Flow Structure Research Articles

Vortex-shedding and bistability in cylinder-flexible plate assembly in a channel

This study numerically investigates the fluid–structure interaction dynamics of a stationary circular cylinder with an attached flexible splitter plate in a confined fluid domain. We explore how variations in Reynolds number (Re), plate length, offset from the channel centerline, and blockage ratio influence the vortex-shedding and oscillatory behavior of the plates in laminar flow. Results indicate that at low Reynolds numbers (Re = 100), there are no vortex shedding or oscillations, while at higher Reynolds (Re = 200 to 300), the shorter plate exhibits first-mode oscillations and symmetry breaking, whereas the longer plate shows only transient second-mode oscillations at Re = 300 that diminish in amplitude, suggesting that increased plate length reduces vortex-induced forces. Dynamic Mode Decomposition (DMD) analysis confirms consistent primary flow structures across different Reynolds numbers, with initial modes encapsulating the majority of the system’s dynamics. In addition to determining the critical Re for vortex-shedding, vortex-induced oscillations and bistability, the study also examines the critical blockage ratios on the symmetry breaking phenomenon, and also shows that plate stability is influenced by domain asymmetry. These insights enhance understanding of the biomechanics of fish-like robots and inform the design and control of bioinspired flexible structures in fluid flows.

Efficient dimension-by-dimension adaptive TENO-based limiter and troubled-cell indicator for nodal-based high-order spectral difference method

A new targeted essentially non-oscillatory (TENO) limiter with adaptive dissipation has been developed for the 3rd- and 4th-order spectral difference method. This limiter can potentially be useful for other nodal-based discontinuous high-order methods as well. Unlike traditional WENO limiters for these methods which limit low-order moments one by one, the new limiter is based on a direct convex combination of reconstruction polynomial candidates. This strategy ensures the good computational efficiency for high order reconstructions. The reconstruction stencils only involve nodal values from the target cell and its neighbors sharing faces with it. The reconstruction employs Hermite polynomials, making the new limiter compact. It can be implemented in a dimension-by-dimension manner for multi-dimensional problems, which is consistent with the spectral difference method. To further enhance efficiency, a TENO-based troubled-cell indicator is also developed to only activate limiters in troubled cells. Extensive one-dimensional and two-dimensional numerical experiments validate the performance of the new TENO-based limiter and indicator. In summary, the limiter is much less dissipative than WENO limiters and can resolve richer small-scale flow structures on coarse meshes. The indicator precisely marks out troubled cells, slightly improving over the KXRCF indicator.

World Intellectual Capital Circulation: Brain Drain, High-Tech Products and Export of Technologies

The purpose of the present research is to reveal the global structure of intellectual capital flows, in which upstream emigration of scientists and researchers from donor countries enriches the intellectual capital and potential of the recipient countries, while intellectual products and technologies from recipient countries go downstream to donor countries. The research uses expert judgement to collect data. Institutional and comparative analyses are used to explain the structure of intellectual capital flows and to identify the reasons for the upstream emigration of intellectual capital and the downstream export of intellectual products. Econometric methods are used to explain the relationships between indices and scores. We reveal that all countries can be conditionally divided into two categories, namely donors and recipients of human intellectual capital. Donors supply scientists and researchers to recipient countries, and recipient countries supply high-tech products to donors. This situation is not only justified from the perspective of the international division of labor, but is also beneficial for both donor and recipient countries, as donors receive the necessary technology from recipients, and recipients replenish their need for scientists to create high-tech products. This constant circulation leads to the further impoverishment of developing countries, while at the same time becoming the basis for the enrichment of highly developed countries. According to the results of the study, we can conclude that three main characteristics act as factors to describe the global flows of intellectual capital: 1. As recipient countries offer better living and working conditions, higher wages and more secure human rights, the outflow of scientists from donor countries seems to be a natural phenomenon. 2. Research shows that donor countries lack the demand for scientists and their development, as these countries receive high technologies and products from recipient countries, which means that donor countries' policy is aimed at reducing their funding for science. 3. On the contrary, the demand for scientists in recipient countries is growing as high-tech products become the main export commodity. Recipient countries of intellectual human capital have no other export opportunities – they are poor in minerals and the high-tech sector is the only way to balance the country's payments.

Influence of periodicity on natural convection in a square porous cavity due to non-uniform heat under LTNE state

In this article, the influence of the local thermal non-equilibrium (LTNE) state on free convection in a square cavity filled with fluid-saturated porous medium is investigated numerically. The steady-state flow is induced due to sinusoidal heat distributed on the side walls of the cavity and insulated of the horizontal walls. The coupled flow governing equations are solved numerically by using the finite volume method (FVM) consisting of the SIMPLER (Semi-Implicit Method for Pressure Linked Equation Revised) Algorithm. The numerical simulations of temperature and stream-function contours are carried out for the non-Darcy model. The developed code is validated with existing numerical and present computed results for the case of a square enclosure associated with non-uniform heat source. Then, the present numerical results are analyzed over a range of physical parameters, like periodicity parameter ( N ≥ 1 ), interface heat transfer coefficient ( 10 − 2 ≤ H ≤ 10 2 ), porosity scaled thermal conductivity ratio ( 10 − 2 ≤ γ ≤ 10 2 ), with a fixed Rayleigh number ( Ra = 10 6 ), Darcy number ( Da = 10 − 4 ), Prandtl number (Pr = 0.71), and porosity ( ε = 0.8 ). To study the impacts of these key parameters on the fluid flow behavior and isotherm patterns of fluid as well as solid phase in the porous-square enclosure. From present numerical experiments that the structure of flow is controlled by multicellular structure with rotating clockwise and anticlockwise directions in the entire results. The flow dynamics are highly affected by the periodicity parameter (N) under LTNE circumstances. The characteristics of the local Nusselt number have the point of inflection and the maximum magnitude of it increases with N. The significant effect of H is found on the heat transfer rate of fluid phase but it is negligible on the heat transfer rate of solid phase. However, the influence of γ is found reverse in nature on the heat transfer rate of fluid as well as solid phase when as compared to the effect of H.

Experimental and numerical study on vibration response, VIV mechanism and aerostatic coefficients of triple-separated decks under different vertical distances

In this study, aerodynamic interference effects (AIE) on the vibration response, aerostatic coefficient (AC) and vortex-induced vibration (VIV) mechanism of the triple-separated decks under different incoming wind directions and vertical distances were investigated via wind tunnel tests and numerical simulations, respectively. The test results show that the AIE increases the displacement of VIV, and the VIV responses reaches maximum value under S/H = −1.0 (S is the vertical distance between the centers of RB and HB decks, and H is the height of RB deck) when the RB deck is on the windward side (the maximum displacements of VIV are 193.86% and 37.30% higher than the case of single RB deck and S/H = 0.0, respectively). The pressure distribution and flow structure show that the scale of vortex that alternately shed off from the tail of the deck becomes stronger and the fluctuating pressure coefficient increases under AIE, which increase the VIV amplitude of the RB deck and cause the VIV of HB decks. The experimental and numerical results indicated that the aerostatic coefficients (AC) of the leeward girder are more affected by the AIE. The interference factor (IF) of drag coefficient (CD) is far less than 1.0 under the case of F-5 (S/H = 0.0).

Numerical Study of the Force Characteristics and Flow Field Patterns of a Cylinder in the Internal Solitary Wave

The density of the ocean is unevenly distributed along the depth direction, showing a stratified structure. When there is an external disturbance, large-scale internal solitary waves are easily generated. The internal solitary waves are bounded by the intermediate pycnocline, and the currents in the upper and lower layers will flow in opposite directions. This generates strong shear forces that threaten the safety of marine structures. In this paper, the flow field distribution characteristics of a cylinder under the action of internal solitary waves at different scales are analyzed as a research object. The whole cylinder is discretized into 40 regions, and the horizontal force applied to each section of the cylinder is extracted. The force characteristics of the cylinder are analyzed. It is concluded that the pressure is the main factor determining the magnitude of the total combined force. In addition, the paper extracts the main flow structures from the modal decomposition point of view and explains the reasons affecting the force behavior of the cylinder.

Aerodynamic noise reduction of high-speed pantograph by introducing planar jet on leeward surface of panhead

Combining the improved delayed detached eddy simulation (IDDES) model and Ffowcs Williams-Hawkings (FW–H) equation, the potential of panhead leeward-side jet in pantograph aerodynamic noise control is numerically investigated. A typical double-strip pantograph is used as the baseline model. Two identical planar jets are arranged on the leeward side of the two strips to achieve active flow control. The results show that the planar jet can reduce the aerodynamic drag of the upstream strip and suppress its lift fluctuation, while the jet does not produce equivalent level of positive effects on the downstream strip. Benefiting from the suppression of lift fluctuation of the upstream strip, the far-field noise of the model equipped with jet achieves a 7 dB reduction in the main direction of panhead lift fluctuation, and the noise on the pantograph side is also reduced by 1–2 dB. The flow-field analysis reveals that the planar jet pushes the coherent flow structures in the panhead's wake downstream, which makes the high-intensity flow-field fluctuation away from the upstream strip. The absence of the positive effect of the jet on wake flow modification of the downstream strip can be attributed to the distinct inflow conditions of the two strips.

Asymptotic profiles of mean zonal flows generated by thermal convection of Boussinesq fluid in a rapidly rotating thin spherical shell

The asymptotic behavior of the profiles of mean zonal flows generated by thermal convection of a Boussinesq fluid in a rapidly rotating thin spherical shell was studied by extending the integration time of the numerical experiments of a previous study under similar conditions. Calculations were performed for the whole globe, as well as for a one-eighth sector region, with various values of the hyper-diffusion parameters. For sufficiently weak hyper-diffusion, a prograde zonal jet and alternating narrow zonal jets appeared at the equator and in the middle and high latitudes, respectively, as reported in the previous study. However, further integrations showed that the middle and high latitude flows are asymptotically accelerated eastward, jet peaks merge, and the banded zonal flow structure eventually disappears. Thus, the rotating thin spherical shell convection model of a Boussinesq fluid used in the previous studies seems inadequate to explain the surface banded structures of Jovian planetary atmospheres without modification of the standard setups. To maintain the alternating jet structure in the middle and high latitudes over the long-term, some sort of scale-independent dissipation process should be specified that prevents the evolution of zonal flows toward the long-term asymptotic state.

Numerical investigation on the transverse jet into a supersonic crossflow with different pressure ratios

The jet can be applied to the yaw control of a projectile, however, the complex interaction of the jet with the supersonic mainstream makes the flow field complex and yaw force unpredictable. To reveal the evolution of flow structures under different pressure ratios (PRs), or momentum flux ratios, a transverse sonic jet injected into a supersonic laminar crossflow has been studied numerically. Large-eddy simulations are employed to simulate the flow fields and evolution tendency of flow structures under different PRs of 10, 50, 100, 300, and 500. Our results show clearly the shock and flow structures of the jet interaction with crossflow under different PRs. Moreover, we find that, with the increase of PR, a larger upstream recirculation zone (RZ) and jet shock core appear, which accelerates the transformation of the bow shock (BoS) and the instability of the jet shear layer due to its stronger interaction with the crossflow. In addition, a high PR also accelerates RZ instability and produces a strong compressing effect on the major counter-rotating vortex pair in the jet flow, which makes the streamwise vortex tube stronger in the wake. These findings provide important information for applications of jet control of projectiles.

Influence of Runner Downstream Structure on the Flow Field in the Draft Tube of a Small-Sized Water Turbine

The flow in the draft tube of the water turbine is affected by the upstream flow and the inherent structure accompanied by various undesirable characteristics, affecting the efficient and stable operation of the water turbine. Changing the flow structure downstream of the runner is an important measure to reduce hydraulic loss in the draft tube and improve stability. In this study, three downstream structures of the runner, namely, the non-locking nut, small locking nut, and extended locking nut are numerically calculated and verified using experimental results. The unstable flow characteristics of the draft tube are analyzed using variations in swirling flow, backflow, pressure gradient, and vortex strip. The results show the non-negligible effect of the locking nut, which significantly reduces the rotational momentum flux at the draft tube inlet, accelerates the decay rate of the swirling flow, and suppresses the generation of axial low pressure. The small locking nut significantly reduces the pressure gradient, shortens the backflow zone, and decreases the backflow velocity. The extended locking nut reduces the backflow zone in some sections and reduces the vortex zone of the straight section but prolongs the backflow zone and increases the backflow velocity.

On the Spanwise Periodicity within the Gap between Two Different-Sized Tandem Circular Cylinders at Re = 3900

Although the spanwise periodicity within the gap between two tandem circular cylinders has been observed by some researchers, there is a lack of systematic research on the properties of this periodicity. For the spanwise periodicity within the gap, this study aims to ascertain its characteristics, its influences on the flow field, and its variation trend with increasing spacing ratio. By numerically simulating the flow around two tandem circular cylinders with a diameter ratio of d/D = 0.6 and seventeen spacing ratios (L/D = 1.00~6.00) at Re = 3900, this study shows four flow regimes: Reattachment Flow (L/D = 1.00~3.15), Bi-stable Flow (L/D = 3.24), Intermittent Lock-in Co-shedding (L/D = 3.30~3.50), and Subharmonic Lock-in Co-shedding (L/D = 4.00~6.00). Further, depending on the spanwise periodicity length of the time-averaged flow structures (i.e., Pz) within the gap, Reattachment Flow is, for the first time, subdivided into three new sub-flow regimes: Small-scale Periodic Reattachment (L/D = 1.00~1.50, Pz/D = (0, 4]), Large-scale Periodic Reattachment (L/D = 2.00~2.25, Pz/D > 4) and Non-periodic Reattachment (L/D = 2.50~3.15, no spanwise periodicity). The formation mechanisms are elaborated by analyzing the combined effect of both the L/D value and the spanwise-averaged time-averaged reattachment angle of the downstream cylinder. Moreover, this study proves that the newly defined Small-scale Periodic Reattachment and Large-scale Periodic Reattachment are responsible for the pronounced asymmetry of the flow along the transverse direction within the gap. In addition, detailed flow properties and statistical parameters are provided for each flow regime, such as velocity, vorticity, force coefficient, separation/reattachment angle, Strouhal number, and Q-criterion.

General formalism for symmetrically structured flows according to constructal Law

Flows from point to line or to surface (and vice versa) that obey a set of constraints are necessarily structured (Constructal Law). We can observe this feature in natural systems, in man-made systems, in the economy and in society. Here we develop a formalism for general application in point to line and point to surface symmetrical flow structures with constraints. We show that flow structuring occurs between successive branching levels, and that it is possible to find general structuring rules of the respective flow tree according to the Constructal Law.

Viscous dissipation and Joule heating in case of variable electrical conductivity Carreau–Yasuda nanofluid flow in a complex wavy asymmetric channel through porous media

This paper focuses on flow structures and thermal fields of the Carreau–Yasuda (CY) nanofluid model through a two-dimensional, wavy, complicated vertical asymmetrical conduit filled with porous elements. Formulations of the viscous dissipation in the case of CY nanofluids are derived and nonlinear radiation flux as well as joule heating are examined. Buongiorno’s nanofluid approach, which involves Brownian motion and thermophoresis aspects is considered. The electrical conductivity of the suspension is considered as a variable where it depends upon the ambient temperature and concentration distributions and the Joule heating impacts are not neglected. The approach of solving the problem is contingent upon converting the system to dimensionless form then the lubrication approach with low magnetic Reynold numbers is applied. Numerical solutions are found for the resultant system, and wide ranges are considered for Weissenberg number We, non-Newtonian parameter n and Darcy number [Formula: see text], namely, [Formula: see text], [Formula: see text] and [Formula: see text], respectively. The major results indicated that gradients of the pressure are higher in case of shear thickening [Formula: see text] comparing to in the instance of shear thinning [Formula: see text]. Also, the velocity is enhanced, close to the channel’s lowest portion, as the Weissenberg number is growing. The variable electrical conductivity gives a higher mass transfer rate compared to the constant property.

Scaling and flow structure of Langmuir turbulence in inertial frames

Abstract This paper provides a framework that unifies the characteristics of Langmuir turbulence, including the vortex force effect, velocity scalings, vertical flow structure, and crosswind spacing between surface streaks. The widely accepted CL2 mechanism is extended to explain the observed maximum alongwind velocity and downwelling velocity below the surface. Balancing the extended mechanism in the Craik-Leibovich equations, the scalings for the along-wind velocity u, cross-wind velocity v, and vertical velocity w are formulated as Here, Uf is the friction velocity, Us is the Stokes drift on the surface, and La = (Uf /Us)1/2 is the Langmuir number. Simulations using the Stratified Ocean Model with Adaptive Refinement in Large Eddy Simulation mode (LES-SOMAR) validate the scalings and reveal physical similarity for velocity and crosswind spacing. The horizontally averaged velocity along the wind ū/U on the surface grows with time, whereas v/V and w/W are confined. The root mean square (rms) of w peaks at wrms/W ≈ 0.85 at a depth of 1.3Zs, where Zs is the e-folding scale of the Stokes drift. The crosswind spacing L grows linearly with time but is finally limited by the depth of the water H, with maximum L/H = 3.3. This framework agrees with measurement collected in six different field campaigns.

Turbulent kinetic energy budget of sediment-laden open-channel flows: bedload-induced wall-roughness similarity

New experiments in highly turbulent, steady, subcritical and uniform water open-channel flows have been carried out to measure the mean turbulent kinetic energy (TKE) budget of sediment-laden boundary layer flows with two sizes (dp = 3 mm and 1 mm) of Plexiglas particles $({\rm relative\ density}\ = 1.192)$ . The experiments covered energetic sediment transport conditions (Shields number of $0.35 < \theta < 1.2$ ) ranging from non-capacity to full-capacity flows in bedload-to-suspension-dominated transport modes (suspension number of $0.5 < {w_s}/{u_\ast } < 1.3$ where ${w_s}$ is the settling velocity and $u_*$ is the friction velocity) and for weakly to highly inertial, finite size turbulence-particle conditions (Stokes number of 0.1 < St < 3.5 and dp/η > 10 where $\eta$ is the Kolmogorov length scale). It was shown that the effects of sediments on the TKE budget are very pronounced in all large particle experiments for which a bedload layer of several grain diameter thickness is developed above the channel bed. When compared with the corresponding reference clear-water flows, the TKE shear-production rate for the 3 mm particle flows is strongly reduced in the wall region corresponding to the bedload layer. This turbulence damping is seen to increase with sediment load until full capacity for flows with constant Shields value, as well as with Shields number value. Inside this damped TKE shear-production zone, a distinct peak of maximal turbulence production appears to coincide with the upper edge of the bedload layer delimited by a sharp gradient in mean sediment concentration. This vertically upshifted peak of TKE production is accompanied by an enhanced net downward oriented TKE flux when compared with the reference clear-water flows. The downward diffused TKE is found to act in the bedload layer as a local energy source in reasonable balance with the sediment transport term. The mechanism behind this downward TKE transport was further analysed on the basis of coherent flow structure dynamics controlled by ejection- and sweep-type events. The agreement between the height of downward directed mean TKE flux and the height below which sweep-type events dominate the Reynolds shear-stress contribution over ejections, revealed the leading role played by sweeps in mean TKE transport. This agreement holds for all reference clear-water flows supporting the well-known wall-roughness-induced dominance of the sweep contribution in turbulent, rough clear-water boundary layer flows. Furthermore, for all 3 mm particle flows, the two referred to transition levels were significantly and similarly upshifted to the upper edge of the bedload layer. Only for these sediment-laden flows, the bedload layer thickness is seen to exceed the wall-roughness sublayer of the reference clear-water flows. This supports a strong analogy between wall-roughness effects in clear-water flows and bedload layer effects in sediment-laden flows, on the mean TKE budget induced by a similarly modified coherent flow structure dynamics. The bedload layer-controlled wall roughness is finally confirmed by the good prediction of the wall-roughness parameter ks of the logarithmic velocity distribution. An empirical formulation fitting the presented measurements is presented, valid over the range of Shields number values covered herein.

Sediment control and flow redistribution with submerged vanes: a review

ABSTRACT The most challenging issues in rivers include sediment management, outer bank erosion, intake choking, channel bed shoaling, and river meandering. This paper provides a concise review of the newly developed sediment and flow control technique known as the Iowa vane or submerged vane. Submerged vanes are small flow training structures designed to redistribute flow and sediment within the channel cross-section. The structural stability and economic feasibility of submerged vanes, which distinguish them from conventional methods such as dikes and groins, have inspired many researchers to study their use and efficiency in river management over many decades. Various hydrodynamic characteristics, such as flow structure, sediment motion, vortex generation, and scouring around submerged vanes and arrays of vanes, have been reviewed. Additionally, various vane parameters that influence these characteristics are also explained. This paper also underscores current limitations in understanding the flow and sediment behavior around submerged vanes, while also providing recommendations for future research in the field.

Investigation of Non-Uniform Inflow Effects on Impeller Forces in Axial-Flow Pumps Operating as Turbines

Due to the existence of an inlet elbow, transmission shaft, and other structural components, the inflow of axial-flow pumps as turbines (PATs) becomes non-uniform, resulting in the complexity of internal flow and adverse effects such as structural vibration. In this paper, numerical methods were employed to explore the non-uniform inflow effects on impeller forces and internal flow field characteristics within an axial-flow PAT. The study results indicated that non-uniform inflow caused uneven pressure distribution inside the impeller, which leads to an imbalance in radial forces and offsetting the center of radial forces. With an increasing flow rate, the asymmetry of radial forces as well as the amplitude of their fluctuations increased. Non-uniform inflow was found to induce unstable flow structures inside the impeller, leading to low-frequency, high-amplitude pressure fluctuations near the hub. Using the enstrophy transport equation, it was shown that the relative vortex generation term played a major part in the spatiotemporal evolution of vortices, with minimal viscous effects.

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 dynamic (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.

Fluidic sealing effect on flow structure in labyrinth shroud with slotted fins

The paper analyses the flow structure of the recently introduced fluidic sealing technique that can limit the leakage flow through the labyrinth seal. The main idea behind the concept is to introduce a high-velocity jet into the gap. The jet is introduced through the slot in the fin of the seal, connecting the upstream surface of the fin with the gap. The jet is driven by the naturally occurring pressure difference, thus the solution is passive. The concept was verified using test section measurements and numerical simulations, proving effectiveness. However, the physical phenomenon standing behind the effectiveness was not studied thoroughly. A deep analysis of the flow structure in the labyrinth seal with fluidic sealing was performed based on RANS results. In addition, LES simulations were performed to allow for even more insight into the flow. The analysis revealed that the fluidic sealing introduces much non-uniformity into the flow, in comparison to the reference configuration, causing intensive mixing. The energy spectrum reveals that increased mixing raises the levels of high-frequency kinetic energy oscillations, which additionally promotes dissipation.

Numerical Study on Hydrodynamic Performance of a Pitching Hydrofoil with Chordwise and Spanwise Deformation

The hydrofoil plays a crucial role in tidal current energy (TCE) devices, such as horizontal-axis turbines (HATs), vertical-axis turbines (VATs), and oscillating hydrofoils. This study delves into the numerical investigation of passive chordwise and spanwise deformations and the hydrodynamic performance of a deformable hydrofoil. Three-dimensional (3D) coupled fluid–structure interaction (FSI) simulations were conducted using the ANSYS Workbench platform, integrating computational fluid dynamics (CFD) and finite element analysis (FEA). The simulation involved a deformable hydrofoil undergoing pitching motion with varying elastic moduli. The study scrutinizes the impact of elastic modulus on hydrofoil deformation, pressure distribution, flow structure, and hydrodynamic performance. Coefficients of lift, drag, torque, as well as their hysteresis areas and intensities, were defined to assess the hydrodynamic performance. The analysis of the correlation between pressure distribution and deformation elucidates the FSI mechanism. Additionally, the study investigated the 3D effects based on the flow structure around the hydrofoil. Discrepancies in pressure distribution along the spanwise direction result from these 3D effects. Consequently, different chordwise deformations of cross-sections along the spanwise direction were observed, contributing to spanwise deformation. The pressure difference between upper and lower surfaces diminished with increasing deformation. Peak values and fluctuations of lift, drag, and torque decreased. This study provides insights for selecting an appropriate elastic modulus for hydrofoils used in TCE devices.