# Effect of V-Shaped Groove Microstructure on Blood Flow Resistance in Bionic Artificial Blood Vessels

Authors: Zhou Li; Yunqing Gu; Lingzhi Yu; Zhuofan Yin; Wenting Wang; Denghao Wu; Jiegang Mou; Shuihua Zheng
Journal: Applied Bionics and Biomechanics
 (2023)

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## Abstract

This study aims to investigate the blood flow in bionic artificial blood vessels and to reduce the resistance to blood flow, the drag reduction characteristics of V-shaped groove drag reduction microstructures in artificial blood vessel structures were investigated in depth. By varying the parameters of incoming flow velocity, groove width, and groove depth, the effect of various variable conditions on the drag reduction effect of the grooves was investigated, and the flow field characteristics and drag reduction effect of the V-shaped groove microstructure in the artificial blood vessel were obtained. A detailed analysis of the effect of velocity and groove size on the drag reduction effect of the groove was also carried out to demonstrate the drag reduction mechanism of the V-shaped groove microstructure and to summarize the variation law of the drag reduction rate of the V-shaped groove. The results show that the resistance reduction rate of the V-shaped groove microstructure decreases with the increase of blood flow velocity, increases with the increase of groove width, and increases and then decreases with the increase of groove depth. The velocity range used in this paper is 0.3–0.6 m/s, the groove width varies from 0 to 0.3 mm, and the groove depth varies from 0 to 0.3 mm.


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## Body

## 1. Introduction

As our people’s living standards improve and their dietary structure changes, poor eating habits and the concept of exercise have caused the incidence of cardiovascular disease to rise [1, 2]. For example, diseases such as atherosclerosis [3] can cause phenomena such as occlusion of the lumen or narrowing of the ducts, leading to increased vascular resistance and endangering people’s lives in serious cases [4, 5]. Therefore, the hemodynamics in blood vessels has been carefully studied in the research fields of biomedicine and biomechanics at home and abroad [6, 7], and the blood flow characteristics and resistance-reducing structures in artificial blood vessels have received increasing attention from researchers [8].The drag reduction techniques have been a hot topic of research for scholars in the fluid and energy fields, with much research on bionic surface groove drag reduction techniques [9, 10], which have been applied to a variety of fields such as aviation and navigation, sports and pipeline transportation, and the biomedical field have also stepped up research and application of bionic drag reduction microstructures [11–14]. Microchannel studies [15] have shown that grooved microstructures can significantly reduce the resistance to flow in channels [16], while microstructures are also highly hemocompatible and inhibit the adhesion of macromolecules in blood [17]. Biomimetic microstructures are often used in biological systems to improve the physical properties of material surfaces by reducing resistance, improving lubrication, and being superhydrophobic [18, 19].With the gradual improvement of the research on trench drag-reducing microstructures, the application of this technology is also being explored. Bixler and Bhushan [20] conducted resistance tests on different structures of bionic microstructures and suggested that the optimal structure size should be selected in conjunction with the actual situation in the practical application of bionic drag-reducing structures. Dean and Bhushan [21] applied microstructures to the study of flow in the pipe and found that the microstructure of the rib surface in the square pipe did not show a good drag reduction effect by comparing the change of pipe pressure drop. Sasamori et al. [22] further investigated the effect of microgroove structures on pipe resistance and obtained a reduction of 11.7% at a Reynolds number equal to 3,400. Since then, the researchers have analyzed the velocity flow field using the 2D PIV technique and demonstrated that the trench surface suppresses the jet and sweep frequencies of the turbulent structure, resulting in a reduction in drag on the turbulent surface. Also, the size of the groove, fluid flow velocity in the pipe, secondary vortices, and Reynolds number are all important factors that affect the effectiveness of the blood flow drag reduction [23, 24]. Among the various microstructures, the V-shaped groove has been proven by most scholars to be the most effective type of groove drag reduction structure [25], but at this stage, there is relatively little research on the design of intravascular bionic microstructures and the optimization of intravascular hemodynamic parameters. One solution to this challenge is to apply V-shaped groove microstructures to bionic artificial blood vessels to reduce the resistance to blood flow through groove drag reduction.In this paper, the application of V-groove microstructures to artificial blood vessels is investigated in detail, and the resistance reduction characteristics of the microstructures are analyzed in detail for the size and flow rate of the bionic artificial blood vessel. Numerical simulations are used to investigate the resistance reduction efficiency and mechanism of the intravascular bionic microstructure, and to investigate the effect of the bionic microstructure on the intravascular hemodynamic parameters. In order to optimize the bionic microarchitecture and its parameters within the artificial blood vessel, reduce the blood flow resistance of the vessel, and provide a basis and design ideas for the development of artificial blood vessels with antistenosis, antiobstruction, and low resistance.


## 2. Materials and Methods

### 2.1. Vascular Model and Computational Domain

In this paper, V-grooves were selected for in-depth study. For this purpose, several sets of simulation experiments were generated by modifying the V-groove depth and width parameters. To meet the requirements of numerical simulations of artificial blood vessels for research purposes, a series of idealized assumptions about the real blood flow environment had to be made. The following assumptions were used: incompressible Newtonian fluid [26], flow as a laminar flow, constant flow [27], rigid tube walls, and no slip. The length of the starting section of fluid laminar flow for the conditions studied in this paper was calculated according to the empirical Equation (1) [28]. A review of the data yielded [29] that the axillary artery diameter was 3.3–5.1 mm, the mean flow velocity was 25–92 cm/s, and the Reynolds number was 249.9–1,421. Reynolds number is a measure of the ratio of fluid inertial force to viscous force, which is a dimensionless number. In this paper, the bionic vessel model was assumed to have a tube diameter of 4 mm, and a maximum Reynolds number of 726 was calculated for a 4 mm diameter vessel with a flow velocity of 0.3–0.6 m/s. The flow was all in laminar flow. The higher the flow velocity, the longer the laminar flow initiation section, with the longest section being 84 mm.(1)L=0.2875dRe,where L is the length of the starting segment (mm), d is the vessel diameter (mm), and Re is the Reynolds number.As the formulae for the laminar flow initiation section are empirical, their calculation results are for experimental reference only and their values differ from the simulation results. It can be determined that in this study, the length of the initial segment of laminar flow is <100 mm in all the segments of the blood vessel where the inlet flow velocity is between 0.3 and 0.6 m/s.Based on the above assumptions about the blood vessel, a model of the biomimetic artificial blood vessel was created, as shown in Figure1. This includes the two-dimensional dimensions of the model, the schematic diagram of the three-dimensional model, and the dimensions of the calculation domain. Taking into account the length of the laminar flow start section at different velocities and the computational performance, the upstream length of the test section was taken as 10l, which is fully sufficient for this study. To avoid exit disturbances, the length is extended downstream of the test section by l. The calculation domain is therefore a tubular cylinder with a total length of 12 l = 120 mm and a diameter of d = 4 mm.Figure 1
Biomimetic artificial blood vessel model: (a) two-dimensional dimensions, (b) three-dimensional schematic, and (c) calculation field size.
(a)(b)(c)The boundary conditions and initial conditions are set as follows: the fluid in the flow field is blood, its density is 1,060 kg/m3, the kinematic viscosity coefficient is 0.0035 m2/s, and the blood temperature is always set to 37°C. The vessel inlet is set as a velocity inlet and the blood enters the calculation domain at a fixed flow rate. The flow velocity was set in the range of 0.3–0.6 m/s, which matched the actual blood flow velocity of the model vessel diameter dimensions. The computational domain exits using the outflow as the boundary condition, which is used for exits where velocity and pressure details are unknown and is appropriate for fully developed flow. Slip-free walls are used in the computational domain for both smooth and bionic microstructure walls. A convergence residual of 10−8 is specified.


### 2.2. Groove Parameter Setting

To meet the feasibility of realistic vessel thickness and to prevent the boundary layer from interfering with each other during the simulation, the trench depth should be set to less than one-tenth of the calculated domain diameter. In this simulation, the calculated domain pipe diameter is 4 mm, and the corresponding groove depthh+ and groove width w+ should be <0.4 mm. The flat plate experiment [30] has demonstrated that too small a groove spacing will interfere with each other and affect its actual resistance reduction effect, so the groove spacing s is uniformly set to 0.3 mm. A schematic diagram of the V-shaped trench structure is shown in Figure 2. At the same time, to ensure that the resistance change of the microstructure is observed and to amplify the drag reduction effect, the number of nonsmooth microstructure grooves is uniformly 10. The 3D model of the trench structure pipe section is shown in Figure 3.Figure 2
Schematic diagram of the bionic V-groove microstructure model.Figure 3
3D schematic of the bionic trench model.Models with groove widths of 0.05, 0.1, 0.15, 0.2, 0.25 and 0.3 mm and groove depths of 0.05, 0.1, 0.15, 0.2, 0.25 and 0.3 mm were set up to investigate the effect of groove size parameters on the drag reduction rate. Flow velocities of 0.3, 0.4, 0.5 and 0.6 m/s were set to investigate the effect of flow velocity on the resistance reduction rate of the grooves. According to Equation (2), the blood flow resistance value of the measured microstructure can be calculated, while the equidistant pressure difference of the smooth part of the same calculation model is calculated for control, which is used to compare the resistance difference between the smooth tube wall and the microstructure surface. The resistance reduction rate can be calculated from Equation (3). The results of all the calculation models are analyzed together to obtain the variation of the V-groove resistance with each parameter of the groove.


### 2.3. Resistance Calculation Method

The controlling equation used for numerical simulations is the incompressible Navier–Stokes (N–S) equation [31]. The resistance of the vessel can be derived from the Hagen–Poiseuille equation [32]. The expression for the vascular resistance Rs is as follows:(2)Rs=ΔpQ=8μLπR4,where L is the length of the circular tube (m), Δp is the pressure drop in the circular pipe section (Pa), Q is the flow rate in the circular tube (m3/s), R is the radius of the circular tube (m), and μ is the dynamic viscosity (kg·(m · s)−1).The resistance reduction rate for microstructures can be obtained by comparing the blood flow resistance of smooth and grooved pipe sections in the same calculation. Using the blood flow resistance of the smooth tube section as the basis for the calculation, the evaluation equation for the resistance reduction rate is as follows:(3)λ=R0−RcR0×100%,where λ is the rate of resistance reduction, R0 is the resistance to blood flow in a smooth tubular segment, and Rc is the resistance to blood flow in a tubular segment with a microstructure.When the resistance reduction rate is positive, the microstructure has a resistance reduction effect and vice versa, it has a resistance increase effect.


### 2.4. Mesh and Calculation Accuracy Validation

The long straight circular tube model has a simple topology and is suitable for structured meshing. Mesh software is used to divide the model into meshes. For vascular cylindrical pipes, the mesh can be generated using the MultiZone method, which automatically decomposes the entire pipe section into multiple regions that can be swept, and then generates a high-quality hexahedral mesh.This paper is a study of the wall resistance of artificial blood vessels, which requires high precision and accuracy of the pipe wall, so the Inflation command was used to refine and encrypt the boundary mesh with eight layers and an expansion rate of 1.1.Simulations were carried out with vessels without the addition of drag-reducing microstructures as calculation objects to verify the computational accuracy of the numerical simulations. The theoretical value of the pressure difference in the vessel segment can be calculated according to the Hagen–Poiseuille Equation (4), which can verify the numerical simulation results in a smooth inner wall vessel. Therefore, in this paper, the pressure drop under the action of a smooth circular tube is obtained using the Poiseuille equation and compared with the numerical simulation of the pressure drop to verify the magnitude of the error in the numerical simulation.(4)Δp=128μLQπd4.When the blood with an inlet velocity of 0.3 m/s flows into the long straight circular tube, the theoretical value of the pressure drop in the 10 mm section of the tube is 21 Pa, calculated according to the Poiseuille equation, and the error in the calculation is very close to the theoretical value when the number of grids is close to 300,000. As the number of grids continues to increase, the error decreases less. For numerical simulation, it is generally considered that an error of <5% can satisfy the calculation requirements.Taking into account the calculation accuracy and calculation time, a mesh size of around 300,000 meshes was finally used in all simulations. The error between the numerical simulation results and the theoretical value is about 3.8%, and this error size can be considered accurate for the numerical simulation calculation results. Although the numerical solution obtained in the numerical simulation has errors, the vascular structure properties obtained with it can represent the actual phenomenon and properties.


## 2.1. Vascular Model and Computational Domain

In this paper, V-grooves were selected for in-depth study. For this purpose, several sets of simulation experiments were generated by modifying the V-groove depth and width parameters. To meet the requirements of numerical simulations of artificial blood vessels for research purposes, a series of idealized assumptions about the real blood flow environment had to be made. The following assumptions were used: incompressible Newtonian fluid [26], flow as a laminar flow, constant flow [27], rigid tube walls, and no slip. The length of the starting section of fluid laminar flow for the conditions studied in this paper was calculated according to the empirical Equation (1) [28]. A review of the data yielded [29] that the axillary artery diameter was 3.3–5.1 mm, the mean flow velocity was 25–92 cm/s, and the Reynolds number was 249.9–1,421. Reynolds number is a measure of the ratio of fluid inertial force to viscous force, which is a dimensionless number. In this paper, the bionic vessel model was assumed to have a tube diameter of 4 mm, and a maximum Reynolds number of 726 was calculated for a 4 mm diameter vessel with a flow velocity of 0.3–0.6 m/s. The flow was all in laminar flow. The higher the flow velocity, the longer the laminar flow initiation section, with the longest section being 84 mm.(1)L=0.2875dRe,where L is the length of the starting segment (mm), d is the vessel diameter (mm), and Re is the Reynolds number.As the formulae for the laminar flow initiation section are empirical, their calculation results are for experimental reference only and their values differ from the simulation results. It can be determined that in this study, the length of the initial segment of laminar flow is <100 mm in all the segments of the blood vessel where the inlet flow velocity is between 0.3 and 0.6 m/s.Based on the above assumptions about the blood vessel, a model of the biomimetic artificial blood vessel was created, as shown in Figure1. This includes the two-dimensional dimensions of the model, the schematic diagram of the three-dimensional model, and the dimensions of the calculation domain. Taking into account the length of the laminar flow start section at different velocities and the computational performance, the upstream length of the test section was taken as 10l, which is fully sufficient for this study. To avoid exit disturbances, the length is extended downstream of the test section by l. The calculation domain is therefore a tubular cylinder with a total length of 12 l = 120 mm and a diameter of d = 4 mm.Figure 1
Biomimetic artificial blood vessel model: (a) two-dimensional dimensions, (b) three-dimensional schematic, and (c) calculation field size.
(a)(b)(c)The boundary conditions and initial conditions are set as follows: the fluid in the flow field is blood, its density is 1,060 kg/m3, the kinematic viscosity coefficient is 0.0035 m2/s, and the blood temperature is always set to 37°C. The vessel inlet is set as a velocity inlet and the blood enters the calculation domain at a fixed flow rate. The flow velocity was set in the range of 0.3–0.6 m/s, which matched the actual blood flow velocity of the model vessel diameter dimensions. The computational domain exits using the outflow as the boundary condition, which is used for exits where velocity and pressure details are unknown and is appropriate for fully developed flow. Slip-free walls are used in the computational domain for both smooth and bionic microstructure walls. A convergence residual of 10−8 is specified.


## 2.2. Groove Parameter Setting

To meet the feasibility of realistic vessel thickness and to prevent the boundary layer from interfering with each other during the simulation, the trench depth should be set to less than one-tenth of the calculated domain diameter. In this simulation, the calculated domain pipe diameter is 4 mm, and the corresponding groove depthh+ and groove width w+ should be <0.4 mm. The flat plate experiment [30] has demonstrated that too small a groove spacing will interfere with each other and affect its actual resistance reduction effect, so the groove spacing s is uniformly set to 0.3 mm. A schematic diagram of the V-shaped trench structure is shown in Figure 2. At the same time, to ensure that the resistance change of the microstructure is observed and to amplify the drag reduction effect, the number of nonsmooth microstructure grooves is uniformly 10. The 3D model of the trench structure pipe section is shown in Figure 3.Figure 2
Schematic diagram of the bionic V-groove microstructure model.Figure 3
3D schematic of the bionic trench model.Models with groove widths of 0.05, 0.1, 0.15, 0.2, 0.25 and 0.3 mm and groove depths of 0.05, 0.1, 0.15, 0.2, 0.25 and 0.3 mm were set up to investigate the effect of groove size parameters on the drag reduction rate. Flow velocities of 0.3, 0.4, 0.5 and 0.6 m/s were set to investigate the effect of flow velocity on the resistance reduction rate of the grooves. According to Equation (2), the blood flow resistance value of the measured microstructure can be calculated, while the equidistant pressure difference of the smooth part of the same calculation model is calculated for control, which is used to compare the resistance difference between the smooth tube wall and the microstructure surface. The resistance reduction rate can be calculated from Equation (3). The results of all the calculation models are analyzed together to obtain the variation of the V-groove resistance with each parameter of the groove.


## 2.3. Resistance Calculation Method

The controlling equation used for numerical simulations is the incompressible Navier–Stokes (N–S) equation [31]. The resistance of the vessel can be derived from the Hagen–Poiseuille equation [32]. The expression for the vascular resistance Rs is as follows:(2)Rs=ΔpQ=8μLπR4,where L is the length of the circular tube (m), Δp is the pressure drop in the circular pipe section (Pa), Q is the flow rate in the circular tube (m3/s), R is the radius of the circular tube (m), and μ is the dynamic viscosity (kg·(m · s)−1).The resistance reduction rate for microstructures can be obtained by comparing the blood flow resistance of smooth and grooved pipe sections in the same calculation. Using the blood flow resistance of the smooth tube section as the basis for the calculation, the evaluation equation for the resistance reduction rate is as follows:(3)λ=R0−RcR0×100%,where λ is the rate of resistance reduction, R0 is the resistance to blood flow in a smooth tubular segment, and Rc is the resistance to blood flow in a tubular segment with a microstructure.When the resistance reduction rate is positive, the microstructure has a resistance reduction effect and vice versa, it has a resistance increase effect.


## 2.4. Mesh and Calculation Accuracy Validation

The long straight circular tube model has a simple topology and is suitable for structured meshing. Mesh software is used to divide the model into meshes. For vascular cylindrical pipes, the mesh can be generated using the MultiZone method, which automatically decomposes the entire pipe section into multiple regions that can be swept, and then generates a high-quality hexahedral mesh.This paper is a study of the wall resistance of artificial blood vessels, which requires high precision and accuracy of the pipe wall, so the Inflation command was used to refine and encrypt the boundary mesh with eight layers and an expansion rate of 1.1.Simulations were carried out with vessels without the addition of drag-reducing microstructures as calculation objects to verify the computational accuracy of the numerical simulations. The theoretical value of the pressure difference in the vessel segment can be calculated according to the Hagen–Poiseuille Equation (4), which can verify the numerical simulation results in a smooth inner wall vessel. Therefore, in this paper, the pressure drop under the action of a smooth circular tube is obtained using the Poiseuille equation and compared with the numerical simulation of the pressure drop to verify the magnitude of the error in the numerical simulation.(4)Δp=128μLQπd4.When the blood with an inlet velocity of 0.3 m/s flows into the long straight circular tube, the theoretical value of the pressure drop in the 10 mm section of the tube is 21 Pa, calculated according to the Poiseuille equation, and the error in the calculation is very close to the theoretical value when the number of grids is close to 300,000. As the number of grids continues to increase, the error decreases less. For numerical simulation, it is generally considered that an error of <5% can satisfy the calculation requirements.Taking into account the calculation accuracy and calculation time, a mesh size of around 300,000 meshes was finally used in all simulations. The error between the numerical simulation results and the theoretical value is about 3.8%, and this error size can be considered accurate for the numerical simulation calculation results. Although the numerical solution obtained in the numerical simulation has errors, the vascular structure properties obtained with it can represent the actual phenomenon and properties.


## 3. Results and Discussion

### 3.1. Effect of Fluid Velocity on the Drag Reduction Effect of Grooves

#### 3.1.1. Different Groove Widths

As can be seen from the figure, almost all models have a drag reduction effect, except for some results forw+ = 0.05 mm, and the drag reduction rate decreases gradually with increasing velocity for all calculated models. In Figure 4(a), the maximum drag reduction is 2.16% and the minimum is 0.18% for a trench width of 0.1 mm and a depth of 0.05–0.3 mm. In Figure 4(b), the maximum resistance reduction is 3.73% and the minimum is 1.86% for a trench width of 0.2 mm and a depth of 0.05–0.3 mm. In Figure 4(c), the maximum resistance reduction is 6.89% and the minimum is 6.1% for a trench width of 0.3 mm and a depth of 0.1–0.3 mm. The curve with h+ = 0.05 mm shows a completely different variation pattern from the other curves, which may be analyzed as the value of depth change is too small and the velocity of v = 0.6 m/s is too large for this size, so the effect of drag reduction decreases sharply. In the three sets of calculation results of groove width w+ = 0.1, 0.2, and 0.3 mm, it can be seen initially that the effect of flow velocity on the drag reduction rate is slightly affected by the model groove width size. When the width w+ is small, the slope of the resistance reduction curve is larger, which indicates that the velocity variation has a greater effect on the magnitude of the resistance reduction, and the resistance reduction rate decreases sharply with the increase of the velocity. On the contrary, when the width w+ is larger, the change curve of drag reduction rate is flatter, which indicates that the effect of speed change on the size of drag reduction rate is smaller and the drag reduction performance is more stable.Figure 4
Variation curves of resistance reduction with velocityv for V-groove microstructures (different groove widths): (a) w+ = 0.1 mm, (b) w+ = 0.2 mm, and (c) w+ = 0.3 mm.
(a)(b)(c)


#### 3.1.2. Different Groove Depths

The values of the resistance reduction rate on the curves show a decreasing trend, except for thew+ = 0.05 mm curve in Figure 5(a), where the w+ = 0.3 mm curve lies above all the curves. In Figure 5(a), the maximum resistance reduction rate is 6.47% for a groove depth of 0.1 mm and a width of 0–0.3 mm, and the resistance increase occurs at a speed of 0.5 m/s and w+ = 0.05 mm, which shows that the size of w+ = 0.05 mm is too small. When the velocity v is >0.5 m/s, the drag reduction effect of the groove under this size is extremely unstable. Figure 5(b) shows a maximum resistance reduction of 6.89% and a minimum reduction of 0.38% for a trench depth of 0.2 mm and a width of 0–0.3 mm. In Figure 5(c), the maximum resistance reduction rate is 6.72% for the groove depth of 0.3 mm and width of 0–0.3 mm, and the curve of w+ = 0.05 mm gradually decreases to a negative value, and the resistance reduction rate hovers around 0, so this size has almost no drag reduction effect.Figure 5
Variation curves of resistance reduction with velocityv for V-groove microstructures (different groove depths): (a) h+ = 0.1 mm, (b) h+ = 0.2 mm, and (c) h+ = 0.3 mm.
(a)(b)(c)The curves in Figure5(a)–5(c) are similar, taking Figure 5(a) as an example, the curve at w+ = 3 mm is located at the uppermost level, indicating that the drag reduction rate is generally high under this condition, and the curve is relatively straight, indicating that the drag reduction effect is highly adaptable to the speed and the drag reduction effect is highly stable; the curve at w+ = 0.05 mm is located at the lowermost level, indicating that the drag reduction rate is generally low under this condition, and the curve decreases extremely fast, indicating that the magnitude of the drag reduction rate under this condition is affected by the speed change, and the drag reduction effect decreases rapidly with the speed increase. The curve at w+ = 0.05 mm is at the bottom, indicating that the drag reduction rate is generally low under this condition, and the curve decreases very fast, indicating that the size of the drag reduction rate under this condition is influenced by the change of speed, and the drag reduction effect decreases rapidly with the increase of speed. Comparing all the curves in Figure 5, it can be found that the curve laws at w+ = 0.05 and h+ = 0.05 mm are different from the other curves and there is no consistent law, and considering the possible errors and accuracy problems in the numerical calculation, it can be considered that the law of resistance reduction almost does not exist in the case of small trench size.


#### 3.1.3. Different Width-to-Depth Ratio

The width-to-depth ratio is also an important influencing factor in many trench structure resistance reduction studies. The relationship between flow velocity and drag reduction for a width-to-depth ratio of 1 : 1 is shown in Figure6(a), where the drag reduction decreases as the inlet velocity increases in a trench with a width of 0.1 mm. The maximum reduction rate of 2.12% is obtained at a velocity of 0.3 m/s. In the 0.2 mm depth trench, the reduction decreases with increasing velocity, with a maximum reduction of 3.87% obtained at a velocity of 0.3 m/s. In the 0.3 mm depth trench, the reduction decreases with increasing velocity, with a maximum reduction of 3.87% obtained at a velocity of 0.3 m/s. In the 0.3 mm depth trench, the reduction rate decreases slightly with increasing speed, but remains above 6%, with a maximum reduction rate of 6.71% obtained at 0.3 mm speed. Combining the above three groove sizes, it can be seen that the resistance reduction rate of the groove decreases with increasing inlet velocity. At a width-to-depth ratio of 1 : 1, a maximum drag reduction of 6.71% is obtained.Figure 6
Variation curves of resistance reduction with velocityv for different groove width-to-depth ratios: (a) 1 : 1 and (b) 2 : 1.
(a)(b)The relationship curve between the flow velocity and the drag reduction rate for a width-to-depth ratio of 2 : 1 is shown in Figure6(b). At a width-to-depth ratio of 2 : 1, the resistance reduction rate decreases as the inlet velocity increases from 0.3 to 0.6 m/s at a groove depth of 0.1 mm, with the maximum resistance reduction rate of 2.09% at a velocity of 0.3 m/s. When the groove depth is 0.2 mm, the resistance reduction rate of the groove microstructure gradually decreases as the initial flow velocity increases, and the maximum resistance reduction rate is 3.62% at a velocity of 0.3 m/s. When the groove depth is 0.3 mm, the resistance reduction rate of the groove microstructure remains at about 6.3% as the initial flow velocity increases, and the maximum resistance reduction rate reaches 6.64% at an initial velocity of 0.3 m/s.The curves of the width-to-depth ratio of the two V-shaped groove structures can be seen that the width-to-depth ratio has less influence on the curves of resistance reduction with speed, and the curves of the two groups are highly similar. When the size of the V-shaped groove is small, the effect of the resistance reduction rate with speed is larger, and when the size of the groove is larger, the effect of the resistance reduction rate with speed is smaller. This indicates that the larger groove sizew+ = 0.3 mm is more suitable for a certain width-to-depth ratio and can maintain excellent resistance reduction over a larger speed range.


### 3.2. Influence of Groove Structure Parameters on the Resistance Reduction Effect

#### 3.2.1. Effect of the V-Groove Widthw

As shown in Figure7, all calculations show that the resistance reduction rate of the trench increases as the trench width increases, keeping all other conditions the same. Except for the h+ = 0.05 mm curve in Figure 7(d), all curves achieve a maximum at w+ = 0.3 mm. The basic characteristics of the curves are relatively similar in all four figures. The slope of the curve from w+ = 0.1 to w+ = 0.2 mm is smaller than the slope of the curve from w+ = 0.2 to w+ = 0.3 mm, indicating that the increase in resistance reduction is more significant when the groove width increases from 0.2 to 0.3 mm.Figure 7
Variation curves of resistance reduction with widthw+ for V-shaped grooves (different flow velocity): (a) v = 0.03 mm, (b) v = 0.04 mm, (c) v = 0.05 mm, and (d) v = 0.06 mm.
(a)(b)(c)(d)At the same time, when the groove widthw+ is small, the curves almost coincide and the resistance reduction rate of the groove depth h+ = 0.2 mm is slightly dominant; when the width w+ is larger, the curve of depth h+ = 0.2 mm is positioned higher than the other curves. This indicates that at smaller trench widths, there is not much difference in the resistance reduction effect of different trench depth microstructures, and at a trench depth of 0.2 mm, the larger the trench width the better the resistance reduction effect. The h+ = 0.05 mm curve in Figure 7(d) is different from the other curves, again indicating that a groove with too small a depth has little or no drag reduction effect and that the lack of drag reduction becomes more apparent as the intravascular flow rate increases. Overall, the width of the V-shaped groove has a greater effect on the resistance reduction rate of the groove, with a 6% difference between the highest and lowest values of resistance reduction in each set of results when all other conditions except the groove width w+ remain unchanged. As the trench width w+ increases, the resistance reduction rate changes more evenly, indicating that the resistance reduction rate is approximately linearly related to the trench width in the test range.Through the four sets of calculation results in Figure7, it can be learned that when the incoming flow velocity gradually increases, the resistance reduction rate of the groove under each condition increases, and the difference is small. Under the condition of constant incoming flow velocity, the groove reduction rate increases with the increase of groove width and reaches the maximum at the groove width of 0.3 mm, when the best reduction effect is achieved. Since the diameter of the axillary artery is 3.3–5.1 mm and the diameter of the vessel selected in this paper is 4 mm, the groove width of 0.3 mm in the groove microstructure can achieve the best reduction effect for this artificial vessel.


#### 3.2.2. Effect of the V-Groove Depthh

In Figure8(a), it can be seen that all other things being equal, the variation in resistance reduction varies slightly from curve to curve as the depth of the groove increases. The curves in Figure 8(a) are positive at all sizes except for the curve for w+ = 0.05 mm, which is negative at h+ = 0.05 mm and shows a resistance reduction effect. Ignoring the resistance reduction data for w+ = 0.05 and h+ = 0.05 mm in Figure 8, the remaining part of the curves show high stability, with a small change in resistance reduction with increasing h+. The curves in the remaining three plots also show the pattern present in Figure 8(a). Comparing the six curves in each graph, the resistance reduction rate from h+ = 0 to h+ = 0.2 mm shows an increasing trend, and the resistance reduction rate from h+ = 0.2 to h+ = 0.3 mm shows a decreasing trend, except for the size involving w+ = 0.05 and h+ = 0.05 mm, which are considered to lose the resistance reduction pattern. When the width is larger, such as w+ = 0.3 mm, the curve change feature is most significant, when the width is smaller, such as w+ = 0.1, w+ = 0.15, and w+ = 0.2 mm, the curve is approximately a straight line, indicating that the drag reduction effect of the groove is less affected by the depth of the groove.Figure 8
Variation curves of resistance reduction with depthh+ for V-shaped grooves: (a) v = 0.03 mm, (b) v = 0.04 mm, (c) v = 0.05 mm, and (d) v = 0.06 mm.
(a)(b)(c)(d)Within the range tested, the effect of groove depth variation on groove resistance reduction is small. The V-shaped groove with a width range of 0.1–0.3 mm for the four velocity conditions showed a gentle resistance reduction curve with <1% fluctuation as the depth increased from 0.1 to 0.3 mm. Of all the resistance reduction results shown, the groove depth with the best reduction is aroundh+ = 0.2 mm. Since the object selected for simulation in this paper is the axillary artery, whose wall thickness is <1 mm, this groove depth greatly satisfies the condition of limited wall thickness of artificial blood vessels, so the corresponding bionic artificial blood vessels can be designed with this groove depth for the groove microstructure, which not only has the best resistance reduction effect, but also can provide convenience and save the manufacturing cost for the artificial blood vessels.


#### 3.2.3. Effect of V-Groove Width-to-Depth Ratio

In the following section, the effect of trench size variation on the resistance reduction rate is investigated by considering both trench width and depth as a single variable of width-to-depth ratio. Two sets of trench size data with the same width-to-depth ratio were obtained from the obtained calculation data, as shown in Figure9, for the variation curve of trench resistance reduction rate with increasing V-shaped trench width and depth in equal ratio.Figure 9
Variation curves of resistance reduction with different width-to-depth ratio: (a) 1 : 1 and (b) 2 : 1.
(a)(b)It can be seen from the graphs that other things being equal, the V-groove resistance reduction rate under various velocity conditions tends to increase as the ratio of groove width and depth increases, and the curves under different velocity conditions in both graphs change from dispersion to concentration. At a groove width ofw+ = 0.3 mm, the curves converge almost to a single point, indicating that at this size, similar resistance reduction rates are obtained for all velocity conditions. At a width-to-depth ratio of 1 : 1, the maximum reduction is 6.72% at an inlet speed of v = 0.3 m/s and a groove width of w+ = 0.3 mm, while the minimum reduction is 0.18% at an inlet speed of 0.6 m/s and a groove width of w+ = 0.1 mm. At a width-to-depth ratio of 2 : 1, the maximum drag reduction is 6.64% at an inlet speed of v = 0.3 m/s and a groove width of w+ = 0.3 mm, and the minimum drag reduction is 0.22% at an inlet speed of 0.6 m/s and a groove width of w+ = 0.1 mm. Comparing Figure 9(a) and 9(b), the curves are similar in shape and the values of the vertical coordinates under the same horizontal coordinate are also extremely similar, so it can be seen that the two sets of width-to-depth ratios tested have a small effect on the resistance reduction rate of the grooves. The width-to-depth ratio of the V-shaped groove represents the size of the groove clamping angle, and for the two width-to-depth ratios shown in the following figure, the angle of 1 : 1 is an acute angle and the angle of 2 : 1 is a 90° angle, no significant resistance reduction rate variation characteristics.In addition, the 36 sets of calculation results completed were summarized and analyzed, and the calculation models withw+ = 0.05 and h+ = 0.05 mm, which may lose the drag reduction law due to their small size, were removed, and multiple combinations of aspect ratios could be found, and the calculation results under various aspect ratios were plotted as scatter plots, as shown in Figure 10. Due to the limited size of the calculations, most of the aspect ratios have only one set of drag reduction data, while aspect ratios such as 1 : 1, 3 : 2, and 2 : 1 have multiple sets of sizes to satisfy the data, so some of the aspect ratio conditions in the graph have multiple corresponding drag reduction values. From the scatter plot in Figure 10, it can be seen that the resistance reduction rate does not show a clear trend as the aspect ratio changes. When the aspect ratio is 1 : 1, the distribution of trench resistance reduction rate varies widely, with a minimum of 2.12% and a maximum of 6.72%. Taking the coordinates of the width-to-depth ratio of 1 : 1 as the boundary, Figure 10 can be divided into two parts, in which the width of the left part is greater than the depth, and the distribution of the resistance reduction rate is scattered, but most of the resistance reduction rate is >4%; the width of the right part is smaller than the depth, and the resistance reduction rate has a decreasing trend, and most of the resistance reduction rate is <4%.Figure 10
Scatter plot of trench resistance reduction for different width-to-depth ratios.When the incoming flow velocity is 0.3 m/s and the width-to-depth ratio is >1, the groove microstructure has a good drag reduction effect, especially when the width-to-depth ratio is 3 : 2, the drag reduction rate of the groove at this time is the largest and the drag reduction effect is the best. The size of the groove and the incoming flow velocity of the bionic vessel at this time are more consistent with the real situation of the axillary artery vasculature selected in this paper, indicating that the artificial vessel with this groove design parameter is more achievable. By continuously optimizing the bionic microarchitecture and its parameters in the artificial blood vessel, we can reduce the resistance to blood flow and provide a basis and design idea for the development of artificial blood vessels with low resistance and long life.


### 3.3. V-Groove Velocity Field Analysis

Based on the results of the V-groove drag rate calculation for the different sizes above, the groove with the largest drag ratew+ = 0.3 and h+ = 0.2 mm and the groove with the smaller drag rate w+ = 0.1 and h+ = 0.1 mm were selected to observe the blood flow pattern near the boundary layer, analyze the blood flow state in the groove and investigate the reasons for the variation of the drag rate.The cloud plot of the velocity variation of blood passing through the V-shaped groove of the drag-reducing microstructure is shown in Figure11. As can be seen from the graphs, the lower drag rate is typically no more than 2.2% for the w+ = 0.1 and h+ = 0.1 mm dimensions, and the best drag rate is achieved for the w+ = 0.3 and h+ = 0.2 mm dimensions, with the drag rate being >6.5%. As can be seen from all velocity clouds, the bionic microstructure alters the original flow characteristics of the smooth tube, resulting in a significant improvement in blood flow characteristics. In the tube segments without microstructures, the high-velocity contour density and the greater thickness of the boundary layer of blood flow resulted in a more variable distribution of blood flow velocities in circular sections within the vessel, with high flow velocities and narrow high-velocity regions at the central axis and an overall nonuniform velocity distribution. The boundary velocity contour density is reduced in tube segments with a trench structure. From the above, it is known that the velocity reduction rate is higher when the velocity is small under the condition of constant size, and correspondingly the velocity cloud pattern of the same size of V-shaped groove at different velocities can be seen from the velocity cloud pattern. As shown in Figure 11(e), at v = 0.3 m/s, the narrow area of maximum velocity at the axis of the vessel is almost completely dissipated and replaced by a smaller maximum velocity at the axis, but the coverage area becomes larger and the distribution of blood flow velocity from the axis to the vessel wall becomes more uniform, with a greater improvement in the drag reduction effect. As the velocity increases, the dampening effect becomes less effective, as shown in Figure 11(f)–11(h), where the change in flow velocity in the axial region of the velocity cloud is less significant than at v = 0.3 m/s as the velocity increases.Figure 11
Velocity clouds of a bionic V-groove microstructured artificial vessel: (a)w+ = 0.1 mm, h+ = 0.1 mm, v = 0.3 m/s; (b) w+ = 0.1 mm, h+ = 0.1 mm, v = 0.4 m/s; (c) w+ = 0.1 mm, h+ = 0.1 mm, v = 0.5 m/s; (d) w+ = 0.1 mm, h+ = 0.1 mm, v = 0.6 m/s; (e) w+ = 0.3 mm, h+ = 0.2 mm, v = 0.3 m/s; (f) w+ = 0.3 mm, h+ = 0.2 mm, v = 0.4 m/s; (g) w+ = 0.3 mm, h+ = 0.2 mm, v = 0.5 m/s; (h) w+ = 0.3 mm, h+ = 0.2 mm, v = 0.6 m/s.
(a)(b)(c)(d)(e)(f)(g)(h)In Figure11, the four cloud plots with dimensions w+ = 0.3 and h+ = 0.2 mm have a smaller velocity gradient along the axial region to the vessel wall and a more uniform velocity distribution compared to the four cloud plots with dimensions w+ = 0.1 and h+ = 0.1 mm at the same velocity. Therefore, it can be known that the presence of V-shaped microstructures improves the velocity distribution of intravascular blood flow, and the dampening effect is related to the uniformity of velocity distribution between the axis and the canal wall. When the maximum velocity at the axis of blood flow in the tube is smaller, and the blood flow velocity in the area close to the vessel wall surface is less obstructed by the wall and the boundary velocity is larger, i.e., when the velocity distribution in the tube cross-section is uniform, the drag reduction effect is good.


## 3.1. Effect of Fluid Velocity on the Drag Reduction Effect of Grooves

### 3.1.1. Different Groove Widths

As can be seen from the figure, almost all models have a drag reduction effect, except for some results forw+ = 0.05 mm, and the drag reduction rate decreases gradually with increasing velocity for all calculated models. In Figure 4(a), the maximum drag reduction is 2.16% and the minimum is 0.18% for a trench width of 0.1 mm and a depth of 0.05–0.3 mm. In Figure 4(b), the maximum resistance reduction is 3.73% and the minimum is 1.86% for a trench width of 0.2 mm and a depth of 0.05–0.3 mm. In Figure 4(c), the maximum resistance reduction is 6.89% and the minimum is 6.1% for a trench width of 0.3 mm and a depth of 0.1–0.3 mm. The curve with h+ = 0.05 mm shows a completely different variation pattern from the other curves, which may be analyzed as the value of depth change is too small and the velocity of v = 0.6 m/s is too large for this size, so the effect of drag reduction decreases sharply. In the three sets of calculation results of groove width w+ = 0.1, 0.2, and 0.3 mm, it can be seen initially that the effect of flow velocity on the drag reduction rate is slightly affected by the model groove width size. When the width w+ is small, the slope of the resistance reduction curve is larger, which indicates that the velocity variation has a greater effect on the magnitude of the resistance reduction, and the resistance reduction rate decreases sharply with the increase of the velocity. On the contrary, when the width w+ is larger, the change curve of drag reduction rate is flatter, which indicates that the effect of speed change on the size of drag reduction rate is smaller and the drag reduction performance is more stable.Figure 4
Variation curves of resistance reduction with velocityv for V-groove microstructures (different groove widths): (a) w+ = 0.1 mm, (b) w+ = 0.2 mm, and (c) w+ = 0.3 mm.
(a)(b)(c)


### 3.1.2. Different Groove Depths

The values of the resistance reduction rate on the curves show a decreasing trend, except for thew+ = 0.05 mm curve in Figure 5(a), where the w+ = 0.3 mm curve lies above all the curves. In Figure 5(a), the maximum resistance reduction rate is 6.47% for a groove depth of 0.1 mm and a width of 0–0.3 mm, and the resistance increase occurs at a speed of 0.5 m/s and w+ = 0.05 mm, which shows that the size of w+ = 0.05 mm is too small. When the velocity v is >0.5 m/s, the drag reduction effect of the groove under this size is extremely unstable. Figure 5(b) shows a maximum resistance reduction of 6.89% and a minimum reduction of 0.38% for a trench depth of 0.2 mm and a width of 0–0.3 mm. In Figure 5(c), the maximum resistance reduction rate is 6.72% for the groove depth of 0.3 mm and width of 0–0.3 mm, and the curve of w+ = 0.05 mm gradually decreases to a negative value, and the resistance reduction rate hovers around 0, so this size has almost no drag reduction effect.Figure 5
Variation curves of resistance reduction with velocityv for V-groove microstructures (different groove depths): (a) h+ = 0.1 mm, (b) h+ = 0.2 mm, and (c) h+ = 0.3 mm.
(a)(b)(c)The curves in Figure5(a)–5(c) are similar, taking Figure 5(a) as an example, the curve at w+ = 3 mm is located at the uppermost level, indicating that the drag reduction rate is generally high under this condition, and the curve is relatively straight, indicating that the drag reduction effect is highly adaptable to the speed and the drag reduction effect is highly stable; the curve at w+ = 0.05 mm is located at the lowermost level, indicating that the drag reduction rate is generally low under this condition, and the curve decreases extremely fast, indicating that the magnitude of the drag reduction rate under this condition is affected by the speed change, and the drag reduction effect decreases rapidly with the speed increase. The curve at w+ = 0.05 mm is at the bottom, indicating that the drag reduction rate is generally low under this condition, and the curve decreases very fast, indicating that the size of the drag reduction rate under this condition is influenced by the change of speed, and the drag reduction effect decreases rapidly with the increase of speed. Comparing all the curves in Figure 5, it can be found that the curve laws at w+ = 0.05 and h+ = 0.05 mm are different from the other curves and there is no consistent law, and considering the possible errors and accuracy problems in the numerical calculation, it can be considered that the law of resistance reduction almost does not exist in the case of small trench size.


### 3.1.3. Different Width-to-Depth Ratio

The width-to-depth ratio is also an important influencing factor in many trench structure resistance reduction studies. The relationship between flow velocity and drag reduction for a width-to-depth ratio of 1 : 1 is shown in Figure6(a), where the drag reduction decreases as the inlet velocity increases in a trench with a width of 0.1 mm. The maximum reduction rate of 2.12% is obtained at a velocity of 0.3 m/s. In the 0.2 mm depth trench, the reduction decreases with increasing velocity, with a maximum reduction of 3.87% obtained at a velocity of 0.3 m/s. In the 0.3 mm depth trench, the reduction decreases with increasing velocity, with a maximum reduction of 3.87% obtained at a velocity of 0.3 m/s. In the 0.3 mm depth trench, the reduction rate decreases slightly with increasing speed, but remains above 6%, with a maximum reduction rate of 6.71% obtained at 0.3 mm speed. Combining the above three groove sizes, it can be seen that the resistance reduction rate of the groove decreases with increasing inlet velocity. At a width-to-depth ratio of 1 : 1, a maximum drag reduction of 6.71% is obtained.Figure 6
Variation curves of resistance reduction with velocityv for different groove width-to-depth ratios: (a) 1 : 1 and (b) 2 : 1.
(a)(b)The relationship curve between the flow velocity and the drag reduction rate for a width-to-depth ratio of 2 : 1 is shown in Figure6(b). At a width-to-depth ratio of 2 : 1, the resistance reduction rate decreases as the inlet velocity increases from 0.3 to 0.6 m/s at a groove depth of 0.1 mm, with the maximum resistance reduction rate of 2.09% at a velocity of 0.3 m/s. When the groove depth is 0.2 mm, the resistance reduction rate of the groove microstructure gradually decreases as the initial flow velocity increases, and the maximum resistance reduction rate is 3.62% at a velocity of 0.3 m/s. When the groove depth is 0.3 mm, the resistance reduction rate of the groove microstructure remains at about 6.3% as the initial flow velocity increases, and the maximum resistance reduction rate reaches 6.64% at an initial velocity of 0.3 m/s.The curves of the width-to-depth ratio of the two V-shaped groove structures can be seen that the width-to-depth ratio has less influence on the curves of resistance reduction with speed, and the curves of the two groups are highly similar. When the size of the V-shaped groove is small, the effect of the resistance reduction rate with speed is larger, and when the size of the groove is larger, the effect of the resistance reduction rate with speed is smaller. This indicates that the larger groove sizew+ = 0.3 mm is more suitable for a certain width-to-depth ratio and can maintain excellent resistance reduction over a larger speed range.


## 3.1.1. Different Groove Widths

As can be seen from the figure, almost all models have a drag reduction effect, except for some results forw+ = 0.05 mm, and the drag reduction rate decreases gradually with increasing velocity for all calculated models. In Figure 4(a), the maximum drag reduction is 2.16% and the minimum is 0.18% for a trench width of 0.1 mm and a depth of 0.05–0.3 mm. In Figure 4(b), the maximum resistance reduction is 3.73% and the minimum is 1.86% for a trench width of 0.2 mm and a depth of 0.05–0.3 mm. In Figure 4(c), the maximum resistance reduction is 6.89% and the minimum is 6.1% for a trench width of 0.3 mm and a depth of 0.1–0.3 mm. The curve with h+ = 0.05 mm shows a completely different variation pattern from the other curves, which may be analyzed as the value of depth change is too small and the velocity of v = 0.6 m/s is too large for this size, so the effect of drag reduction decreases sharply. In the three sets of calculation results of groove width w+ = 0.1, 0.2, and 0.3 mm, it can be seen initially that the effect of flow velocity on the drag reduction rate is slightly affected by the model groove width size. When the width w+ is small, the slope of the resistance reduction curve is larger, which indicates that the velocity variation has a greater effect on the magnitude of the resistance reduction, and the resistance reduction rate decreases sharply with the increase of the velocity. On the contrary, when the width w+ is larger, the change curve of drag reduction rate is flatter, which indicates that the effect of speed change on the size of drag reduction rate is smaller and the drag reduction performance is more stable.Figure 4
Variation curves of resistance reduction with velocityv for V-groove microstructures (different groove widths): (a) w+ = 0.1 mm, (b) w+ = 0.2 mm, and (c) w+ = 0.3 mm.
(a)(b)(c)


## 3.1.2. Different Groove Depths

The values of the resistance reduction rate on the curves show a decreasing trend, except for thew+ = 0.05 mm curve in Figure 5(a), where the w+ = 0.3 mm curve lies above all the curves. In Figure 5(a), the maximum resistance reduction rate is 6.47% for a groove depth of 0.1 mm and a width of 0–0.3 mm, and the resistance increase occurs at a speed of 0.5 m/s and w+ = 0.05 mm, which shows that the size of w+ = 0.05 mm is too small. When the velocity v is >0.5 m/s, the drag reduction effect of the groove under this size is extremely unstable. Figure 5(b) shows a maximum resistance reduction of 6.89% and a minimum reduction of 0.38% for a trench depth of 0.2 mm and a width of 0–0.3 mm. In Figure 5(c), the maximum resistance reduction rate is 6.72% for the groove depth of 0.3 mm and width of 0–0.3 mm, and the curve of w+ = 0.05 mm gradually decreases to a negative value, and the resistance reduction rate hovers around 0, so this size has almost no drag reduction effect.Figure 5
Variation curves of resistance reduction with velocityv for V-groove microstructures (different groove depths): (a) h+ = 0.1 mm, (b) h+ = 0.2 mm, and (c) h+ = 0.3 mm.
(a)(b)(c)The curves in Figure5(a)–5(c) are similar, taking Figure 5(a) as an example, the curve at w+ = 3 mm is located at the uppermost level, indicating that the drag reduction rate is generally high under this condition, and the curve is relatively straight, indicating that the drag reduction effect is highly adaptable to the speed and the drag reduction effect is highly stable; the curve at w+ = 0.05 mm is located at the lowermost level, indicating that the drag reduction rate is generally low under this condition, and the curve decreases extremely fast, indicating that the magnitude of the drag reduction rate under this condition is affected by the speed change, and the drag reduction effect decreases rapidly with the speed increase. The curve at w+ = 0.05 mm is at the bottom, indicating that the drag reduction rate is generally low under this condition, and the curve decreases very fast, indicating that the size of the drag reduction rate under this condition is influenced by the change of speed, and the drag reduction effect decreases rapidly with the increase of speed. Comparing all the curves in Figure 5, it can be found that the curve laws at w+ = 0.05 and h+ = 0.05 mm are different from the other curves and there is no consistent law, and considering the possible errors and accuracy problems in the numerical calculation, it can be considered that the law of resistance reduction almost does not exist in the case of small trench size.


## 3.1.3. Different Width-to-Depth Ratio

The width-to-depth ratio is also an important influencing factor in many trench structure resistance reduction studies. The relationship between flow velocity and drag reduction for a width-to-depth ratio of 1 : 1 is shown in Figure6(a), where the drag reduction decreases as the inlet velocity increases in a trench with a width of 0.1 mm. The maximum reduction rate of 2.12% is obtained at a velocity of 0.3 m/s. In the 0.2 mm depth trench, the reduction decreases with increasing velocity, with a maximum reduction of 3.87% obtained at a velocity of 0.3 m/s. In the 0.3 mm depth trench, the reduction decreases with increasing velocity, with a maximum reduction of 3.87% obtained at a velocity of 0.3 m/s. In the 0.3 mm depth trench, the reduction rate decreases slightly with increasing speed, but remains above 6%, with a maximum reduction rate of 6.71% obtained at 0.3 mm speed. Combining the above three groove sizes, it can be seen that the resistance reduction rate of the groove decreases with increasing inlet velocity. At a width-to-depth ratio of 1 : 1, a maximum drag reduction of 6.71% is obtained.Figure 6
Variation curves of resistance reduction with velocityv for different groove width-to-depth ratios: (a) 1 : 1 and (b) 2 : 1.
(a)(b)The relationship curve between the flow velocity and the drag reduction rate for a width-to-depth ratio of 2 : 1 is shown in Figure6(b). At a width-to-depth ratio of 2 : 1, the resistance reduction rate decreases as the inlet velocity increases from 0.3 to 0.6 m/s at a groove depth of 0.1 mm, with the maximum resistance reduction rate of 2.09% at a velocity of 0.3 m/s. When the groove depth is 0.2 mm, the resistance reduction rate of the groove microstructure gradually decreases as the initial flow velocity increases, and the maximum resistance reduction rate is 3.62% at a velocity of 0.3 m/s. When the groove depth is 0.3 mm, the resistance reduction rate of the groove microstructure remains at about 6.3% as the initial flow velocity increases, and the maximum resistance reduction rate reaches 6.64% at an initial velocity of 0.3 m/s.The curves of the width-to-depth ratio of the two V-shaped groove structures can be seen that the width-to-depth ratio has less influence on the curves of resistance reduction with speed, and the curves of the two groups are highly similar. When the size of the V-shaped groove is small, the effect of the resistance reduction rate with speed is larger, and when the size of the groove is larger, the effect of the resistance reduction rate with speed is smaller. This indicates that the larger groove sizew+ = 0.3 mm is more suitable for a certain width-to-depth ratio and can maintain excellent resistance reduction over a larger speed range.


## 3.2. Influence of Groove Structure Parameters on the Resistance Reduction Effect

### 3.2.1. Effect of the V-Groove Widthw

As shown in Figure7, all calculations show that the resistance reduction rate of the trench increases as the trench width increases, keeping all other conditions the same. Except for the h+ = 0.05 mm curve in Figure 7(d), all curves achieve a maximum at w+ = 0.3 mm. The basic characteristics of the curves are relatively similar in all four figures. The slope of the curve from w+ = 0.1 to w+ = 0.2 mm is smaller than the slope of the curve from w+ = 0.2 to w+ = 0.3 mm, indicating that the increase in resistance reduction is more significant when the groove width increases from 0.2 to 0.3 mm.Figure 7
Variation curves of resistance reduction with widthw+ for V-shaped grooves (different flow velocity): (a) v = 0.03 mm, (b) v = 0.04 mm, (c) v = 0.05 mm, and (d) v = 0.06 mm.
(a)(b)(c)(d)At the same time, when the groove widthw+ is small, the curves almost coincide and the resistance reduction rate of the groove depth h+ = 0.2 mm is slightly dominant; when the width w+ is larger, the curve of depth h+ = 0.2 mm is positioned higher than the other curves. This indicates that at smaller trench widths, there is not much difference in the resistance reduction effect of different trench depth microstructures, and at a trench depth of 0.2 mm, the larger the trench width the better the resistance reduction effect. The h+ = 0.05 mm curve in Figure 7(d) is different from the other curves, again indicating that a groove with too small a depth has little or no drag reduction effect and that the lack of drag reduction becomes more apparent as the intravascular flow rate increases. Overall, the width of the V-shaped groove has a greater effect on the resistance reduction rate of the groove, with a 6% difference between the highest and lowest values of resistance reduction in each set of results when all other conditions except the groove width w+ remain unchanged. As the trench width w+ increases, the resistance reduction rate changes more evenly, indicating that the resistance reduction rate is approximately linearly related to the trench width in the test range.Through the four sets of calculation results in Figure7, it can be learned that when the incoming flow velocity gradually increases, the resistance reduction rate of the groove under each condition increases, and the difference is small. Under the condition of constant incoming flow velocity, the groove reduction rate increases with the increase of groove width and reaches the maximum at the groove width of 0.3 mm, when the best reduction effect is achieved. Since the diameter of the axillary artery is 3.3–5.1 mm and the diameter of the vessel selected in this paper is 4 mm, the groove width of 0.3 mm in the groove microstructure can achieve the best reduction effect for this artificial vessel.


### 3.2.2. Effect of the V-Groove Depthh

In Figure8(a), it can be seen that all other things being equal, the variation in resistance reduction varies slightly from curve to curve as the depth of the groove increases. The curves in Figure 8(a) are positive at all sizes except for the curve for w+ = 0.05 mm, which is negative at h+ = 0.05 mm and shows a resistance reduction effect. Ignoring the resistance reduction data for w+ = 0.05 and h+ = 0.05 mm in Figure 8, the remaining part of the curves show high stability, with a small change in resistance reduction with increasing h+. The curves in the remaining three plots also show the pattern present in Figure 8(a). Comparing the six curves in each graph, the resistance reduction rate from h+ = 0 to h+ = 0.2 mm shows an increasing trend, and the resistance reduction rate from h+ = 0.2 to h+ = 0.3 mm shows a decreasing trend, except for the size involving w+ = 0.05 and h+ = 0.05 mm, which are considered to lose the resistance reduction pattern. When the width is larger, such as w+ = 0.3 mm, the curve change feature is most significant, when the width is smaller, such as w+ = 0.1, w+ = 0.15, and w+ = 0.2 mm, the curve is approximately a straight line, indicating that the drag reduction effect of the groove is less affected by the depth of the groove.Figure 8
Variation curves of resistance reduction with depthh+ for V-shaped grooves: (a) v = 0.03 mm, (b) v = 0.04 mm, (c) v = 0.05 mm, and (d) v = 0.06 mm.
(a)(b)(c)(d)Within the range tested, the effect of groove depth variation on groove resistance reduction is small. The V-shaped groove with a width range of 0.1–0.3 mm for the four velocity conditions showed a gentle resistance reduction curve with <1% fluctuation as the depth increased from 0.1 to 0.3 mm. Of all the resistance reduction results shown, the groove depth with the best reduction is aroundh+ = 0.2 mm. Since the object selected for simulation in this paper is the axillary artery, whose wall thickness is <1 mm, this groove depth greatly satisfies the condition of limited wall thickness of artificial blood vessels, so the corresponding bionic artificial blood vessels can be designed with this groove depth for the groove microstructure, which not only has the best resistance reduction effect, but also can provide convenience and save the manufacturing cost for the artificial blood vessels.


### 3.2.3. Effect of V-Groove Width-to-Depth Ratio

In the following section, the effect of trench size variation on the resistance reduction rate is investigated by considering both trench width and depth as a single variable of width-to-depth ratio. Two sets of trench size data with the same width-to-depth ratio were obtained from the obtained calculation data, as shown in Figure9, for the variation curve of trench resistance reduction rate with increasing V-shaped trench width and depth in equal ratio.Figure 9
Variation curves of resistance reduction with different width-to-depth ratio: (a) 1 : 1 and (b) 2 : 1.
(a)(b)It can be seen from the graphs that other things being equal, the V-groove resistance reduction rate under various velocity conditions tends to increase as the ratio of groove width and depth increases, and the curves under different velocity conditions in both graphs change from dispersion to concentration. At a groove width ofw+ = 0.3 mm, the curves converge almost to a single point, indicating that at this size, similar resistance reduction rates are obtained for all velocity conditions. At a width-to-depth ratio of 1 : 1, the maximum reduction is 6.72% at an inlet speed of v = 0.3 m/s and a groove width of w+ = 0.3 mm, while the minimum reduction is 0.18% at an inlet speed of 0.6 m/s and a groove width of w+ = 0.1 mm. At a width-to-depth ratio of 2 : 1, the maximum drag reduction is 6.64% at an inlet speed of v = 0.3 m/s and a groove width of w+ = 0.3 mm, and the minimum drag reduction is 0.22% at an inlet speed of 0.6 m/s and a groove width of w+ = 0.1 mm. Comparing Figure 9(a) and 9(b), the curves are similar in shape and the values of the vertical coordinates under the same horizontal coordinate are also extremely similar, so it can be seen that the two sets of width-to-depth ratios tested have a small effect on the resistance reduction rate of the grooves. The width-to-depth ratio of the V-shaped groove represents the size of the groove clamping angle, and for the two width-to-depth ratios shown in the following figure, the angle of 1 : 1 is an acute angle and the angle of 2 : 1 is a 90° angle, no significant resistance reduction rate variation characteristics.In addition, the 36 sets of calculation results completed were summarized and analyzed, and the calculation models withw+ = 0.05 and h+ = 0.05 mm, which may lose the drag reduction law due to their small size, were removed, and multiple combinations of aspect ratios could be found, and the calculation results under various aspect ratios were plotted as scatter plots, as shown in Figure 10. Due to the limited size of the calculations, most of the aspect ratios have only one set of drag reduction data, while aspect ratios such as 1 : 1, 3 : 2, and 2 : 1 have multiple sets of sizes to satisfy the data, so some of the aspect ratio conditions in the graph have multiple corresponding drag reduction values. From the scatter plot in Figure 10, it can be seen that the resistance reduction rate does not show a clear trend as the aspect ratio changes. When the aspect ratio is 1 : 1, the distribution of trench resistance reduction rate varies widely, with a minimum of 2.12% and a maximum of 6.72%. Taking the coordinates of the width-to-depth ratio of 1 : 1 as the boundary, Figure 10 can be divided into two parts, in which the width of the left part is greater than the depth, and the distribution of the resistance reduction rate is scattered, but most of the resistance reduction rate is >4%; the width of the right part is smaller than the depth, and the resistance reduction rate has a decreasing trend, and most of the resistance reduction rate is <4%.Figure 10
Scatter plot of trench resistance reduction for different width-to-depth ratios.When the incoming flow velocity is 0.3 m/s and the width-to-depth ratio is >1, the groove microstructure has a good drag reduction effect, especially when the width-to-depth ratio is 3 : 2, the drag reduction rate of the groove at this time is the largest and the drag reduction effect is the best. The size of the groove and the incoming flow velocity of the bionic vessel at this time are more consistent with the real situation of the axillary artery vasculature selected in this paper, indicating that the artificial vessel with this groove design parameter is more achievable. By continuously optimizing the bionic microarchitecture and its parameters in the artificial blood vessel, we can reduce the resistance to blood flow and provide a basis and design idea for the development of artificial blood vessels with low resistance and long life.


## 3.2.1. Effect of the V-Groove Widthw

As shown in Figure7, all calculations show that the resistance reduction rate of the trench increases as the trench width increases, keeping all other conditions the same. Except for the h+ = 0.05 mm curve in Figure 7(d), all curves achieve a maximum at w+ = 0.3 mm. The basic characteristics of the curves are relatively similar in all four figures. The slope of the curve from w+ = 0.1 to w+ = 0.2 mm is smaller than the slope of the curve from w+ = 0.2 to w+ = 0.3 mm, indicating that the increase in resistance reduction is more significant when the groove width increases from 0.2 to 0.3 mm.Figure 7
Variation curves of resistance reduction with widthw+ for V-shaped grooves (different flow velocity): (a) v = 0.03 mm, (b) v = 0.04 mm, (c) v = 0.05 mm, and (d) v = 0.06 mm.
(a)(b)(c)(d)At the same time, when the groove widthw+ is small, the curves almost coincide and the resistance reduction rate of the groove depth h+ = 0.2 mm is slightly dominant; when the width w+ is larger, the curve of depth h+ = 0.2 mm is positioned higher than the other curves. This indicates that at smaller trench widths, there is not much difference in the resistance reduction effect of different trench depth microstructures, and at a trench depth of 0.2 mm, the larger the trench width the better the resistance reduction effect. The h+ = 0.05 mm curve in Figure 7(d) is different from the other curves, again indicating that a groove with too small a depth has little or no drag reduction effect and that the lack of drag reduction becomes more apparent as the intravascular flow rate increases. Overall, the width of the V-shaped groove has a greater effect on the resistance reduction rate of the groove, with a 6% difference between the highest and lowest values of resistance reduction in each set of results when all other conditions except the groove width w+ remain unchanged. As the trench width w+ increases, the resistance reduction rate changes more evenly, indicating that the resistance reduction rate is approximately linearly related to the trench width in the test range.Through the four sets of calculation results in Figure7, it can be learned that when the incoming flow velocity gradually increases, the resistance reduction rate of the groove under each condition increases, and the difference is small. Under the condition of constant incoming flow velocity, the groove reduction rate increases with the increase of groove width and reaches the maximum at the groove width of 0.3 mm, when the best reduction effect is achieved. Since the diameter of the axillary artery is 3.3–5.1 mm and the diameter of the vessel selected in this paper is 4 mm, the groove width of 0.3 mm in the groove microstructure can achieve the best reduction effect for this artificial vessel.


## 3.2.2. Effect of the V-Groove Depthh

In Figure8(a), it can be seen that all other things being equal, the variation in resistance reduction varies slightly from curve to curve as the depth of the groove increases. The curves in Figure 8(a) are positive at all sizes except for the curve for w+ = 0.05 mm, which is negative at h+ = 0.05 mm and shows a resistance reduction effect. Ignoring the resistance reduction data for w+ = 0.05 and h+ = 0.05 mm in Figure 8, the remaining part of the curves show high stability, with a small change in resistance reduction with increasing h+. The curves in the remaining three plots also show the pattern present in Figure 8(a). Comparing the six curves in each graph, the resistance reduction rate from h+ = 0 to h+ = 0.2 mm shows an increasing trend, and the resistance reduction rate from h+ = 0.2 to h+ = 0.3 mm shows a decreasing trend, except for the size involving w+ = 0.05 and h+ = 0.05 mm, which are considered to lose the resistance reduction pattern. When the width is larger, such as w+ = 0.3 mm, the curve change feature is most significant, when the width is smaller, such as w+ = 0.1, w+ = 0.15, and w+ = 0.2 mm, the curve is approximately a straight line, indicating that the drag reduction effect of the groove is less affected by the depth of the groove.Figure 8
Variation curves of resistance reduction with depthh+ for V-shaped grooves: (a) v = 0.03 mm, (b) v = 0.04 mm, (c) v = 0.05 mm, and (d) v = 0.06 mm.
(a)(b)(c)(d)Within the range tested, the effect of groove depth variation on groove resistance reduction is small. The V-shaped groove with a width range of 0.1–0.3 mm for the four velocity conditions showed a gentle resistance reduction curve with <1% fluctuation as the depth increased from 0.1 to 0.3 mm. Of all the resistance reduction results shown, the groove depth with the best reduction is aroundh+ = 0.2 mm. Since the object selected for simulation in this paper is the axillary artery, whose wall thickness is <1 mm, this groove depth greatly satisfies the condition of limited wall thickness of artificial blood vessels, so the corresponding bionic artificial blood vessels can be designed with this groove depth for the groove microstructure, which not only has the best resistance reduction effect, but also can provide convenience and save the manufacturing cost for the artificial blood vessels.


## 3.2.3. Effect of V-Groove Width-to-Depth Ratio

In the following section, the effect of trench size variation on the resistance reduction rate is investigated by considering both trench width and depth as a single variable of width-to-depth ratio. Two sets of trench size data with the same width-to-depth ratio were obtained from the obtained calculation data, as shown in Figure9, for the variation curve of trench resistance reduction rate with increasing V-shaped trench width and depth in equal ratio.Figure 9
Variation curves of resistance reduction with different width-to-depth ratio: (a) 1 : 1 and (b) 2 : 1.
(a)(b)It can be seen from the graphs that other things being equal, the V-groove resistance reduction rate under various velocity conditions tends to increase as the ratio of groove width and depth increases, and the curves under different velocity conditions in both graphs change from dispersion to concentration. At a groove width ofw+ = 0.3 mm, the curves converge almost to a single point, indicating that at this size, similar resistance reduction rates are obtained for all velocity conditions. At a width-to-depth ratio of 1 : 1, the maximum reduction is 6.72% at an inlet speed of v = 0.3 m/s and a groove width of w+ = 0.3 mm, while the minimum reduction is 0.18% at an inlet speed of 0.6 m/s and a groove width of w+ = 0.1 mm. At a width-to-depth ratio of 2 : 1, the maximum drag reduction is 6.64% at an inlet speed of v = 0.3 m/s and a groove width of w+ = 0.3 mm, and the minimum drag reduction is 0.22% at an inlet speed of 0.6 m/s and a groove width of w+ = 0.1 mm. Comparing Figure 9(a) and 9(b), the curves are similar in shape and the values of the vertical coordinates under the same horizontal coordinate are also extremely similar, so it can be seen that the two sets of width-to-depth ratios tested have a small effect on the resistance reduction rate of the grooves. The width-to-depth ratio of the V-shaped groove represents the size of the groove clamping angle, and for the two width-to-depth ratios shown in the following figure, the angle of 1 : 1 is an acute angle and the angle of 2 : 1 is a 90° angle, no significant resistance reduction rate variation characteristics.In addition, the 36 sets of calculation results completed were summarized and analyzed, and the calculation models withw+ = 0.05 and h+ = 0.05 mm, which may lose the drag reduction law due to their small size, were removed, and multiple combinations of aspect ratios could be found, and the calculation results under various aspect ratios were plotted as scatter plots, as shown in Figure 10. Due to the limited size of the calculations, most of the aspect ratios have only one set of drag reduction data, while aspect ratios such as 1 : 1, 3 : 2, and 2 : 1 have multiple sets of sizes to satisfy the data, so some of the aspect ratio conditions in the graph have multiple corresponding drag reduction values. From the scatter plot in Figure 10, it can be seen that the resistance reduction rate does not show a clear trend as the aspect ratio changes. When the aspect ratio is 1 : 1, the distribution of trench resistance reduction rate varies widely, with a minimum of 2.12% and a maximum of 6.72%. Taking the coordinates of the width-to-depth ratio of 1 : 1 as the boundary, Figure 10 can be divided into two parts, in which the width of the left part is greater than the depth, and the distribution of the resistance reduction rate is scattered, but most of the resistance reduction rate is >4%; the width of the right part is smaller than the depth, and the resistance reduction rate has a decreasing trend, and most of the resistance reduction rate is <4%.Figure 10
Scatter plot of trench resistance reduction for different width-to-depth ratios.When the incoming flow velocity is 0.3 m/s and the width-to-depth ratio is >1, the groove microstructure has a good drag reduction effect, especially when the width-to-depth ratio is 3 : 2, the drag reduction rate of the groove at this time is the largest and the drag reduction effect is the best. The size of the groove and the incoming flow velocity of the bionic vessel at this time are more consistent with the real situation of the axillary artery vasculature selected in this paper, indicating that the artificial vessel with this groove design parameter is more achievable. By continuously optimizing the bionic microarchitecture and its parameters in the artificial blood vessel, we can reduce the resistance to blood flow and provide a basis and design idea for the development of artificial blood vessels with low resistance and long life.


## 3.3. V-Groove Velocity Field Analysis

Based on the results of the V-groove drag rate calculation for the different sizes above, the groove with the largest drag ratew+ = 0.3 and h+ = 0.2 mm and the groove with the smaller drag rate w+ = 0.1 and h+ = 0.1 mm were selected to observe the blood flow pattern near the boundary layer, analyze the blood flow state in the groove and investigate the reasons for the variation of the drag rate.The cloud plot of the velocity variation of blood passing through the V-shaped groove of the drag-reducing microstructure is shown in Figure11. As can be seen from the graphs, the lower drag rate is typically no more than 2.2% for the w+ = 0.1 and h+ = 0.1 mm dimensions, and the best drag rate is achieved for the w+ = 0.3 and h+ = 0.2 mm dimensions, with the drag rate being >6.5%. As can be seen from all velocity clouds, the bionic microstructure alters the original flow characteristics of the smooth tube, resulting in a significant improvement in blood flow characteristics. In the tube segments without microstructures, the high-velocity contour density and the greater thickness of the boundary layer of blood flow resulted in a more variable distribution of blood flow velocities in circular sections within the vessel, with high flow velocities and narrow high-velocity regions at the central axis and an overall nonuniform velocity distribution. The boundary velocity contour density is reduced in tube segments with a trench structure. From the above, it is known that the velocity reduction rate is higher when the velocity is small under the condition of constant size, and correspondingly the velocity cloud pattern of the same size of V-shaped groove at different velocities can be seen from the velocity cloud pattern. As shown in Figure 11(e), at v = 0.3 m/s, the narrow area of maximum velocity at the axis of the vessel is almost completely dissipated and replaced by a smaller maximum velocity at the axis, but the coverage area becomes larger and the distribution of blood flow velocity from the axis to the vessel wall becomes more uniform, with a greater improvement in the drag reduction effect. As the velocity increases, the dampening effect becomes less effective, as shown in Figure 11(f)–11(h), where the change in flow velocity in the axial region of the velocity cloud is less significant than at v = 0.3 m/s as the velocity increases.Figure 11
Velocity clouds of a bionic V-groove microstructured artificial vessel: (a)w+ = 0.1 mm, h+ = 0.1 mm, v = 0.3 m/s; (b) w+ = 0.1 mm, h+ = 0.1 mm, v = 0.4 m/s; (c) w+ = 0.1 mm, h+ = 0.1 mm, v = 0.5 m/s; (d) w+ = 0.1 mm, h+ = 0.1 mm, v = 0.6 m/s; (e) w+ = 0.3 mm, h+ = 0.2 mm, v = 0.3 m/s; (f) w+ = 0.3 mm, h+ = 0.2 mm, v = 0.4 m/s; (g) w+ = 0.3 mm, h+ = 0.2 mm, v = 0.5 m/s; (h) w+ = 0.3 mm, h+ = 0.2 mm, v = 0.6 m/s.
(a)(b)(c)(d)(e)(f)(g)(h)In Figure11, the four cloud plots with dimensions w+ = 0.3 and h+ = 0.2 mm have a smaller velocity gradient along the axial region to the vessel wall and a more uniform velocity distribution compared to the four cloud plots with dimensions w+ = 0.1 and h+ = 0.1 mm at the same velocity. Therefore, it can be known that the presence of V-shaped microstructures improves the velocity distribution of intravascular blood flow, and the dampening effect is related to the uniformity of velocity distribution between the axis and the canal wall. When the maximum velocity at the axis of blood flow in the tube is smaller, and the blood flow velocity in the area close to the vessel wall surface is less obstructed by the wall and the boundary velocity is larger, i.e., when the velocity distribution in the tube cross-section is uniform, the drag reduction effect is good.


## 4. Conclusion

(1)
The curve patterns atw+ = 0.05 and h+ = 0.05 mm differed greatly from the other curves, and the drag reduction pattern was almost nonexistent. Besides, almost all models have the effect of drag reduction, and the drag reduction rate of V-shaped groove microstructure decreases with the increase of intravascular blood flow velocity, and the effect of width-to-depth ratio on the curve of drag reduction rate with velocity is small.(2)
The resistance reduction rate is approximately linearly related to the width of the groove. When the widthw+ is small, the speed variation has a greater influence on the size of the resistance reduction rate, and the resistance reduction rate decreases sharply as the speed increases; on the contrary, when the width w+ is larger, the speed variation has less influence on the size of the resistance reduction rate, and the resistance reduction performance is more stable. The drag reduction rate under the condition of w+ = 3 mm is generally higher and the drag reduction effect is the best.(3)
The effect of trench depth variation on the trench resistance reduction rate is small, and the resistance reduction rate curve is smooth with fluctuation value of <1%. Among all the results, the groove depth with the best effect is aroundh+ = 0.2 mm.(4)
Atv = 0.3 m/s, the distribution of blood flow velocity from the axis toward the vessel wall becomes more uniform, and there is a greater improvement in the resistance reduction effect at this point. The maximum reduction rate of 6.89% was obtained at a groove width of 0.3 mm, a groove depth of 0.2 mm, and a flow velocity of 0.3 m/s.



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*Source: 7861408-2023-03-13.xml*