Vorticity Magnitude Research Articles

Asymptotic Representation of Vorticity and Dissipation Energy in the Flux Problem for the Navier–Stokes Equations in Curved Pipes

This study explores the problem of describing viscous fluid motion for Navier–Stokes equations in curved channels, which is important in applications like hemodynamics and pipeline transport. Channel curvature leads to vortex flows and closed vortex zones. Asymptotic models of the flux problem are useful for describing viscous fluid motion in long pipes, thus considering geometric parameters like pipe diameter and characteristic length. This study provides a representation for the vorticity vector and energy dissipation in the flow problem for a curved channel, thereby determining the magnitude of vorticity and energy dissipation depending on the channel’s central line curvature and torsion. The accuracy of the asymptotic formulas are estimated in terms of small parameter powers. Numerical calculations for helical tubes demonstrate the effectiveness of the asymptotic formulas.

A comprehensive investigation on the internal flow and outflow characteristics of GDI elliptical divergent nozzles

The substantial demand for enhanced combustion efficiency and achieving near-zero emissions in GDI engines has spurred the introduction of a novel approach employing elliptical divergent nozzle spray technology. This innovative method, which marries the elliptical shape with a divergent nozzle, not only elevates downstream atomization quality but also mitigates nozzle tip wetting. Nevertheless, there exists a dearth of documented research regarding the internal flow and outflow characteristics related to the atomization potential of elliptical divergent nozzles. Numerical investigations have been carried out to scrutinize alterations in the three-dimensional cavitation morphology, the dispersion of turbulent vortex structures, and the nozzle exit flow parameters across a range of cavitation number conditions for both circular and elliptical divergent nozzles. The research findings demonstrate that the cavitation intensity of the elliptical divergent nozzle consistently surpasses that of the circular divergent nozzle. Also, the elliptical divergent nozzle consistently exhibits a greater number of turbulent vortex structures compared to the circular divergent nozzle across all cavitation number conditions. Additionally, as the cavitation number decreases, the difference in turbulence vorticity magnitude between the exits of the circular and elliptical divergent nozzles gradually increases. Furthermore, the elliptical diverging orifices are more susceptible to cavitation compared to their circular counterparts. The elliptical divergent nozzle outperforms the circular nozzle with a substantial 24.6% increase in exit velocity, especially at a cavitation number of 1.016.

Pulverized coal combustion in boundary layer turbulence using direct numerical simulation

The present study investigates pulverized coal combustion under oxy-fuel conditions interacting with turbulent boundary layer flows over a flat plate using direct numerical simulation (DNS). The coal particles are tracked in the Lagrangian framework while the flow is solved in an Eulerian way. Three cases with reacting particles, inert particles and single-phase flows were performed. The interplay between pulverized coal combustion, turbulent boundary layer flows and the wall was examined. It was shown that the coal particles first ignite in the outer layer of the boundary layer turbulence, where individual coal particle ignition occurs. The wall-normal velocity in the reacting case is larger compared with that of the non-reacting cases due to flow acceleration induced by combustion. The volatile matter mass fraction is high in the inner layer in the downstream region. However, the heat release rate is low due to the cold wall effect. The strong correlation between the wall heat flux and streak structures in the near-wall region is observed in all cases. The values of radiative heat transfer are similar in the upstream region of both the cases with reacting and inert particles. However, as combustion occurs and particle temperature increases in the reacting case, the radiative heat transfer from particles to the wall increases significantly in the downstream region. Particle accumulation due to turbophoresis in the near-wall region is analyzed. It was shown that the magnitude of streamwise vorticity is attenuated by coal combustion. Therefore, particle wall-accumulation is less prominent in the reacting case compared with the inert case.

Luminescence anisotropy and vorticity magnitude of a free turbulent jet

In the field of experimental fluid dynamics, the direct measurement of vorticity remains a challenge, even though it plays a crucial role in understanding turbulent flows. The present study explores the influence of the rotation of nanoparticles on their luminescence anisotropy as a potential novel measurement method. This relation opens a new field of flow diagnostics, based on the measurement of polarized intensity components. Potentially, the method allows for the direct measurement of the vorticity. For this, the canonical flow in this study is a turbulent round jet at ${{Re}} = {12\,000}$ and 14 400. It is confirmed that the flow regime has an influence on the luminescence anisotropy. Using a model of such deterministic rotations according to another work by the authors (Schmidt & Rösgen, Phys. Rev. Res., vol. 5, no. 3, 2023, 033006), the magnitude of the vorticity components is computed, since the presented set-up is limited to sensing the magnitude of these quantities. The computed components indicate the self-similarity of the vorticity magnitude. A large-eddy simulation is conducted for comparison with the experiments, demonstrating good agreement.

Shear-thinning stimulative fluid breakup in 3D pore-throat

In polymer flooding, the primary attentions focused on the influence of polymer concentration and the elasticity on fluid breakup. However, the shear-thinning characteristic can also significantly affect the apparent viscosity of the fluid. We simulated the breakup process of the dispersed phase in both shear-thinning and Newtonian fluids by using volume of fluid method, encompassing various viscosity ratios, capillary numbers, and rheological parameters. The critical conditions of capillary number and viscosity ratio for breakup of the dispersed phase were obtained, indicating that the dispersed phase was more prone to breakup in shear-thinning fluids. The mechanism of fluid breakup induced by shear-thinning was examined through the analysis of viscosity, pressure, and the magnitude of vorticity. Attributed to heightened destabilization in the radial direction and diminished viscous forces, fluid breakup processes were enhanced by lower zero-shear viscosity and reduced power-law index. The fluid breakup caused by the radial instability of shear-thinning fluids is distinguishing from the classical Roof snap-off theory. Inspiring by these results, enhancing rheological parameters such as power-law index and zero-shear viscosity in designing polymer flooding technique can accelerate the occurrence of the breakup process, thereby achieving control over the oil recovery process.

Entrainment and bulk flow characteristics of heated and unheated transient plumes using direct numerical simulations

An off-source volumetrically heated turbulent transient plume, known as transient diabatic plume (TDP), is compared with an unheated transient plume (TP). Both the TDP and TP are simulated using direct numerical simulations at a source Reynolds number (Re) of 2000. The flow is sufficiently resolved till the Kolmogorov (η) scale. The radius of the TP shows a self-similar behavior of linear increase with height after about five diameters from the source hot-patch. However, the velocity does not show a self-similar behavior. The addition of off-source buoyancy in the TDP triples the vertical velocity and also causes an order of magnitude increase in the vorticity magnitude (ω) due to the effect of the baroclinic torque. Compared to the TP, the entrainment coefficient and radius of the TDP increase and this shows enhanced entrainment due to heating. The transient flows fields are analyzed using local scales based on integral quantities of volume, momentum, and buoyancy. Normalizing the vorticity with these integral scales results in a more uniform scaled ωl for both flows. Hence, for both TP and TDP, we use the same values of ωl to quantify the inner and outer boundaries of the turbulent non-turbulent layer (TNTL). The width of the TNTL (δTNTL) decreases by ∼25% due to heating. The conditionally averaged velocity profiles suggest that very close to the outer irrotational boundary (IB) of the TNTL, the TDP exhibits stronger updrafts and downdrafts in comparison to the TP. Entrainment is studied using the mean relative velocity (⟨vn⟩) defined at the IB. The analysis of the components of ⟨vn⟩ reveal that the viscous diffusion component, which is of the order of the Kolmogorov velocity (uη), is balanced by the baroclinic and viscous dissipation components, while the inviscid term is negligible in comparison.

Large Eddy Simulation of the Flow around a Generic Submarine under Straight-Ahead and 10° Yaw Conditions

Aiming towards a better understanding of the flow field around a fully appended Joubert BB2 submarine model, and in order to complement the experimental investigations of the wake of the hydroplanes and sail, large eddy simulation (LES) with the dynamic Smagorinsky model was conducted. Three sets of grids with a maximum grid number of up to 228 million were designed to perform the LES simulation for the Joubert BB2 under 10° yaw conditions, with a freestream Reynolds number based on the local freestream velocity and a hull length of ReL = 2.2 × 107. Comparisons of the wake of the cruciform appendage were made with experiments to verify the computational accuracy and to examine the influence of the spatial resolution. A satisfactory result was more representative of the experiments with the improvement in grid spatial resolution. The evolution characteristics of three co-rotating vortices originating from the cruciform appendage under the most refined grid arrangement are further described in detail under straight-ahead and 10° yaw conditions. The comparison results show that, in the core-flow region, the resultant velocity, vorticity magnitude, and TKE were stronger and the wake was more complicated under 10° yaw conditions. Tip vortex tracking under 10° yaw conditions exhibited significant three-dimensional characteristics as the wake developed downstream.

Influence of jet flow on hydrodynamic performance of a ducted propeller

This study introduces a concept that jet technology in the aeronautical field is used for active flow control to improve the hydrodynamic performance of a ducted propeller. Jet flow is added in front of the ducted propeller, and it produces a circumferential velocity that is opposite to the rotation direction of the rotor. An international standard ducted propeller was adopted to demonstrate this concept. The unsteady Reynolds-averaged Navier–Stokes method and the shear stress transport k−ω turbulence model were employed for the simulations. The open-source platform OpenFOAM was utilized. The overall efficiency η0 of the ducted propeller first increases and then decreases with increasing the jet flow velocity Rjf from 1 to 3 and the distance L to the rotation center from 0.2D to 0.4D. When the jet flow is at the optimal condition of Rjf=2 and L=0.3D, the maximum efficiency improvement of 3.1% is achieved for the ducted propeller. The reason is that the jet flow contributes to a pressure increase in the flow through the rotor. This effect is related to tip and hub vortices, which are disrupted by the jet flow and have relatively low vorticity magnitudes compared to the reference case without jet. The findings in this study have the potential to advance the development of active flow control technology for ships.

Numerical simulation of hydrodynamic performance of pump-jet propulsor with serrated trailing-edge duct under different working conditions

Pump-Jet Propulsors (PJPs) have excellent propulsion performance, but the duct makes the internal flow and vortex distribution of PJP more complex. This work presents a serrated modification of the duct trailing-edge of the rear-stator PJP. A Suboff submarine is used to provide wake for PJP, and the propulsion performance and flow field of PJP in self-propelled state are analyzed. In addition, the hydrodynamic coefficients and vorticity fields of two PJPs in oblique flow are compared. The results indicate that the serrated structure can reduce the vorticity magnitude behind the duct, accelerate the shedding of PJP tailing vortex. In direct flow, the higher the inflow velocity, the better the effect of the serrated structure on weakening the wake vortex, which can reduce the vorticity by up to 52.4%. However, the propulsion efficiency of the modified PJP is reduced, but it is within 3%. In oblique flow, the hydrodynamic coefficient and propulsion efficiency of the two PJPs are significantly reduced, and the efficiency of the modified PJP is better than that of the original PJP. The larger the inflow angle, the more obvious the effect of the serrated structure on weakening the wake vortex, and the smaller the loss of propulsion performance.

Valvular and ascending aortic hemodynamics of the On-X aortic valved conduit by same-day echocardiography and 4D flow MRI.

This study aims to assess whether the On-X aortic valved conduit better restores normal valvular and ascending aortic hemodynamics than other commonly used bileaflet mechanical valved conduit prostheses from St. Jude Medical and Carbomedics by using same-day transthoracic echocardiography (TTE) and 4D flow magnetic resonance imaging (MRI) examinations. TTE and 4D flow MRI were performed back-to-back in 10 patients with On-X, six patients with St. Jude (two) and Carbomedics (four) prostheses, and 36 healthy volunteers. TTE evaluated valvular hemodynamic parameters: transvalvular peak velocity (TPV), mean and peak transvalvular pressure gradient (TPG), and effective orifice area (EOA). 4D flow MRI evaluated the peak systolic 3D viscous energy loss rate (VELR) density and mean vorticity magnitude in the ascending aorta (AAo). While higher TPV and mean and peak TPG were recorded in all patients compared to healthy subjects, the values in On-X patients were closer to those in healthy subjects (TPV 1.9 ± 0.3 vs. 2.2 ± 0.3 vs. 1.2 ± 0.2 m/s, mean TPG 7.4 ± 1.9 vs. 9.2 ± 2.3 vs. 3.1 ± 0.9 mmHg, peak TPG 15.3 ± 5.2 vs. 18.9 ± 5.2 vs. 6.1 ± 1.8 mmHg, p < 0.001). Likewise, while higher VELR density and mean vorticity magnitude were recorded in all patients than in healthy subjects, the values in On-X patients were closer to those in healthy subjects (VELR: 50.6 ± 20.1 vs. 89.8 ± 35.2 vs. 21.4 ± 9.2 W/m3, p < 0.001) and vorticity (147.6 ± 30.0 vs. 191.2 ± 26.0 vs. 84.6 ± 20.5 s-1, p < 0.001). This study demonstrates that the On-X aortic valved conduit may produce less aberrant hemodynamics in the AAo while maintaining similar valvular hemodynamics to St. Jude Medical and Carbomedics alternatives.

Inflow-velocity and rotational effects on revolving and translating wings

An aspect ratio 9.5 rectangular wing is articulated in revolving and translating motions at a 45° angle of incidence and Reynolds number Re=O(300). The effects of rotational (Coriolis and centripetal) accelerations and relative inflow velocity profile on vorticity transport within the leading-edge vortex (LEV) system are independently investigated. For the range of displacements studied (180° rotation and corresponding translational displacement), a stably attached leading-edge vortex (LEV) is observed when rotational accelerations and/or a linearly varying inflow velocity profile is present; however, the inflow velocity profile has a stronger effect on stability of the LEV. LEV vorticity magnitude and lift are significantly augmented when both factors are included (i.e., the full revolving wing case). Vorticity transport analyses are conducted in a planar control region two chords from the axis of rotation, where LEV stability is typically observed on revolving wings at high incidence and at an equivalent spanwise position in the translating case. The fully revolving wing case exhibits a substantially larger leading-edge shear-layer vorticity flux than the other cases, whereas Coriolis tilting makes little contribution to regulation of LEV strength. A correlation is found between the spanwise convective flux and tilting flux contributions in all cases. Decomposition of the spanwise convective flux term demonstrates that the two phenomena are kinematically linked and, together, define a new out-of-plane convective flux term that captures the essence of the spanwise convective flux. The role of this term and the effect of rotational accelerations on it are examined.

Experimental investigation on the ferrofluid flow in a horizontal mini channel under the constant magnetic field using PIV

Applying the magnetic field alters the flow characteristics of the ferrofluids, chiefly accounting for heat transfer augmentation. To elucidate how changes in flow characteristics enhance heat transfer, the impact of a constant magnetic field on the laminar ferrofluid (Fe3O4/water nanofluid) flow inside a mini channel is visualized and quantitatively investigated through the PIV method. Experiments are accomplished at the magnetic flux density of 3200 G and the magnetic particle concentration of 0.0014 wt% for 0.30≤Re≤62.5. The effects of the magnetic field are scrutinized on the flow patterns and velocity profiles. The results indicate that at Re=0.30, the region of influence of the magnet is considerable, inducing a y-velocity component, which accelerates the fluid and improves heat transfer. At Re=31.5, two quasi-symmetrical recirculation zones are observed, enhancing the fluid mixing. Additionally, though diminishing the magnetic field effects, raising the Re number from 31.5 to 62.5 increases the overall vorticity magnitude by 45.5%.

A comparative analysis of internal flow and spray characteristics in triangular orifices with diesel and biodiesel

This paper presents an inquiry into the internal flow and spray behavior of diesel and biodiesel in a triangular orifice, using experimental and numerical methods. The inner flow was analyzed through the implementation of Large Eddy Simulation model. Furthermore, two high-speed cameras were utilized to capture spray images of the major and minor axes of the triangle-shaped nozzle simultaneously. The investigation revealed that, in comparison to diesel, biodiesel exhibited a higher discharge coefficient. Additionally, the vorticity magnitudes and turbulence vortex structures for biodiesel were consistently lower than those for diesel. The use of biodiesel can hinder the occurrence of cavitation. Moreover, it was observed that the triangular spray cone angle displayed axis-switching phenomena for both fuels. The axis-switching phenomenon is suppressed by using biodiesel. The research also discovered that the triangular biodiesel spray has a longer spray tip penetration and a smaller angle in all view planes. This could be attributed to the higher viscosity and surface tension of biodiesel, as well as the inhibition of the spray axis-switching during the injection, leading to an increase in the spray tip penetration and a decrease in the spray cone angle for biodiesel.

Effect of stenotic shapes and arterial wall elasticity on the hemodynamics

The present study employs an arbitrary Lagrangian–Eulerian fluid–structure interaction approach to investigate pulsatile blood flow through a deformable stenosed channel. The flow is modeled by solving the incompressible continuity and momentum equations using finite element-based commercial solver COMSOL Multiphysics®. In this work, we explore the effects of different stenotic shapes—elliptical, round, and sinusoidal, degrees of stenosis (30%, 50%, and 70%), and arterial wall stiffnesses—0.5, 1.5, and 2.5 MPa on the velocity profile, pressure and wall shear stress distribution, and wall deformation. The oscillatory shear index (OSI) is analyzed to predict further plaque formation in the stenosed artery. We find that the flow velocity, wall shear stress, and pressure difference across the stenosed region increase with an increase in the stenotic severity and artery stiffness. The velocity profiles intersect at a radial location in the stenotic region termed critical radius, where relative magnitudes get reversed. With the increase in stenotic severity, the wall displacement decreases at the throat and increases at the upstream side. With the increase in wall stiffness, the wall deformation decreases, and shear stress increases, thereby increasing the pressure drop across the stenosed region. At a lower mass flow rate and a higher degree of stenosis, the vortices are formed upstream and downstream of the stenosed region for all stenotic shapes. The vorticity magnitude is found to be more than 21% higher for sinusoidal stenotic shape than round and elliptical ones. The effect of stenotic profile on the pressure drop characteristics shows that blood experiences maximum wall shear stress for the sinusoidal stenotic geometry, whereas the pressure drop is the maximum for the elliptical stenotic shape. The elliptical stenotic shape is more prone to further plaque formation than round and sinusoidal stenotic shapes. At lower Womersley number (Wo=2.76) corresponding to 60 beats per min heart beat rate, secondary vortices are formed downstream of the channel, causing higher OSI.

Numerical investigation of the flow characteristics of supercritical carbon dioxide in a high-speed rotating annular gap

The flow characteristics of Taylor–Couette–Poiseuille flow induced by supercritical carbon dioxide in an annular gap play a pivotal role in determining the overall performance of the rotating machinery. To accurately design the structural components of rotating machinery and enhance its efficiency, this study employs the large eddy simulation method to investigate the flow behavior of Taylor–Couette–Poiseuille flow with supercritical carbon dioxide within an annular gap. The results reveal that vortices are predominantly generated near the inner wall. Initially, the flow exhibits small swirl vortices, spiral ring vortices, and annular vortices along the flow direction. As the flow progresses, these small vortices at the inlet region transition into hairpin swirl vortices. Finally, turbulent flow disturbances lead to the fragmentation and merging of spiral and annular vortices, resulting in a flow field characterized by high-frequency hairpin swirl vortices and small vortices with strong randomness. An increase in the swirl number causes the initial position of the Taylor vortex to shift toward the inlet, while the turbulent kinetic energy is more active on the outer wall side than the inner wall side. Along the flow direction, the vortices experience a developmental process involving stabilization, diffusion, and mixing. Varying the radius ratio affects the magnitude of vorticity, reduces velocity fluctuations in a regular pattern, and alters the distribution of helicity bands from wide and sparse to compact and dense groupings. As the axial Reynolds number increases, the magnitude of vortices grows, leading to more severe velocity fluctuations and the transformation of the helicity bands from a regular annular pattern to fluctuating vortices bands, accompanied by a decrease in helicity.

Subvortices within a Numerically Simulated Tornado: The Role of Unstable Vortex Rossby Waves

Abstract Multiple subvortices corresponding to suction vortices in observations are obtained within a simulated tornado for the EF4 tornado case of Funing, China, on 23 June 2016. Within the simulation, the tornado evolves from a one-cell structure with vorticity maximum at its center to a two-cell structure with a ring of vorticity maximum. Five well-defined subvortices develop along the ring. The radial profile of tangential wind across the vorticity ring satisfies the necessary condition of barotropic instability associated with phase-locked, counterpropagating vortex Rossby waves (VRWs) along the ring edges. The phased-locked waves revolve around the parent vortex at a speed less than the maximum azimuthal-mean tangential velocity, agreeing with theoretically predicted VRW phase speed. The radii within which the wave activities are confined are also correctly predicted by the VRW theory where radial group velocity approaches zero. Several other characteristics related to the simulated subvortices agree with VRW theories also. The most unstable azimuthal wavenumber depends on the width and the relative magnitude of vorticity of the vortex ring. Their values estimated from the simulation prior to subvortex formation correctly predict wavenumber 5 as the most unstable. The largest contribution to wave kinetic energy is diagnosed to be from the radial shear of azimuthal wind term, consistent with barotropic instability. Vorticity diagnostics show that vertical vorticity stretching is the primary vorticity source for the intensification and maintenance of the simulated subvortices. Significance Statement Multiple subvortices or suction vortices in tornadoes can produce extreme damage but their cause is not well understood. An intense tornado from China that developed five strong subvortices, along a vorticity ring a distance from the tornado vortex center, was successfully simulated. By examining the propagation and other characteristics of these subvortices and comparing them with theoretical models of vortex Rossby waves (VRWs) that have been studied mostly in the context of typhoons/hurricanes, it is believed that nonlinear growth of unstable VRWs associated with barotropic instability is the primary reason for the development of subvortices within the tornado. The conclusion is further supported by analyses of the primary source of wave growth energy. Vertical vorticity stretching is the main vorticity source for intensifying and maintaining the subvortices at their development and mature stages. The unstable growth of VRWs as the cause of tornado suction vortices has not been analyzed in detail for realistic tornadoes until now.

Study on the Suppression Effect on Vortex-Induced Vibration of Double-Deck Truss Girder by the Spatial Position of the Deflector Plate

This paper carried out wind tunnel tests and numerical analysis to study the effect of the spatial position of deflector plates on the vortex-induced vibration (VIV) of a double-deck truss girder. The wind tunnel tests found that setting the web deflector plate and the lower chord deflector plate significantly suppressed the VIV. In order to study the suppression mechanism of the deflector plate on VIV, numerical simulations were conducted using the computational fluid dynamics (CFD) method. We analyzed the suppression mechanism of the deflector plate on VIV by combining the vertical amplitude obtained by numerical simulation with the change in the vorticity magnitude and direction. The results showed that the flow velocity around the lower surface of the airflow was reduced, resulting in significantly lower vorticity at the exact position of the lower chord deflector plate and web deflector plate section compared to the original section. The web deflector plate and the lower chord deflector plate broke the vortex shedding mode in the wake flow region, and the vortex shedding frequency was far away from the self-oscillation frequency of the double-deck truss girder, thus suppressing the VIV.

Experimental and numerical study on explosion behavior of hydrogen-air mixture in an obstructed closed chamber

The flame evolution, flame front speed and pressure dynamics are investigated through experimental and simulation analysis. The effects of the obstacle on velocity vector field and vorticity field are analyzed. The results indicate that a rise in blockage ratio causes a rapid rise in flame front speed. The turbulent combustion, flame backflow, and overpressure are significantly enhanced as obstacle distance and blockage ratio increase. The jet flame results in a surge in flame front speed, and a momentary increase in pressure rise. The flame-vortex interaction causes strong turbulent combustion and a rapid overpressure increase. The overpressure displays regular periodic fluctuations and high-frequency oscillations with high amplitudes, which can be attributed to the dynamic and impulsive responses. The vortex results in the formation of a curled flame with high localized vorticity. The backflow flame, exhibiting an extremely high vorticity magnitude, is induced by the overall pressure gradient and flow field recirculation.

ANALIZA NUMERICĂ A UNEI NOI CONFIGURAŢII DE TURBINE EOLIENE CU AX VERTICAL

Governmental incentives, technological progress, and lowering costs have made renewable energy more accessible and more affordable for residential areas. Switching to renewable energy sources not only reduces greenhouse gas emissions but also provides long-term financial gains, energy independence, and a cleaner environment for communities. In this study, a numerical analysis of a vertical-axis wind turbine layout that is easily adaptable to populated areas was conducted. Among the results are the variation of the torque coefficient during the course of a complete 360-degree rotation and the vorticity magnitude evolution at the nominal point. In order to validate the numerical results, a test campaign will be conducted inside the wind tunnel as part of further study. This campaign will be carried out using an experimental small-scale model.

High hemodynamic stresses induce aneurysms at internal carotid artery bends

To investigate the role of hemodynamic stresses in initiating cerebral aneurysms at bends of internal carotid artery (ICA). Sixty-one patients with 68 aneurysms at ICA bends were retrospectively enrolled as the experiment group. Among the 61 patients, 30 normal ICAs without aneurysms were chosen as the control. All patients had 3-dimensional angiography and CFD analysis. The bending angle was significantly (P &lt; .0001) smaller in the experiment than control group (131.2º ± 14.9º vs 150.3º ± 9.5º). The dynamic pressure, shear stress, vorticity magnitude and strain rate were the least at direct flow impinging center where the total pressure was very high. The dynamic stress, shear stress, strain rate and gradients of total pressure except for gradient 1 were significantly (P &lt; .05) greater at the aneurysm site than at all the other sites. The total pressure at the aneurysm site was greater (P &lt; .05) than at 1 lateral location and at the distal area but smaller (P &lt; .05) than at the proximal area. The dynamic pressure, shear stress, strain rate and gradient of total pressure at the aneurysm site were significantly (P &lt; .001) greater than on the aneurysm dome. The hemodynamic stresses were all significantly (P &lt; .01) greater at the aneurysm site in the experiment group than at the site corresponding to the aneurysm in the control group. Aneurysms at the ICA bends are caused by direct flow impingement and increased hemodynamic stresses, and smaller arterial bending angles result in abnormally enhanced hemodynamic stresses to initiate an aneurysm near the flow impingement area.