3D Vortex Structures Research Articles

Insights into turbulent airflow structures in blind headings under different ventilation duct distances

The paper explores the 3D stationary vortex structure of turbulent airflow near the dead-end face of a blind heading, ventilated via a forcing ventilation system. Despite its significance in blind heading ventilation, previous studies primarily focused on temporal dynamics of harmful impurities, overlooking flow structure details crucial for mass transfer processes. Our study delves into the ventilation flow structure across diverse parameters of the auxiliary ventilation system. Alongside standard flow visualization tools, we introduce three dimensionless indicators to comprehensively characterize flow structure, facilitating analysis of its variations with parameter changes and quantitative evaluation of system efficiency. Analysis revealed the formation of a single large-scale vortex within the entire range of considered ventilation system parameters in the heading. This vortex induces a significant increase in air circulation, approximately 2.5–3.5 times greater than airflow emerging from the ventilation duct’s end, thus intensifying mass transfer processes within the heading. We found that ventilation efficiency of the dead-end face zone in a blind heading with a 29.2 m² cross-section decreases linearly with increasing distance between the ventilation duct’s end and the dead-end face. However, compensating for this distance by increasing duct velocity is feasible, bearing significant implications for mine ventilation safety, particularly in ventilating blind headings with distant ducts from the dead-end face.

Simulation Analysis of Charge and Flow Features in a Needle-to-Ring Electrohydrodynamic Actuator

Three-dimensional (3D) numerical studies closer to real physical scenarios have received increasing academic attention for providing a better design reference for electrohydrodynamic (EHD) pumping technology. A 3D computational model of a cylindrical EHD cascade actuator based on needle-to-ring electrodes is established in this paper, in which the effects of injection, field-enhanced dissociation, and surface charge accumulation are jointly involved. We explore the strongly coupling behavior of the EHD flow pattern with charge motion in an isothermal incompressible dielectric liquid, analyzing the flow rate, dynamic pressure, and current. It is found that an asymmetrical 3D vortex structure appears within the 2D axisymmetric actuator body, which is attributed to the motion of opposite charges.

Hydrodynamic performance of manta rays swimming in staggered arranged group

To investigate the hydrodynamic performance of manta rays swimming in staggered arranged group, a morphological and kinematic model of manta rays is developed based on biological observations, and then a numerical calculation method is established for group swimming of manta rays based on the Immersed Boundary Method and the Sphere function-based Gas Kinetic Scheme (IB-SGKS). The group swimming of two manta rays with a fixed vertical spacing of 0.1 times the body thickness, and a flow direction spacing of 0—1.5 times the body length is systematically investigated. The average thrust/efficiency of the group system and each individual in the group are analyzed by combining the global three-dimensional (3D) vortex structure and the characteristic cross-section two-dimensional (2D) vortex structure. The numerical results are shown below. When the streamwise spacing between individuals is small, the propulsive performance decreases sharply compared with swimming alone; as the streamwise spacing increases, the propulsive performance of the leader manta ray is consistently better than that of swimming alone, with the maximum thrust enhanced up to 11.24% when <i>D</i><sub><i>x</i></sub> = 0.4BL, and the maximum efficiency is enhanced up to 3.58% when <i>D</i><sub><i>x</i></sub> = 0.3BL; with the increase of the streamwise spacing, in the thrust/efficiency curves of the follower manta ray appears volatility, with the maximum thrust enhanced to 48.14% when <i>D</i><sub><i>x</i></sub> = 0.4BL and the maximum efficiency reached to 12.39% when <i>D</i><sub><i>x</i></sub> = 0.5BL; the system average thrust and efficiency enhancement both reach their corresponding maximum values, specifically, 29.69% and 6.77%, when <i>D</i><sub><i>x</i></sub> = 0.4BL, which is because the tail vortex of the leading manta ray just passes through the front edge of the follower manta ray and directly acts on the tip vortex that initially falls off from the follower manta rays, thus substantially increasing their vortex energy.

On the distributed blowing control of flow around a square cylinder at a low Reynolds number

This paper numerically investigates the distributed blowing control of the flow around a square cylinder at a low Reynolds number of Re=200. The air holes are placed at the windward or leeward stagnation points. The control effect of the unsteady aerodynamic forces is notably different with different spanwise distributions of air holes, which is represented by the dimensionless air hole area ratio G. The simulation results indicate that the windward blowing control (WBC) shows better control effect than the leeward blowing control (LBC) in reducing the time-averaged drag coefficient Cd¯ of the square cylinder while the fluctuating lift coefficient Cl′ can be significantly suppressed by the LBC. Besides, the surface pressure distribution, the turbulence kinetic energy (TKE) and Reynolds shear stress (RSS) distributions and the shedding vortices in the wake are analysed and compared in detail under different control conditions. Finally, through the instantaneous 3D vortex structures and the spanwise fluctuating velocity w′ distribution in the flow field, the suppression of the unsteady aerodynamic forces is mainly related to the 3D vortex pairs induced by the blowing jet.

Flow mechanism and heat transfer characteristic of sweeping jet impinging on confined concave surfaces

The sweeping jet actuator (SJA), a type of fluid oscillator, has attracted considerable attention in the areas of enhanced heat transfer and flow control. In this study, an unsteady Reynolds-averaged Navier–Stokes numerical investigation (k–ω baseline) was conducted to evaluate the flow mechanisms and heat transfer characteristics of a sweeping jet (SJ) on a confined concave surface. A conventional oscillating jet with a unit aspect ratio was used to generate the SJ. The heat transfer at the target surface and the flow details inside the flow field are discussed in detail to analyze the mechanism of the effect of SJ on impinging cooling. First, an appropriate numerical model was selected based on a comparison with a previous experiment. Subsequently, the time-averaged and time-resolved flow field and heat transfer results were investigated at three target distances for three different Reynolds numbers. The unsteady time-averaged results show that the SJ exhibits better heat transfer performance at higher Reynolds numbers and narrower target spacings than circle jet, which improves by 13% at Re = 30 000, H/D = 1. Subsequently, the turbulent kinetic energy and velocity loss theories were combined to compare the time-averaged and time-resolved flow field details of the two jets. The heat transfer characteristics of the target surface and the flow details inside the flow field in time and space were effectively correlated. Finally, the topology and three-dimensional (3D) vortex structure inside the confined channel were remodeled to better understand the unsteady sweeping process and provide theoretical support for subsequent applications.

Hybrid turbulence models for flows around a stationary smooth circular cylinder

The aim of this paper is to evaluate the accuracy, stability and efficiency of the different hybrid turbulence models via the benchmark computations of flows around a stationary smooth circular cylinder. The hybrid turbulence models have been validated and applied a lot in turbine flow, combustion, aerodynamic and aeroacoustic problems, while not much in hydrodynamic problems. In order to verify the simulation performance of the newly proposed hybrid strategies, this paper uses the SST-PANS, SST-SAS and SST-IDDES to compare the numerical simulation of the large separation flow problem. The model performance is assessed by a detailed comparison of predictions regarding the turbulence characteristics, the hydrodynamic characteristics, and the distribution of eddy-viscosity. The self-developed CFD solver, vim-FOAM-SJTU, is used in the present simulations. From the assessment, it is confirmed that the hybrid models have the abilities to calculate the small-scale motions, and all models can be employed to predict the unsteady characteristics of wake vortices advantageously. Both the SST-PANS and SST-IDDES models can capture complex flow structures and physics mechanism. The SAS model using the Lvk scale with features of local-adaptive and grid-independent can predict the eddy-viscosity reasonable. When the constant Cs = 0.11 contained in the Lvk limiter is modified to be Cs = 0.08, SST-SAS is also able to achieve better performance in the same mesh. The hybrid model can calculate and simulate the 3D vortex structure well, which is closer to the real physical phenomenon. And SST-IDDES has the best simulation results. The numerical results from SST-IDDES show its comparable capabilities for simulation of massively separated hydrodynamic flows and its potential application in the prediction of industrial turbulent flows for vortex-induced motions (VIM).

Effects of corner chamfers on the extreme pressures on a square cylinder at incidence to a uniform flow

Wind-induced damages to cladding, glass curtain walls, and windows on surfaces of buildings demand further investigation of extreme pressures on a square prism. The flow physics of extreme wind pressures on a square cylinder has not yet been clarified, especially as they relate to corner modifications and flow incidence. Large-eddy simulation is utilized to investigate uniform flow past a standard square cylinder and a chamfered cylinder with a chamfer ratio of 1/7. The Reynolds number is fixed at 22,000, and the incidence angle ranges from 0° to 45°. The flow mechanism of extreme pressures is studied through analyses of instantaneous flow structures. The influences of corner modifications on extreme pressures are further investigated. The results show that extreme negative pressures are strong in the non-Gaussian regions, which are observed at the rear corners and sides of the two cylinders and change dramatically as the incidence changes. Two types of flow structures are responsible for the extreme pressures, namely, the intermittent rear-corner vortices caused by reverse-flow separation and the Karman vortices near the rear side. The distribution of extreme pressures is highly three-dimensional, owing to 3D vortex structures at a high Reynolds number. By introducing chamfers, the strength and spanwise variations in the corner vortex are reduced, and extreme pressures are weakened.

Drag Reduction Characteristics of Bionic Structure Composed of Grooves and Mucous Membrane Acting on Turbulent Boundary Layer

The biological surface structure comprising fish scales and a mucous membrane exhibits good turbulent drag reduction ability. Based on this structure, a bionic frictional drag reduction model composed of a grooved structure and mucous membrane was established herein, and its efficacy in reducing the resistance of a turbulent boundary layer was analyzed. Accordingly, the drag reduction performance of the bionic structure was investigated through large eddy simulations. The results revealed that the mucous membrane was evenly distributed on the groove wall through secretion, and effectively improved the drag reduction rate of the groove wall. The bionic grooves and mucous membrane structure successfully inhibited the turbulent kinetic energy, turbulence intensity, and Reynolds stress. The grooved structure improved the shape of the Λ vortex structure and the mucous membrane reduced the number of three-dimensional (3D) vortex structures. Furthermore, the streak structure near the bionic structure wall was reduced and its shape was regularized, which intuitively demonstrates the turbulence suppression ability of the proposed bionic structure. This paper presents the results of a hydrodynamic analysis of the frictional drag reduction characteristics of a bionic structure consisting of grooves and viscous membranes acting on the turbulent boundary layer of a wall.

Pressure Fluctuation on the Blade of a Axial Fan Driven in a Cooling System Enclosure

W Suppressing the pressure fluctuations distributed on the blade surface of an axial fan is applied as one of the means to reduce the noise generated in the cooling system of construction machinery. For that purpose, it is effective to use computational fluid dynamics (CFD) to capture the 3D vortex structure around a fan blade. However, while there have been many reports on the flow field formed around the blades of a fan alone or an axial fan with a duct-shaped shroud, the influence of the vortex structure formed at the actual operating point of the axial fan on the pressure fluctuation on the blade surface has not been sufficiently discussed. In this study, the three-dimensional vortex structure around the fan blade installed in the cooling system is investigated, and in particular, the influence of the wing tip leakage vortex on the pressure fluctuation on the fan blade surface is clarified. Wing tip leakage vortex that flow from forward in the direction of rotation of the fan interfere with a blade while oscillating periodically in the y-axis direction. The oscillation of the forward wing tip leakage vortex causes the separation position of the newly formed wing tip leakage vortex to change, and as a result, the pressure fluctuation increases at the tip of the blade suction surface near the separation position.

Evolution characteristics of 3D vortex structures in stratified swirling flames studied by dual-plane stereoscopic PIV

Stratified swirling flames are typically formed in centrally-staged combustors of modern aero engines. The pilot flame plays an indispensable role in stabilizing the stratified swirling flame. Evolutions of the primary recirculation zone (PRZ) and vortices in the central shear layer (CSL) notably affect dynamics of the pilot flame. This work employed a dual-plane stereoscopic particle image velocimetry (DP-s-PIV) to investigate the evolution characteristics of three-dimensional vortex structures in stratified swirling flows/flames at different Re numbers and working conditions. Time-resolved measurements obtained temporal evolutions of vortex structures and the scanning process resolved time-averaged volumetric flow fields under different working conditions. Results show that the flame-induced flow acceleration near the burner outlet enhances the vorticity and the strain rate of the central shear layer (CSL), where a precessing vortex core (PVC) resides and its dynamics is strongly coupled with the primary recirculation zone (PRZ). The lengths of the PRZ in swirling flames were found to be smaller than that of the swirling flow, owing to the reduced swirl intensity and the enhanced turbulent-induced momentum transport. Furthermore, statistical analyses based on the instantaneous flow fields of the reacting cases demonstrated that the averaged vorticity magnitude and averaged turbulent kinetic energy (TKE) for vortices in the CSL essentially obey the linear dependency and square dependency with the Re number, respectively. And, there exists a linear correlation between the average turbulent kinetic energy and averaged vorticity magnitude for vortices in the CSL. This implies that the enhanced vortices due to the flame-induced effect downstream of the pilot stage is the main source for local turbulence generation in stratified swirling flames.

LES study on the working mechanism of large-scale precessing vortices and energy separation process of Ranque-Hilsch vortex tube

In this paper, a large eddy simulation model (LES) was adopted to analyse the large-scale precessing vortices and energy separation in a Ranque–Hilsch vortex tube. By comparing the time-averaged axial velocity field between the Laser Doppler velocimetry data and the numerical results, the feasibility of the LES model was confirmed. The 2D instant flow field presents two vortex structures of secondary circulation flow at the cold end, and precessing vortices inside the tube. It also reveals two opposite flows in the axial and radial directions, and the precessing vortices formed by the reverse flow turn towards the main flow. Then, the 3D coherent structure inside the vortex tube was obtained by the vortex identification method for the first time. The basic vortex structure inside the vortex tube consists of the vortex body, detached vortex, and fragmentised detached vortex. Through the evolution of the 3D vortex structure, it was found that the detached vortices experienced a life cycle of growth, shedding, fragmenting, and vanishing. Benefitting from the vortex shedding processes, the precessing vortices overcame the adverse radial pressure gradient and drove part of the reverse flow towards the main flow from the low-pressure zone to the high-pressure zone. Through these processes, the vortex core precession that drives the reciprocating motion of the gas parcels near the reverse flow boundary was established, and energy could be transferred from the inner layer to the outer layer through a heat pump cycle.

Thermally activated flux motion in optimally electron-doped (Ca0.85La0.15)10(Pt3As8)(Fe2As2)5 and Ca10(Pt3As8)((Fe0.92Pt0.08)2As2)5 single crystals

The temperature dependence of the electric resistivity measured in various magnetic fields was analyzed by the vortex glass theory and the thermally activated flux motion (TAFM) theory. The vortex glass-to-vortex liquid (GTL) transition Tg obtained from the analysis shows a temperature dependence of BgT=B01-T/Tcm. The vortex liquid region is divided into the critical region existing in a finite temperature region just above Tg and the TAFM region present in the finite temperature region above it. In the critical region, the activation energy is expressed as Ueff=kBTTc-T/(Tc-Tg), whereas in the TAFM region, the activity energy is expressed as temperature-nonlinear UT,B=U0B1-tq. In the GTL transition, (Ca0.85La0.15)10(Pt3As8)(Fe2As2)5 maintains the 3D vortex structure without exhibiting dimension crossover of the vortex, but Ca10(Pt3As8)((Fe0.92Pt0.08)2As2)5 exhibits the dimension crossover from the 3D vortex glass to the 2D vortex liquid.

Three-dimensional biological hydrodynamics study on various types of batoid fishlike locomotion

Three-dimensional (3D) fluid-structure-interaction simulations are conducted for real and hypothetical batoid-fish-like swimming, using a unified 3D kinematic model; proposed here. The combined effect of batlike flapping and fishlike undulation results in various types of 3D vortex structures that are correlated with the propulsive performance parameters and can be used for an efficient design of underwater vehicles.

Computational Model Construction and Analysis of the Hydrodynamics of a Rhinoptera Javanica

In this study, numerical simulations are employed to investigate the hydrodynamic performance and wake topology of a swimming Rhinoptera javanica. The study is motivated by the quest to understand the hydrodynamics of median and paired fin(MPF) mode with both spanwise and chordwise flexibility. The simulations employ an immersed boundary(IB)-simplified sphere function-based gas kinetic scheme(SGKS) method that allows us to simulate flows with complex moving boundaries on fixed Cartesian grids. A computational model is constructed based on biological data. The evolution of the hydrodynamic force and 3D vortex structures are presented. Besides, the effect of frequency and amplitude are also discussed to explain some behaviors of the actual Rhinoptera javanica. This work can provide a baseline for the design of a bio-inspired underwater vehicle.

Evolution of the Diffusion-Induced Flow over a Disk Submerged in a Stratified Viscous Fluid

The paper presents the results of the mathematically simulated evolution of a 3D diffusion-induced flow over a disk (with diameter d and thickness H = 0.76 d) immersed in a linearly density-stratified incompressible viscous fluid (described by a system of the Navier–Stokes equations in the Boussinesq approximation). The disk rests at the level of the neutral buoyancy (coinciding with its symmetry axis z) and disturbs the homogeneity of the background diffusion flux in the fluid forming a complex system of slow currents (internal gravitational waves). Over time, two thin horizontal convection cells are formed at the upper and lower parts of the disk stretching parallel to the z axis and adjacent to the base cell with thickness d/2. This work is the first to analyze in detail the fundamental mechanism for the formation of each new half-wave near the vertical axis x (passing through the center of the disk) during half the buoyancy period of the fluid Tb. This mechanism is based on gravitational instability. The emergence of this instability is first detected at 0.473Tb at a height of 3.9 d above the center of the disk. The same mechanism is also implemented over the place where the body moves in the horizontal direction. The 3D vortex structure of the flow is visualized by constructing the isosurfaces of the imaginary part of the complex-conjugate eigenvalues of the velocity gradient tensor. In mathematical simulation, we employed a numerical method SMIF that has proved itself over three decades with an explicit hybrid finite-difference scheme for the approximation of the convective terms of the equations (second-order approximation, monotonicity).

Numerical simulation of turbulence arising in the free convection boundary layer after a cross row of rectangular obstacles

The contribution covers results of direct numerical simulation of transitional processes and turbulence developing in the vertical-plate free convection boundary layer downstream of a periodic row of 3D obstacles. The Prandtl number is set at 0.7. Periodicity conditions are prescribed in the spanwise direction. Steamwise position of the obstacles being spanwise-elongated rectangular parallelepipeds corresponds either to the local Rayleigh number, Rax equal to 109 or to Rax = 2.5·108 . In the first (basic) case, 3D vortex structures of a wide spectrum start to develop at a relatively short distance from the obstacles. The largest-in-size vortices, occupying the outer part of the layer, have a hairpin-like shape, and their heads are oriented opposite to the main flow direction. Steamwise evolution of the transitional and turbulent flow structure is analysed based on iso-surfaces of the Q-criterion covering the flow region up to Rax = 2.6·1010. The predicted mean Nusselt number dependence on Rax is in a good agreement with the known measurement data, both for the transitional and the turbulent flow regions. For the second case, nonlinear spatial development of a nearly 2D instability wave occupying a large portion of the computational domain is predicted. Rapid destruction of this wave and occurrence of chaotic 3D eddies are observed in this case at Rax = 3 • 109.

A new passive control technique for the suppression of vortex-induced motion in deep-draft semisubmersibles

The control of vortex-induced motion (VIM) of deep-draft semisubmersibles has recently emerged as a serious concern in offshore semisubmersible platforms subjected to high ocean currents. With the increased draft of semisubmersibles, the coherent wake vortex fields behind the multi-column platforms become quite significant, which increase the impact of the coupled fluid-structure dynamics on the platform motion. In particular, the effective mitigation of the synchronization of wake vortices in a deep-draft semisubmersible is important for the reliable station-keeping and to extend the fatigue life of risers and mooring systems. The present study aims at the development of a passive control technique for the vortex synchronization of deep-draft semisubmersibles (DDS) via continuous cross-sectional twisting of the rounded square column along the spanwise direction. The computations are performed using a hybrid URAN-LES turbulence model based on the finite volume method. A validation study of the numerical results is performed with the available experimental data for the stationary and vibrating configurations of deep-draft semisubmersible. To begin, we first examine the VIM performance of a single column of the semisubmersible with a twisted angle of 45 °. We next examine the design of twisted column to understand its effect on the vorticity dynamics and the VIM response characteristics. In comparison to the untwisted square-column configuration, the twisted column produces the reduction in the transverse (sway) VIM amplitude up to 90% at the peak lock-in condition. The streamwise (surge) amplitude for the twisted-column semisubmersible is also found to be reduced by approximately 1/3 of the amplitude of the square-column counterpart. The twisted surface on the column results in a continuous spanwise (column-wise) variation of the shear-layer separation points. The three-dimensional (3D) variation of separation lines and the pressure distribution along the twisted and the square columns are analyzed to understand the underlying mechanism of the VIM suppression. We find that the modification of vortex shedding due to the variation in the separation line along the twisted column significantly influences the mean and fluctuating hydrodynamic forces. We extend the twisted column concept to the deep-draft semisubmersibles and demonstrate its effectiveness to produce a remarkable degree of VIM suppression. We explore the effects of the orientation of twisted columns and the incidence angle of the oncoming flow and present the 3D wake vortex structures and the motion histories of the DDS configuration.

Chaos in breaking waves

This study investigates the chaotic behavior of breaking waves by laboratory experiments and numerical modeling. Repeated laboratory runs with different initial velocity perturbations show that the wave profile before the wave breaks can be accurately reproduced, but the subsequent breaking process varies among runs, indicating the lack of repeatability of breaking waves in reality. Numerical simulations based on the Smoothed Particle Hydrodynamics method are further carried out to examine the repeatability of wave breaking process. Consistent with the laboratory observation, multiple numerical simulations with variations in initial conditions present highly repeatable velocity field and free surface profile in the potential flow region but considerable variation at the breaking and post-breaking processes. Comparison also shows that 3D vortex structures induced by breaking waves are different among cases. Analysis of particle trajectory reveals that there is a similar trajectory thus a minor trajectory divergence among particles that are initially located at the pre-breaking region and the flume bottom, which are not directly impacted by the breaking process. However, a much more significant particle trajectory divergence is observed among particles that are initially located at the wave-splash region and the bore propagation region. The rate of divergence of particle trajectory under breaking waves is further examined by computing the Lyapunov exponent, a widely used indicator of chaos. This study reveals that different initial velocity perturbations lead to variations of near-surface velocity at the onset of wave breaking, which eventually cause the development of drastically different breaking wave jets and splashes. Therefore, the process of wave breaking, like many other dynamic processes in nature, exhibits a chaotic behavior.

DDES with adaptive coefficient for stalled flows past a wind turbine airfoil

A new delayed detached eddy simulation method with adaptive coefficient (DDES-AC) is proposed to overcome the transition delay from Reynolds-averaged Navier–Stokes (RANS) to large eddy simulation (LES) in the simulation of the mild, moderate separation, and dynamic stall flows past a wind turbine airfoil (NACA0015). The coefficient CDES is designed to be adaptive with the flow patterns, quasi-2D or 3D vortex structures, which aids in reducing the modelled eddy viscosity in the initial region of the separated shear layer. The DDES-AC is proved to be effective in the simulation of a fully attached plate flow without additional skin friction loss and a NACA0015 airfoil with a mild trailing edge separation. It also outperforms the DDES in moderate separation at an angle of attack beyond the static stall. The DDES presents “delay behaviour” in the dynamic stall simulation, resulting in an underestimation of the drag and pitching moment peaks and a deferred recovery of those in the downstroke. However, the DDES-AC improves the prediction accuracy and agrees excellently with the available experiment data.

Suppression of vortex-induced vibration of a square cylinder via continuous twisting at moderate Reynolds numbers

Vortex-induced vibration (VIV) of elastic structures with a square-shaped prismatic column exposed to flow has a significant impact on many aspects of structural design and stability. The main aim of the present numerical study is to investigate an alternative design of square column for minimizing the impact of VIV on the elastic structures. The numerical study is carried out at moderate Reynolds numbers (1000 ≤ Re ≤ 22000). For both stationary and freely vibrating square cylinders, a systematic validation of the numerical results is performed with the available experimental data. In particular, various turbulence models are explored to assess their effectiveness to capture the separated wake flow dynamics behind the square cylinder. The simulation results via k−ω SST-SAS (Scale Adaptive Simulation) model are found closer to the reported measurements for both stationary and vibrating cases. After establishing the validity of our numerical methodology, the VIV simulations of twisted square cylinders with different twisted angles are performed at the moderate Reynolds numbers. In comparison to the square cylinder counterpart, the results of the twisted square cylinder demonstrate good controlling effect on the VIV response at two oncoming flow directions (0° and 45°). The twisted surface of the cylinder causes the variation of separation or vortex shedding points as well as the frequency of vortex shedding, which in turn affect the distributions of hydrodynamic forces along the cylinder. The power spectral analysis of hydrodynamic forces of twisted square cylinder indicates that the twisted surface has a significant influence on the frequencies of both drag and lift forces. Finally, comparisons of the detailed flow patterns, the 3D vortex structures and the vortex-shedding modes between square and twisted cylinders are presented in detail.