Vortex Structures Research Articles

Quantum turbulence in superfluid helium: Decay and energy spectrum

The paper presents a comprehensive numerical study of the free decay of vortex tangle in superfluid helium. The initial vortex tangle represents one of the stationary configurations of loops in a counterflow with a laminar normal fluid component. The calculations are carried out in the framework of the vortex line method using the full Biot–Savart law over a wide range of temperatures. The aim of the study is to identify the role of various factors introduced into the numerical procedures (removal of small loops and segments during reconnections, the addition of and exclusion of vortex points on loops) and to determine the evolution of energy spectrum during the decay of quantum turbulence. A statistical approach is used to calculate the kinetic energy distribution on length scales. The calculations are carried out using periodic boundary conditions in a cube. The results show that, in agreement with the Feynman–Vinen theory, initially the rates of reduction in vortex line density at different temperatures are the same. However, when the vortex structure becomes rarefied, the influence of the mutual friction force becomes apparent, in agreement with Schwarz's theory. Statistical method for determining the energy spectrum is used. The Kolmogorov spectrum is not observed during decays at any temperature.

Hovering flapping wings with dynamic twist

The role of (active) dynamic wing twist on aerodynamic performance of three-dimensional hovering flapping flight is explored using numerical simulations. A variety of cases with different pitch angles and with (flexible wings) or without (rigid wings) dynamic twist are compared. The results show that changes in aerodynamic performance due to dynamic twist are comparable to those obtained without twist (rigid wing cases) by pitching the whole wing and that lift and lift-to-power ratio generally collapse onto a single curve when plotted as a function of the mid-stroke pitch angle at 2/3 wing radius. However, in some cases dynamic twist yields enhanced time-averaged efficiency. Using the force and power partitioning method, it is shown that this enhancement results from the absence of vortical structures near the wing root lower surface and to the presence of an extended leading edge vortex on the wing upper surface, when compared to the most efficient rigid wing case. These differences in flow topology lead to enhanced lift during the early phase of the strokes without changes in power consumption.

Coherent vortical structures in fluids and plasmas

Coherent vortical structures in fluids and plasmas

A conditional deep learning model for super-resolution reconstruction of small-scale turbulent structures in particle-Laden flows

Super-resolution reconstruction of turbulent flows using deep learning has gained significant attention, yet challenges remain in accurately capturing physical small-scale structures. This study introduces the Conditional Enhanced Super-Resolution Generative Adversarial Network (CESRGAN) for reconstructing high-resolution turbulent velocity fields from low-resolution inputs. CESRGAN consists of a conditional discriminator and a conditional generator, the latter being called CoGEN. CoGEN incorporates subgrid-scale (SGS) turbulence kinetic energy as conditional information, improving the recovery of small-scale turbulent structures with the desired level of energy. By being aware of SGS turbulence kinetic energy, CoGEN is relatively insensitive to the degree of detail in the input. As shown in the paper, its advantages become more pronounced when the model is applied to heavily filtered input. We evaluate the model using direct numerical simulation (DNS) data of forced homogeneous isotropic turbulence. The analysis of Q-criterion isosurfaces, energy spectra, and probability density functions shows that the proposed CoGEN reconstructs fine-scale vortical structures more precisely and captures turbulent intermittency better compared to the traditional generator. Particle-pair dispersion simulations validate the physical fidelity of CoGEN-reconstructed fields, closely matching DNS results across various Stokes numbers and filtering levels. This paper demonstrates how incorporating available physical information enhances super-resolution models for turbulent flows.

Study of unsteady shear flow near stall in a shrouded supercritical carbon dioxide centrifugal compressor

This study investigates the unsteady shear flow patterns and their relation with the aerodynamic instability of a shrouded supercritical carbon dioxide (SCO2) centrifugal compressor impeller using the dynamic mode decomposition method combined with detached eddy simulation. The results demonstrate that discrete shedding vortex array in the blade tip region is the dominant mode of the SCO2 shrouded centrifugal compressor impeller, with a frequency of 0.5 times the blade passing frequency. In contrast, the main flow structures in the identical impeller using ideal air consist of small-scale shedding vortices near the suction surface and the separated secondary flow. Further analysis of flow field details indicates that the shedding vortex structure inside the shrouded centrifugal impeller originates from the Kelvin–Helmholtz instability generated on the shear interface between the mainstream and the recirculation flow. The greater shear intensity within the SCO2 centrifugal impeller is the reason for the evident occurrence of vortex shedding phenomena in its flow field. Additionally, during the transition from near-stall to stall, vortex pairing phenomena happens at the throat of the centrifugal impeller due to evolutional behaviors of the vortexes. The occurrence of vortex pairing leads to faster blockage of the blade tip region and then the secondary flow spillage over to adjacent passage, ultimately resulting in reverse flow in the blade tip region and extensive blockage at the impeller inlet. The unsteady shear flow evolution clearly demonstrates the processes of stall in SCO2 shrouded impellers.

Study on micromechanical behavior and energy evolution of granular material generated by latent diffusion model under rotation of principal stresses

In this study, advanced image processing technology is used to analyze the three-dimensional sand composite image, and the topography features of sand particles are successfully extracted and saved as high-quality image files. These image files were then trained using the latent diffusion model (LDM) to generate a large number of sand particles with real morphology, which were then applied to numerical studies. The effects of particle morphology on the macroscopic mechanical behavior and microscopic energy evolution of sand under complex stress paths were studied in detail, combined with the circular and elliptical particles widely used in current tests. The results show that with the increase of the irregularity of the sample shape, the cycle period and radius of the closed circle formed by the partial strain curve gradually decrease, and the center of the circle gradually shifts. In addition, the volume strain and liquefaction strength of sand samples increase with the increase of particle shape irregularity. It is particularly noteworthy that obvious vortex structures exist in the positions near the center where deformation is severe in the samples of circular and elliptical particles. However, such structures are difficult to be directly observed in sample with irregular particles. This phenomenon reveals the influence of particle morphology on the complexity of the mechanical behavior of sand, providing us with new insights into the understanding of the response mechanism of sand soil under complex stress conditions.

Novel passive flow control method using leading-edge prism-shaped cylinder: Performance enhancement of vertical-axis wind turbines

Due to periodic dynamic stall at low tip speed ratios (TSRs), vertical-axis wind turbines (VAWTs) experience notable performance challenges during rotation, which leads to fluctuations in torque and a decrease in energy capture. This research aims to boost the aerodynamic performance of Darrieus VAWTs by employing a leading-edge (LE) prism cylinder (PC) to enhance energy extraction. This novel small-scale device functions as a passive method for controlling flow separation, aiming to energize the boundary layer and adjust the pressure distribution on the blades. Its effectiveness depends on factors such as size, shape, and placement, necessitating careful optimization. A three-dimensional (3D) computational fluid dynamics (CFD) analysis, combined with Taguchi optimization and analysis of variance, is conducted to determine the optimal design parameters for the LE PC tool. This 3D CFD method captures the full complexity of flow dynamics, including vortex structures and wake behavior, leading to more accurate wind turbine performance predictions than two-dimensional (2D) CFD models. The results highlight the crucial role of PC size (Factor A), which contributes nearly 85% to the total contribution factor, while the angle of PC influence is minimal. The optimized rotor demonstrates a 36% increase in maximum average power coefficient (CP) compared to an uncontrolled rotor at TSR = 1.5. However, the effectiveness of this control method diminishes at higher TSRs because the blades encounter angles of attack below the critical stall angle throughout the rotation cycle, naturally preventing flow separation and making the flow separation control method unnecessary. The PC installed on the optimized blade delays flow separation to 55% of the blade chord length, compared to 40% for the base blade. Consequently, the rotor operates efficiently, ensuring consistent, and reliable power generation without flow separation issues.

Impact of density ratio on droplet dynamics in pulsating flow

Secondary atomization is extensively studied by investigating a droplet subjected to a steady air/gas stream. However, droplets are often subjected to unsteady or pulsating flows, such as in aero-engines or rockets, because of thermo-acoustic instabilities in the combustion chambers. The investigation focuses on the droplet dynamics and breakup in a pulsating flow for a range of density ratios (ρr), 1000 to 10, under sinusoidal airflow of different amplitudes and frequencies as compared to the dynamics in a steady flow. The volume of fluid multiphase model tracks the liquid–gas interface, and the governing equations are solved using the finite volume method. The two-dimensional axisymmetric pulsating simulations demonstrate accuracy comparable to the corresponding three-dimensional simulations at a much lower computational cost and are used for parametric studies. The droplets under the pulsating flow show a wavy surface, and larger vortex structures are observed during the deceleration period. At a high-density ratio (1000), pulsating flow enhances droplet deformation for a faster breakup, with the flow amplitude having more impact than its frequency. For a medium-density ratio (100), where breakup occurs under steady flow, droplet breakup is inhibited in the pulsating flow at low amplitude and high frequency. In the case of a low-density ratio (10), there is no breakup under steady flow, but pulsating flow promotes breakup, except at low amplitude and high frequency. The droplet breakup is always achieved for the highest amplitude, while lower frequencies push the liquid mass from the center of the droplet to the rim.

Inner–outer interaction of unsteady turbulent flow inside duct with wall corrugations: Augmentation and saturation

This study investigates the inner–outer interaction of the unsteady turbulent flow inside a duct with wall corrugations, where “inner” refers to the trapped flow in a corrugation-induced cavity array and “outer” relates to the mainstream flow transporting through a circular duct. Configurations with different pitch–diameter ratios (P/D) are used to demonstrate the effect of the cavity flow pattern on the mainstream flow variations. An improved delayed detached-eddy simulation with dynamic blending function is performed to acquire high-fidelity turbulent flow data, in which dynamic evolution of multi-scale vortex structures containing hairpin vortices and vortex fragments is clearly resolved. The subsequent statistical analysis reveals a nonlinear variation tendency of the inner–outer interaction intensity, experiencing sudden augmentation first and then a gradual attenuation toward the final saturation. Comparatively, a larger pitch ratio results in a stronger interaction under the effect of bicentric recirculation zones within the cavity array. Moreover, a proper orthogonal decomposition analysis allows for the visualization of energetic flow structures, as consistent velocity variations throughout the duct volume are identified for a larger pitch ratio, while discontinuity at the duct termination is found for a smaller pitch ratio. Finally, an advanced elliptical model based on the spatiotemporal cross correlation analysis is proposed to examine the convection velocity and sweeping velocity of the interactive mainstream flow and cavity flow. The results highlighted the presence of first-augmented and then saturated dynamics and kinematics inside the duct with the cavity array.

Numerical study of transition hydraulic jumps in different types of stilling basins using lattice Boltzmann methods

Transition hydraulic jumps, also known as low-Froude number jumps, have been less studied compared to high Froude number jumps, despite their significance in high-discharge and low-head dams. A three-dimensional (3D) Lattice Boltzmann method simulation was conducted to investigate submerged transition hydraulic jumps in both normal and expanded stilling basins, focusing on turbulent flow characteristics such as velocity fields, vorticity features, pressure fluctuations, and coherent structures. In expanded basins, two symmetric separated rollers were observed, with the rollers detaching from the submerged jump as the width of basin increased. The length of submerged roller in normal basins is observed as Lr/Ht = 6.19, while it is decreased to Lr/Ht = 4 in expanded basins because of the occurrence of roller lateral diffusion toward sidewalls. The transition of vortex structures from y- to z-vortical was analyzed, and three-dimensional shear layers are captured using the iso-surface of vorticity magnitude ω = 6.5. To further describe the internal structure of turbulence within the transition hydraulic jump, the coherent flow structures are qualitatively examined using the Ω criterion that is the third generation of vortex identification technique. Pressure fluctuations in low-Froude number stilling basins, described using root mean square (RMS), are first presented. High patches of RMS are found in the flow fields and at the bottom of basins, and it is qualitatively noted that shear effects make great contributions to the pressure fluctuations. Distribution of bottom pressure fluctuation RMS in different types of basin was also analyzed. The peak RMS value occurs at the ogee region of the weir, specifically at x/L = −0.2, and it is mainly affected by the width of expansion. Bottom pressure fluctuation RMS decreases in the following order: Normal, 5 m gradual expansion, 10 m gradual expansion, 5 m sudden expansion, and 10 m sudden expansion, due to the lateral diffusion of rollers toward sidewalls. This research introduces an innovative numerical simulation approach to studying pressure fluctuations, offering valuable insights for hydraulic engineering applications.

Near wake evolution of a tidal stream turbine due to asymmetric sheared turbulent inflow with different integral length scales

Tidal stream turbines deployed at highly energetic open water sites are subjected to sheared inflow in the rotor plane. The inflow shear is expected to cause asymmetric loading on the rotor blades and affect the downstream wake. In the current study, two different turbulent inflow conditions, static-high shear and dynamic shear, were generated via an active-grid turbulence generator. A 1:20 scaled three-bladed horizontal axis tidal turbine model was tested in those conditions. The results were compared to a quasi-laminar case with no imposed turbulence or shear. The results show that the high shear reduces the average performance, with a drop of up to 16% in the optimal power coefficient. Besides, the shear profiles increase torque fluctuations and induce significant differences in wake hydrodynamics between the high-speed (upper) and low-speed (lower) regions. The large integral length scales further enhance the load fluctuations perceived by the rotor but have a negligible effect on the mean wake field quantities. The wake recovery was found to be ∼2 to 4 times faster in the upper half region than in the lower region in the near wake. The lower half region featured a faster breakdown of tip vortex structure and a rapid drop of swirl number, a phenomenon conjectured to be a consequence of the strong turbulence intensities and Reynolds stresses in the lower half region. The sheared turbulent inflow also results in a very intensive energy redistribution process towards large-scale, low-frequency motions, which is important to the downstream turbines.

Influence of porous material on the flow behind a backward-facing step: experimental study

We investigate effect of porous insert located upstream of the separation edge of a backward-facing step (BFS) in early transitional regime as a function of Reynolds number. This is an example of hydrodynamic system that is a combination of separated shear flow with large amplification potential and porous materials known for efficient flow destabilisation. Spectral analysis reveals that dynamics of BFS is dominated by spectral modes that remain globally coherent along the streamwise direction. We detect two branches of characteristic frequencies in the flow and with Hilbert transform we characterise their spatial support. For low Reynolds numbers, the dynamics of the flow is dominated by lower frequency, whereas for sufficiently large Reynolds numbers cross-over to higher frequencies is observed. Increasing permeability of the porous insert results in decrease in Reynolds number value, at which frequency cross-over occurs. By comparing normalised frequencies on each branch with local stability analysis, we attribute Kelvin–Helmholtz and Tollmien–Schlichting instabilities to upper and lower frequency branches, respectively. Finally, our results show that porous inserts enhance Kelvin–Helmholtz instability and promote transition to oscillator-type dynamics. Specifically, the amplitude of vortical (BFS) structures associated with higher-frequency branch follows Landau model prediction for all investigated porous inserts.

LOSS BREAKDOWN IN AXIAL TURBINES: A NEW METHOD FOR VORTEX LOSS AND WAKE DETECTION FROM 3D RANS SIMULATIONS

Abstract To enhance turbine efficiency, it is essential to mitigate the losses generated by irreversible phenomena in turbine flows, including boundary layers, shock waves, vortices, and trailing edge wakes. Fast and accurate detection of losses is crucial from the earliest design stages, where reduced-order models based on oversimplified correlations are employed. This requires a deep understanding of the physics behind loss-generating mechanisms, attainable by examining the 3D flow. While existing criteria can identify various phenomena, accurately quantifying vortex-generated losses remains challenging, as these losses frequently extend beyond the vortical structure. This paper provides a straightforward and effective approach to localize and assess vortex-related losses. The method is grounded in Zlatinov's decomposition of the entropy generation rate into a streamwise and secondary flow component. A criterion based on vortex kinematics evaluates the vortex's strength, enabling the determination of its spatial influence and contribution to overall losses. To validate the method, a post-processing code is developed to perform loss breakdown, using existing identification criteria and new techniques introduced within this work, particularly for wake detection. 3D RANS simulations on various configurations, from simple curved ducts to nozzle guide vanes, allow to gradually test and validate the computational tool. Results confirm that the highest entropy generation rates occur outside the vortical structure and show good ability to identify both the vortex shape and its area of influence in terms of losses. A significant improvement in predicting vortex losses is observed, especially for turbine blades with leakage vortices.

Connectivity between the solar photosphere and chromosphere in a vortical structure

Context. High-resolution solar observations have revealed the existence of small-scale vortices, as seen in chromospheric intensity maps and velocity diagnostics. Frequently, these vortices have been observed near magnetic flux concentrations, indicating a link between swirls and the evolution of the small-scale magnetic fields. Vortices have also been studied with magneto-hydrodynamic (MHD) numerical simulations of the solar atmosphere, revealing their complexity, dynamics, and magnetic nature. In particular, it has been proposed that a rotating magnetic field structure driven by a photospheric vortex flow at its footprint produces the chromospheric swirling plasma motion. Aims. We present a complete and comprehensive description of the time evolution of a small-scale magnetic flux concentration interacting with the intergranular vortex flow and affected by processes of intensification and weakening of its magnetic field. In addition, we study the chromospheric dynamics associated with the interaction, including the analysis of a chromospheric swirl and an impulsive chromospheric jet. Methods. We studied observations taken with the CRisp Imaging SpectroPolarimeter (CRISP) instrument and the CHROMospheric Imaging Spectrometer (CHROMIS) at the Swedish Solar Telescope (SST) in April 2019. The data were recorded at quiet-Sun disc centre, consisting of full Stokes maps in the Fe I line at 6173 Å and in the Ca II infrared triplet line at 8542 Å, as well as spectroscopic maps in the lines of Hα 6563 Å and Ca II K 3934 Å. Utilising the multi-wavelength data and performing height-dependent Stokes inversion, based on methods of local correlation tracking and wavelet analysis, we studied several atmospheric properties during the event lifetime. This approach allowed us to interpret the spatial and temporal connectivity between the photosphere and the chromosphere. Results. We identified the convective collapse process as the initial mechanism of magnetic field intensification, generating a re-bound flow moving upwards within the magnetic flux concentration. This disturbance eventually steepens into an acoustic shock wave that dissipates in the lower chromosphere, heating it locally. We observed prolonged magnetic field amplification when the vortex flow disappears during the propagation of the upward velocity disturbance. We propose that this type of magnetic field amplification could be attributed to changes in the local vorticity. Our analysis indicates the rotation of a magnetic structure that extends from the photosphere to the chromosphere, anchored to a photospheric magnetic flux concentration. It appears to be affected by a propagating shock wave and its subsequent dissipation process could be related to the release of the jet.

Analysis of Unsteady Flow and Interstage Interference of Pressure Pulsation of Two-Stage Pump as Turbine Under Turbine Model

The process pump as turbine (PPAT) serves as a crucial component for recovering high-pressure energy from mediums used in chemical and refining processes. Ensuring the long-term safe and stable operation of PPAT in high-temperature and high-pressure environments is essential, with pressure pulsation being one of its most significant external characteristic indicators. This study investigates the evolution of vortex structure distribution and the generation and propagation mechanisms of pressure pulsation in a two-stage PPAT operating in turbine mode. Results indicate that the uniformity of the pressure coefficient (Cp) gradient distribution is poorer in the first stage runner compared to the second stage, with a larger distribution area of high-strength vortices. In the draft tube, vortex strength increases with rising flow rates, and the flow around the circular cylinder on one side gradually develops to both sides. In the two-stage diffusers, the primary source of pressure pulsation is the dynamic and static interference effect between the two impellers and the corresponding diffuser tongue. The interstage interference with a frequency of n*15fn is most pronounced in the inflow runner, gradually weakening along the flow direction, and ultimately disappearing in the draft tube. In addition, more low-frequency signals with a frequency of 0.5fn are captured in the draft tube under large flow conditions, which is mainly generated by the vortex band in the draft tube. The low-frequency pulsation energy is high and the attenuation is slow, which has a great destructive effect on the energy recovery system of the PPAT.

Simulation Analysis of 3-D Airflow and Temperature Uniformity of Paddy in a Laboratory Drying Oven.

This study analyzed the effects of airflow characteristics on the temperature distribution and drying uniformity of paddy during convective drying. Simulations of the drying process with varying airflow inlet and outlet positions were conducted using COMSOL Multiphysics 6.1 software. The determination coefficient (R2) between the simulated data and experimental values of Sample1 (S1), Sample2 (S2), and Sample3 (S3) was calculated, and its average values were 0.964, 0.963, 0.963, and 0.967, respectively. This study demonstrates that the airflow direction and outlet location have a significant impact on the temperature uniformity of the paddy. The vortex structure generated by the obstruction of the sidewalls and paddy influences both the airflow and temperature distribution within the drying chamber. When the outlet was on the left side and the inlet airflow was in a vertical orientation (VO), the temperature distribution of the paddy exhibited higher temperatures in the edge regions and lower temperatures in the center, with a maximum temperature difference of around 16 °C. The time required for the temperature to reach equilibrium with the outlet positioned on the left was 28.6% shorter than with the outlets positioned in the center or on both sides. Moreover, the temperature uniformity of the three paddy samples was better under this condition. The developed model accurately reflected the paddy drying process. It could also be used to analyze the optimal heating uniformity, providing a technical basis for the design of grain dryers.

Numerical study on the combustion characteristics and performances of single and multi-injectors in a scramjet combustor

The present study numerically investigates the combustion characteristics and performance of a direct-connect gaseous hydrogen-fueled scramjet combustor depending on the injector scheme. A comprehensive numerical simulation was conducted with an improved delayed detached eddy simulation (IDDES) approach. The framework utilized a high-order accurate numerical scheme to ensure the high fidelity of the results. A total of ten cases were considered combining two injector schemes and five injection pressure conditions. Each injector scheme had a similar range of global equivalence ratios. Numerical results revealed the differences in the local dynamics of the counter-rotating vortex pair. The multi-injector case did not maintain the jet's systemic vortex structure, which plays a primary role in the fuel-air mixing and burning. It owes to the interactions between the jet-jet and the jet-wall surface, where the interaction leads to the loss of momentum. This characteristic of the multi-injector makes the fuel-air mixing contact surface get closer to a thin-flat layer, resulting in the flame being anchored on a flat shear layer over the entire combustor. As a result, the combustion efficiency of the multi-injector is much lower than that of the single injector under a similar equivalence ratio range. Present results indicate that the multi-injector, which is expected to increase the combustion performance by maximizing the fuel-air contact surface, may operate in contrast to its original anticipation under certain configurations and conditions. It also suggests that optimizing the combustion performance requires careful design of injector distributions considering the distances and interactions between injector-to-injector and injector-to-wall.

Application of partial wave analysis in multiphoton pair production

Electron-positron pair production is investigated in the multiphoton regime under polarized fields. Partial wave analysis can be applied to reveal the momentum spectral structure and identify the positions of valleys/peaks of the multiphoton rings by combining with CP conservation. Moreover, considering the spin states of created pairs in partial wave analysis, the particle orbital angular momentum associated with the valleys/peaks can also be identified from multiphoton rings. It is found that the approximate analytical treatments for angular distribution by using partial wave analysis are consistent with those of the numerical calculation using the Dirac-Heisenberg-Wigner formalism. The results are helpful for understanding the angular momentum information in momentum spectra, and they also have an implication for revealing the vortex structure near the valleys where the amplitude nearly vanishes. Published by the American Physical Society 2024

Large-eddy simulation of tip clearance cavitating flow around a hydrofoil

Large-eddy simulations of tip clearance cavitating flow between a National Advisory Committee for Aeronautics 0012 hydrofoil and the endwall have been performed to investigate the effects of cavitation on vortical structures, turbulence statistics and hydrofoil performance within the tip clearance region. The wall-adapting local eddy-viscosity model is employed to compute the subgrid-scale stress, and the Zwart-Gerber-Belamri cavitation model is used to predict the cavitating flow. The simulation results show that cavitation has insignificant effects on the tip clearance flow structures and the wandering motion of the tip leakage vortex (TLV). Detailed analysis of turbulence statistics indicates that the turbulent kinetic energy and pressure fluctuation inside the TLV core are significantly increased under the effect of cavitation. In addition, it is found that cavitation enhances the unstable wall-normal motion of the TLV, leading to the enhancement of turbulence near the TLV core. The hydrofoil performance affected by cavitation is also investigated, showing that the lift and drag forces acting on the hydrofoil is substantially reduced due to the cavitation.

Study on vortex structure and hydrodynamic characteristics of water-exit projectile with shoulder ventilation

During the vertical motion of a water-exit projectile, the gas stored inside is expelled from the shoulder under the effect of pressure differential, forming a ventilated cavity covering the surface of the projectile. This paper explores the vortex structure characteristics of the surface ventilated cavity through numerical simulation and summarizes its impact on the hydrodynamic characteristics of the water-exit projectile. It was found that the end of the shoulder ventilated cavity presents a periodic vortex shedding form. And the existence of the shoulder ventilated cavity can reduce the vertical resistance of the projectile, improve the vertical movement speed, and play a role in load reduction and drag reduction. Additionally, the lateral displacement of the projectile at the moment of water exit decreases by approximately 45.2%, and the deviation angle reduces by about 55.6%, significantly improving the stabilization of its water exit posture. This indicates that the presence of the shoulder ventilated cavity can effectively enhance the hydrodynamic performance of the projectile.