Particle Image Research Articles

Proper orthogonal decomposition analysis for two-dimensional wake transition behind a NACA 0012 airfoil in a soap film

Abstract An experimental study has been conducted to analyze the flow characteristics around a NACA 0012 airfoil in a horizontal soap film tunnel. The investigation involves both the qualitative observations and the quantitative measurements at various angles of attack (0° to 20°) for Reynolds numbers ∼ 3000 and 5000. Flow visualizations were carried out using the interference technique, while particle image velocimetry (PIV) was used for velocity field measurements. The study examines the two-dimensional wake transition of the NACA 0012 airfoil under different Reynolds numbers and angles of attack in a soap film tunnel. Results indicate that changes in the trailing flow within the soap film are primarily influenced by the Reynolds number and angle of attack. The visualization of the flow exposes different states of wakes and their corresponding flow structures. At lower angles of attack α ≤ 6°, vortex shedding occurs in an alternating mode, while at intermediate angles (8° to 16°), the wake widens. The vortices exhibit more chaotic and turbulent behavior at higher angles of attack, i.e., α ≥ 16°. Furthermore, the study indicates that the same wake transition takes place at lower angles of attack as Reynolds numbers rise.

Investigation of droplet splashing behavior during oblique jet impact onto a wall

For the issue of jet impingement on the wall in industrial cooling processes, an experimental setup based on high-speed photography for oblique jet impingement onto the wall was constructed. The experimental focus was on the study of liquid droplet splashing behavior after oblique jet impingement on the wall, discussing the liquid droplet splashing behavior under three jet impingement modes: Rayleigh regime, first wind-induced regime, and secondary wind-induced regime. By employing methods such as trajectory imaging and particle image velocity for liquid droplet parameter image measurement, obtaining the particle size, velocity, and distribution of splashed droplets after oblique jet impact on walls under different working conditions. The impact of jet impingement velocity and angle on droplet splashing parameters was analyzed. The results showed that when the impingement point is before the breakup length, with increasing flow velocity, the surface wave of the liquid column, and the spreading liquid film became more pronounced, but the loss of liquid-phase components due to splashing was relatively small. When the impingement point is after the breakup length, the secondary breakup resulting in a “crown”-shaped liquid film after droplet impingement leads to a significant loss of liquid-phase components through splashing. As the inlet velocity of the jet increases, there is a decreasing trend in droplet size and an increasing trend in droplet velocity. With an increase in jet angle, there is a decreasing trend in droplet size and velocity. Based on the concentration, size, and velocity distribution characteristics of splashing droplets, the area after oblique jet impingement on the wall can be divided into the impingement zone, low-concentration low-velocity zone, high-concentration high-velocity zone, and lateral splashing zone. This has significant implications for understanding the splashing mechanism after oblique jet impingement on the wall and optimizing operating conditions.

A simple hot wire temperature drift correction based on temperature sensitivity applied to a turbulent shear layer

A procedure is proposed to correct temperature drift for hot wire anemometry measurements in turbulent fields where the facility is not equipped with temperature control. The procedure consists of evaluating the wire sensitivity to the temperature by building a voltage-temperature curve. The voltages of both the calibration points and the measurement points are corrected, shifting the voltage values to an arbitrary reference temperature. The correction can be applied to the instantaneous voltages by performing synced temperature measurements with constant current anemometry or constant voltage anemometry cold wire. The efficacy of the method is tested on a turbulent shear layer that develops on the side of an open jet wind tunnel not equipped with temperature control. The velocity statistics show a good match with respect to reference particle image velocimetry measurements, evidencing the self-similarity of the shear layer in contrast with the non-corrected data and the data corrected using the semi-empirical and analytical relation based on King's law modification. A correction based only on the temperature statistics shows indistinguishable results with respect to the instantaneous correction.

Comparative study of analytical models with linear and quadratic pressure drop conditions on a perforated plate in water waves

Proper pressure drop conditions are essential in predicting hydrodynamic performance of perforated structures in the framework of a potential flow theory. In this study, we investigate water waves passing through a perforated plate with various pressure drop models to examine how pressure drop conditions affect the hydrodynamic performance of perforated structures. We derive the analytical solutions of waves across the perforated plate by adopting three commonly pressure drop conditions, including one linear pressure drop condition (LPDC), and two quadratic pressure drop conditions (QPDCs). A series of laboratory experiments are conducted to validate the present theoretical results. We compare the hydrodynamic performance between the experimental data and the theoretical solutions with the three different pressure drop models, typically for wave reflection coefficients, dynamic pressures, and velocity fields measured by the technique of particle image velocimetry in the experiments. It is found that the existing pressure drop models can predict well wave reflection coefficients, dynamic pressure, and velocity profiles at certain conditions. However, the linear wave solutions associated with LPDC or QPDCs generally underpredict the amplitude of particle velocity near the free surface on the perforated plate. This underestimation increases largely as the wave steepness increases. The LPDC performance relies much on the selection of empirical coefficients. For the QPDCs, the analytical models show deviated results from the experimental data for wave reflection coefficients when the wave steepness is relatively low.

An experimental investigation of supersonic conical cooling films with angles of attack

While the flow mechanisms of two-dimensional supersonic cooling films have been studied in-depth, this paper used the nanoparticle planar laser scattering and particle image velocimetry techniques to investigate the flow of supersonic conical cooling films at different angles of attack (AOAs). The mainstream Mach number was Ma∞=3.8, and the supersonic conical cooling film was tangentially injected via a precisely calibrated Maj=2.8 annular nozzle. Initially, the streamwise boundary layer transition process without cooling film injection was analyzed. The boundary layer transition on the leeward side occurred prematurely, whereas on the windward side, the transition process was notably delayed. Subsequently, the supersonic conical cooling film flow was qualitatively and quantitatively evaluated from the perspectives of turbulent structures, and the time-averaged and statistical characteristics of the velocity field. On the windward side, as the ratio of static pressure decreased, the effective cooling length also decreased with an increase in AOA. On the leeward side, at a small positive AOA, the supersonic conical cooling film mixed with the low-energy fluid within the thickened inner layer of the mainstream boundary layer, which mitigated the growth rate of the mixing layer and ultimately enhanced the effective cooling length. With a further increase in AOA, the supersonic conical cooling film experienced the three-dimensional detrimental effects of crossflow-separation vortices and downwash mainstream on the leeward surface, resulting in a decrease in the effective cooling length.

Magnetic Anisotropy Dominates over Physical and Magnetic Structure in Performance of Magnetic Nanoflowers

Magnetic nanoparticles are indispensable in many biomedical applications, but it remains unclear how the composition and structure will influence the application specific performance. We consider two compositions, ferrite and cobalt ferrite, synthesized under conditions that create aggregated multi‐core nanoparticles, called nanoflowers. Each nanoflower has an ionic surfactant or dextran to provide colloid stability in water. The composition, but not the coating, greatly impacts the heating output and the magnetic particle imaging tracer quality (with cobalt ferrite significantly reduced compared to ferrite). The cobalt ferrite nanoflowers have a core/shell structure with a reduced magnetization, which limits the effective magnetic anisotropy of the individual cobalt ferrite nanoflowers as well as the magnetic interactions among the nanoflowers. Both limitations significantly reduce the overall increase in the magnetic anisotropy with increasing magnetic field and consequently the nanoflowers’ efficacy for heating and imaging. Despite this, the formation of denser‐packed clusters and chains with external magnetic field in the ionic surfactant‐cobalt ferrite nanoflowers overcomes some of the shell's detrimental effects, resulting in better heating and imaging properties compared to the dextran‐cobalt ferrite. In short, the magnetic anisotropy dominates over physical and magnetic structure in the performance of the studied nanoflowers for heating and imaging applications.

Study of the Flow Characteristics of Pumped Media in the Confined Morphology of a Ferrofluid Pump With Annular Microscale Constraints

Abstract The driving mechanism of ferrofluid micropumps under the constraints of an annular microscale morphology is not fully understood. The gap between microfabrication technology and the fundamental theory of microfluidics has become a substantial obstacle to the development and application of ferrofluid micropumps. In this study, we first theoretically analyzed the Knudsen numbers of millimeter-scale microfluids using Jacobson's molecular hard sphere model, obtaining the initial conclusion that liquid flow conforms to the continuum hypothesis in geometric morphologies with characteristic dimensions greater than 7 × 10−8 m. Subsequently, using a microscopic lens combined with the particle image velocimetry optical measurement method, the flow patterns in millimeter-scale annular flow channels were captured and we observed wall slip phenomena in which the slip length of the millimeter-scale channel approached the micron level. The slip velocity and flowrate through the cross section of the microscale channel followed a logarithmic function relationship and could be divided into rapid growth, slow growth, and stable stages. As the characteristic scale of the channel was further reduced, the linear relationship between the slip velocity and cross-sectional flowrate in the rapid growth stage was broken, and the nonlinear relationship approximated an exponential function. Finally, a theoretical model for the flow behavior of the driving fluid in a ferrofluid micropump was established using slip boundary conditions. The flow patterns in microscale ring flow under slip conditions conformed to a quadratic function.

Improvement in the Number of Velocity Vector Acquisitions Using an In-Picture Tracking Method for 3D3C Rainbow Particle Tracking Velocimetry

Particle image velocimetry and particle tracking velocimetry (PTV) have developed from two-dimensional two-component (2D2C) velocity vector measurements to 3D3C measurements. Rainbow particle tracking velocimetry is a low-cost 3D3C measurement technique adopting a single color camera. However, the vector acquisition rate is not so high. To increase the number of acquired vectors, this paper proposes a high probability and long-term tracking method. First, particles are tracked in a raw picture instead of in three-dimensional space. The tracking is aided by the color information. Second, a particle that temporarily cannot be tracked due to particle overlap is compensated for using the positional information at times before and after. The proposed method is demonstrated for flow under a rotating disk with different particle densities and velocities. The use of the proposed method improves the tracking rate, number of continuous tracking steps, and number of acquired velocity vectors. The method can be applied under the difficult conditions of high particle density (0.004 particles per pixel) and large particle movement (maximum of 60 pix).

Effects of cohesion and viscosity on lava dome growth following repose

Lava domes result from effusive eruption of high viscosity lava. These viscous lava extrusions range in shape from flat-topped domes with small height-to-width aspect ratios, to spine-like columns exhibiting large height-to-width aspect ratios. A primary control on morphology during early dome growth is thought to be the variation in rheological characteristics of extruded material. In this work, we present new scaled analogue models of lava dome growth that consider extrusion of a frictional plastic upper-conduit plug followed by viscous magma. We simulate the brittle plug using a sand-plaster mixture, the cohesion of which is varied by plaster content. We model the magma using sugar syrup, the viscosity of which is controlled by the weight percent of added crystalline sugar. The models both qualitatively and quantitatively reproduce part of the spectrum of natural dome morphology not previously obtained in most past analogue modelling studies. Model aspect ratios of 0.02 to 0.9 capture approximately 90 % of the reported aspect ratio variation in nature. Increasing plug cohesion results in extrusions with higher aspect ratios and spinier morphologies. Low viscosity fluid typically erupts through the brittle dome, whilst high viscosity fluid tends to promote endogenous growth or emerge as exogenous lobes. Particle Image Velocimetry shows that fracture localisation at the dome surface is cohesion-dependent, and eruption of fluid follows shear fractures within the dome. Where fluid remains contained within the dome, we see lateral spread leading to a wider and flatter dome morphology. Evolution of lava dome morphology, deformation, and associated hazards is guided by the complex rheological properties of the extruded material; we suggest that during episodic dome growth, these properties are largely defined in the conduit prior to their eruption.

Combining Computational Fluid Dynamics and Experimental Data to Understand Fish Schooling Behavior.

Understanding the flow physics behind fish schooling poses significant challenges due to the difficulties in directly measuring hydrodynamic performance and the three-dimensional, chaotic, and complex flow structures generated by collective moving organisms. Numerous previous simulations and experiments have utilized computational, mechanical, or robotic models to represent live fish. And existing studies of live fish schools have contributed significantly to dissecting the complexities of fish schooling. But the scarcity of combined approaches that include both computational and experimental studies, ideally of the same fish schools, has limited our ability to understand the physical factors that are involved in fish collective behavior. This underscores the necessity of developing new approaches to working directly with live fish schools. An integrated method that combines experiments on live fish schools with computational fluid dynamics (CFD) simulations represents an innovative method of studying the hydrodynamics of fish schooling. CFD techniques can deliver accurate performance measurements and high-fidelity flow characteristics for comprehensive analysis. Concurrently, experimental approaches can capture the precise locomotor kinematics of fish and offer additional flow information through particle image velocimetry (PIV) measurements, potentially enhancing the accuracy and efficiency of CFD studies via advanced data assimilation techniques. The flow patterns observed in PIV experiments with fish schools and the complex hydrodynamic interactions revealed by integrated analyses highlight the complexity of fish schooling, prompting a reevaluation of the classic Weihs model of school dynamics. The synergy between CFD models and experimental data grants us comprehensive insights into the flow dynamics of fish schools, facilitating the evaluation of their functional significance and enabling comparative studies of schooling behavior. In addition, we consider the challenges in developing integrated analytical methods and suggest promising directions for future research.

Strongly Interacting Nanoferrites for Magnetic Particle Imaging and Spatially Resolved Thermometry.

High-crystal-quality nanoferrites with short surface ligands (oleic acid) were recently shown to exhibit enhanced sensitivity and spatial resolution, likely due to chain formation (uniaxial assemblies of particles) for magnetic particle imaging (MPI). Here, we develop a simple one-pot thermal decomposition approach to produce ferrite (iron oxide) magnetic nano-objects (MNOs) that strongly interact magnetically and have good synthetic reproducibility. The ferrite MNOs were physically characterized by X-ray diffraction, Raman spectroscopy, transmission electron microscopy, and dynamic light scattering. The MNOs were magnetically characterized by magnetometry and magnetic particle spectroscopy (MPS) to study their interactions, dynamics, and suitability for spatially resolved magnetic thermometry. The MNOs were synthesized in a range of sizes between 12 nm and 27 nm, showing that MNOs below a minimum size do not exhibit dynamic interactions/significant increased response and that a larger field is required for chain formation as size increases. In addition to size effects, we explore the role of ligand length, environment (liquid vs solid), and concentration on the proposed chain formation. The experimental results were then correlated to micromagnetic simulations to gain further insight into the formation of chains. Compared to some existing MPI tracers, our ferrite MNOs exhibit enhanced signal (up to about 37×) and spatial resolution (up to about 9×) under certain limited (ferrite-MNO optimal) field and frequency conditions used. MPS as a function of temperature and drive field amplitude was performed, showing promise for spatially resolved thermometry. These results confirm the importance of tuning the frequency and amplitude of the drive field for optimal imaging/thermal performance.

Investigating lubricant behavior in a partially flooded tapered roller bearing: Validation of a multiphase CFD solver for aerated oil sump via particle image velocimetry studies and high-speed camera acquisitions

In the recent years, the efficacy of utilizing sapphire outer rings as a viable tool for experimentally observing oil flows within rolling bearings has been demonstrated. However, in previous studies, such approach was applied under fully-flooded lubrication conditions exclusively. This paper presents the outcomes of observations and measurements conducted under oil-bath lubrication conditions of a vertical-axis Tapered Roller Bearing (TRB). The experimental work encompasses four operational speeds ranging from 1000 min−1 to 2500 min−1, and two oil levels, i.e. 10% and 100% of the bearing width. Pictures were captured using an High-Speed Camera (HSC) for a qualitative inspection. Particle Image Velocimetry (PIV) measurements were conducted for a quantitative assessment of the oil velocity fields. The findings reveal specific lubricant flows, highlight aeration, and show particular vorticity patterns that intensify with increasing speed. These experimentally obtained results align with Computational Fluid Dynamics (CFD) simulations conducted using a specially developed model in OpenFOAM®, leveraging a solver that accounts for aeration.

Flow data forecasting for the junction flow using artificial neural network

The present study aims to predict the flow characteristics downstream of a cylinder, which is the result of junction flow using an Artificial Neural Network (ANN) algorithm. The training and test datasets were obtained through Particle Image Velocimetry (PIV) experiments. The experiments were conducted at Reynolds numbers Re = 1.5 x 103 and 4 x 103 based on the cylinder diameter (D) at dimensionless measurement heights (Z = h/D) of Z1 = 0.06, Z2 = 0.4, Z3 = 0.8, and Z4 = 1.6 respectively. While the X- and Y-coordinate and dimensionless measurement location (Z) variables are employed as inputs to the ANN model, the output variables are vorticity ⟨ω⟩, streamwise velocity ⟨u⟩, and transverse velocity ⟨v⟩, which are derived from the time-averaged flow data. Modeling flow characteristics with easily obtainable independent variables without flow and physical properties was considered. Three various training algorithms such as Levenberg Marquardt (LM), Resilient Backpropagation (RP), and Scaled Conjugate Gradient (SCG) were employed to assess and compare their prediction performance. The results indicate that the LM learning algorithm outperforms the RP and SCG algorithms, especially at low Reynolds (Re) numbers. The ANN model, trained with the LM algorithm, exhibits significant success, achieving R = 0.9816 correlation coefficient (R), MAE = 2.4250 m/s Mean Absolute Error (MAE), and RMSE = 3.3541 m/s Root Mean Square Error (RMSE) for streamwise velocity ⟨u⟩ data. Notably, the LM algorithm for the testing process demonstrates the best predictions at Re = 1.5x103, yielding R = 0.9779, MAE = 2.7417 m/s, and RMSE = 3.7493 m/s. The ANN-LM model's patterns closely align with experimental results, affirming its accuracy, which proves that the prediction of time-averaged velocity data solely based on spatial coordinates as input can be achieved successfully.

On the role of temperature in the response of air-backed composites to hydrodynamic loading: An experimental study

Understanding the role of temperature in the dynamic response of composite plates is critical for naval systems operating in extreme environments like the Arctic. Despite the advantages of composite materials in improving corrosion resistance and enabling the customization of material properties to their environment, their behavior at cold temperature, especially under dynamic loading, remains elusive. This research gap hinders the effective use of composite materials in extreme environments. Here, we study the dynamic response of air-backed fiberglass epoxy plates under hydrodynamic loading at room temperature and 4∘C. By employing digital image correlation and particle image velocimetry, we investigated the interplay between fluid–structure interactions and cold temperatures. Our findings reveal the critical role of temperature in shaping the dynamic response of air-backed composites through changes in the stiffness and damping properties. At cold temperature, the plate experiences a larger (smaller) deformation in the initial (latter) phase of the dynamic response. Furthermore, we observed a pronounced coupling between the structural response and the flow physics, with peaks of the hydrodynamic loading synchronized with the peak deflections. Our results underscore the importance of considering temperature in the design of naval systems for extreme environments, providing key insights into fluid–structure interactions at cold temperature.

Continuous Casting Tundish Dead Volume Study by Physical Modeling and Computational Investigation

Flow efficiency in a two‐strand continuous casting tundish is studied by analyzing the residential time distribution (RTD) curves in a small‐scale tundish water model using a conductive NaCl solution tracer. The velocity fields in the tundish water model are measured by particle image velocimetry, which is used to validate the results of the mathematical model in the article. It is found that the tracer concentration has a significant impact on the predicted dead volume fraction in the RTD analysis. Validated mathematical modeling of the computational fluid dynamics (CFD) technology is performed to explore the root cause of the defective results in the RTD analysis. It is found that the flow inside the tundish is sensitive to density variations caused by the injected tracer. A denser tracer will stay lower in the tundish by gravity and flow out of the tundish more quickly. A proper tracer concentration in the water model experiments is discussed to visualize the dead volume and improve tundish furniture design efficiently for future work, a new method using CFD modeling is proposed in this article, which can directly demonstrate the dead volume's location.

Control of a Circular Jet with a Disk-Type Bluff Body Using a Dielectric Barrier Discharge Plasma Actuator

In this study, a disk-type bluff body was installed at the upper part of a nozzle exit, and the circular jet inside the nozzle was controlled using a dielectric barrier discharge (DBD) plasma actuator (DBD-PA). The effects of the changes in the excitation frequency of the jet induced by the DBD-PA on the jet diffusion were elucidated. The experiments included visualization of the jet cross-section, particle image velocimetry analysis, and velocity measurements using an I-type hot-wire anemometer. When the DBD-PA was driven at a specific burst frequency (900–1400 Hz), a lock-in phenomenon occurred, in which the frequency of vortices generated in the initial jet coincided with the burst frequency. This lock-in phenomenon suppressed the merging of vortices by generating vortices at regular intervals. When vortex merging was suppressed, the jet was less likely to be entrained into the recirculation flow generated by the bluff body, thereby increasing the downstream jet width and average flow rate.

Quantification of the hetero-contact formation process for a CuO/CeO2 hetero-aggregate model system prepared by double flame spray pyrolysis

In hetero-aggregates, different materials form sintered hetero-contacts, which lead to new material properties. In this study, the influence of process parameters on the formation of hetero-contacts in Double Flame Spray Pyrolysis (DFSP) was quantified. The mixing of jets was monitored by Particle Image Velocimetry (PIV) measurements as well as by thermocouples and compared to the single flame setting. Overlap of the jets was evaluated using tracers to visualize the mixing zone. Ten CuO/CeO2 model material samples were prepared with different flame inclination angles, nozzle distances and different particle volume fractions. Mixing on hetero-aggregate level was quantified using Convolutional Neural Network (CNN) evaluations of STEM images, Temperature-Programmed Reduction (TPR) and Differential Centrifugal Sedimentation (DCS) disk centrifugation to determine cluster sizes and hetero-coordination numbers as mixing quantifiers. Here, good correlations between the differently measured quantifiers were observed.

Comparison Study of Hydrodynamic Characteristics in Different Swimming Modes of Carassius auratus

This study utilized particle image velocimetry (PIV) to analyze the kinematic and hydrodynamic characteristics of juvenile goldfish across three swimming modes: forward swimming, burst and coast, and turning. The results demonstrated that C-shaped turning exhibited the highest speed, enabling rapid and agile maneuvers for predator evasion. Meanwhile, forward swimming was optimal for sustained locomotion, and burst-and-coast swimming was suited for predatory behaviors. A vorticity analysis revealed that vorticity around the tail fin was the primary source of propulsive force, corroborating the correlation between vorticity magnitude and propulsion found in previous research. The findings emphasize the crucial role of the tail fin in swimming efficiency and performance. Future research should integrate ethology, biomechanics, and physiology to deepen the understanding of fish locomotion, potentially informing the design of efficient biomimetic underwater robots and contributing to fish conservation efforts.

Flow Field Characteristics at the Spanwise Edge of a Vegetative Canopy Model

This study investigates the complex flow field across a spanwise vegetative model canopy edge focusing on turbulent transport processes. Utilizing stereoscopic particle image velocimetry, the three velocity components were measured in wall-parallel planes at various elevations within canopy across the spanwise canopy edge. Conventional ensemble averaged results were contrasted with those obtained by conditionally averaged flow properties across instantaneous internal interfaces in the flow to understand their contribution to the ensemble average. The conditional average captured the strong gradients in mean velocities, Reynolds stresses, vorticity, swirling strength, and turbulent kinetic energy production across the dynamically changing instantaneous interface. In contrast, the conventional ensemble average smeared out the strong gradients. Small magnitudes of advective terms in the turbulent kinetic energy transport equation suggested weak secondary transverse flows in the present model canopy. The turbulent flow structure across the spanwise canopy edge was further investigated using Quadrant-Hole analysis for both averaging approaches. Conventional ensemble averaged results indicated a shift from sweep to ejection dominance when moving from canopy into the open patch, while the conditional average showed only sweep dominated transport. In contrast to a homogeneous canopy layout, below canopy height at the canopy edge, sweeps and ejections lose their dominance in vertical turbulent transport. The present results show that the dynamics of internal interfaces govern the ensemble averaged results and a possible implementation into existing models is proposed. The present results are expected to increase understanding of spanwise turbulent transport and aid in developing strategies to mitigate desertification.

A study on the wake structure of an ascending submersible with silk flexible appendages using continuous wavelet transform and dynamic mode decomposition

This study proposed a new method for installing silk flexible appendages on the surface of the submersible to modify the wake structure of ascending submersibles, and explored a method of drag reduction of ascending submersible. A comparative analysis of the flow structure of submersibles with varying appendage lengths was conducted to understand the disturbance characteristics of the wake flow structure of submersible, and the high-speed particle image velocimetry (PIV) measurement experiment was conducted at a Reynolds number of 6456. Analysis of the time-averaged flow field showed that the flexible appendages could disrupt the two large-scale vortices in the wake of the submersibles during the sailing process, but this ability diminished with increasing appendage length. Furthermore, continuous wavelet transform (CWT) and dynamic mode decomposition (DMD) were used to analyze the mechanism behind this phenomenon. The analysis results showed that flexible appendages based on CWT had an inhibitory effect on large-scale flow, and this effect gradually decreased with increasing appendage length. The results indicate that the flexible appendages can disrupt the wake vortex structure, reduce vortex energy, and facilitate the transition from large-scale vortex to small-scale vortex. Additionally, excessive disturbance is generated in the wake region when the flexible appendage is too long, hindering the shedding of small-scale vortices and resulting in an increase.