Leading Edge Region Research Articles

Endwall film-cooling in a cascade with filleted vane, upstream discrete slots, and holes

ABSTRACT In vane cascades, large filleted vanes influence aerodynamics, while upstream endwall film-cooling arrangement impacts aero-thermal performance. This study explores experimental investigations on endwall flows and film-cooling effectiveness in a filleted vane cascade using discrete slots and holes. Two fillet profiles are examined covering the leading-edge area to either the throat or 62% of the axial chord. Film-cooling employs two slots and two rows of holes in the leading-edge region with inlet blowing ratios ranging from 1.0 to 2.8. Results show variations in total pressure loss and Nusselt number between filleted and un-filleted vanes, highlighting optimal film-cooling effectiveness with the smaller fillet profiles.

Aerodynamic performance evaluation of subsonic compressor cascade blade with leading-edge damage

Abstract Material loss at the leading edge of in-service gas-turbine engine blades is detrimental to the aerodynamic performances of compressors. In this study, computational simulations and experiments using pneumatic probes were conducted to measure the total pressure loss of compressor cascade blades with material loss at their leading edges. The correlations between blade leading-edge damage geometries and cascade blade total pressure losses were analyzed. The geometrical features of blade leading-edge damage that most affect the cascade blade total pressure loss were distinguished, and the influences of leading-edge damage region cross-sectional shapes on the cascade blade total pressure loss were examined. Two methods for evaluating the total pressure loss of damaged cascade blades were developed using experimental and numerical data. In the first method, an attempt is made to correlate the cascade blade total pressure loss with a characteristic parameter that is defined using scale and angle parameters of the leading-edge damage region. The second method is based on the probability distribution function as well as the critical loss boundary of the geometrical parameters of the leading-edge damage region. The results of this study provide a better understanding of the influence of damaged leading edges on compressor cascade blade aerodynamic performance and can help establish low-cost methods for the estimation of compressor performance degradation.

Modified Target Pressure Distribution for Supersonic Natural Laminar Flow Wing Design

Natural laminar flow (NLF) is an important technique for reducing drag of the next-generation supersonic transport aircraft. However, achieving NLF on supersonic transport wings is challenging due to the large swept angles and high-Reynolds-number conditions, which significantly amplify Tollmien–Schlichting (TS) and crossflow (CF) instabilities. To address this problem, this paper proposes a modified target pressure distribution to attenuate the TS and CF instabilities. Compared with conventional targets defined using empirical functions, it is derived in two steps: the first step is to prescribe an initial flat target pressure distribution with a narrow leading-edge flow acceleration region and conduct inverse designs; the second step is to modify the target pressure distribution according to the stability analysis results of the designed wing in order to achieve a balance of disturbance growth at positive and negative wave angles. The proposed approach is validated on a 60°-swept infinite-span wing at Ma=2 and Re=1.39×107. Results demonstrate that TS and CF instabilities are well-suppressed under the modified target pressure distribution, with the transition location delayed from xtr/c=0.26 on the baseline wing to xtr/c=0.95 on the designed wing, suggesting that the proposed method is effective for NLF design on supersonic highly swept wings.

A new approach to account for turbulence distortion effect on Amiet's leading-edge noise prediction

A turbulent inflow distorts as it approaches an airfoil's leading edge (LE), which is an important phenomenon influencing the airfoil LE noise. This mechanism is not yet fully understood and is not accounted for in Amiet's theory for LE noise. Thus, the main contribution of this paper is to discuss a possible new approach to account for turbulence distortion in Amiet's LE noise model. The analysis is based on wind tunnel experiments performed for four NACA airfoil geometries. Hot-wire anemometry and a microphone array were used to evaluate the turbulence in the LE region and the radiated noise, respectively. Turbulent inflow was generated with a rod and a grid. Based on the measured turbulence data, a formulation that describes the turbulence length scale near the airfoil LE is introduced, which yields more accurate noise predictions when used in combination with Amiet's model. The proposed approach to estimate LE noise consists of using an appropriate turbulence spectrum formulation for the distorted turbulence and the proposed expression to determine the turbulence length scale near the airfoil LE, yielding a maximum discrepancy between measured and predicted LE noise of 4dB for a rod Strouhal number from 0.3 to 3.

Enhanced cooling performance of blade tip slot cooling: Effect of slot open length

Addressing the critical challenge of thermal load-induced damage in turbine blade tips, this study aims to elucidate the effects of slot open length on film cooling effectiveness (FCE) across turbine blade tips with Pressure Side (PS) and Suction Side (SS) slots considering the application of additive manufacturing to turbine blade tips. Employing a linear cascade setup and the pressure sensitive paint (PSP) technique, we examined and quantified cooling performance across turbine blade tips with PS or SS slots at various slot open lengths. We revealed that while short slot open lengths enhance FCE at the leading edge (LE) due to increased averaged blowing ratios, they fail to adequately cover the trailing edge (TE) region. This decrease in cooling performance is largely attributable to the mixing of coolant with hot gas. In contrast, longer slot open lengths achieve a consistent FCE distribution across the blade tip despite a slight decrease in FCE at the LE region. The study suggests that integrating additional thermal design strategies, such as partition walls with slots, could effectively manage hot gas behaviors, thus enhancing the overall cooling design of turbine blade tips. This research makes a significant contribution to the field of turbine blade tip cooling design, providing insights into optimizing cooling performance through advanced slot configurations enabled by additive manufacturing technologies.

Attenuation of boundary-layer instabilities for natural laminar flow design on supersonic highly swept wings

To meet the challenge of drag reduction for next-generation supersonic transport aircraft, increasing attention has been focused on Natural Laminar Flow (NLF) technology. However, the highly swept wings and high-Reynolds-number conditions of such aircraft dramatically amplify Crossflow (CF) instabilities inside boundary layers, making it difficult to maintain a large laminar flow region. To explore novel NLF designs on supersonic wings, this article investigates the mechanisms underlying the attenuation of Tollmien–Schlichting (TS) and CF instabilities by modifying pressure distributions. The evolution of TS and CF instabilities are evaluated under typical pressure distributions with different leading-edge flow acceleration region lengths, pressure coefficient slopes and pressure coefficient deviations. The results show that shortening the leading-edge flow acceleration region and using a flat pressure distribution are favorable for suppressing CF instabilities, and keeping a balance of disturbance growth between positive and negative wave angles is favorable for attenuating TS instabilities. Based on the uncovered mechanisms, a strategy of supersonic NLF design is proposed. Examination of the proposed strategy at a 60° sweep angle and Ma = 2 presents potential to exceed the conventional NLF limit and achieve a transition Reynolds number of 17.6 million, which can provide guidance for NLF design on supersonic highly swept wings.

Dissecting tumor microenvironment from spatially resolved transcriptomics data by heterogeneous graph learning

Spatially resolved transcriptomics (SRT) has enabled precise dissection of tumor-microenvironment (TME) by analyzing its intracellular molecular networks and intercellular cell-cell communication (CCC). However, lacking computational exploration of complicated relations between cells, genes, and histological regions, severely limits the ability to interpret the complex structure of TME. Here, we introduce stKeep, a heterogeneous graph (HG) learning method that integrates multimodality and gene-gene interactions, in unraveling TME from SRT data. stKeep leverages HG to learn both cell-modules and gene-modules by incorporating features of diverse nodes including genes, cells, and histological regions, allows for identifying finer cell-states within TME and cell-state-specific gene-gene relations, respectively. Furthermore, stKeep employs HG to infer CCC for each cell, while ensuring that learned CCC patterns are comparable across different cell-states through contrastive learning. In various cancer samples, stKeep outperforms other tools in dissecting TME such as detecting bi-potent basal populations, neoplastic myoepithelial cells, and metastatic cells distributed within the tumor or leading-edge regions. Notably, stKeep identifies key transcription factors, ligands, and receptors relevant to disease progression, which are further validated by the functional and survival analysis of independent clinical data, thereby highlighting its clinical prognostic and immunotherapy applications.

Reynolds number sensitivity of the vortex dynamics around a long-span rail-cum-road bridge girder with three separated boxes

The novel separated three-box girder is gradually adopted for very long-span cable-stayed bridges due to its excellent flutter stability. Due to its special design of cross section, it exhibits notable Reynolds number effects in the flow patterns and vortex dynamics when subject to incoming flow. To explore its Reynolds number sensitivity, this paper performs a three-dimensional large eddy simulation (LES) on the flow around a static long-span rail-cum-road bridge girder with three separated boxes at different Reynolds numbers. The overall centre height H of the bridge model is chosen as the characteristic length, and the investigated Reynolds number regime falls into the regime of 1e2≤Re≤2.8e4. Through the analysis of the flow characteristics of three distinct regions in the flow field(the windward leading edge region, the gap region and the wake region), a successive transition of the wake flow, gap flow, and leading edge shear flow is observed with increasing Reynolds number. The surrounding flow patterns are divided by different Reynolds number regimes as: laminar separation at the trailing edge (Re<5e2); simultaneous instability of the gap shear layer and the wake (5e2≤Re<1e3); restabilisation of the upstream gap shear layer (1e3≤Re<3e3); secondary instability of the upstream gap shear layer and transition of the wake (3e3≤Re<8e3); transition of the separated shear layer at the leading edge (8e3≤Re≤2.8e4). This paper reveals in detail the complex vortex dynamics in the surrounding flow field of the special cross section with three separated boxes.

Validation of a RANS Turbulence Model for a S833 Wind Turbine Airfoil With a Trailing Edge Flap Using Oil Visualization and Pressure Taps

Abstract The aerodynamics of a small wind turbine blade was captured using a γ–Reθ k–ω shear stress transport transitional turbulence model tuned with production limiter coefficients at a Reynolds number of 1.70×105. The computational fluid dynamics simulations were validated against wind tunnel experiments that included airfoil pressure tap measurements and surface oil flow visualization (SOFV) to capture the flow field. The uniqueness of this blade included a trailing edge flap that was 20% of the chord controlled using a servomotor. The test matrix included angles of attack (AOA) between 1 deg and 7 deg with flap angles of 10 deg in the upward and downward position. Two locations were always observed on the airfoil: a leading edge region of high shear and a midsection of flow separation. Within the flow separation section, two distinct regions existed: a complete detachment of flow from the airfoil surface creating a stagnation region which was followed by a reverse flow region. A third location of flow reattachment near the trailing edge was observed for all cases excluding a downward angled trailing edge flap. The utilization of the flap resulted in changes to the size of the separation zone and the movement of the separation zone along the chord. The numerical skin friction coefficient, oil residue profiles from the SOFV, and pressure tap measurements all showed onset of separation locations on the chord within 10%. The computational fluid dynamics model also predicted the coefficient of pressure across the chord of the airfoil within 10% in comparison to the experimental measurements.

Effects of Flow Pulsation and Surface Geometry On Heat Transfer Performance in a Channel with Teardrop-Shaped Dimples Measured by Transient Technique

Abstract This study focuses on the heat transfer performance of a pulsating flow over a channel surface with teardrop-shaped dimples. Heat transfer measurements were performed by a transient technique with compensation of three-dimensional heat conduction under a bulk Reynolds number of 25,000. Seven types of surfaces with the teardrop-shaped dimples were examined, where dimple arrangement (in-line/staggered) and inclination angle (0-60 deg) were varied. A pulsating flow with the Strouhal number of 0.15 was generated by vibrating a rubber film section on the channel wall using a vibration generator. The pulsation amplitude was evaluated by calculating the root-mean-square value of the phase averaged velocity. Two conditions of the pulsation amplitudes were examined (0.09 and 0.12 of mean velocity). The results showed that the surface-averaged Nusselt number and friction factor for the pulsating flow increased from those for the steady flow. The highest increases of the surface-averaged Nusselt number and heat transfer efficiency index appeared in the 30deg in-line arrangement, and those were 16.1% and 9.8%, respectively, at most as compared with the steady case. Due to the flow pulsation, the local Nusselt number was enhanced at the leading-edge region of the dimples, and supplementary RANS/URANS results showed that the flow separation size was shrunk by the flow pulsation there.

Effects of Flow Pulsation and Surface Geometry on Heat Transfer Performance in a Channel With Teardrop-Shaped Dimples Investigated by Large Eddy Simulation

Abstract Large eddy simulation was performed to investigate heat transfer performance of a pulsating flow over teardrop-shaped dimples. A total of six geometries of dimpled surfaces were examined for dimple arrangements of in-line/staggered/original and dimple inclination angle of 0–60 deg. Pulsating flows were generated by sinusoidally varying the volume-averaged velocity. The pulsation frequency and amplitude were changed for the Strouhal number of 0–0.60 and the root-mean-square velocity amplitude normalized by the bulk flow velocity of 0–0.14. The results showed that the surface-averaged Nusselt number and friction factor were larger for the pulsating flow case than for the steady flow case. The surface-averaged Nusselt number ratio and the friction factor increased with the Strouhal number up to the Strouhal number of 0.30. For the Strouhal number larger than 0.30, they decreased with the Strouhal number or stayed almost constant. Consequently, the heat transfer efficiency index increased with the Strouhal number. The increase in the local Nusselt number ratio due to the flow pulsation was observed at the leading-edge region of the dimples. The results of the streamlines near the dimple showed that the swirling separation bubble was located closer to the leading-edge region due to the pulsation, which resulted in the increase of the absolute values of the turbulent heat flux and the local Nusselt number ratio.

ViCTORIA project: The LOFAR view of environmental effects in Virgo cluster star-forming galaxies

Context. Environmental effects such as ram pressure stripping (RPS) shape the evolution of galaxies in dense regions. Aims. We used the nearby Virgo cluster as a laboratory to study the environmental effects on the nonthermal components of star-forming galaxies. Methods. We constructed a sample of 17 RPS galaxies in the Virgo cluster and a statistical control sample of 119 nearby galaxies from the Herschel Reference Survey. All objects in these samples were detected in LOFAR 144 MHz observations and come with Hα and/or far-UV star formation rate (SFR) estimates. Results. We derived the radio–SFR relations, confirming a clearly super-linear slope of ≈1.4. We found that Virgo cluster RPS galaxies have radio luminosities that are a factor of 2−3 larger than galaxies in our control sample. We also investigated the total mass-spectral index relation, where we found a relation for the Virgo cluster RPS galaxies that is shifted to steeper spectral index values by 0.17 ± 0.06. Analyzing the spatially resolved ratio between the observed and the expected radio emission based on the hybrid near-UV + 100 μm SFR surface density, we generally observed excess radio emission all across the disk with the exception of a few leading-edge radio-deficient regions. Conclusions. The radio excess and the spectral steepening for the RPS sample could be explained by an increased magnetic field strength if the disk-wide radio enhancement is due to projection effects. For the galaxies that show the strongest radio excesses (NGC 4330, NGC 4396 and NGC 4522), a rapid decline in the SFR (tquench ≤ 100 Myr) could be an alternative explanation. We disfavor shock acceleration of electrons as a cause for the radio excess since it cannot easily explain the spectral steepening and radio morphology.

Aerodynamic design of a high-efficiency two-stage axial turbine, using streamline curvature method and performance optimisation by clocking of stator blades

Abstract Aerodynamic design of a high-efficiency two-stage axial turbine is carried out using a hybrid method through implantation of a two-step design procedure. In the first step, the well-known streamline curvature (SLC) and free vortex (FV) methods are properly combined to establish three-dimensional geometries of the blades at each row and to obtain the flow field properties. The second step is provided to obtain the highest aerodynamic efficiency by optimum clocking of the second stator blades relative to the first ones through executing steady and unsteady computational fluid dynamics (CFD) of three-dimensional viscous flow. Slight discrepancies were observed between gas dynamics results of the SLC and those of CFD. Total pressure and temperature at the turbine outlet, obtained from SLC method, differed from those obtained by 3D-CFD technique by 13.06% and 1.88% respectively. Aerodynamic efficiency of the turbine is obtained about 91.83%, based on 3D-CFD. Time-averaged results showed that under the optimum clocking of the second row stator blades, inlet total pressure and output power of the second rotor increase by 0.23%, and 0.93%, respectively, in comparison to the worst clocking case. These augmentations resulted in increased total to total efficiency of the second stage by 0.444%. Additionally, the total output power of the two stages increased by 0.71% through the optimum clocking. Modeling the unsteady wake flow trajectory within the blades passages confirmed that all of these beneficial effects happen if the upstream wake impinges on the leading edge region of the second stator blades.

Clocking effects on aerodynamics of a gas turbine low pressure axial turbine, part 2: Unsteady simulation

Unsteady, viscous compressible flow is numerically simulated within first two stages of a low pressure turbine of a gas turbine engine under different clocking of its stator blades rows. Zonal DES turbulence modeling has been used for flow simulations. Time-dependent wake flow trajectory is modeled and visualized within the blades passages. All characteristics of the passage wake flow, including its V-shape motion, re-orientation, elongation, expansion, and stretching, are properly simulated. Unsteady flow field results together with those of general aerodynamic performance of the optimum and worst clocking cases are presented and compared with each other. Analyses of the flow simulation results showed that the optimum clocking of the blades rows occurs while the upstream wake flow impinges on the downstream stator blade leading edge region. Final results demonstrated that under the optimum clocking of the second stator, the inlet total pressure of the second rotor blades row and its output power increase by 0.1% and 0.336%, respectively. Consequently, efficiency of the second stage increases by 0.35%. In addition, total output power of the whole two stages increases by 0.237%.

Analysis of turbulence distortion effects on flow-induced noise prediction for propeller blade sections

Amiet's leading-edge (LE) noise prediction model estimates the noise generated by inflow turbulence interacting with an infinitely thin flat plate. Previous studies showed that Amiet's theory underpredicts foil LE noise levels for high frequencies because the inflow turbulence is distorted by the mean flow acceleration in the foil LE region and this effect is not accounted for in the model. Recent investigations proposed a method to account for turbulence distortion in Amiet's model, showing good agreement with experimental data for airfoils. In the current study, we will discuss and analyze the influence of this new method on the noise prediction for propeller blade sections operating under realistic inflow conditions. In addition, the comparison of LE and trailing-edge (TE) noise is analyzed. The analysis is performed for the BB2 hull and the S7692 propeller, considering blade sections located at 70% and 90% of the propeller radius. The input for the noise prediction is determined numerically. The results show that the noise prediction accounting for the turbulence distortion most strongly affects the LE noise in the high-frequency range and the frequency where the dominant noise-generation mechanism shifts from the LE to the TE.

Numerical study of inflow turbulence distortion and noise for airfoils

In this work, the interaction of grid-generated turbulence with airfoils of different thicknesses, namely, a National Advisory Committee for Aeronautics (NACA) 0008 and a NACA 0018, is investigated, leading to a deeper understanding of the influence of the airfoil geometry on the near-field flow and on the far-field pressure fluctuations. Experimentally validated lattice-Boltzmann simulations are used to analyze the flow properties in the leading-edge (LE) vicinity. The analysis of the velocity fluctuations near the LE shows that momentum is transferred from the streamwise to the transverse velocity for the NACA 0008 airfoil interacting with a large turbulence length scale. This mechanism changes with the increase in the airfoil thickness because the inflow turbulence length scale becomes comparable to the airfoil thickness in the LE region, resulting in a higher concentration of vortices near the LE oriented in the transverse direction, creating high-velocity fluctuations in the spanwise direction. The near- and far-field pressure fluctuations are analyzed to understand the impact of the inflow turbulence distortion on these parameters and the limitations of analytical methods for real airfoils. Results show that the wall-pressure fluctuations are affected by the turbulence distortion in the LE region. Thick airfoils have noise directivity patterns significantly different compared to the Amiet predictions for higher frequencies, radiating higher noise levels upstream of the LE than the thin airfoil. This is likely associated with a drastic change in the pressure fluctuation distribution near the airfoil LE region, attributed to the change in the distortion of the vortical structures in the LE area.

Receptivity and Stability Theory Analysis of a Transonic Swept Wing Experiment

Surface suction provides an efficient way to delay boundary layer transitions. In order to verify the suction effects and determine the mechanism of suction control in transonic swept wing boundary layers, wind tunnel transition measurements in a hybrid laminar flow control (HLFC) wind tunnel model uses an infrared thermography technique in the Aircraft Research Association (ARA) 2.74 m × 2.44 m low turbulence level transonic wind tunnel. Based on the experimental data of stationary crossflow dominant transitions without and with surface suction in transonic swept wing boundary layers, in this paper, the effects on the receptivity and linear and nonlinear evolution of stationary crossflow vortices have been analyzed with the consideration of curvature. Theoretical analysis agreed with the experimental observations in regard to the transition delay caused by boundary layer suction near the leading-edge region.

Conjugate Heat Transfer Evaluation of Turbine Blade Leading-Edge Swirl and Jet Impingement Cooling With Particulate Deposition

Abstract Internal cooling structures for gas turbine engines are becoming more complicated to push the hot gas temperature as high as possible, which, however, allows particulates drawn into the coolant air to be more readily to deposit within these passages and thus greatly affect their flow loss and thermal performance. In this study, internal swirl cooling and jet impingement cooling subjected to particulate deposition were evaluated and compared using a conjugate heat transfer method, with an emphasis on the thermal effects of the insulative deposits. To accomplish the goal, an unsteady conjugate mesh morphing simulation framework was developed and validated, which involved particle tracking in an unsteady fluid flow, particle–wall interaction modeling, conjugate mesh morphing of both fluid and solid domains, and a deposit identification method. The swirl and the jet impingement cooling configurations modeled the internal cooling passage for the leading-edge region of a turbine blade and were investigated in a dust-laden coolant environment at real engine conditions. Coupling effects between the dynamic deposition process and the unsteady flow inside the two cooling channels were examined and the insulative effects of the deposits were quantified by comparing the temperatures on the external and internal surfaces of the metal channel walls, as well as on the deposit layers. Results demonstrated the ability of the newly developed, unsteady conjugate simulation framework to identify the deposits from the original bare wall surface and to predict the insulation effects of the deposits in the dynamic deposition process. The dust almost covered the entire impingement channel, while deposits were only seen in the vicinity of the jets in the swirl channel. Despite this, a dramatical decrease of convection heat transfer was found in the swirl channel because the swirling flow was sensitive to the interruption of the deposits. In contrast, the deposits improved the heat transfer rate in the impingement channel. When the thermal effects of the deposit layer were taken into account, the wall temperatures of both two cooling geometries were substantially elevated, exceeding the allowable temperature of the metal material. Due to the denser deposit coverage, the impingement channel wall had a greater temperature increase than the swirl channel. In terms of flow loss, the presence of the deposits inhibited the swirl intensity by interrupting the swirling flow and thus reduced the friction loss, whereas the pressure loss was improved by the deposits in the impingement cooling.

An arc-tenon attachment for nickel-based single crystal turbine blade with improved high-temperature fretting fatigue performance

Nickel-based single crystal (NBSC) turbine blade tenon is prone to fretting fatigue failure. In this study, an arc-tenon attachment was proposed and its fretting fatigue life increased by up to 408.18 % at 600 ℃ compared with the plane-tenon structure under the applied peak stress of 65 MPa. The arc-tenon attachment could effectively reduce the maximum von-Mises stresses and resolved shear stresses near the contact region, regulating the stress distribution and reducing the stress gradient, which was beneficial to alleviating the activation of octahedral slip systems and delaying crack initiation, thereby improving the fretting fatigue life at high temperature. Meanwhile, high temperature promoted the formation of oxide layer on the contact surface, providing low coefficient of friction and further reducing the contact stress. The large resolved shear stress near the contact leading edge region facilitated the activation of octahedral slip systems, then the resultant multiple slip lines sheared both the γ matrix phase and γ′ precipitates. The further growth of the slip lines accelerated the fretting fatigue crack initiation and propagation. The arc-tenon attachment could provide long fretting fatigue life and showed great potential in engineering application.

Investigation on transition characteristics of laminar separation bubble on a hydrofoil

The phenomenon of water–jet pump stall can be ascribed to the development of blade boundary layer separation with the transition process playing a significant role in this separation. The hydrofoil is usually used as a simplified model of the water–jet pump impeller blade, and its flow field characteristics have important reference values for analyzing the impeller flow. Based on the transition model and the dynamic mode decomposition method, this article presents the results of a study that was carried out on the stall characteristics of the NACA0009 blunt trailing edge hydrofoil. The transition characteristics of hydrofoil surfaces at different angles of attack (AoA)and Chord-based Reynolds numbers (ReL) are obtained. The hydrofoil boundary layer transition is dominated by natural transition as the AoA is less than 4°, while the transition is dominated by leading-edge separation-induced transition as the AoA is greater than 4°. The investigation yields the dynamic properties of the LSB (Laminar Separation Bubble) as the AoA is varied. The phenomenon known as the deep stall is distinguished by the movement of the stall vortex toward the upstream direction near the trailing-edge region, where it merges with the LSB in the leading-edge region. This phenomenon leads to oscillations in the lift and drag coefficients. The relationship between the LSB and the trailing-edge stall vortex is established using DMD (Dynamic Mode Decomposition) methods. As the phenomenon of the deep stall occurs, it can be observed that the modal energy of the leading-edge LSB is comparatively higher than the modal energy of the trailing-edge stall vortex, inducing the dominant role of the LSB and the movement toward the trailing-edge region and, consequently, the phenomenon of trailing-edge vortex shedding in the hydrofoil. The findings of this study could be guidance for the design of fluid machinery blades.