and mucus release rate. Both approaches indicated that the best drag reduction performance occurs at a water flow velocity of 2 m/s and a mucus flow rate of 0.1 m/s. Experimental results show that the maximum drag reduction rate reached 28.5%, with the flexible structure demonstrating a significantly higher drag reduction effect compared to the non-flexible structure. This enhanced performance is attributed to the alteration of the near-wall boundary layer flow and the hydrophobic properties of PDMS, which reduce fluid contact. Additionally, low-speed vortices near the structure facilitate the conversion of sliding friction at the solid-liquid interface into rolling friction between two liquid interfaces, further effectively reducing drag. This biomimetic structure not only optimizes energy efficiency and extends operational duration, but also improves cruising speed and maneuverability.