A study on the drag reduction characteristics of flexible appendage submersibles during dives

A study on the drag reduction characteristics of flexible appendage submersibles during dives | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A study on the drag reduction characteristics of flexible appendage submersibles during dives Shan WANG, Fei YAN, Gangqing ZHANG, Rui ZHU, Lei LI, Jian ZHANG This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6162883/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study presents a novel method for installing flexible appendages (hairs) on the surface of a submersible to reduce its drag as it descends from the surface to the seafloor. First, the changes in drag, Reynolds stress, turbulent kinetic energy, and time-averaged streamlines of the flow field before and after the addition of hair appendages to the submersible were analyzed using a six-component sensor and particle image velocimetry (PIV). The results indicate that, with optimal hair appendages, the drag of the submersible is reduced by 8.7% compared to a conventional submersible (0 L ), and the intensity and extent of the two large-scale eddies in the flow field decrease. Subsequently, the energy spectrum of the flow field, the dominant modes of the flow, and the energy distribution within the vortex core before and after the addition of hair appendages were analyzed using Fourier transform and proper orthogonal decomposition (POD). The results show that hair appendages of optimal length can reduce vortex frequency and energy in the flow field of a submersible. It was also found that hair appendages were able to alter the intrinsic period of the time coefficient and amplify its peak, leading to the emergence of more complex flow features. Submersible Flexible appendage Drag reduction Fourier transform POD Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Figure 19 1 Introduction Deep-submersible technology can be utilized for exploring the ocean and exploiting its resources, which holds significant importance for the advancement of marine science and technology civilization [1] . There are very few submersibles worldwide capable of conducting deep-sea exploration, each with varying depths of descent and capabilities. However, they all encounter the common issue of extended descending times, which not only impacts operational efficiency but also causes discomfort to the crew. Rapid descending technology represents a key future development direction for submersibles, with enhancing hydrodynamic performance being pivotal to improving descent speeds [2] . Numerous studies have been undertaken in the United States, such as DOER Marine's Deep search, Cameron's Deepsea Challenge and Hawkes Ocean Technologies' Deep Flight Challenger [3–4] . China's "Jiao long" has also conducted extensive research on hydrodynamic performance during its development, achieving breakthroughs in 16 key technologies including hydrodynamic motion in nonlinear environments and characteristics of unpowered descending motions [5] . Increasing the descending speed of a submersible is a common method to optimize drag performance. It mainly includes groove surface drag reduction, flexible surface drag reduction, appendage drag reduction, superhydrophobic coating drag reduction [6] . The concept of reducing the drag on a channel surface by mimicking the structure of sharkskin was widely explored in the field of cylindrical flow research [7] . However, the majority of surface drag reduction techniques are designed to operate under specific flow conditions, and any alteration to the flow direction may render the original optimized drag reduction structure either inapplicable or invalid. Flexible surface drag reduction could control the boundary layer [8] , while superhydrophobic surface drag reduction reduced the adhesion and viscosity of fluids on the surface [9] . However, both face challenges in durability, economy, and manufacturing processes. As an important method to enhance the fluid performance of submersibles, the drag reduction appendage method offers advantages such as environmental friendliness, cost-effectiveness, and ease of installation. Currently, most drag-reducing appendages are rigid airfoils [10–12] . Although they are effective in reducing drag, they are mostly suitable for straight-line navigation and are not very effective in reducing drag when submerging. Additionally, the pressure changes during the movement of rigid appendages can unbalance forces on both sides, leading to pitching and yawing of the submersible. In addition, rigid appendages increase the weight of submersibles, which are prone to wear in high-pressure deep-sea environments and are expensive to maintain. In recent years, the drag reduction method using flexible appendages has gained prominence in fluid dynamics. Tian et al. added closed soft filaments to the back side of the plate, and the maximum drag reduction effect was about 10% [13–14] . Mao et al. after securing flexible filaments within a cylinder, observed three distinct swing modes: oscillation mode, undulation mode, and vortex leading mode [15–16] . They found that oscillation and undulation modes were more effective in reducing drag compared to the vortex leading mode. Furthermore, pairing flexible filaments with different phases yielded better drag reduction effects than pairing those with the same phase. Baena et al. achieved drag reduction by attaching a flexible plate behind a blunt body, demonstrating that quasi-static parallel plate devices positively influence the drag coefficient of slender blunt bodies [17] . These studies have yielded significant advancements in the field of fluid dynamics. Inspired by research on drag reduction using flexible appendages in cylindrical and plate flow fields, a method for reducing drag with flexible appendages is proposed. When selecting flexible appendages for submersibles, considerations should include hydrophobicity, elasticity, and toughness [18] . Optimal hydrophobic performance can minimize the appendage's impact on the submersible itself. Meanwhile, good elasticity and toughness enable flexible appendages to maintain stable performance under complex working conditions. Hair exhibits a certain level of hydrophobicity [19] , with a density ranging from 1.00 to 1.40 g/cm³. Its surface is composed of numerous scale-like cuticles, which create small gaps between them [20] , thereby preventing water from adhering to the hair. Additionally, these cuticles are typically arranged in overlapping layers and tilted towards the direction of hair growth [21] , facilitating easier movement of water molecules across the hair's surface. The cuticles are primarily composed of keratin, rich in hydrophobic amino acids, which contributes to the hydrophobic nature of hair strands [22] . Hair is a multi-layered structure known for its excellent structural elasticity and ability to store energy [23–25] , with a Young's modulus of approximately 4.39 GPa. Furthermore, keratin is a protein with a cross-linked structure that enhances strength and toughness [26] . At the microscopic level, internal hydrogen bonds and disulfide bonds further bolster the elasticity and toughness of hair strands, enabling them to withstand deformation such as stretching and bending [27–30] . In summary, due to its favorable hydrophobicity, elasticity, and toughness, coupled with a density close to that of water, hair is considered a suitable material for flexible appendage in this study. The wake characteristics of the submersible with flexible hair appendages are more complex than those in traditional flow fields, so further study is needed to understand their influence on the wake characteristics of the submersible. The post-processing technology of the flow field can handle acquired image data, eliminating noise and errors to obtain more reliable flow field data. Fourier transform focuses on frequency domain analysis, widely applied in flow field and mechanical monitoring [31–33] . Liu et al. utilized the Fourier transform method to decompose flow fields at various scales [34] , successfully applying it to both two-dimensional and three-dimensional flow field data, thereby validating its reliability in flow field analysis. Proper orthogonal decomposition (POD) reduces high-dimensional flow field data to lower dimensions, thereby simplifying data complexity. Through POD decomposition, the primary modes in the flow field—the modes with the highest energy are extracted, while modes with lower energy are disregarded [35] . Li et al. analyzed the wake of a square column using the POD method [36] . Alzabari et al. employed the POD method to investigate vortex shedding in cylindrical wakes [37] . Hiroka used the POD method to examine wake structures of short cylinders in three-dimensional flow fields [38] . Jing et al. utilized the POD method to identify the existence of antisymmetric and symmetric shedding modes of wake vortex under different conditions in their experimental study of flow around a square column controlled by an oscillating jet [39] . This study presents a method to reduce the drag of a submersible during its descent from the surface to the seafloor by installing hair appendages on its surface. First, drag changes, Reynolds number stresses, turbulent kinetic energy, and time-averaged streamlines of the flow field—both before and after the addition of these hair appendages—were analyzed using a six-component sensor and particle image velocimetry (PIV). Subsequently, the energy spectrum of the submersible, the dominant flow field modes, and the energy distribution at the vortex center—both before and after the addition of the hair appendages—were analyzed using Fourier transform and proper orthogonal decomposition (POD). 2 Experimental setups 2.1 Experimental models The submersible model selected in this study was L = 22 cm and D = 6 cm . The hair model was shown in Fig. 1 . Through the study of the submersible, it was found that the vortex center and the high-energy area in the flow field appeared in the midship and stern of the submersible, so hair appendages were installed on both sides of the midship and stern. Through continuous experiments, it was found that the effect was more obvious when 12 silks were installed in the midship of the submersible and 5 silks were installed in the stern, among which the silks were 0.025 L apart, totaling 34 silks, as shown in Fig. 2 . 2.2 Test condition and scheme This paper mainly studies the descent condition of a submersible and conducts experiments based on the Reynolds similarity criterion. Specifically, the model Reynolds number ( \(\:{Re}_{m}\) ) is 6456, while the prototype Reynolds number ( \(\:{Re}_{p}\) ) ranges from 0 to 322,000. To satisfy the Reynolds similarity criterion, the model's geometric scale, flow velocity, and fluid properties are chosen such that the Reynolds numbers of the model and the prototype are in proportion. The model Reynolds number falls within the range of the prototype's Reynolds number, ensuring that the flow characteristics are dynamically similar according to the Reynolds similarity criterion. In the experimental procedure, the installation position, quantity, and other experimental parameters of hair on the submersible remained unchanged. The hair length was set to 0.4 L initially, with 0.05 L being cut off after each test. A total of 9 sets of experiments were conducted, varying the hair length from 0.4 L to 0 L . The hair length of 0 L represented the conventional submersible and served as the control group for testing. The resistance and lift force of the submersible under vertical descending conditions were measured using a force characteristic test system. Based on the experimental results, the optimal hair length for drag reduction was determined as the ideal length for the hair appendages. Next, the descending angles of the submersible were adjusted by changing the dip angle, as shown in Fig. 3 . The resistance changes of conventional submersibles and hair appendages under different angles were measured. This further explored the actual drag reduction effectiveness of the hair appendages across various operational conditions. 2.3 High speed PIV measurement The schematic view of the experimental configuration is shown in Fig. 4 a. The PIV system is implemented using a continuous laser and a high-speed camera. The high-speed camera used in this experiment (FASTCAM_Mini_AX100) has a maximum resolution of 2048×2048 pixels and a maximum frame rate of 4000 fps. The model of six-degree-of-freedom sensor is DYDW-005, the measuring force range is 0 ~ 2 N , and the measuring accuracy is ± 0.15% FS. The laser power is 5 W , which can produce sheet light with a width of 0.5 to 2 mm to illuminate the tracer particles in the water. The tracer particle size is 20 µm . This experiment was conducted on the flow direction plane (x, y), the camera resolution was set to 1920×1280, and the frame rate was set to 1000 fps. The experiment was conducted in the circulating water channel, and an experimental site device diagram was shown in Fig. 4 b. And the experimental section of the flume is 2.5 m , the cross-sectional area of the experimental section is 0.3 m² , and the spreading width is 0.6 m (free liquid surface). The wall thickness is 0.01 m , the maximum flow rate of the circulating flume is 0.7 m/s , and the maximum turbulence degree is 4%. 3 Results and discussion 3.1 Force Analysis Figure 5 illustrates the variation of drag and lift (forces acting perpendicular to the direction of fluid motion) with hair length during a submersible dive. As hair length increases, both drag and lift forces initially decrease and then increase. At a hair length of 0.3 L , the drag and lift forces during the submersible's vertical descent are minimized, showing a reduction of 8.7% in drag and 10.9% in lift compared to a conventional submersible (0 L ). As the length of the hair appendages continued to increase, both the drag and lift of the submersible also increased to some extent. This suggests that the length of the hair appendages has a noticeable impact on the actual drag reduction. Based on the conclusion from Fig. 5 , a hair length equivalent to 0.3 L is selected for the hair appendages in the drag test. Drag tests of the submersible are conducted at descending dip angles of 0°, 5°, 10°, 15°, 20°, 25°, and 30°, with the results shown in Fig. 6 . Across all dip angles, the hair appendages consistently reduce drag, demonstrating their adaptability to various operational conditions. However, within the range of 0° to 30°, the effectiveness of the selected hair appendages in reducing resistance decreases as the longitudinal angles increase, suggesting that their resistance reduction capability is influenced by operational conditions. 3.2 Lift power spectrum analysis The lift power spectral density provides a more intuitive understanding of the variation in the submersible’s lift force across different frequency ranges, aiding in the evaluation and optimization of its stability, maneuverability, and control performance. A six-component sensor is used to monitor the lift variation of the submersible with hair appendage lengths of 0.1 L , 0.2 L , 0.3 L , and the control group of 0 L , with a measurement frequency of 100 Hz and a monitoring period of 60 s. The measured lift data are Fourier transformed to obtain the lift power spectrum, as shown in Fig. 7 . After the addition of hair appendages, the lift energy during submersible dives shifted and primarily remained in the low-frequency region. This suggests that the lift changes generated by the submersible’s motion are largely influenced by lower-frequency flows, typically associated with large-scale turbulent structures in the flow field. However, a notable decrease in the dominant frequency occurs when the hair appendages reach lengths of 0.2 L and 0.3 L . This indicates a stabilization of the eddy and turbulent structures in the flow field. The presence of hair appendages likely alters the shear layer structure of the fluid, reducing turbulence intensity. As a result, the flow field becomes more stable, which helps reduce the drag force on the submersible. 3.3 Analysis of Flow field structure Time-averaged streamlines help visualize both the distribution and direction of fluid motion within a flow field. They also provide insight into the structure and morphology of fluid flow, including vortices, separation regions, and other features. Figure 8 illustrates the time-averaged streamlines before and after integrating hair appendages into submersibles. For the 0L submersible (Fig. 8 a), strong and widespread vortex regions appeared in both the bow and stern flow fields, indicating unstable flow characteristics around the submersible's surface and the generation of intense eddies. After the installation of hair appendages (Fig. 8 b-d), when 0.1 L of hair appendages were added, there was little significant change in the overall flow length of the flow field. However, the normal length of the swirling region in the stern increased slightly, while the normal length of the swirling region in the bow decreased slightly. This suggests that the hair appendages mildly reduced fluid disturbances at the bow, while at the stern, the increased normal length of the swirl region is likely due to stronger shear effects caused by the hair appendages, which altered the flow pattern and slightly enlarged the swirl region. When 0.2 L of hair appendages were added, the flow field characteristics remained similar to those at 0.3 L . The transom vortex region's flow pattern resembled the previous vortex characteristics, and at this stage, the normal length of the vortex region at the stern increased further, while the vortex region at the bow continued to shrink. The normal lengths and areas of the vortex regions at both the bow and stern became nearly equal. This indicates that as the length of the hair appendages increased, the vortex regions gradually narrowed, resulting in weakened fluid diffusion. However, the narrowing of the wake region at the stern means that fluid flow becomes more concentrated, which could potentially complicate the flow field structure. Figure 9 illustrates the normalized root mean square velocity before and after adding hair appendages to the submersible. For the 0 L submersible (Fig. 9 a), two distinct low-velocity regions are present in the bow and stern flow fields. The low-velocity region in the stern extends significantly toward the bow, a result of the interaction between the submersible and the surrounding fluid, which generates strong vortices and flow resistance. This interaction leads to reduced flow velocities near the submersible. Additionally, a larger high-velocity zone appears beneath the bow, likely due to the disturbed fluid creating turbulence in that area. For the submersible with hair appendages (Fig. 9 b-d), the velocity in the high-velocity zone at the bow decreases as the length of the hair appendages increases. After adding 0.1 L of hair appendages, the low-speed zone in the wake flow does not change significantly, suggesting that the hair appendages have a minimal impact on the wake flow at this stage. Their effect may only slightly mitigate the vortex's destructive influence without significantly altering the low-speed zone. When 0.2 L of hair appendages are added, the low-speed region of the wake flow decreases. By the time the appendage length reaches 0.3 L , the low-speed region of the wake flow remains similar to that observed with 0.2 L . As the appendage length continues to increase, their effect on the flow field gradually lessens, likely due to the stabilization of the flow field structure. This pattern aligns with the results seen in Fig. 8 d. The Reynolds stress ( \(\:R=\stackrel{-}{{u}^{{\prime\:}}{v}^{{\prime\:}}}\) ) is a key parameter that characterizes turbulent motion. Figure 10 illustrates the normalized Reynolds stress distribution of the submersible before and after adding various lengths of hair appendages. In the case of the 0L submersible (Fig. 10 a), the bow flow field displays a prominent positive Reynolds stress region, which indicates the presence of turbulence and instability at the front of the submersible. Similarly, the stern flow field shows a broad negative Reynolds stress region, signaling that the flow at the rear is also disturbed and turbulent. This behavior aligns with the trends observed in Fig. 8 a, supporting the consistency of the turbulence and flow disturbances across different data representations. For the submersible with hair appendages (Fig. 10 b-d), the addition of 0.1 L of hair appendages leads to a reduction in the positive Reynolds stress in the bow wake and a decrease in the extent of the negative Reynolds stress region in the stern flow field. This suggests that the turbulence and disturbance intensity are suppressed, resulting in a more orderly flow. As the hair appendages increase to 0.2 L , the positive Reynolds stress in the bow flow field continues to decrease, and the absolute value of the negative Reynolds stress in the stern flow field also decreases. This indicates a further reduction in turbulence intensity and energy loss in the wake region, leading to a significant improvement in flow stability. When the hair appendages are increased to 0.3 L , the positive Reynolds stress in the bow wake continues to decrease, and the location of the maximum positive Reynolds stress shifts farther from the submersible. This suggests that the turbulence intensity near the surface of the submersible continues to diminish, and as the length of the appendages increases, the flow becomes more stabilized. The disturbed region moves farther from the submersible. Additionally, the absolute value of the negative Reynolds stress in the stern wake continues to decrease, further weakening turbulence intensity and promoting a smoother, more orderly flow. Turbulent kinetic energy ( \(\:TKE=0.5{{u}^{{\prime\:}}}^{2}+0.5{{v}^{{\prime\:}}}^{2}\) ) is a key indicator of the conversion and dissipation processes of energy within turbulent flow. Figure 11 shows the normalized distribution of TKE before and after the addition of hair appendages to the submersibles. For the 0 L submersible (Fig. 11 a), the turbulent kinetic energy distribution is wide, with the high-energy region predominantly located at the stern. This suggests stronger vorticity and energy conversion in the stern area. In contrast, the bow region shows a smaller high-energy area, indicating a more stable flow with fewer disturbances. For the submersible with hair appendages (Fig. 11 b-d), adding 0.1 L of hair appendages results in a decrease in turbulent kinetic energy in the bow's wake region and an increase in the amidships. There is no significant change in the transom, indicating that the short appendages do not notably enhance flow field vortices. When the appendage length increases to 0.2 L , the turbulent kinetic energy in the bow wake gradually expands, likely due to increased peripheral fluid disturbance, which induces stronger reflux and vortex activity, thereby enhancing the turbulent kinetic energy in the bow. When the addition of 0.3 L of hair appendages, both the bow and stern regions experience a decrease in turbulent kinetic energy, while the amidships remains unchanged. The maximum turbulent kinetic energy of the flow field drops from 0.114 to 0.102, reflecting a 10.5% reduction. This indicates that the optimal length of hair appendages improves the flow state, reduces the generation of turbulent kinetic energy, enhances flow stability, and lowers flow resistance. The transient streamline diagram illustrates the fluid flow conditions and vortex structure in the flow field. Figure 12 shows the transient streamlines before and after the installation of hair appendages on the submersible. For the 0 L submersible (Fig. 12 a), two large vortices formed at the bow and stern, causing increased drag due to flow separation. After adding 0.1 L of hair appendages (Fig. 12 b), the wake region slightly narrowed, but the stern vortex structure remained largely unchanged, indicating that the short hair appendages had a limited effect and did not significantly alter the boundary layer or flow pattern to prevent the formation of large vortices. With 0.2 L of hair appendages (Fig. 12 c), the large stern vortices decomposed into multiple smaller vortices, and energy was dissipated through a high-frequency mechanism. This suggests that the hair appendages suppressed the formation of large vortices and promoted small vortex generation by exchanging elastic vibration and fluid momentum, in line with the turbulence energy cascade theory. With 0.3 L of hair appendages (Fig. 12 d), the bow vortex region decreased, the stern vortex lengthened, and the intersection of the bow and stern vortices shifted towards the bow. This indicates that the optimal hair appendage length improved the boundary layer behavior, reduced flow separation, and helped guide the fluid transition from the bow to the stern more effectively. 3.4 Fourier transform analysis of energy spectrum of vortex center The energy spectrum of the vortex center provides insights into the distribution of energy within the vortex. Thus, the vortex centroids in the flow field regions at the bow (0.3 L , 0.1 L ) and stern (0.2 L , 0.8 L ) of the submersible were monitored separately. The monitoring was conducted at a frequency of 1000 Hz over a duration of 7.2 seconds. Figure 13 illustrates the energy spectrum of the vortex centers in the flow field at the bow, both before and after the installation of the hair appendages on the submersible. For the 0 L submersible, the vortex frequency in the bow flow field is 1.37 Hz , with an energy of 178.3. Upon adding 0.1 L hair appendages, the vortex frequency in the bow flow field decreased to 1.24 Hz , with an associated energy of 150.3, representing a 9.5% decrease in frequency and a 15.7% decrease in energy compared to the conventional submersible (0 L ). With 0.2 L hair appendages, the vortex frequency further decreased to 1.09 Hz , and the energy dropped to 142.4, indicating a 20.4% reduction in frequency and a 20.1% reduction in energy compared to the conventional submersible (0 L ). After adding 0.3 L of hair appendages, the vortex frequency in the bow flow field was further reduced to 0.96 Hz , with an energy of 128.2, reflecting a 29.9% reduction in frequency and a 28.1% reduction in energy compared to the conventional submersible (0 L ). The experimental data clearly demonstrate that as the length of the hair appendages increases, both the vortex frequency and energy in the bow flow field exhibit a distinct decreasing trend. Figure 14 illustrates the energy spectrum at the center of the vortex in the transom flow field of the submersible before and after the installation of the hair appendages. For the 0 L submersible, the vortex frequency in the transom flow field is 0.96 Hz , with an energy of 157.7. After the addition of 0.1 L of hair appendages, the vortex frequency remains at 0.96 Hz , but the energy decreases to 146.4, representing a 7.2% reduction in energy compared to the conventional submersible (0 L ). With the addition of 0.2 L of hair appendages, the vortex frequency drops to 0.69 Hz , and the energy further decreases to 120.9, indicating a 28.1% reduction in frequency and a 23.3% reduction in energy compared to the conventional submersible (0 L ). When 0.3 L of hair appendages are added, the vortex frequency decreases to 0.55 Hz , with an energy of 108.2. Compared to the conventional submersible (0 L ), this results in a 42.7% reduction in frequency and a 31.4% reduction in energy. These results indicate that the appropriate length of hair appendages can effectively reduce the vortex frequency and energy in the submersible’s flow field. The vortex frequency and energy are minimized when the hair appendage length is 0.3 L , which is consistent with the trends observed in Figs. 10 d and 11 d. 3.5 POD flow field analysis By performing proper orthogonal decomposition (POD) of the flow field, we can simplify the complex problem into a series of intrinsic modes, facilitating a better understanding of its structural and dynamic properties. In this paper, we analyze the POD decomposition of the wake flow field both before and after the addition of hair appendages of varying lengths to the submersible. Figure 15 illustrates the energy distribution corresponding to each order of the POD modes. The figure shows that energy is primarily concentrated in the first-order modes, indicating a significant hierarchical and structured flow field. In contrast, the second and higher-order modes contain relatively less energy, suggesting that the influence of small-scale vortices is weaker compared to the large-scale dominant flow features. Consequently, the first-order and second-order modes offer a good representation for understanding the behavior of the flow field. Figure 16 illustrates the velocity field reconstruction for the POD first-order modes. For the 0L submersible (Fig. 16 a), large high-velocity regions are observed in the wake flow at the bow and amidships, consistent with the trend in Fig. 9 a. After adding 0.1 L hair appendages (Fig. 16 b), the high-velocity region in the wake flow was significantly reduced, while a large high-velocity backflow region appeared at the bow, indicating that the hair appendages altered the large-scale flow characteristics. When 0.2 L of appendages were added (Fig. 16 c), the high-speed region gradually extended from the bow to amidships, and the backflow region decreased, suggesting that fluid separation was suppressed and flow stability improved. After adding 0.3 L hair appendages (Fig. 16 d), the flow characteristics were similar to those of 0.2 L , but the intensity increased significantly. This may be because the 0.3 L hair appendages optimize the vortex structure, enabling more effective conversion and utilization of the fluid's kinetic energy. At this point, the energy in the flow field is further concentrated in the first-order mode, reinforcing the dominant flow features, which is consistent with the phenomenon observed in Fig. 15 . The second-order modes of the proper orthogonal decomposition (POD) represent the low-energy modes in the flow field, revealing secondary flow structures that are neglected by the first-order modes, particularly local vortices and details of the complex flow. Figure 17 illustrates the velocity field reconstruction for the second-order modes of the POD. For the 0L submersible (Fig. 17 a), a high-velocity region is evident in the bow, while the central wake region exhibits a large backflow, suggesting that the flow structure in these areas is quite complex. After adding 0.1 L hair appendages (Fig. 17 b), the high-velocity region in the bow gradually shifts along the flow direction. This shift can be attributed to the appendages altering the fluid momentum distribution, which results in adjustments to both the flow direction and velocity. Additionally, new high-speed backflow regions appear at the bow and amidships, indicating that the vortex structure and wake behavior of the flow field have become more complicated, potentially increasing flow instability in these regions. With the addition of 0.2 L hair appendages (Fig. 17 c), the high-velocity region extends continuously from the bow, and the backflow region extends toward the stern. This suggests that the hair appendages enhance fluid mobility and make the flow structure more interactive. When the appendages are further increased to 0.3 L (Fig. 17 d), the flow characteristics become similar to those observed with 0.2 L appendages. This indicates that the effects of the hair appendages on the flow structure tend to stabilize within this range, likely due to the flow field reaching steady-state equilibrium. Consequently, changes in flow characteristics are no longer significant, though the actual performance may still differ. The time coefficients of the POD decomposition reveal the time evolution characteristics of different flow modes in the flow field, which are crucial for understanding vortex structures and flow stability. Figure 18 illustrates the time coefficients of the POD first-order modes. It is evident that these coefficients exhibit clear periodic changes, indicating that the main flow modes (e.g., the primary vortex) in the flow field evolve periodically over a specific timescale. The waveforms of the submersible's time coefficient exhibit different fluctuation patterns depending on the length of the hair appendages. Notably, when the appendage length is 0.3L, the waveform of the time coefficient is almost 180° out of phase with the waveforms under other conditions. This suggests that the nonlinear effects in the flow field become more pronounced as the appendage length increases. Furthermore, the peak value of the time coefficient for the first-order POD mode increases with the addition of hair appendages. The peak intensity of this coefficient reflects the strength of the vortex structure in the flow field, indicating that the appendages enhance the vortex contribution to the main flow modes. This increase in vortex intensity may lead to the development of more complex flow features. Figure 19 illustrates the time coefficients for the second-order modes of POD. In POD analysis, these time coefficients typically reflect small-scale, rapidly changing dynamic processes within the system. By analyzing their variations, insights can be gained into the dynamic behavior of the second-order vibration modes and their contribution to the system's response. In this study, the time coefficients of the second-order modes reveal the dynamic properties of the local vortex phenomenon in the submersible wake flow field. Compared to the first-order modes, the time coefficients of the second-order modes exhibit more violent fluctuations, though with smaller amplitudes. This suggests a more dispersed energy distribution and more frequent dynamic changes, reflecting the system's fluctuations and energy exchanges on shorter time scales. Additionally, the trends in the amplitudes of the POD first-order and second-order modal time coefficients align with the POD modal energy distributions shown in Fig. 15 , further validating the analytical results regarding intermodal energy conversion and coupling effects. 4 Conclusions In this study, the effects of hair appendages on the drag and flow field characteristics of a submersible under diving conditions are investigated using particle image velocimetry (PIV), Fourier transform (FT), and proper orthogonal decomposition (POD) techniques. The results show that the optimal length of hair appendages can effectively reduce the drag force on the submersible and significantly improve the flow characteristics of its flow field, particularly when the length of the hair appendages is 0.3 L . The main findings are as follows: The drag results show that hair appendages are beneficial for submersibles, reducing both drag and lift during the dive. The mean flow field analysis reveals that the hair appendages can disrupt large eddies in the flow. Turbulent kinetic energy and Reynolds stress analyses show that the hair appendages, as flexible structures, can absorb some of the pulsation energy, thereby reducing the turbulence intensity in the submersible's flow field region. Through the Fourier-transformed energy spectrum at the vortex center, it was found that hair appendages reduce both the vortex frequency and vortex energy in the submersible's flow field. POD analyses show that hair appendages can disrupt the intrinsic period of the time coefficients and amplify their peaks, resulting in the emergence of more complex flow features. Declarations Author Contribution Shan WANG was the main author, responsible for the overall conception, literature review, data analysis, methodology design, and preparation and revision of the final manuscript.2. Fei YAN provided financial support and resources and contributed to the discussion and optimization of experimental designs.3. Gangqing ZHANG participated in the preliminary study design discussion and validated the data results.4. Rui ZHU performed language editing and format checking to ensure the manuscript met the journal's submission requirements.5. Lei LI contributed to the initial study design discussion and provided suggestions for the theoretical framework.6. Jian ZHANG participated in the study discussion and provided guidance for the final version of the paper. Acknowledgments The author wishes to acknowledge the support given to him by the Major Basic Research Project of the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (24KJA130001). References Q. N. XU, Z. HU, C. YE, et al., Present situation and prospect of deep-sea manned submersible technology and its application, Science and Technology Foresight. 2022, 1(2): 36–48. Z. W. LI, W. C. CUI., Study on the resistance performance for the third generation of manned submersible with full ocean depth, "The Deepsea Challenge", Chinese Journal of Hydrodynamics. 2013, 28(01): 1–9. L. Taylor, T. Lawson., Project Deepsearch: An innovative solution for accessing the oceans, Marine Technology Society Journal, 2009, 43(5): 169–177. G. Hawkes., The old arguments of manned versus unmanned systems are about to become irrelevant: new technologies are game changers, Marine Technology Society Journal, 2009, 43(5): 164–168. Q. N. XU, H. Y. ZHANG., Development and application of jiao long manned submersible, Science. 2014, 66(02): 11–13. M. Mo, W. Zhao, Z. Chen., Research status of Marine drag reduction technology, Tri. 2015, 35(04): 505–515. P. Y. Guo, Y. Zhang, M. Z. Zhang, H. B. Hu., Experimental study of aeration reduction on hydrophilic-superhydrophobic interphase surfaces, Chinese Journal of Technology and Applied Mechanics. 2024, 56(1): 94–100. H. Zhou, D. Shen, G. Tian., Biomechanical characteristics of puffer skin for flexible surface drag reduction, Mechanics of Advanced Materials and Structures. 2019, 28(11): 1–7. Z. Wang, J. Kong, Q. Zhou., Natural superhydrophobic surfaces and application, Journal of Physics: Conference Series. 2022, 2390(1): 012115. M. Hadipour., Investigation of sweep angle effects on a submarine hydrodynamic drag using computational fluid dynamics, Jordan Journal of Mechanical & Industrial Engineering. 2015, 9(3): 209–216. G. L. Zhou, P. Wang, C. Y. Guo, C. Wang., Research on the impact of underwater stern foil on the ship resistance performance, Journal of Ship Mechanics. 2022, 26(07): 962–968. M. M. Zheng, Y. D. Liu, Y. Y. Tang, Y. J. Wang, Y. P. He., Two-dimensional hydrofoil hydrodynamic performance and waveform evolution studies in density stratification and homogeneous fluid, Ocean Engineering. 2022, 263: 112366. S. Gao, S. Pan, H. C. Wang, X. L. Tian., Shape deformation and drag variation of a coupled rigid-flexible system in a flowing soap film, Physical Review Letters. 2020, 125(3): 034502. X. L. Tian., Review of " flexible coating reduces drag", Journal of Shanghai Jiao Tong University. 2021, 55(02): 213–214. Q. Mao, Y. Liu, H. J. Sung., Drag reduction by flapping a flexible filament behind a stationary cylinder, Physics of Fluids. 2022, 34(8): 087123. Q. Mao, Y. Liu, H. J. Sung., Drag reduction by flapping a pair of flexible filaments behind a cylinder, Physics of Fluids. 2023, 35(3): 033602. C. G. Baena, J. I. J. González, C. M. Bazán., Drag reduction of a blunt body through reconfiguration of rear flexible plates, Physics of Fluids. 2021, 33(4): 045102. B. W. Song, Y. H. Guo, Z. Z. Luo, X. H. Xu, Y. Wang., Investigation about drag reduction annulus experiment of hydrophobic surface, Acta Physica Sinica. 2013, 62(15): 154701. Michael K, Sabri A, Harald K, et al., Distribution and localization of hydrophobic and ionic chemical groups at the surface of bleached human hair fibers, Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2018, 538: 262–269. Z. Nan, H. Liu, G. Archana, et al., Facile and efficient enzymatic methods for harvesting or removal of cuticle cells from human hair shafts, Journal of Natural Fibers, 2022, 19(15): 11036–11049. Y. H. Zhang, S. M. Zhang, Z. Fan, et al., A scanning electron microscopic comparative observation on the hairs of hairy men and the controls, Chinese Journal of Anatomy. 1988, (02): 98–100. Hitoshi M, Daisuke S, Yuri O, et al., Impact of protein carbonylation on the chemical characteristics of the hair surface, International Journal of Cosmetic Science. 2021, 43(6): 764–771. Hironori T, Kento F, Hitoshi S, et al., Structural elasticity for tensile deformation of a single human hair and the comparison with it for the bending deformation, Journal of the Mechanical Behavior of Biomedical Materials. 2021, 113: 104166. Hironori T, Kento F., Division of force among layers constituting human hair during bending and tension, Journal of the Mechanical Behavior of Biomedical Materials. 2022, 133: 105346. J F W, Gabriele W, Hans-Martin H, et al., Analysis of the torsional storage modulus of human hair and its relation to hair morphology and cosmetic processing, Journal of Cosmetic Science. 2014, 65(2): 59–68. C. H. Lee. A. P. Coulombe., Self-organization of keratin intermediate filaments into cross-linked networks, The Journal of Cell Biology. 2009, 186(3): 9–21. E. Antunes, F. C. Cruz, G. N. Azoia, et al., Insights on the mechanical behavior of keratin fibrils, International Journal of Biological Macromolecules. 2016, 89: 477–483. W. Qu, X. Guo., G. Xu., et al., Improving the mechanical properties of damaged hair using low-molecular weight hyaluronate, Molecules. 2022, 27(22): 7701–7701. Fernandes, Cavaco-Paulo., Protein disulphide isomerase-mediated grafting of cysteine-containing peptides onto over-bleached hair, Biocatalysis and Biotransformation. 2012, 30(1): 10–19. G. Zeng, Y. Zhou, Y. Liang, et al., A hair fiber inspired bio-based adhesive with high bonding strength and mildew tolerance, Chemical Engineering Journal. 2022, 434: 134632. J. Wang, S. Luan, J. Zhu, et al., Fourier mode decomposition of unsteady flows in a single injection port fluidic thrust vectoring nozzle, International Journal of Aeronautical and Space Sciences. 2020: 1–16. Waleed K. A., Mahmoud A. A., M. Z. A. Fourier decomposition and anisotropic diffusion filtering of forced turbulence, International Journal of Applied Mechanics. 2017, 09(08): 1750121. X. Y. Zhao, X. Q. Chen., Z. Q. Gong., et al., RecFNO: A resolution-invariant flow and heat field reconstruction method from sparse observations via Fourier neural operator, International Journal of Thermal Sciences. 2024, 195: 108619. L. Liu, Y. Chen, X. Xie., Spatial scale decomposition of flow field based on multidimensional Fourier analysis, Journal of Fudan (Natural Science Edition). 2014, 53(05): 616–625. Q. Zhang, Y. Liu, S. Wang., The identification of coherent structures using proper orthogonal decomposition and dynamic mode decomposition, Journal of Fluids and Structures. 2014, 49: 53–72. M. Li, Q. Li, H. Shi, et al., Effects of free-stream turbulence on the near wake flow and aerodynamic forces of a square cylinder, Journal of Fluids and Structures. 2022, 114: 103748. A. Fawaz, A. M. E. Catherine. W, P. Ouio., Unsteady vortex shedding dynamics behind a circular cylinder in very shallow free-surface flows, Computers and Fluids. 2023, 260: 105918. R. Hiroka., Three-dimensional wake structures over a short cylinder having a fore angled hole, Ocean Engineering. 2023, 271: 113713. Z. Jing, W. Wang, X. Wen., Experimental study of square column winding by oscillating jets, Thermal Power Engineering. 2024, 39(01): 108–118. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6162883","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":425083637,"identity":"a74d7632-3271-44a0-94d6-1ec90df5645b","order_by":0,"name":"Shan WANG","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA00lEQVRIiWNgGAWjYBACNvmD7T8+GNjU8zMzHyBOC58E8wHJGQVpCZLtbAnEaZGTYEuQ5vlwOMHgPI8BkQ6T7jEw4DE4nCfZzPPxxhsGOzndBkJaZM4YJEgYpBfzM/NutpzDkGxsdoCQFoYcgwMGBtaMM5t5t0nzMBxI3EaEFsOGBANmxg2HeZ4RqUUiLZnhgIFzIlALG5FaeA4fY2wwSDOWbGYztpxjQIRf5Nsb25j//LGR4+c//PDGmwo7OYJaUIAEsVGDrIVUHaNgFIyCUTAiAAAGxj34firE/QAAAABJRU5ErkJggg==","orcid":"","institution":"Jiangsu University of Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"Shan","middleName":"","lastName":"WANG","suffix":""},{"id":425083638,"identity":"7e74c0aa-7c0b-40da-b6c7-bd8e04142b0c","order_by":1,"name":"Fei YAN","email":"","orcid":"","institution":"Jiangsu University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Fei","middleName":"","lastName":"YAN","suffix":""},{"id":425083639,"identity":"8fe054d9-d850-4dd9-adb4-e42dd4d61d55","order_by":2,"name":"Gangqing ZHANG","email":"","orcid":"","institution":"Jiangsu University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Gangqing","middleName":"","lastName":"ZHANG","suffix":""},{"id":425083640,"identity":"8694a9d1-80ac-43bc-8d79-3c46778a5456","order_by":3,"name":"Rui ZHU","email":"","orcid":"","institution":"Jiangsu University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Rui","middleName":"","lastName":"ZHU","suffix":""},{"id":425083641,"identity":"1d1ff4e0-b3ed-497a-8732-cdf4ec79edbf","order_by":4,"name":"Lei LI","email":"","orcid":"","institution":"Jiangsu University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Lei","middleName":"","lastName":"LI","suffix":""},{"id":425083642,"identity":"4bb62f26-78f5-484e-9880-2430824c31b8","order_by":5,"name":"Jian ZHANG","email":"","orcid":"","institution":"Jiangsu University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Jian","middleName":"","lastName":"ZHANG","suffix":""}],"badges":[],"createdAt":"2025-03-05 13:08:25","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6162883/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6162883/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":78226274,"identity":"8cfc8396-d730-47b8-8d84-2682291ed3f6","added_by":"auto","created_at":"2025-03-11 06:59:06","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":224255,"visible":true,"origin":"","legend":"\u003cp\u003eHair strands under a laser microscope.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6162883/v1/839f2fbe9684f2f5e6db9d22.png"},{"id":78226309,"identity":"ebea77bd-be78-485c-a7f9-e6cef24d7493","added_by":"auto","created_at":"2025-03-11 06:59:07","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":222308,"visible":true,"origin":"","legend":"\u003cp\u003eSubmersible with hair appendage.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6162883/v1/44ecd5e7e4c1a3cb37469ce8.png"},{"id":78226276,"identity":"433d1087-bbd6-4d57-ae0f-7d679e5d0e9d","added_by":"auto","created_at":"2025-03-11 06:59:06","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":395015,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagram of the longitudinal inclination of the submersible dive.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6162883/v1/878c40d749ab8809473940bb.png"},{"id":78226279,"identity":"e7b7370e-d768-4466-a539-dd9e9be6f7ec","added_by":"auto","created_at":"2025-03-11 06:59:06","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":327955,"visible":true,"origin":"","legend":"\u003cp\u003eTest system of force and flow field of submersible.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-6162883/v1/18828fd131b83e97de8ecbd5.png"},{"id":78227033,"identity":"65693eae-9c82-4c21-a5ec-19ed0f8099c1","added_by":"auto","created_at":"2025-03-11 07:07:06","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":27637,"visible":true,"origin":"","legend":"\u003cp\u003eVariation of drag and lift with hair length during submersible dives.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-6162883/v1/9c42dd137adc983814e8d8a4.png"},{"id":78227035,"identity":"19432333-ef40-4e17-af51-a73ef0697b8f","added_by":"auto","created_at":"2025-03-11 07:07:06","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":59464,"visible":true,"origin":"","legend":"\u003cp\u003eDrag test of the submersible at different inclinations under diving conditions.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-6162883/v1/f08d61b19a6e5e590c41d558.png"},{"id":78227037,"identity":"9e6caae4-cd4f-47d4-8970-a630258e1277","added_by":"auto","created_at":"2025-03-11 07:07:06","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":1780444,"visible":true,"origin":"","legend":"\u003cp\u003ePower spectrum of lift of submersibles with different hair appendages.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-6162883/v1/3d78d508aada1ac9a639de71.png"},{"id":78227036,"identity":"291122fa-11ac-4c24-a3f0-b740556a77f0","added_by":"auto","created_at":"2025-03-11 07:07:06","extension":"jpeg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":167322,"visible":true,"origin":"","legend":"\u003cp\u003eTime-averaged streamlines and vortex cloud of submersibles with different hair appendages: (a) 0 \u003cem\u003eL\u003c/em\u003e (b) 0.1 \u003cem\u003eL\u003c/em\u003e (c) 0.2 \u003cem\u003eL\u003c/em\u003e (d) 0.3 \u003cem\u003eL\u003c/em\u003e.\u003c/p\u003e","description":"","filename":"8.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6162883/v1/e27714a5331316529240451c.jpeg"},{"id":78227052,"identity":"af100aa7-346c-492c-8b1c-5665accaa288","added_by":"auto","created_at":"2025-03-11 07:07:07","extension":"jpeg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":106540,"visible":true,"origin":"","legend":"\u003cp\u003eNormalized root-mean-square velocity cloud of submersibles with different hair appendages: (a) 0 \u003cem\u003eL\u003c/em\u003e(b) 0.1 \u003cem\u003eL\u003c/em\u003e (c) 0.2 \u003cem\u003eL\u003c/em\u003e (d) 0.3 \u003cem\u003eL\u003c/em\u003e.\u003c/p\u003e","description":"","filename":"9.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6162883/v1/1d295ee1f2477f82e0eb7f73.jpeg"},{"id":78227051,"identity":"16427c0a-b114-4ab6-91ce-d6c122b81300","added_by":"auto","created_at":"2025-03-11 07:07:07","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":721255,"visible":true,"origin":"","legend":"\u003cp\u003eNormalized Reynolds stress distributions of submersibles with different hair appendages: (a) 0 \u003cem\u003eL\u003c/em\u003e (b) 0.1 \u003cem\u003eL\u003c/em\u003e (c) 0.2 \u003cem\u003eL\u003c/em\u003e (d) 0.3 \u003cem\u003eL\u003c/em\u003e.\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-6162883/v1/425bd350718d969d8b68da0c.png"},{"id":78226291,"identity":"09e386ec-2c31-416e-b941-18a782a06881","added_by":"auto","created_at":"2025-03-11 06:59:06","extension":"jpeg","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":160460,"visible":true,"origin":"","legend":"\u003cp\u003eNormalized turbulent kinetic energy distribution of submersibles with different hair appendages: (a) 0 \u003cem\u003eL\u003c/em\u003e(b) 0.1 \u003cem\u003eL\u003c/em\u003e (c) 0.2 \u003cem\u003eL\u003c/em\u003e (d) 0.3 \u003cem\u003eL\u003c/em\u003e.\u003c/p\u003e","description":"","filename":"11.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6162883/v1/8de7e8b5d9531e71e2af27eb.jpeg"},{"id":78227045,"identity":"4435262f-2a1b-4b19-85e8-5a3a1eda047f","added_by":"auto","created_at":"2025-03-11 07:07:06","extension":"jpeg","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":171977,"visible":true,"origin":"","legend":"\u003cp\u003eInstantaneous flow lines of submersibles with different hair appendages: (a) 0 \u003cem\u003eL\u003c/em\u003e(b) 0.1 \u003cem\u003eL\u003c/em\u003e (c) 0.2 \u003cem\u003eL\u003c/em\u003e (d) 0.3 \u003cem\u003eL\u003c/em\u003e.\u003c/p\u003e","description":"","filename":"12.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6162883/v1/4e0b9c287df20b84922d3332.jpeg"},{"id":78226308,"identity":"7eab8408-77df-44d1-8b6a-ec756416455b","added_by":"auto","created_at":"2025-03-11 06:59:07","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":137842,"visible":true,"origin":"","legend":"\u003cp\u003eBow region vortex center energy spectrum of submersibles with different hair appendages.\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-6162883/v1/f73ab6f5ad506ca4f487bebc.png"},{"id":78229587,"identity":"f0a70362-7ff1-4bed-a0ce-75becf80e7ca","added_by":"auto","created_at":"2025-03-11 07:23:06","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":139071,"visible":true,"origin":"","legend":"\u003cp\u003eStern vortex center energy spectrum of submersibles with different hair appendages.\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-6162883/v1/f8aeb7e0d303bd0f4c1b1820.png"},{"id":78226282,"identity":"c75b2ed3-45ff-4907-aea6-0c5c66b249a8","added_by":"auto","created_at":"2025-03-11 06:59:06","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":41606,"visible":true,"origin":"","legend":"\u003cp\u003eEnergy share of each order of modality for POD of submersibles with different hair appendages.\u003c/p\u003e","description":"","filename":"15.png","url":"https://assets-eu.researchsquare.com/files/rs-6162883/v1/956e052f31ed926e5270ebe6.png"},{"id":78228464,"identity":"1f39d523-2050-4fae-ae60-11feff2b69a7","added_by":"auto","created_at":"2025-03-11 07:15:06","extension":"png","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":832183,"visible":true,"origin":"","legend":"\u003cp\u003eFirst-order tangential fluctuating velocity cloud image of submersibles with different hair appendages: (a) 0 \u003cem\u003eL\u003c/em\u003e (b) 0.1 \u003cem\u003eL\u003c/em\u003e (c) 0.2 \u003cem\u003eL\u003c/em\u003e (d) 0.3 \u003cem\u003eL\u003c/em\u003e.\u003c/p\u003e","description":"","filename":"16.png","url":"https://assets-eu.researchsquare.com/files/rs-6162883/v1/040566f9104ebca0c724c7c1.png"},{"id":78226295,"identity":"c1c442de-665f-4f6e-b556-40b8689b1738","added_by":"auto","created_at":"2025-03-11 06:59:06","extension":"png","order_by":17,"title":"Figure 17","display":"","copyAsset":false,"role":"figure","size":894128,"visible":true,"origin":"","legend":"\u003cp\u003eSecond-order normal fluctuating velocity cloud image of submersibles with different hair appendages: (a) 0 \u003cem\u003eL\u003c/em\u003e (b) 0.1 \u003cem\u003eL\u003c/em\u003e (c) 0.2 \u003cem\u003eL\u003c/em\u003e (d) 0.3 \u003cem\u003eL\u003c/em\u003e.\u003c/p\u003e","description":"","filename":"17.png","url":"https://assets-eu.researchsquare.com/files/rs-6162883/v1/305d055f0983399e901fef8f.png"},{"id":78226290,"identity":"3176f3d9-5436-4c1b-a27b-241a70bd1a1d","added_by":"auto","created_at":"2025-03-11 06:59:06","extension":"png","order_by":18,"title":"Figure 18","display":"","copyAsset":false,"role":"figure","size":189644,"visible":true,"origin":"","legend":"\u003cp\u003eFirst-order modality time coefficients of submersibles with different hair appendages: (a) 0 \u003cem\u003eL\u003c/em\u003e(b) 0.1 \u003cem\u003eL\u003c/em\u003e (c) 0.2 \u003cem\u003eL\u003c/em\u003e (d) 0.3 \u003cem\u003eL\u003c/em\u003e.\u003c/p\u003e","description":"","filename":"18.png","url":"https://assets-eu.researchsquare.com/files/rs-6162883/v1/be4ff31f4f4d0d1f48608659.png"},{"id":78229684,"identity":"97781555-d41e-4fc2-a542-94fc7c1c9d75","added_by":"auto","created_at":"2025-03-11 07:23:14","extension":"png","order_by":19,"title":"Figure 19","display":"","copyAsset":false,"role":"figure","size":211934,"visible":true,"origin":"","legend":"\u003cp\u003eSecond-order modality time coefficients of submersibles with different hair appendages: (a) 0 \u003cem\u003eL\u003c/em\u003e (b) 0.1 \u003cem\u003eL\u003c/em\u003e (c) 0.2 \u003cem\u003eL\u003c/em\u003e (d) 0.3 \u003cem\u003eL\u003c/em\u003e.\u003c/p\u003e","description":"","filename":"19.png","url":"https://assets-eu.researchsquare.com/files/rs-6162883/v1/50f75c3acedf5b9cf0a87b4c.png"},{"id":81917693,"identity":"83cb08e1-cb2c-41b8-84b9-34f39e7d65fb","added_by":"auto","created_at":"2025-05-04 19:31:23","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":7120411,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6162883/v1/1a2403ad-3570-4822-aaeb-ea339b26b09e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A study on the drag reduction characteristics of flexible appendage submersibles during dives","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eDeep-submersible technology can be utilized for exploring the ocean and exploiting its resources, which holds significant importance for the advancement of marine science and technology civilization \u003csup\u003e[1]\u003c/sup\u003e. There are very few submersibles worldwide capable of conducting deep-sea exploration, each with varying depths of descent and capabilities. However, they all encounter the common issue of extended descending times, which not only impacts operational efficiency but also causes discomfort to the crew. Rapid descending technology represents a key future development direction for submersibles, with enhancing hydrodynamic performance being pivotal to improving descent speeds \u003csup\u003e[2]\u003c/sup\u003e. Numerous studies have been undertaken in the United States, such as DOER Marine's Deep search, Cameron's Deepsea Challenge and Hawkes Ocean Technologies' Deep Flight Challenger \u003csup\u003e[3\u0026ndash;4]\u003c/sup\u003e. China's \"Jiao long\" has also conducted extensive research on hydrodynamic performance during its development, achieving breakthroughs in 16 key technologies including hydrodynamic motion in nonlinear environments and characteristics of unpowered descending motions \u003csup\u003e[5]\u003c/sup\u003e. Increasing the descending speed of a submersible is a common method to optimize drag performance. It mainly includes groove surface drag reduction, flexible surface drag reduction, appendage drag reduction, superhydrophobic coating drag reduction \u003csup\u003e[6]\u003c/sup\u003e. The concept of reducing the drag on a channel surface by mimicking the structure of sharkskin was widely explored in the field of cylindrical flow research \u003csup\u003e[7]\u003c/sup\u003e. However, the majority of surface drag reduction techniques are designed to operate under specific flow conditions, and any alteration to the flow direction may render the original optimized drag reduction structure either inapplicable or invalid. Flexible surface drag reduction could control the boundary layer \u003csup\u003e[8]\u003c/sup\u003e, while superhydrophobic surface drag reduction reduced the adhesion and viscosity of fluids on the surface \u003csup\u003e[9]\u003c/sup\u003e. However, both face challenges in durability, economy, and manufacturing processes.\u003c/p\u003e \u003cp\u003eAs an important method to enhance the fluid performance of submersibles, the drag reduction appendage method offers advantages such as environmental friendliness, cost-effectiveness, and ease of installation. Currently, most drag-reducing appendages are rigid airfoils \u003csup\u003e[10\u0026ndash;12]\u003c/sup\u003e. Although they are effective in reducing drag, they are mostly suitable for straight-line navigation and are not very effective in reducing drag when submerging. Additionally, the pressure changes during the movement of rigid appendages can unbalance forces on both sides, leading to pitching and yawing of the submersible. In addition, rigid appendages increase the weight of submersibles, which are prone to wear in high-pressure deep-sea environments and are expensive to maintain.\u003c/p\u003e \u003cp\u003eIn recent years, the drag reduction method using flexible appendages has gained prominence in fluid dynamics. Tian et al. added closed soft filaments to the back side of the plate, and the maximum drag reduction effect was about 10% \u003csup\u003e[13\u0026ndash;14]\u003c/sup\u003e. Mao et al. after securing flexible filaments within a cylinder, observed three distinct swing modes: oscillation mode, undulation mode, and vortex leading mode \u003csup\u003e[15\u0026ndash;16]\u003c/sup\u003e. They found that oscillation and undulation modes were more effective in reducing drag compared to the vortex leading mode. Furthermore, pairing flexible filaments with different phases yielded better drag reduction effects than pairing those with the same phase. Baena et al. achieved drag reduction by attaching a flexible plate behind a blunt body, demonstrating that quasi-static parallel plate devices positively influence the drag coefficient of slender blunt bodies \u003csup\u003e[17]\u003c/sup\u003e. These studies have yielded significant advancements in the field of fluid dynamics.\u003c/p\u003e \u003cp\u003eInspired by research on drag reduction using flexible appendages in cylindrical and plate flow fields, a method for reducing drag with flexible appendages is proposed. When selecting flexible appendages for submersibles, considerations should include hydrophobicity, elasticity, and toughness \u003csup\u003e[18]\u003c/sup\u003e. Optimal hydrophobic performance can minimize the appendage's impact on the submersible itself. Meanwhile, good elasticity and toughness enable flexible appendages to maintain stable performance under complex working conditions. Hair exhibits a certain level of hydrophobicity \u003csup\u003e[19]\u003c/sup\u003e, with a density ranging from 1.00 to 1.40 g/cm\u0026sup3;. Its surface is composed of numerous scale-like cuticles, which create small gaps between them \u003csup\u003e[20]\u003c/sup\u003e, thereby preventing water from adhering to the hair. Additionally, these cuticles are typically arranged in overlapping layers and tilted towards the direction of hair growth \u003csup\u003e[21]\u003c/sup\u003e, facilitating easier movement of water molecules across the hair's surface. The cuticles are primarily composed of keratin, rich in hydrophobic amino acids, which contributes to the hydrophobic nature of hair strands \u003csup\u003e[22]\u003c/sup\u003e. Hair is a multi-layered structure known for its excellent structural elasticity and ability to store energy \u003csup\u003e[23\u0026ndash;25]\u003c/sup\u003e, with a Young's modulus of approximately 4.39 GPa. Furthermore, keratin is a protein with a cross-linked structure that enhances strength and toughness \u003csup\u003e[26]\u003c/sup\u003e. At the microscopic level, internal hydrogen bonds and disulfide bonds further bolster the elasticity and toughness of hair strands, enabling them to withstand deformation such as stretching and bending \u003csup\u003e[27\u0026ndash;30]\u003c/sup\u003e. In summary, due to its favorable hydrophobicity, elasticity, and toughness, coupled with a density close to that of water, hair is considered a suitable material for flexible appendage in this study. The wake characteristics of the submersible with flexible hair appendages are more complex than those in traditional flow fields, so further study is needed to understand their influence on the wake characteristics of the submersible.\u003c/p\u003e \u003cp\u003eThe post-processing technology of the flow field can handle acquired image data, eliminating noise and errors to obtain more reliable flow field data. Fourier transform focuses on frequency domain analysis, widely applied in flow field and mechanical monitoring \u003csup\u003e[31\u0026ndash;33]\u003c/sup\u003e. Liu et al. utilized the Fourier transform method to decompose flow fields at various scales \u003csup\u003e[34]\u003c/sup\u003e, successfully applying it to both two-dimensional and three-dimensional flow field data, thereby validating its reliability in flow field analysis. Proper orthogonal decomposition (POD) reduces high-dimensional flow field data to lower dimensions, thereby simplifying data complexity. Through POD decomposition, the primary modes in the flow field\u0026mdash;the modes with the highest energy are extracted, while modes with lower energy are disregarded \u003csup\u003e[35]\u003c/sup\u003e. Li et al. analyzed the wake of a square column using the POD method \u003csup\u003e[36]\u003c/sup\u003e. Alzabari et al. employed the POD method to investigate vortex shedding in cylindrical wakes \u003csup\u003e[37]\u003c/sup\u003e. Hiroka used the POD method to examine wake structures of short cylinders in three-dimensional flow fields \u003csup\u003e[38]\u003c/sup\u003e. Jing et al. utilized the POD method to identify the existence of antisymmetric and symmetric shedding modes of wake vortex under different conditions in their experimental study of flow around a square column controlled by an oscillating jet \u003csup\u003e[39]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThis study presents a method to reduce the drag of a submersible during its descent from the surface to the seafloor by installing hair appendages on its surface. First, drag changes, Reynolds number stresses, turbulent kinetic energy, and time-averaged streamlines of the flow field\u0026mdash;both before and after the addition of these hair appendages\u0026mdash;were analyzed using a six-component sensor and particle image velocimetry (PIV). Subsequently, the energy spectrum of the submersible, the dominant flow field modes, and the energy distribution at the vortex center\u0026mdash;both before and after the addition of the hair appendages\u0026mdash;were analyzed using Fourier transform and proper orthogonal decomposition (POD).\u003c/p\u003e"},{"header":"2 Experimental setups","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Experimental models\u003c/h2\u003e \u003cp\u003eThe submersible model selected in this study was \u003cem\u003eL\u003c/em\u003e\u0026thinsp;=\u0026thinsp;22 \u003cem\u003ecm\u003c/em\u003e and \u003cem\u003eD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;6 \u003cem\u003ecm\u003c/em\u003e. The hair model was shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Through the study of the submersible, it was found that the vortex center and the high-energy area in the flow field appeared in the midship and stern of the submersible, so hair appendages were installed on both sides of the midship and stern. Through continuous experiments, it was found that the effect was more obvious when 12 silks were installed in the midship of the submersible and 5 silks were installed in the stern, among which the silks were 0.025 \u003cem\u003eL\u003c/em\u003e apart, totaling 34 silks, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Test condition and scheme\u003c/h2\u003e \u003cp\u003eThis paper mainly studies the descent condition of a submersible and conducts experiments based on the Reynolds similarity criterion. Specifically, the model Reynolds number (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Re}_{m}\\)\u003c/span\u003e\u003c/span\u003e) is 6456, while the prototype Reynolds number (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Re}_{p}\\)\u003c/span\u003e\u003c/span\u003e) ranges from 0 to 322,000. To satisfy the Reynolds similarity criterion, the model's geometric scale, flow velocity, and fluid properties are chosen such that the Reynolds numbers of the model and the prototype are in proportion. The model Reynolds number falls within the range of the prototype's Reynolds number, ensuring that the flow characteristics are dynamically similar according to the Reynolds similarity criterion. In the experimental procedure, the installation position, quantity, and other experimental parameters of hair on the submersible remained unchanged. The hair length was set to 0.4 \u003cem\u003eL\u003c/em\u003e initially, with 0.05 \u003cem\u003eL\u003c/em\u003e being cut off after each test. A total of 9 sets of experiments were conducted, varying the hair length from 0.4 \u003cem\u003eL\u003c/em\u003e to 0 \u003cem\u003eL\u003c/em\u003e. The hair length of 0 \u003cem\u003eL\u003c/em\u003e represented the conventional submersible and served as the control group for testing. The resistance and lift force of the submersible under vertical descending conditions were measured using a force characteristic test system. Based on the experimental results, the optimal hair length for drag reduction was determined as the ideal length for the hair appendages. Next, the descending angles of the submersible were adjusted by changing the dip angle, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The resistance changes of conventional submersibles and hair appendages under different angles were measured. This further explored the actual drag reduction effectiveness of the hair appendages across various operational conditions.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 High speed PIV measurement\u003c/h2\u003e \u003cp\u003eThe schematic view of the experimental configuration is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea. The PIV system is implemented using a continuous laser and a high-speed camera. The high-speed camera used in this experiment (FASTCAM_Mini_AX100) has a maximum resolution of 2048\u0026times;2048 pixels and a maximum frame rate of 4000 fps. The model of six-degree-of-freedom sensor is DYDW-005, the measuring force range is 0\u0026thinsp;~\u0026thinsp;2 \u003cem\u003eN\u003c/em\u003e, and the measuring accuracy is \u0026plusmn;\u0026thinsp;0.15% FS. The laser power is 5 \u003cem\u003eW\u003c/em\u003e, which can produce sheet light with a width of 0.5 to 2 \u003cem\u003emm\u003c/em\u003e to illuminate the tracer particles in the water. The tracer particle size is 20 \u003cem\u003e\u0026micro;m\u003c/em\u003e. This experiment was conducted on the flow direction plane (x, y), the camera resolution was set to 1920\u0026times;1280, and the frame rate was set to 1000 \u003cem\u003efps.\u003c/em\u003e\u003c/p\u003e \u003cp\u003eThe experiment was conducted in the circulating water channel, and an experimental site device diagram was shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb. And the experimental section of the flume is 2.5 \u003cem\u003em\u003c/em\u003e, the cross-sectional area of the experimental section is 0.3 \u003cem\u003em\u0026sup2;\u003c/em\u003e, and the spreading width is 0.6 \u003cem\u003em\u003c/em\u003e (free liquid surface). The wall thickness is 0.01 \u003cem\u003em\u003c/em\u003e, the maximum flow rate of the circulating flume is 0.7 \u003cem\u003em/s\u003c/em\u003e, and the maximum turbulence degree is 4%.\u003c/p\u003e \u003c/div\u003e"},{"header":"3 Results and discussion","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Force Analysis\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e illustrates the variation of drag and lift (forces acting perpendicular to the direction of fluid motion) with hair length during a submersible dive. As hair length increases, both drag and lift forces initially decrease and then increase. At a hair length of 0.3 \u003cem\u003eL\u003c/em\u003e, the drag and lift forces during the submersible's vertical descent are minimized, showing a reduction of 8.7% in drag and 10.9% in lift compared to a conventional submersible (0 \u003cem\u003eL\u003c/em\u003e). As the length of the hair appendages continued to increase, both the drag and lift of the submersible also increased to some extent. This suggests that the length of the hair appendages has a noticeable impact on the actual drag reduction.\u003c/p\u003e \u003cp\u003eBased on the conclusion from Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, a hair length equivalent to 0.3 \u003cem\u003eL\u003c/em\u003e is selected for the hair appendages in the drag test. Drag tests of the submersible are conducted at descending dip angles of 0\u0026deg;, 5\u0026deg;, 10\u0026deg;, 15\u0026deg;, 20\u0026deg;, 25\u0026deg;, and 30\u0026deg;, with the results shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. Across all dip angles, the hair appendages consistently reduce drag, demonstrating their adaptability to various operational conditions. However, within the range of 0\u0026deg; to 30\u0026deg;, the effectiveness of the selected hair appendages in reducing resistance decreases as the longitudinal angles increase, suggesting that their resistance reduction capability is influenced by operational conditions.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Lift power spectrum analysis\u003c/h2\u003e \u003cp\u003eThe lift power spectral density provides a more intuitive understanding of the variation in the submersible\u0026rsquo;s lift force across different frequency ranges, aiding in the evaluation and optimization of its stability, maneuverability, and control performance. A six-component sensor is used to monitor the lift variation of the submersible with hair appendage lengths of 0.1 \u003cem\u003eL\u003c/em\u003e, 0.2 \u003cem\u003eL\u003c/em\u003e, 0.3 \u003cem\u003eL\u003c/em\u003e, and the control group of 0 \u003cem\u003eL\u003c/em\u003e, with a measurement frequency of 100 \u003cem\u003eHz\u003c/em\u003e and a monitoring period of 60 s. The measured lift data are Fourier transformed to obtain the lift power spectrum, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. After the addition of hair appendages, the lift energy during submersible dives shifted and primarily remained in the low-frequency region. This suggests that the lift changes generated by the submersible\u0026rsquo;s motion are largely influenced by lower-frequency flows, typically associated with large-scale turbulent structures in the flow field. However, a notable decrease in the dominant frequency occurs when the hair appendages reach lengths of 0.2 \u003cem\u003eL\u003c/em\u003e and 0.3 \u003cem\u003eL\u003c/em\u003e. This indicates a stabilization of the eddy and turbulent structures in the flow field. The presence of hair appendages likely alters the shear layer structure of the fluid, reducing turbulence intensity. As a result, the flow field becomes more stable, which helps reduce the drag force on the submersible.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Analysis of Flow field structure\u003c/h2\u003e \u003cp\u003eTime-averaged streamlines help visualize both the distribution and direction of fluid motion within a flow field. They also provide insight into the structure and morphology of fluid flow, including vortices, separation regions, and other features. Figure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e illustrates the time-averaged streamlines before and after integrating hair appendages into submersibles. For the 0L submersible (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ea), strong and widespread vortex regions appeared in both the bow and stern flow fields, indicating unstable flow characteristics around the submersible's surface and the generation of intense eddies. After the installation of hair appendages (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eb-d), when 0.1 \u003cem\u003eL\u003c/em\u003e of hair appendages were added, there was little significant change in the overall flow length of the flow field. However, the normal length of the swirling region in the stern increased slightly, while the normal length of the swirling region in the bow decreased slightly. This suggests that the hair appendages mildly reduced fluid disturbances at the bow, while at the stern, the increased normal length of the swirl region is likely due to stronger shear effects caused by the hair appendages, which altered the flow pattern and slightly enlarged the swirl region. When 0.2 \u003cem\u003eL\u003c/em\u003e of hair appendages were added, the flow field characteristics remained similar to those at 0.3 \u003cem\u003eL\u003c/em\u003e. The transom vortex region's flow pattern resembled the previous vortex characteristics, and at this stage, the normal length of the vortex region at the stern increased further, while the vortex region at the bow continued to shrink. The normal lengths and areas of the vortex regions at both the bow and stern became nearly equal. This indicates that as the length of the hair appendages increased, the vortex regions gradually narrowed, resulting in weakened fluid diffusion. However, the narrowing of the wake region at the stern means that fluid flow becomes more concentrated, which could potentially complicate the flow field structure.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e illustrates the normalized root mean square velocity before and after adding hair appendages to the submersible. For the 0 \u003cem\u003eL\u003c/em\u003e submersible (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003ea), two distinct low-velocity regions are present in the bow and stern flow fields. The low-velocity region in the stern extends significantly toward the bow, a result of the interaction between the submersible and the surrounding fluid, which generates strong vortices and flow resistance. This interaction leads to reduced flow velocities near the submersible. Additionally, a larger high-velocity zone appears beneath the bow, likely due to the disturbed fluid creating turbulence in that area. For the submersible with hair appendages (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eb-d), the velocity in the high-velocity zone at the bow decreases as the length of the hair appendages increases. After adding 0.1 \u003cem\u003eL\u003c/em\u003e of hair appendages, the low-speed zone in the wake flow does not change significantly, suggesting that the hair appendages have a minimal impact on the wake flow at this stage. Their effect may only slightly mitigate the vortex's destructive influence without significantly altering the low-speed zone. When 0.2 \u003cem\u003eL\u003c/em\u003e of hair appendages are added, the low-speed region of the wake flow decreases. By the time the appendage length reaches 0.3 \u003cem\u003eL\u003c/em\u003e, the low-speed region of the wake flow remains similar to that observed with 0.2 \u003cem\u003eL\u003c/em\u003e. As the appendage length continues to increase, their effect on the flow field gradually lessens, likely due to the stabilization of the flow field structure. This pattern aligns with the results seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ed.\u003c/p\u003e \u003cp\u003eThe Reynolds stress (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:R=\\stackrel{-}{{u}^{{\\prime\\:}}{v}^{{\\prime\\:}}}\\)\u003c/span\u003e\u003c/span\u003e) is a key parameter that characterizes turbulent motion. Figure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e illustrates the normalized Reynolds stress distribution of the submersible before and after adding various lengths of hair appendages. In the case of the 0L submersible (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003ea), the bow flow field displays a prominent positive Reynolds stress region, which indicates the presence of turbulence and instability at the front of the submersible. Similarly, the stern flow field shows a broad negative Reynolds stress region, signaling that the flow at the rear is also disturbed and turbulent. This behavior aligns with the trends observed in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ea, supporting the consistency of the turbulence and flow disturbances across different data representations. For the submersible with hair appendages (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003eb-d), the addition of 0.1 \u003cem\u003eL\u003c/em\u003e of hair appendages leads to a reduction in the positive Reynolds stress in the bow wake and a decrease in the extent of the negative Reynolds stress region in the stern flow field. This suggests that the turbulence and disturbance intensity are suppressed, resulting in a more orderly flow. As the hair appendages increase to 0.2 \u003cem\u003eL\u003c/em\u003e, the positive Reynolds stress in the bow flow field continues to decrease, and the absolute value of the negative Reynolds stress in the stern flow field also decreases. This indicates a further reduction in turbulence intensity and energy loss in the wake region, leading to a significant improvement in flow stability. When the hair appendages are increased to 0.3 \u003cem\u003eL\u003c/em\u003e, the positive Reynolds stress in the bow wake continues to decrease, and the location of the maximum positive Reynolds stress shifts farther from the submersible. This suggests that the turbulence intensity near the surface of the submersible continues to diminish, and as the length of the appendages increases, the flow becomes more stabilized. The disturbed region moves farther from the submersible. Additionally, the absolute value of the negative Reynolds stress in the stern wake continues to decrease, further weakening turbulence intensity and promoting a smoother, more orderly flow.\u003c/p\u003e \u003cp\u003eTurbulent kinetic energy (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:TKE=0.5{{u}^{{\\prime\\:}}}^{2}+0.5{{v}^{{\\prime\\:}}}^{2}\\)\u003c/span\u003e\u003c/span\u003e) is a key indicator of the conversion and dissipation processes of energy within turbulent flow. Figure\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e shows the normalized distribution of TKE before and after the addition of hair appendages to the submersibles. For the 0 \u003cem\u003eL\u003c/em\u003e submersible (Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003ea), the turbulent kinetic energy distribution is wide, with the high-energy region predominantly located at the stern. This suggests stronger vorticity and energy conversion in the stern area. In contrast, the bow region shows a smaller high-energy area, indicating a more stable flow with fewer disturbances. For the submersible with hair appendages (Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003eb-d), adding 0.1 \u003cem\u003eL\u003c/em\u003e of hair appendages results in a decrease in turbulent kinetic energy in the bow's wake region and an increase in the amidships. There is no significant change in the transom, indicating that the short appendages do not notably enhance flow field vortices. When the appendage length increases to 0.2 \u003cem\u003eL\u003c/em\u003e, the turbulent kinetic energy in the bow wake gradually expands, likely due to increased peripheral fluid disturbance, which induces stronger reflux and vortex activity, thereby enhancing the turbulent kinetic energy in the bow. When the addition of 0.3 \u003cem\u003eL\u003c/em\u003e of hair appendages, both the bow and stern regions experience a decrease in turbulent kinetic energy, while the amidships remains unchanged. The maximum turbulent kinetic energy of the flow field drops from 0.114 to 0.102, reflecting a 10.5% reduction. This indicates that the optimal length of hair appendages improves the flow state, reduces the generation of turbulent kinetic energy, enhances flow stability, and lowers flow resistance.\u003c/p\u003e \u003cp\u003eThe transient streamline diagram illustrates the fluid flow conditions and vortex structure in the flow field. Figure\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e shows the transient streamlines before and after the installation of hair appendages on the submersible. For the 0 \u003cem\u003eL\u003c/em\u003e submersible (Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003ea), two large vortices formed at the bow and stern, causing increased drag due to flow separation. After adding 0.1 \u003cem\u003eL\u003c/em\u003e of hair appendages (Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003eb), the wake region slightly narrowed, but the stern vortex structure remained largely unchanged, indicating that the short hair appendages had a limited effect and did not significantly alter the boundary layer or flow pattern to prevent the formation of large vortices. With 0.2 \u003cem\u003eL\u003c/em\u003e of hair appendages (Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003ec), the large stern vortices decomposed into multiple smaller vortices, and energy was dissipated through a high-frequency mechanism. This suggests that the hair appendages suppressed the formation of large vortices and promoted small vortex generation by exchanging elastic vibration and fluid momentum, in line with the turbulence energy cascade theory. With 0.3 \u003cem\u003eL\u003c/em\u003e of hair appendages (Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003ed), the bow vortex region decreased, the stern vortex lengthened, and the intersection of the bow and stern vortices shifted towards the bow. This indicates that the optimal hair appendage length improved the boundary layer behavior, reduced flow separation, and helped guide the fluid transition from the bow to the stern more effectively.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Fourier transform analysis of energy spectrum of vortex center\u003c/h2\u003e \u003cp\u003eThe energy spectrum of the vortex center provides insights into the distribution of energy within the vortex. Thus, the vortex centroids in the flow field regions at the bow (0.3 \u003cem\u003eL\u003c/em\u003e, 0.1 \u003cem\u003eL\u003c/em\u003e) and stern (0.2 \u003cem\u003eL\u003c/em\u003e, 0.8 \u003cem\u003eL\u003c/em\u003e) of the submersible were monitored separately. The monitoring was conducted at a frequency of 1000 \u003cem\u003eHz\u003c/em\u003e over a duration of 7.2 seconds. Figure\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e illustrates the energy spectrum of the vortex centers in the flow field at the bow, both before and after the installation of the hair appendages on the submersible. For the 0 \u003cem\u003eL\u003c/em\u003e submersible, the vortex frequency in the bow flow field is 1.37 \u003cem\u003eHz\u003c/em\u003e, with an energy of 178.3. Upon adding 0.1 \u003cem\u003eL\u003c/em\u003e hair appendages, the vortex frequency in the bow flow field decreased to 1.24 \u003cem\u003eHz\u003c/em\u003e, with an associated energy of 150.3, representing a 9.5% decrease in frequency and a 15.7% decrease in energy compared to the conventional submersible (0 \u003cem\u003eL\u003c/em\u003e). With 0.2 \u003cem\u003eL\u003c/em\u003e hair appendages, the vortex frequency further decreased to 1.09 \u003cem\u003eHz\u003c/em\u003e, and the energy dropped to 142.4, indicating a 20.4% reduction in frequency and a 20.1% reduction in energy compared to the conventional submersible (0 \u003cem\u003eL\u003c/em\u003e). After adding 0.3 \u003cem\u003eL\u003c/em\u003e of hair appendages, the vortex frequency in the bow flow field was further reduced to 0.96 \u003cem\u003eHz\u003c/em\u003e, with an energy of 128.2, reflecting a 29.9% reduction in frequency and a 28.1% reduction in energy compared to the conventional submersible (0 \u003cem\u003eL\u003c/em\u003e). The experimental data clearly demonstrate that as the length of the hair appendages increases, both the vortex frequency and energy in the bow flow field exhibit a distinct decreasing trend.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e illustrates the energy spectrum at the center of the vortex in the transom flow field of the submersible before and after the installation of the hair appendages. For the 0 \u003cem\u003eL\u003c/em\u003e submersible, the vortex frequency in the transom flow field is 0.96 \u003cem\u003eHz\u003c/em\u003e, with an energy of 157.7. After the addition of 0.1 \u003cem\u003eL\u003c/em\u003e of hair appendages, the vortex frequency remains at 0.96 \u003cem\u003eHz\u003c/em\u003e, but the energy decreases to 146.4, representing a 7.2% reduction in energy compared to the conventional submersible (0 \u003cem\u003eL\u003c/em\u003e). With the addition of 0.2 \u003cem\u003eL\u003c/em\u003e of hair appendages, the vortex frequency drops to 0.69 \u003cem\u003eHz\u003c/em\u003e, and the energy further decreases to 120.9, indicating a 28.1% reduction in frequency and a 23.3% reduction in energy compared to the conventional submersible (0 \u003cem\u003eL\u003c/em\u003e). When 0.3 L of hair appendages are added, the vortex frequency decreases to 0.55 \u003cem\u003eHz\u003c/em\u003e, with an energy of 108.2. Compared to the conventional submersible (0 \u003cem\u003eL\u003c/em\u003e), this results in a 42.7% reduction in frequency and a 31.4% reduction in energy. These results indicate that the appropriate length of hair appendages can effectively reduce the vortex frequency and energy in the submersible\u0026rsquo;s flow field. The vortex frequency and energy are minimized when the hair appendage length is 0.3 \u003cem\u003eL\u003c/em\u003e, which is consistent with the trends observed in Figs.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003ed and \u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003ed.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.5 POD flow field analysis\u003c/h2\u003e \u003cp\u003eBy performing proper orthogonal decomposition (POD) of the flow field, we can simplify the complex problem into a series of intrinsic modes, facilitating a better understanding of its structural and dynamic properties. In this paper, we analyze the POD decomposition of the wake flow field both before and after the addition of hair appendages of varying lengths to the submersible. Figure\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e illustrates the energy distribution corresponding to each order of the POD modes. The figure shows that energy is primarily concentrated in the first-order modes, indicating a significant hierarchical and structured flow field. In contrast, the second and higher-order modes contain relatively less energy, suggesting that the influence of small-scale vortices is weaker compared to the large-scale dominant flow features. Consequently, the first-order and second-order modes offer a good representation for understanding the behavior of the flow field.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e16\u003c/span\u003e illustrates the velocity field reconstruction for the POD first-order modes. For the 0L submersible (Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e16\u003c/span\u003ea), large high-velocity regions are observed in the wake flow at the bow and amidships, consistent with the trend in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003ea. After adding 0.1 \u003cem\u003eL\u003c/em\u003e hair appendages (Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e16\u003c/span\u003eb), the high-velocity region in the wake flow was significantly reduced, while a large high-velocity backflow region appeared at the bow, indicating that the hair appendages altered the large-scale flow characteristics. When 0.2 \u003cem\u003eL\u003c/em\u003e of appendages were added (Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e16\u003c/span\u003ec), the high-speed region gradually extended from the bow to amidships, and the backflow region decreased, suggesting that fluid separation was suppressed and flow stability improved. After adding 0.3 \u003cem\u003eL\u003c/em\u003e hair appendages (Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e16\u003c/span\u003ed), the flow characteristics were similar to those of 0.2 \u003cem\u003eL\u003c/em\u003e, but the intensity increased significantly. This may be because the 0.3 \u003cem\u003eL\u003c/em\u003e hair appendages optimize the vortex structure, enabling more effective conversion and utilization of the fluid's kinetic energy. At this point, the energy in the flow field is further concentrated in the first-order mode, reinforcing the dominant flow features, which is consistent with the phenomenon observed in Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThe second-order modes of the proper orthogonal decomposition (POD) represent the low-energy modes in the flow field, revealing secondary flow structures that are neglected by the first-order modes, particularly local vortices and details of the complex flow. Figure\u0026nbsp;\u003cspan refid=\"Fig17\" class=\"InternalRef\"\u003e17\u003c/span\u003e illustrates the velocity field reconstruction for the second-order modes of the POD. For the 0L submersible (Fig.\u0026nbsp;\u003cspan refid=\"Fig17\" class=\"InternalRef\"\u003e17\u003c/span\u003ea), a high-velocity region is evident in the bow, while the central wake region exhibits a large backflow, suggesting that the flow structure in these areas is quite complex. After adding 0.1 \u003cem\u003eL\u003c/em\u003e hair appendages (Fig.\u0026nbsp;\u003cspan refid=\"Fig17\" class=\"InternalRef\"\u003e17\u003c/span\u003eb), the high-velocity region in the bow gradually shifts along the flow direction. This shift can be attributed to the appendages altering the fluid momentum distribution, which results in adjustments to both the flow direction and velocity. Additionally, new high-speed backflow regions appear at the bow and amidships, indicating that the vortex structure and wake behavior of the flow field have become more complicated, potentially increasing flow instability in these regions. With the addition of 0.2 \u003cem\u003eL\u003c/em\u003e hair appendages (Fig.\u0026nbsp;\u003cspan refid=\"Fig17\" class=\"InternalRef\"\u003e17\u003c/span\u003ec), the high-velocity region extends continuously from the bow, and the backflow region extends toward the stern. This suggests that the hair appendages enhance fluid mobility and make the flow structure more interactive. When the appendages are further increased to 0.3 \u003cem\u003eL\u003c/em\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig17\" class=\"InternalRef\"\u003e17\u003c/span\u003ed), the flow characteristics become similar to those observed with 0.2 \u003cem\u003eL\u003c/em\u003e appendages. This indicates that the effects of the hair appendages on the flow structure tend to stabilize within this range, likely due to the flow field reaching steady-state equilibrium. Consequently, changes in flow characteristics are no longer significant, though the actual performance may still differ.\u003c/p\u003e \u003cp\u003eThe time coefficients of the POD decomposition reveal the time evolution characteristics of different flow modes in the flow field, which are crucial for understanding vortex structures and flow stability. Figure\u0026nbsp;\u003cspan refid=\"Fig18\" class=\"InternalRef\"\u003e18\u003c/span\u003e illustrates the time coefficients of the POD first-order modes. It is evident that these coefficients exhibit clear periodic changes, indicating that the main flow modes (e.g., the primary vortex) in the flow field evolve periodically over a specific timescale. The waveforms of the submersible's time coefficient exhibit different fluctuation patterns depending on the length of the hair appendages. Notably, when the appendage length is 0.3L, the waveform of the time coefficient is almost 180\u0026deg; out of phase with the waveforms under other conditions. This suggests that the nonlinear effects in the flow field become more pronounced as the appendage length increases. Furthermore, the peak value of the time coefficient for the first-order POD mode increases with the addition of hair appendages. The peak intensity of this coefficient reflects the strength of the vortex structure in the flow field, indicating that the appendages enhance the vortex contribution to the main flow modes. This increase in vortex intensity may lead to the development of more complex flow features.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig19\" class=\"InternalRef\"\u003e19\u003c/span\u003e illustrates the time coefficients for the second-order modes of POD. In POD analysis, these time coefficients typically reflect small-scale, rapidly changing dynamic processes within the system. By analyzing their variations, insights can be gained into the dynamic behavior of the second-order vibration modes and their contribution to the system's response. In this study, the time coefficients of the second-order modes reveal the dynamic properties of the local vortex phenomenon in the submersible wake flow field. Compared to the first-order modes, the time coefficients of the second-order modes exhibit more violent fluctuations, though with smaller amplitudes. This suggests a more dispersed energy distribution and more frequent dynamic changes, reflecting the system's fluctuations and energy exchanges on shorter time scales. Additionally, the trends in the amplitudes of the POD first-order and second-order modal time coefficients align with the POD modal energy distributions shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e, further validating the analytical results regarding intermodal energy conversion and coupling effects.\u003c/p\u003e \u003c/div\u003e"},{"header":"4 Conclusions","content":"\u003cp\u003eIn this study, the effects of hair appendages on the drag and flow field characteristics of a submersible under diving conditions are investigated using particle image velocimetry (PIV), Fourier transform (FT), and proper orthogonal decomposition (POD) techniques. The results show that the optimal length of hair appendages can effectively reduce the drag force on the submersible and significantly improve the flow characteristics of its flow field, particularly when the length of the hair appendages is 0.3 \u003cem\u003eL\u003c/em\u003e. The main findings are as follows:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe drag results show that hair appendages are beneficial for submersibles, reducing both drag and lift during the dive. The mean flow field analysis reveals that the hair appendages can disrupt large eddies in the flow.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eTurbulent kinetic energy and Reynolds stress analyses show that the hair appendages, as flexible structures, can absorb some of the pulsation energy, thereby reducing the turbulence intensity in the submersible's flow field region.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThrough the Fourier-transformed energy spectrum at the vortex center, it was found that hair appendages reduce both the vortex frequency and vortex energy in the submersible's flow field.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003ePOD analyses show that hair appendages can disrupt the intrinsic period of the time coefficients and amplify their peaks, resulting in the emergence of more complex flow features.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eShan WANG was the main author, responsible for the overall conception, literature review, data analysis, methodology design, and preparation and revision of the final manuscript.2. Fei YAN provided financial support and resources and contributed to the discussion and optimization of experimental designs.3. Gangqing ZHANG participated in the preliminary study design discussion and validated the data results.4. Rui ZHU performed language editing and format checking to ensure the manuscript met the journal's submission requirements.5. Lei LI contributed to the initial study design discussion and provided suggestions for the theoretical framework.6. Jian ZHANG participated in the study discussion and provided guidance for the final version of the paper.\u003c/p\u003e\u003ch2\u003eAcknowledgments\u003c/h2\u003e \u003cp\u003eThe author wishes to acknowledge the support given to him by the Major Basic Research Project of the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (24KJA130001).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eQ. N. XU, Z. HU, C. YE, et al., Present situation and prospect of deep-sea manned submersible technology and its application, Science and Technology Foresight. 2022, 1(2): 36\u0026ndash;48.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZ. W. LI, W. C. CUI., Study on the resistance performance for the third generation of manned submersible with full ocean depth, \"The Deepsea Challenge\", Chinese Journal of Hydrodynamics. 2013, 28(01): 1\u0026ndash;9.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eL. Taylor, T. Lawson., Project Deepsearch: An innovative solution for accessing the oceans, Marine Technology Society Journal, 2009, 43(5): 169\u0026ndash;177.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eG. Hawkes., The old arguments of manned versus unmanned systems are about to become irrelevant: new technologies are game changers, Marine Technology Society Journal, 2009, 43(5): 164\u0026ndash;168.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eQ. N. XU, H. Y. ZHANG., Development and application of jiao long manned submersible, Science. 2014, 66(02): 11\u0026ndash;13.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eM. Mo, W. Zhao, Z. Chen., Research status of Marine drag reduction technology, Tri. 2015, 35(04): 505\u0026ndash;515.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eP. Y. Guo, Y. Zhang, M. Z. Zhang, H. B. Hu., Experimental study of aeration reduction on hydrophilic-superhydrophobic interphase surfaces, Chinese Journal of Technology and Applied Mechanics. 2024, 56(1): 94\u0026ndash;100.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eH. Zhou, D. Shen, G. Tian., Biomechanical characteristics of puffer skin for flexible surface drag reduction, Mechanics of Advanced Materials and Structures. 2019, 28(11): 1\u0026ndash;7.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZ. Wang, J. Kong, Q. Zhou., Natural superhydrophobic surfaces and application, Journal of Physics: Conference Series. 2022, 2390(1): 012115.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eM. Hadipour., Investigation of sweep angle effects on a submarine hydrodynamic drag using computational fluid dynamics, Jordan Journal of Mechanical \u0026amp; Industrial Engineering. 2015, 9(3): 209\u0026ndash;216.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eG. L. Zhou, P. Wang, C. Y. Guo, C. Wang., Research on the impact of underwater stern foil on the ship resistance performance, Journal of Ship Mechanics. 2022, 26(07): 962\u0026ndash;968.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eM. M. Zheng, Y. D. Liu, Y. Y. Tang, Y. J. Wang, Y. P. He., Two-dimensional hydrofoil hydrodynamic performance and waveform evolution studies in density stratification and homogeneous fluid, Ocean Engineering. 2022, 263: 112366.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eS. Gao, S. Pan, H. C. Wang, X. L. Tian., Shape deformation and drag variation of a coupled rigid-flexible system in a flowing soap film, Physical Review Letters. 2020, 125(3): 034502.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eX. L. Tian., Review of \" flexible coating reduces drag\", Journal of Shanghai Jiao Tong University. 2021, 55(02): 213\u0026ndash;214.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eQ. Mao, Y. Liu, H. J. Sung., Drag reduction by flapping a flexible filament behind a stationary cylinder, Physics of Fluids. 2022, 34(8): 087123.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eQ. Mao, Y. Liu, H. J. Sung., Drag reduction by flapping a pair of flexible filaments behind a cylinder, Physics of Fluids. 2023, 35(3): 033602.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eC. G. Baena, J. I. J. Gonz\u0026aacute;lez, C. M. Baz\u0026aacute;n., Drag reduction of a blunt body through reconfiguration of rear flexible plates, Physics of Fluids. 2021, 33(4): 045102.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eB. W. Song, Y. H. Guo, Z. Z. Luo, X. H. Xu, Y. Wang., Investigation about drag reduction annulus experiment of hydrophobic surface, Acta Physica Sinica. 2013, 62(15): 154701.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMichael K, Sabri A, Harald K, et al., Distribution and localization of hydrophobic and ionic chemical groups at the surface of bleached human hair fibers, Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2018, 538: 262\u0026ndash;269.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZ. Nan, H. Liu, G. Archana, et al., Facile and efficient enzymatic methods for harvesting or removal of cuticle cells from human hair shafts, Journal of Natural Fibers, 2022, 19(15): 11036\u0026ndash;11049.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eY. H. Zhang, S. M. Zhang, Z. Fan, et al., A scanning electron microscopic comparative observation on the hairs of hairy men and the controls, Chinese Journal of Anatomy. 1988, (02): 98\u0026ndash;100.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHitoshi M, Daisuke S, Yuri O, et al., Impact of protein carbonylation on the chemical characteristics of the hair surface, International Journal of Cosmetic Science. 2021, 43(6): 764\u0026ndash;771.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHironori T, Kento F, Hitoshi S, et al., Structural elasticity for tensile deformation of a single human hair and the comparison with it for the bending deformation, Journal of the Mechanical Behavior of Biomedical Materials. 2021, 113: 104166.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHironori T, Kento F., Division of force among layers constituting human hair during bending and tension, Journal of the Mechanical Behavior of Biomedical Materials. 2022, 133: 105346.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJ F W, Gabriele W, Hans-Martin H, et al., Analysis of the torsional storage modulus of human hair and its relation to hair morphology and cosmetic processing, Journal of Cosmetic Science. 2014, 65(2): 59\u0026ndash;68.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eC. H. Lee. A. P. Coulombe., Self-organization of keratin intermediate filaments into cross-linked networks, The Journal of Cell Biology. 2009, 186(3): 9\u0026ndash;21.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eE. Antunes, F. C. Cruz, G. N. Azoia, et al., Insights on the mechanical behavior of keratin fibrils, International Journal of Biological Macromolecules. 2016, 89: 477\u0026ndash;483.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eW. Qu, X. Guo., G. Xu., et al., Improving the mechanical properties of damaged hair using low-molecular weight hyaluronate, Molecules. 2022, 27(22): 7701\u0026ndash;7701.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFernandes, Cavaco-Paulo., Protein disulphide isomerase-mediated grafting of cysteine-containing peptides onto over-bleached hair, Biocatalysis and Biotransformation. 2012, 30(1): 10\u0026ndash;19.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eG. Zeng, Y. Zhou, Y. Liang, et al., A hair fiber inspired bio-based adhesive with high bonding strength and mildew tolerance, Chemical Engineering Journal. 2022, 434: 134632.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJ. Wang, S. Luan, J. Zhu, et al., Fourier mode decomposition of unsteady flows in a single injection port fluidic thrust vectoring nozzle, International Journal of Aeronautical and Space Sciences. 2020: 1\u0026ndash;16.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWaleed K. A., Mahmoud A. A., M. Z. A. Fourier decomposition and anisotropic diffusion filtering of forced turbulence, International Journal of Applied Mechanics. 2017, 09(08): 1750121.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eX. Y. Zhao, X. Q. Chen., Z. Q. Gong., et al., RecFNO: A resolution-invariant flow and heat field reconstruction method from sparse observations via Fourier neural operator, International Journal of Thermal Sciences. 2024, 195: 108619.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eL. Liu, Y. Chen, X. Xie., Spatial scale decomposition of flow field based on multidimensional Fourier analysis, Journal of Fudan (Natural Science Edition). 2014, 53(05): 616\u0026ndash;625.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eQ. Zhang, Y. Liu, S. Wang., The identification of coherent structures using proper orthogonal decomposition and dynamic mode decomposition, Journal of Fluids and Structures. 2014, 49: 53\u0026ndash;72.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eM. Li, Q. Li, H. Shi, et al., Effects of free-stream turbulence on the near wake flow and aerodynamic forces of a square cylinder, Journal of Fluids and Structures. 2022, 114: 103748.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eA. Fawaz, A. M. E. Catherine. W, P. Ouio., Unsteady vortex shedding dynamics behind a circular cylinder in very shallow free-surface flows, Computers and Fluids. 2023, 260: 105918.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eR. Hiroka., Three-dimensional wake structures over a short cylinder having a fore angled hole, Ocean Engineering. 2023, 271: 113713.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZ. Jing, W. Wang, X. Wen., Experimental study of square column winding by oscillating jets, Thermal Power Engineering. 2024, 39(01): 108\u0026ndash;118.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Submersible, Flexible appendage, Drag reduction, Fourier transform, POD","lastPublishedDoi":"10.21203/rs.3.rs-6162883/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6162883/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study presents a novel method for installing flexible appendages (hairs) on the surface of a submersible to reduce its drag as it descends from the surface to the seafloor. First, the changes in drag, Reynolds stress, turbulent kinetic energy, and time-averaged streamlines of the flow field before and after the addition of hair appendages to the submersible were analyzed using a six-component sensor and particle image velocimetry (PIV). The results indicate that, with optimal hair appendages, the drag of the submersible is reduced by 8.7% compared to a conventional submersible (0 \u003cem\u003eL\u003c/em\u003e), and the intensity and extent of the two large-scale eddies in the flow field decrease. Subsequently, the energy spectrum of the flow field, the dominant modes of the flow, and the energy distribution within the vortex core before and after the addition of hair appendages were analyzed using Fourier transform and proper orthogonal decomposition (POD). The results show that hair appendages of optimal length can reduce vortex frequency and energy in the flow field of a submersible. It was also found that hair appendages were able to alter the intrinsic period of the time coefficient and amplify its peak, leading to the emergence of more complex flow features.\u003c/p\u003e","manuscriptTitle":"A study on the drag reduction characteristics of flexible appendage submersibles during dives","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-03-11 06:59:01","doi":"10.21203/rs.3.rs-6162883/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"03ed0431-7fb0-4c48-ae99-a2fbc7c99764","owner":[],"postedDate":"March 11th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-05-04T19:23:12+00:00","versionOfRecord":[],"versionCreatedAt":"2025-03-11 06:59:01","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6162883","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6162883","identity":"rs-6162883","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}