Abstract
Erosion is an inevitable and persistent form of wear, which predominantly occurs on curved surfaces within the realm of fluid machinery. To address this issue, we have developed a novel model incorporating two bionic elements, namely bionic arrangement and bionic morphology, and applied it to explore the erosion resistance of cylindrical surfaces. Specifically, the bionic arrangement is inspired by the phyllotaxis arrangement observed in plants, while the bionic morphology involves the incorporation of convex unit morphology found in desert organisms. Employing a comprehensive approach encompassing erosion testing and numerical analysis, we established two comparative test groups that differed in terms of arrangement and distribution density. This comprehensive analysis sheds light on the erosion resistance mechanism inherent in the combined bionic model. The findings of this study hold significant theoretical implications for the advancement of bionic anti-erosion technology and its practical applications in engineering.
1 Introduction
Erosive wear is a form of wear caused by the impact of multi-phase flow media (such as solid particles, water droplets, and air bubbles) on the target material's surface. This interaction leads to material loss. Given the inherent presence of impurities within multi-phase flows, erosive wear represents a pervasive and inevitable form of wear encountered in engineering applications.
Given the acute depletion of conventional energy sources, namely oil, coal, natural gas, and others, researchers are increasingly focusing their attention on the potential of alternative ocean-based energy sources for human consumption. Tidal energy is gradually considered by researchers as one of the most promising energy sources for research and development [1,2]. As a result, the use of fluid machines such as tidal turbines has gradually increased in demand, and researchers have conducted extensive research and design optimization of tidal turbines [3–7]. The presence of impurities in seawater results in severe erosive wear on the blades of tidal turbines and other fluid machines operating in such environments. This phenomenon significantly diminishes the operational lifespan of these devices. However, there is relatively little research by researchers on the erosive wear of tidal turbines [8–10]. Likewise, the blades of wind turbines, aircraft engines, and helicopters are prone to enduring erosive wear, posing a significant threat to the operational longevity of these apparatus [11–15].
Furthermore, pipeline transportation, a crucial method of transporting traditional energy sources like oil and gas, is susceptible to erosive wear damage. Currently, researchers have predominantly concentrated on investigating erosive wear of pipeline inner wall [16–19], with limited attention given to the damage incurred by the outer wall [20]. The transition from terrestrial to maritime energy harvesting has led to the emergence of a sophisticated and multifaceted landscape for pipeline transportation. It is therefore essential to investigate the erosive wear occurring on the outer wall of the pipeline. Moreover, the outer wall of the subsea pipeline undergoes erosion from seawater when the inner wall of the pipeline is affected by erosive wear damage. Consequently, subsea pipelines are more susceptible to erosive wear damage than other pipeline types. Nevertheless, the majority of current research on submarine pipelines has focused on the study of erosion phenomena on the inner cylindrical surface of the pipelines themselves [21–25].
Considering the aforementioned challenges associated with erosive wear on diverse curved surfaces, it is imperative to identify effective measures for its mitigation. Given the existence of various curved surfaces, this paper focuses on investigating erosive wear on a representative and standardized type of curved surface—the cylindrical surface. Currently, the primary methods employed to alleviate erosive wear in fluid equipment involve the application of surface coatings and composite materials [8–10,13]. Additionally, numerous scholars have employed the use of machined microstructures on the surface of components with the objective of enhancing their lubrication and wear resistance [26–28]. At the same time, bionics offers new solutions for the design of anti-wear surface structures.
Natural erosion occurs due to factors like wind, sand, and rain. Over time, certain organisms have developed mechanisms to reduce erosion damage. Desert organisms, including scorpions, lizards, and tamarisks, exhibit distinct morphological adaptations on their body surfaces, such as convex units, pits, and grooves [29–31]. Similarly, benthic marine organisms, including shellfish species like Scapharca subcrenata, Rapana venosa, and Acanthochiton rubrolineatus, exhibit bionomic structures characterized by ribbing and nodules [32,33]. Scholars have shown that these unique forms have excellent erosion resistance and have attempted to apply them in practice [34]. Our group has carried out theoretical studies on combinatorial bionics and also applied them to anti-wear structures [35–37].
Given the fact that the outer surface of submarine pipelines is also a prominent area prone to erosion, this study proposes a novel bionic erosion resistance model for cylindrical surfaces based on the concept of combined bionics. This study investigates the erosion resistance mechanism of outer circular surfaces with bionic morphology and arrangement through experimental research and numerical analysis. It contributes to the comprehensive study of the combined bionic model for erosive wear resistance on various surface morphologies and offers an effective solution to lessen erosive wear damage on cylindrical surfaces of fluid machinery.
2 Design of Combined Bionic Samples
To mitigate erosive wear on the cylindrical surface, we developed a combined bionic model. We organized the morphology of the convex unit morphology, which was extracted from the surface of desert creatures (such as the Tamarisk and Scorpion), on the target material in accordance with the phyllotaxis arrangement. In the following, we will provide a detailed elaboration on these two bionic objects.
2.1 Phyllotaxis Arrangement.
In the previous observation and study of phyllotaxis arrangement, it was determined that the phyllotaxis arrangement exhibits a high degree of uniformity. Furthermore, its application in surface structure design can effectively guide fluid movement [41]. Our innovative approach involves integrating the bionic arrangement into the investigation of erosive wear resistance in cylindrical surfaces, offering a novel strategy to mitigate erosive wear in engineering applications.
2.2 Convex Unit Morphology.
The desert environment is the closest environment to the gas–solid two-phase erosion environment in nature. In order to find the bionic prototype, our research group has conducted separate investigations on the erosion of desert organisms, including scorpions, lizards, tamarisks, and others [29–31]. Our study revealed the presence of convex unit morphology on the body surfaces of desert organisms, particularly scorpions and tamarisks, as depicted in Fig. 1(b). According to the research, the non-smooth surface of the desert organism's body surface can create a layer of “air film” on its body surface, thereby protecting the body surface from erosion by sand. Nevertheless, the previous study did not delve into the arrangement of the convex unit morphology on the test sample. Consequently, in this study, we utilize a bionic arrangement to apply convex unit morphology to a cylindrical surface. Through erosion studies, we optimize the erosion resistance of the convex unit form to mitigate damage on the cylindrical surface.
2.3 Combined Bionic Sample Design.
In order to explore the influence of different arrangements and densities on the erosion resistance of the combined bionic model, the samples of different arrangements and densities were designed respectively.
In this study on arrangement methods, we organized the convex unit morphology based on two commonly used methods: uniform arrangement and interlaced arrangement. Subsequently, we created two bionic samples on the cylindrical surface. We compared these two bionic samples with the combined bionic samples to investigate the impact of the arrangement method on the erosion resistance. Simultaneously, we employed the smooth cylindrical surface sample as a reference to measure the erosion resistance of bionic samples. To aid subsequent elaboration, we designated the combined bionic sample (PC), the uniform arrangement bionic sample (UC), and the interlaced arrangement bionic sample (IC), as shown Fig. 2.
Additionally, the impact of convex unit morphology arrangement density on erosion resistance in the combined bionic samples has been investigated. Notably, the phyllotactic coefficient h in the phyllotaxis arrangement serves as the parameter regulating the density of convex unit morphology distribution in the combined bionic model. To accomplish this, we selected five distinct groups based on the phyllotactic coefficient (h = 0.7–1.1 mm) and subsequently fabricated combined bionic samples exhibiting varying arrangement densities of convex unit morphology, as shown Fig. 3.
The curved samples possess an outer diameter, R1 = 30 mm, an inner diameter, R2 = 25 mm, and a convex unit radius r = 2.5 mm. In the comparison test group, the density of convex units in the PC, UC, and IC samples was controlled at to ensure the validity of the experiment.
In addition, all the samples were designed to be fabricated using light-curing 3D printing technology. The samples were made using R4600 resin, an ABS-like 3D light modeling resin. The material characteristics of R4600 resin can be found in Table 1.
R4600 resin material characteristics
Parameters | Values |
---|---|
Hardness (shore D) | 76–86 |
Poisson’s ratio | 0.4–0.42 |
Tensile modulus (MPa) | 2559–2678 |
Tensile strength (MPa) | 38–56 |
Bending modulus (MPa) | 2670–2758 |
Bending strength (MPa) | 69–73 |
Parameters | Values |
---|---|
Hardness (shore D) | 76–86 |
Poisson’s ratio | 0.4–0.42 |
Tensile modulus (MPa) | 2559–2678 |
Tensile strength (MPa) | 38–56 |
Bending modulus (MPa) | 2670–2758 |
Bending strength (MPa) | 69–73 |
3 Experiment Design
The erosion test is the most commonly employed method for the investigation of erosion phenomena. The observation of the surface of the eroded sample after the completion of the erosion experiment enables the visualization of the wear phenomenon produced by solid particles on the surface of the sample. In this study, the surface morphology of the eroded sample and the mass removed were employed as the criteria for the evaluation of the erosion resistance of the sample surface morphology. The motion of solid particles and gases in gas–solid two-phase flow experiments is so complex that it is difficult to observe them. In order to study the erosion factors, an erosion model for a gas–solid two-phase flow environment was established, using numerical simulation techniques to assist the study of the erosion damage mechanism and to understand the erosion damage process more clearly. The experimental and numerical simulation setups are described in the following sections.
3.1 Design of Erosion Test.
To carry out the gas–solid two-phase flow erosion test on the samples, an erosion test bench was designed (Fig. 4). The structure of the erosion test bench comprises several components, namely, air compressor 1, pressure regulating valve 2, nozzle 3, sandbox 4, angle adjuster 5, fixture for sample 6, screw 7, collector 8, and other components.
The extent of erosive wear damage varies significantly depending on the erosion parameters of erosive angles. To examine the correlation between the erosion resistance of the combined bionic model and the erosive angle, three erosive angles were chosen to conduct gas–solid two-phase flow erosion tests on the samples. The remaining parameters of the erosion environment were standardized. The parameters for the erosion test were designed and are presented in Table 2.
Erosion test parameters
Erosion parameters | Values |
---|---|
Particle type | Corundum |
Particle shape | Irregular |
Particle size | 80Mesh |
Erosive angle | |
Mass flowrate | 10 g/s |
Test temperature | Room temperature |
Nozzle to sample distance | 250 mm |
Erosion parameters | Values |
---|---|
Particle type | Corundum |
Particle shape | Irregular |
Particle size | 80Mesh |
Erosive angle | |
Mass flowrate | 10 g/s |
Test temperature | Room temperature |
Nozzle to sample distance | 250 mm |
Given that SiC is the hardest particle among the many impurities present in the erosion environment, SiC was chosen as the erosion particle for this experiment. In consideration of the reduction in sample size employed in this experiment relative to that of the actual pipe, a relatively small size was selected for the erosion particles. Furthermore, the erosion speed of this experiment is 30 ± 2 m/s.
The removal quality is a significant indicator for assessing the erosion resistance of the sample in the erosion test. We conducted measurements of the removal quality for the samples undergoing the gas–solid two-phase flow erosion test. At 30-second intervals, we determined the weight of the eroded samples and documented their removal mass. Each sample underwent these procedures 12 times in total. Subsequently, the experimental eroded samples were photographed by microscope for microscopic morphology.
3.2 Numerical Analysis Design.
Numerical analysis plays a crucial role in investigating the mechanism of erosion resistance. In this paper, the combined bionic model is analyzed utilizing the computational fluid dynamics (CFD) module (fluent) within the ansys software. CFD can simulate the erosion removal mass of the sample and the fluid trajectory to assist in the interpretation of the erosion text phenomena.
In CFD analysis, the quality of the meshing significantly affects the outcome of numerical simulations. In this study, we employed a tetrahedral mesh to mesh the model and subdivided the surface of the sample. The computational model consisted of approximately 2.1 million divided meshes. The minimum mesh quality is maintained above 0.25, and the maximum skewness is kept below 0.85.
Erosive wear is a highly intricate form of wear influenced by numerous factors that impact the extent of erosion damage. Given the multitude of influential factors in the erosion process, we contend that a universal erosion model cannot be applied to all erosion processes.
Turbulence is commonly observed when erosive fluids impinge on the surface of the target. Turbulence refers to the flow state in which fluid particles undergo intermixing while in motion. Turbulence is typically calculated in engineering using the transient Navier–Stokes equations for time averaging. These equations are augmented by the turbulent kinetic energy equations and turbulent dissipation rate equations to represent the characteristics of turbulence. The realizable k–ε turbulence model is employed to conduct transient analysis of gas–solid two-phase flow. This involves solving the continuous-phase flow using the Navier–Stokes equations and tracking the trajectory of erosive particles in the flow field using the discrete phase model (DPM) within the Lagrangian reference system.
The flow of erosive fluid is influenced by the shape of the fluid domain in numerical analysis. To mitigate the impact of fluid domain shape on the erosive fluid, a cylindrical shape was chosen for the fluid domain calculation, as depicted in Fig. 5. The inlet boundary of the fluid domain was designated as a velocity inlet, with an inlet velocity set to 30 m/s, while the outlet boundary was set as a standard pressure outlet, incorporating a wall roughness of Ra = 0.5 µm. Subsequently, the collision equation between the erosive particles and the wall will be elucidated.
We also established parameters for numerical analysis to examine the correlation between the extent of erosion damage and the variation in the erosion angle of the samples, utilizing the erosion test parameters. Table 3 presents the pertinent parameters for the numerical analysis.
Numerical analysis parameters
Parameters | Values |
---|---|
Erosive angle | 30–90 deg (every 10 deg is a test group) |
Erosive velocity | 30 m/s |
Particle mass flowrate | 0.01 kg/s |
Particle material density | 2650 kg/m3 |
Particle distribution type | Uniform |
Particle diameter | 1.78 × 10−4 m |
Parameters | Values |
---|---|
Erosive angle | 30–90 deg (every 10 deg is a test group) |
Erosive velocity | 30 m/s |
Particle mass flowrate | 0.01 kg/s |
Particle material density | 2650 kg/m3 |
Particle distribution type | Uniform |
Particle diameter | 1.78 × 10−4 m |
4 Results and Discussion
Previous studies on erosion have revealed that samples exhibit a higher mass of removal during the initial erosion phase [34,44]. Scholars have referred to this phase as the “run-in” phase. Nevertheless, the erosion process is characterized by its extensive duration and gradual nature. The run-in phase, in comparison to the erosion process, can be considered negligible. To mitigate the impact of the run-in phase on the test results, all test samples underwent pre-erosion, effectively circumventing the influence of the run-in phase.
The removal mass of all samples was obtained through the erosion test conducted at various angles. Figure 6 illustrates the removal mass data for the comparison test group of the arrangement. It is noteworthy that the removal mass represents the mean value obtained from 12 measurements of the samples, and the error bar indicates the deviation of the removal mass values from the mean value, as depicted in Fig. 6. Concurrently, during the measurement of the removal mass, it was observed that the values of the 12 measurements for all test samples exhibited variation within a specific range. In essence, the mass of the sample undergoes a nearly linear decrease during the erosion test.
The comparison of removal masses between the samples revealed that the bionic samples in the arrangement comparison test group exhibited smaller removal masses compared to the smooth samples. Evidently, all the bionic samples were designed to be erosion-resistant. Concurrently, we observed a varying degree of mass removal reduction in all samples as the erosion angle increased. Our conclusion aligns with the findings of previous researchers studying the erosion of plastic materials [45–47]. Furthermore, we determined that the PC samples exhibited the smallest removal mass across all erosive angles. In other words, a combined bionic model exhibiting excellent resistance to erosion on cylindrical surfaces has been designed.
Subsequently, we examined the surface morphology of the samples in the comparison test group based on the arrangement method. Then, we analyzed the mechanism of the combined bionic model to mitigate erosion damage on the cylindrical surface. The surface morphology of the samples was observed using an optical microscope before and after experiencing erosion, as depicted in Fig. 7.

Surface morphology of the test samples: (a)–(d) surface morphology of the sample after erosion damage, (e) surface morphology of the sample without erosion damage, and (f) surface morphology of the convex unit of the sample without erosion damage
The surface morphology of the sample was examined, revealing that the processing method resulted in the presence of striped morphology on the undamaged surface of the sample (Figs. 7(e) and 7(f)). Subsequent to the erosion test, erosion caused the destruction of a significant portion of the striped morphology on the sample's surface. The convex unit morphology exhibited more pronounced erosion damage on the surface morphology facing the direction of erosion and on the surface morphology preceding it, as depicted in Figs. 7(a) and 7(b). However, it was also observed that the convex unit morphology exhibits striped morphology on the opposite side of the erosion direction and on the surface morphology of the corresponding region, as depicted in Figs. 7(c) and 7(d). Thus, the convex unit morphology provides some protection for these areas. The mechanism of erosion resistance conferred by the convex unit morphology is illustrated in Fig. 1(b). This demonstrates that the convex unit morphology in the combined bionic model exhibits resistance to erosion, and its erosion resistance mechanism aligns with the findings of our prior study [35,36].
The erosion clouds of the test samples were obtained using CFD, which are illustrated in Fig. 8. It is noteworthy that the regions predominantly affected by erosion damage in the erosion clouds align with the areas obtained in Fig. 7. Furthermore, the variation in erosion rates among the acquired samples corresponds to the removal mass data presented in Fig. 6. Consequently, we employ CFD analysis to elucidate the factors contributing to the differences in erosion resistance among the samples.
The erosion damage area on the sample surface varies with the erosive angle, as observed from the erosion clouds. As the erosive angle increases, the sample surface exhibits a progressive increase in the severity of erosion damage, with the middle area being less affected compared to the areas on the two sides.
As the impact angle increases, the degree of erosion damage on the sample surface gradually decreases. It is noteworthy that with an increase in impact angle, the erosion of the sample surface is primarily concentrated on both sides of the sample. This phenomenon can be attributed to the curved nature of the cylindrical surface. When a fluid makes contact with the sample surface, the trajectory is altered, which in turn affects the erosion of the sample surface.
The angle of impact of the particles on the two sides of the sample is relatively minor in comparison to the central area of the sample, as illustrated in Fig. 9. Furthermore, given that the sample is composed of plastic, the particles are more readily able to inflict damage when the impact angle is minimal. At high-impact angles, the sample primarily exhibits elastic deformation rather than material loss upon particle impact [48].
A comparison was made between the erosion clouds (Fig. 8) of the bionic samples. The erosion damage on the PC samples exhibited greater uniformity compared to the UC and IC samples, particularly at the erosive angle of 30 deg. This can be attributed to the phyllotaxis arrangement in the combined bionic model. A prior study demonstrated the favorable diverting flow properties of the phyllotaxis arrangement [41]. The trajectory figure of fluid flow on the sample surface was obtained in the comparison test group, as depicted in Fig. 10, which clearly illustrates the higher flowrates of the fluid on the surface of the PC sample in comparison to the other samples. The phyllotaxis arrangement exhibits favorable diverting flow characteristics when compared to the other two arrangements. Consequently, this property facilitates a reduction in unnecessary collisions of erosive particles on the surface, thereby mitigating erosion damage to the PC sample.
The bionic perspective provides a comprehensive explanation for this property. To illustrate this, we consider the example of plant leaves. Plant leaves serve a protective role by safeguarding against the damaging effects of wind, sand, and rain erosion. Nevertheless, the leaves exhibit relative fragility. Consequently, through prolonged evolution, the phyllotaxis arrangement has developed remarkable flow-diverting characteristics. This reduction in moving resistance significantly minimizes the impact of wind, sand, and rain on the plants.
Additionally, erosion tests were conducted on samples of varying densities. Figure 11 illustrates the removal mass data of the density comparison test group. The data in Fig. 11 represent the average values of the 12 removal mass measurements, with error bars indicating the degree of dispersion from the mean.
The data figure reveals a correlation between the density of the convex unit morphology distribution and the decreasing removal mass of the sample at varying erosive angles. It can be observed that higher density corresponding to greater erosion resistance. Furthermore, it was observed that the removal mass of all samples decreased as the erosive angle increased. This finding aligns with the conclusions drawn from the comparison test group of arrangement methods.
A CFD test was conducted to investigate the relationship between the distribution density of convex unit morphology and the erosion resistance of the sample. The test samples with a phyllotactic coefficient h = 0.2–1.1 mm were chosen for numerical analysis. Figure 12 illustrates the relationship between the distribution density of convex unit morphology and the erosion rate.
With decreasing phyllotactic coefficient, we observed an exponential-like increase in the number of convex units. Concurrently, as the number of convex units increased dramatically, we observed a decrease in the erosion rate of the sample. The sample exhibits the lowest erosion rate at a specific phyllotactic coefficient h = 0.3 mm. Nevertheless, as the phyllotactic coefficient further decreases, the erosion rate of the sample increases in tandem with the number of convex units. Through observation of the sample at the specific phyllotactic coefficient h = 0.3 mm, we noticed a closely arranged morphology of convex units. Further reduction in the phyllotactic coefficient leads to the overlapping of convex unit morphologies, resulting in an increased erosion rate of the sample. The overlap of convex unit morphologies weakens their erosion resistance.
5 Conclusion
This paper presents a combined bionic model, utilizing “arrangement + morphology” and employing bionics to mitigate erosion damage in samples with circular cylindrical surfaces. The conducted erosion tests and numerical simulations have collectively yielded the following conclusions:
All the bionic samples designed in this paper possess inherent erosion resistance. Among them, the cylindrical surface incorporating two bionic elements demonstrates exceptional erosion resistance. It enhances erosion resistance by 9.32–16.44%, at varying erosive angles respectively.
Both bionic elements actively contribute to erosion resistance. The phyllotaxis arrangement diverts and guides the erosive fluid, mitigating multiple erosions. The convex unit morphology protects the area backside to the erosion direction, thereby reducing erosion damage.
In the combined bionic model, the distribution density of convex units indirectly reflects its erosion resistance. Within a specific range, a higher distribution density of convex units improves the erosion resistance of the model. However, if the distribution densities of the convex units overlap, it leads to a reduction in the erosion resistance of the convex unit morphology itself.
This study contributes to the advancement of the bionic erosion resistance theory and introduces novel concepts for erosion resistance research in the energy and chemical industry. Subsequently, we will explore the bionic erosion resistance of irregular surfaces, thus establishing a more comprehensive theoretical foundation for the practical implementation of bionic erosion resistance.
Acknowledgment
This work was supported by the National Natural Science Foundation of China (Grant No. 52105294), the Jilin Scientific and Technological Development Program (Grant Nos. 20210508034RQ and YDZJ202201ZYTS380), and the China Postdoctoral Science Foundation (Grant No. 2019M661205).
Conflict of Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Data Availability Statement
The authors attest that all data for this study are included in the paper.
Nomenclature
- h =
phyllotactic coefficient (mm)
- n =
order number of the phyllotactic points
- E =
erosive damage (kg/m2)
- R0 =
radius of the base circle (mm)
- νp =
particle impact velocity (m/s)
- α =
spiral angle of the phyllotaxis arrangement (deg)
- θ =
particle impact angle (deg)
- IC =
sample interlaced arrangement bionic sample
- PC =
sample combined bionic sample
- UC =
sample uniform arrangement bionic sample