Vortex Street Research Articles

A numerical study on the oscillatory dynamics of tip vortex cavitation

In this paper, we numerically study the mechanism of the oscillatory flow dynamics associated with the tip vortex cavitation (TVC) over an elliptical hydrofoil section. Using our recently developed three-dimensional variational multiphase flow solver, we investigate the TVC phenomenon at Reynolds number $Re = 8.95 \times 10^5$ via dynamic subgrid-scale modelling and the homogeneous mixture theory. To begin, we examine the grid resolution requirements and introduce a length scale considering both the tip vortex strength and the core radius. This length scale is then employed to non-dimensionalize the spatial resolution in the tip vortex region, the results of which serve as a basis for estimation of the required mesh resolution in large eddy simulations of TVC. We next perform simulations to analyse the dynamical modes of tip vortex cavity oscillation at different cavitation numbers, and compare them with the semi-analytical solution. The breathing mode of cavity surface oscillation is extracted from the spatial-temporal evolution of the cavity's effective radius. The temporally averaged effective radius demonstrates that the columnar cavity experiences a growth region followed by decay as it progresses away from the tip. Further examination of the characteristics of local breathing mode oscillations in the growth and decay regions indicates the alteration of the cavity's oscillatory behaviour as it travels from the growth region to the decay region, with the oscillations within the growth region being characterized by lower frequencies. For representative cavitation numbers $\sigma \in [1.2,2.6]$ , we find that pressure fluctuations exhibit a shift of the spectrum towards lower frequencies as the cavitation number decreases, similar to its influence on breathing mode oscillations. The results indicate the existence of correlations between the breathing mode oscillations and the pressure fluctuations. While the low-frequency pressure fluctuations are found to be correlated with the growth region, the breathing mode oscillations within the decay region are related to higher-frequency pressure fluctuations. The proposed mechanism can play an important role in developing mitigation strategies for TVC, which can reduce the underwater radiated noise by marine propellers.

Computational Analysis of Flow Around Two Wall-Mounted Trapezoidal Bluff Bodies Arranged in Tandem Position

Abstract Flow around two identical wall-mounted trapezoidal bluff bodies, arranged in tandem, is numerically investigated at a Reynolds number of 750,000. The investigation employs Reynolds-averaged Navier–Stokes (RANS) equations and the k–ω SST turbulence model. The effect due to the change of the angular orientation of the inclined faces (α) of this bluff body and the pitch distance (L/D) on hydrodynamic quantities and turbulence quantities is investigated. Furthermore, the drag coefficient and Strouhal number have also been evaluated to understand the vortex shedding and flow pattern-related phenomena. For d and intermediate types of bluff bodies, the streamwise mean velocity, cross-stream mean velocity, turbulence kinetic energy, and recirculation length decrease with the increase of α or L/D. Significant changes are also observed in the case of Strouhal number. Reduction in drag coefficient and recirculation length is observed with increased L/D at a constant α for d-type bluff bodies. The change of α and L/D also creates the formation of a periodic von Kármán vortex street at downstream of the second bluff body in the case of L/D = 7, making the flows more complex and unstable. The maximum size of the recirculation bubble occurs in the case of L/D = 10 at α = 30 deg. The investigation provides valuable insight into the complex dynamics of tandem configurations of wall-mounted bluff bodies.

The impact of finite span and wing-tip vortices on a turbulent NACA0012 wing

High-fidelity simulations are conducted to investigate the turbulent boundary layers around a finite-span NACA0012 wing with a rounded wing-tip geometry at a chord-based Reynolds number of $Re_c=200\,000$ and at various angles of attack up to $10^\circ$ . The study aims to discern the differences between the boundary layers on the finite-span wing and those on infinite-span wings at equivalent angles of attack. The finite-span boundary layers exhibit: (i) an altered streamwise and a non-zero spanwise pressure gradient as a result of the variable downwash induced by the wing-tip vortices (an inviscid effect typical of finite-span wings); (ii) differences in the flow history at different wall-normal distances, caused by the variable flow angle in the wall-normal direction (due to constant pressure gradients and variable momentum normal to the wall); (iii) laminar flow entrainment into the turbulent boundary layers near the wing tip (due to a laminar–turbulent interface); and (iv) variations in boundary layer thickness across the span, attributed to the variable wall-normal velocity in that direction (a primarily inviscid effect). These physical effects are then used to explain the differences in the Reynolds stress profiles and other boundary layer quantities, including the reduced near-wall peak of the streamwise Reynolds stress and the elevated Reynolds stress levels near the boundary layer edge, both observed in the finite-span wings. Other aspects of the flow, such as the downstream development of wing-tip vortices and their interactions with the surrounding flow, are reserved for future investigations.

Kármán Vortex Street in Bose-Einstein Condensate with PT Symmetric Potential

Abstract Kármán vortex street not only exists in nature, but also widely appears in engineering practice, which is of great significance for understanding superfluid. And parity-time (PT) symmetric potential provides a good platform for the study of Kármán vortex street. In this paper, different patterns of vortex shedding formed behind PT symmetric potential in Bose-Einstein condensate (BEC) are
simulated numerically. Kármán vortex street and others are discovered to emerge in the wake of a moving obstacle with appropriate parameters. Compared with BEC without PT symmetric potential, the frequency and amplitude of the drag force are more complex. The parametric regions of the combined modes are scattered around the Kármán vortex street. Numerical simulations indicate that the imaginary part of the PT symmetric potential affects the vortex structure patterns. Finally, we proposed an experimental protocol that may observe Kármán vortex street.

Mesh Refinement Investigation to Simulate Tip Vortex Cavitation under Non-Cavitating Conditions

Mesh Refinement Investigation to Simulate Tip Vortex Cavitation under Non-Cavitating Conditions

Analysis and control of hydrofoil vortex-induced vibration

This paper primarily investigates the relationship between the wake vortices and vortex-induced vibrations in hydrofoil structures, as well as explores effective methods to suppress structural vibrations in hydrofoils using a piezoelectric control system. By combining CFD simulations with PIV experiments, the study compared the vortex characteristics at the trailing edge of hydrofoils with different geometries. Furthermore, by integrating the results from the water tank experiments, the research revealed the sensitivity of vortex-induced resonance to the regularity and periodicity of the von Kármán vortex street. Subsequently, the FxLMS algorithm was fine-tuned based on a phenomenological model of vortex-induced resonance. Active control experiments on vortex-induced vibrations of the hydrofoil were conducted using a piezoelectric control system built on this algorithm, achieving a maximum vibration reduction rate of 56%. Finally, the instability and limitations of the control effectiveness were analyzed, and future research directions were proposed to improve control strategies and the system's temporal responsiveness.

A rapid aerodynamic noise prediction model for multi-rotor unmanned aircraft systems with inclusion of wake effect

In this work, the effect of wake on the rotor aerodynamics and aeroacosutics is studied based on an efficient rapid prediction model, which incorporates the induced effects of tip vortex on the blades into the blade element momentum theory. The tip vortex model is estimated using the free vortex wake method. The aerodynamic flow variables, as well as the unsteady loadings due to the radial flow and induction of tip vortices, are employed to model to equivalent sources and, therefore, noise emission, using Goldstein's acoustic analogy. The comparison between the hybrid algorithm and blade element momentum theory shows that the wake effect is not significant in the case of axial flow only. During forward flight conditions, the wake vortex correction greatly affects high frequency harmonics. In addition, a preliminary case study of a quad-rotor vehicle is also discussed, demonstrating the proposed low-fidelity computational framework is helpful for low-noise design and operation of the multi-rotor UAS vehicles.

Analysis of the flow induced vibration transition sustained by a hydrofoil

Hydrofoils sustain severe flow induced vibrations when a hydrodynamic excitation source couples with a natural frequency, a phenomenon called lock-in responsible for early fatigue and acoustic radiations. The present paper focuses on the fluid-structure interaction during the transition between a non-resonant and a lock-in regimes. Tests were performed in the hydrodynamic tunnel of the French Naval Academy Research Institute with a truncated NACA 66-306 hydrofoil for chord-based Reynolds numbers ranging between 255000 and 374000 at zero angle of attack. Laser vibrometry, particle image velocimetry and spectral proper orthogonal decomposition were used to investigate the fluid-structure interaction mechanisms. The analysis has highlighted a transition between a low magnitude vibration regime occurring at Reynolds 255000 and a lock-in regime occurring at Reynolds 374000. A primary excitation source has been associated with Karman vortex shedding. Also, during the lock-in, a specific type of vortices is observed at a characteristic frequency equal to twice the Karman vortex shedding frequency. Also, a flow recirculation region located in close vicinity of the trailing-edge is reinforced at this particular regime. The understanding of the mechanisms leading to high magnitude vibrations will reduce the acoustic radiations and enhance the efficiency of next generation hydrofoils.

The mechanism of aerodynamic performance enhancement of flapping wings with spanwise active deformation

The single stiffness makes the micro-air vehicles (MAVs) only to show excellent flight performance in a specific flow field environment. The MAVs should have the ability to actively deform to adapt to different application scenarios. This study investigates the effects of spanwise active deformation amplitude (ψmax), phase difference (φP), and Strouhal number (St) on the aerodynamic loads and vortex of a wing through numerical simulations. Under the condition of Re= 1000, numerical simulations were conducted on a rectangular wing with an aspect ratio of 4 during the flapping process. The study reveals that moderate spanwise deformation can increase the thrust of the wing and improve propulsion efficiency (ηP). Within the study's scope, the thrust coefficient increases monotonically and linearly with the deformation, but the propulsion efficiency improves only within a limited parameter range. By observing the vortex under different spanwise deformations and monitoring the forces at different positions of the wing, it was found that active deformation can enhance the strength of the leading-edge vortex (LEV) and the wingtip vortex (TV), thereby enhancing the generation of thrust. The results also indicate that the enhancement of LEV is achieved through the coupling between LEV and secondary vortex. At different Strouhal numbers, improvements in ηP can only be achieved through the combined effects of increased vortex strength and optimal vortex residence time. Additionally, it was observed that at lower St, TV can switch from contributing thrust to causing drag.

Comprehensive Influence of Dimensionless Wave Velocity and Expansion Ratio on Energy Absorption Characteristics of Variable Wavelength Traveling Wave Turbine

Based on the traveling wave motion of fish, this paper introduces a new type of variable wavelength traveling wave turbine that significantly differs from traditional turbine designs in its mechanical structure. By developing a two-dimensional traveling wavy plate model and conducting numerical simulations, this study investigates the relationship between the dimensionless wave velocity, variable wavelength coefficient, and expansion ratio, as well as their combined effects on the energy absorption characteristics of the variable wavelength traveling wave turbine. The results reveal that energy absorption efficiency peaks at an optimal dimensionless wave velocity, which is unaffected by changes in the variable wavelength coefficient. Furthermore, the expansion ratio significantly influences both the dimensionless wave velocity and the variable wavelength coefficient, with an optimal ratio of π* = 2.5 achieving 90.42% efficiency. The energy absorption characteristics of the plate with a larger variable wavelength coefficient are found to be constrained by the expansion ratio. Additional analysis reveals that flow characteristics, such as the pressure distribution, vortex street, and velocity field surrounding the traveling wavy plate, are closely related to its energy absorption performance. These findings provide valuable insights for the design of variable wavelength traveling wave turbine.

Control of the von Kármán vortex street with focusing and vectoring of jet using synthetic jet array

In the present study, a novel flow control technique based on jet focusing and vectoring from a synthetic jet array (SJA) for controlling the wake of a bluff body is proposed and demonstrated. A numerical investigation into the flow past a square cylinder modified by the SJA has been carried out at a free stream Reynolds Number of 100. The SJA consists of four independently controlled synthetic jet actuators operating at a peak velocity of eight times the free stream and fifteen times the natural vortex shedding frequency of the square cylinder. The SJA is operated in two different regimes; a focusing regime involving phase delay (Δφ) with non-linear variation between the actuators and a vectoring regime with a linear phase delay without changing the geometric or operating parameters of the SJA. It has been found that jet focusing is able to reduce the coefficient of drag by as much as 43% for Δφ=90°. Focusing is also observed to reduce the fluctuations in the wake velocity with the maximum reduction in fluctuations also corresponding to Δφ=90°. Jet vectoring is able to deflect the von Kármán vortex street in a singular direction along with shifting of the front stagnation point with maximum deflection for Δφ=60°. Furthermore, vectoring leads to an asymmetry in the wake velocity field with the shifting of the velocity deficit region in the direction of the vectoring along with an asymmetry in the wake velocity fluctuations. This novel approach toward synthetic jet induced active flow control allows for greater manipulation of the flow field characteristics of bluff bodies than present methods with applications in areas of underwater and micro air vehicle maneuvering, automobile, and building aerodynamics among others.

On plunging using double-peak kinematics

This study investigates the thrust generation mechanism and performance of a plunging airfoil undergoing double-peak periodic motion, specifically utilizing superposition of the regular sinusoidal waveform with another less-weighted faster one. It is revealed that the proposed waveform produces 200% more thrust when compared to sinusoidal plunging with a small efficiency difference. Also, it produces two vortex pairs (2P) per cycle all over the plunging frequency-amplitude space, instead of the reverse von Karman vortices. Using this proposed waveform, the 2P wake is generated through interaction of three types of vortices shed during plunging, opposing the regular 2P pattern found in the literature.

Investigation of various winglets using computational fluid dynamics for subsonic aircraft

Abstract The tiny, upturned, or downturned extensions at the tips of an aircraft’s wings are designated as winglets. By minimizing drag and improving fuel efficiency, they are introduced to increase the aircraft’s aerodynamic efficiency. Winglets are now a day’s employed in the commercial aircraft to minimise the induced effect caused by wing tip vortices produced at low subsonic speeds. In this article, we have selected NACA 2412, from which we have created a swept back wing with a 20-degree sweep angle that has eight distinct winglet configurations. SolidWorks 2023 is used for design work, and ANSYS 19.2 is used for analysis. The analysis is carried out by changing the angle of attack (AOA) from -6 degrees to 20 degrees with an incremental step of 2 degrees. Here, we have used the k-epsilon turbulence model to capture the turbulence and 100 m/s velocity is maintained throughout the analysis. From this analysis, a potential solution of aerodynamic co-efficient (lift, drag, cl, cd and cl/cd) are being observed. Blended winglet with cant angle 35 degrees produces high lift-to-drag ratio compared with another winglet configuration. The insights gained from the study are plotted in various graphs such as cl vs alpha, cd v/s alpha and cl/cd v/s alpha and the CFD results show a considerable improvement in aircraft’s performance after using winglets. Aluminium alloy’s high strength to weight ratio, robust corrosion resistance, enhanced conductivity, and outstanding ductility qualities will make it easier for us to manufacture winglets in the future.

Volumetric wake investigation of a free-flying quadcopter using Shake-The-Box Lagrangian particle tracking

The Shake-The-Box technique was applied to experimentally quantify the time-resolved volumetric flow field around a free-flying quadcopter UAV with an overall span of about 0.5 m. State-of-the-art LED illumination and high-speed camera equipment was combined with modern Lagrangian tracer particle tracking and data assimilation techniques, facilitating a measurement volume larger than 1.5m3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${1.5}\\,{\\hbox {m}^3}$$\\end{document}. The setup allowed for both hover and limited maneuvering of the quadcopter, while resolving even small details of the complex interactional aerodynamics. In hover out of ground effect, the four individual rotor wakes merged into a single jet within a few rotor radii below the rotor planes. Evaluating the mass and momentum fluxes over suitable control volumes yields accurate estimates for the quadcopter’s total thrust, the asymmetric thrust distribution between front and back rotors, and the entrainment of external flow through turbulent mixing. Hover in ground effect decreases the power requirement and induces recirculating flow in the center of the four rotors. The outwash pattern is non-uniform with jets developing between the rotors and pointing in radially outward directions. Forward flight cases result in a skewed, rapidly merging wake flanked by the roll-up of two “supervortices” similar to the wingtip vortices of fixed-wing vehicles.

Comparison of rotor hovering aerodynamic performance in free-surface and ground effects using numerical methods

The aerodynamic performance of the rotor hovering on the air–water free-surface, which is significant for cross-medium unmanned aerial vehicles, is merely studied. In this study, a compressible two-phase flow model is used to compare the aerodynamic performance in the free-surface effect (FSE) and the ground effect (GE) with various dimensionless distances, γ, between the rotor and the ground (or free-surface). According to the results, the vortex core in FSE moves further in both vertical and radial directions than in GE for the early stages. Additionally, the blade surface is separated into three parts. In zone I, the aerodynamic performance is mostly determined by proximity effects. For both FSE and GE, the downward induced velocity at the rotor disk rises with increasing γ, leading to a decrease in the sectional thrust coefficient CT,S. By the way, CT,S is larger in FSE. In zone III, the aerodynamic performance is mostly governed by the blade tip vortex. The trend of aerodynamic performance with γ is reversed compared with zone I. The above-mentioned two opposing tendencies result in a smaller rotor thrust in FSE than in GE within the range of 0.60≤γ≤3.00, but a higher rotor thrust in FSE within the range of γ≤0.60.

Blade Airfoil Optimization and Its Impact on Vertical Axis Wind Turbine Performance

Abstract Amidst the emergence of crises in petroleum prices and supply, the imperative for the development of clean energy has become increasingly apparent. Vertical axis wind turbines (VAWT), as a type of wind turbine, still grapple with challenges such as low wind energy utilization and sensitivity to dynamic wind speeds. This study focuses on optimizing the airfoil of a two-dimensional vertical axis wind turbine and analyzes the performance variations in a three-dimensional model. Following the optimization, the average power coefficients of the dual-blade two-dimensional VAWT increased by 7.9% and 4%, respectively, while those of the dual-blade three-dimensional model rose by 7.9% and 1.2%. However, the performance of the three-dimensional model was compromised due to the influence of tip vortices, resulting in inferior performance compared to the two-dimensional model. Both three-dimensional optimized blade designs exhibited a substantial reduction in the flow separation region downstream and improved pressure distribution fluctuations caused by the shedding of tip vortices, leading to decreased pressure differentials. Along the spanwise section, the power coefficient gradually decreased from the central segment to the tip segment. Notably, the power coefficient of the optimized blades at the tip segment increased significantly, accompanied by an augmented pressure differential between the upper and lower surfaces. This augmentation contributed to a significant enhancement in lift, thereby facilitating the rotation of the vertical axis wind turbine.

Multiscale modeling of cavitation around high-speed object based on Euler-Lagrange model and overset mesh

Abstract Cavitation is a common phenomenon, which usually occurs inside the high-speed liquid or at the liquid-solid interface. The unsteady behaviors of cavitating flow, such as shedding and collapse, can cause intense pressure fluctuations and reduce the stability of devices such as under-water high-speed vehicles. In addition, cavitating flow changes the dynamic characteristics of the liquid and causes vibration of the structure as well, making it extremely difficult in achieving precise control. Using OpenFOAM, the present work employs the large eddy simulation (LES) approach to investigate the characteristics of the unsteady cavitating flow around a high-speed under-water object with using the overset mesh technology. The volume of fluid (VOF) approach jointed with the Lagrangian discreate bubble model (DBM) is used for capturing the multiscale cavitation features. The Schnerr & Sauer model is applied for the mass transfer between water and vapor in macroscale, while the Reynolds-Pel equation is incorporated for the growing and collapsing of microscale bubbles. Due to the difficulty in incorporating the multi-scale method into the problems with mesh motion, the present work employs the overset mesh method. Compared with the published small-scale water tank experiment, the LES simulation results fit well with the experimental phenomena, and the DBM can capture the small bubbles accurately. On the basis of model verification, the mechanisms of cavitation forming and collapsing is investigated and the effect of cavitation shedding on the motion of the object is also studied. Moreover, the nucleation, growth, collapse of bubbles, and the interaction between discrete bubbles and large cavities can be well revealed. Further, the multi-scale Euler-Lagrange model is also applied in the rotating propeller, the generation of tip vortex cavitation which is hard to be captured by traditional models is well presented.

Time-Resolved Flowfield and Acoustic Measurements of a Ducted and Unducted Rotor

The impact of adding a duct to an 18.5″ diameter, triple-bladed, electrically driven rotor operating up to Mtip=0.5 at static conditions is investigated experimentally to identify the source mechanisms governing the measured acoustic differences. An unducted rotor is characterized by strong, coherent tip vorticity that interacts with each blade passing, generating high-amplitude harmonic tones. The addition of the duct results in tonal broadening and an increase of the primary and harmonic tone amplitudes. Up to a 15 dB increase in broadband noise across the entire frequency range is measured. High-speed particle imaging velocimetry up to 6.4 kHz is employed to acquire phase-locked and ensemble-averaged measurements of the velocity, vorticity, and turbulence fields. While it is often theorized that a duct can shield lateral acoustic radiation, this study finds that the ducted rotor is louder across all operating regimes, and the noise increases with tip Mach number. The ducted rotor dissipates the coherent tip vorticity into incoherent turbulence intensity due to the interaction of the vortices with the duct internal walls, contributing to a strong broadband noise increase and tonal broadening. The ducted rotor broadband noise increase is due to the rotor interacting with a more turbulent inflow condition and increased turbulence intensity throughout the plume shear layer.

Comprehensive study of vortices interaction and blades height effect in a Darrieus vertical axis wind turbine with J‐type blades

AbstractThere is a growing demand to improve the performance of vertical axis wind turbines to facilitate their commercialization for application in urban areas. This study utilizes a 3D numerical analysis to examine the influence of different vortices generated on turbine efficiency with straight and J‐type blades. The numerical simulation of this study employs the Reynolds‐Averaged Navier–Stokes equations and ‎sliding ‎mesh techniques ‎to more accurately model the rotational motion of blades about the turbine axis in relation to the ‎wind. Comparing the output ‎torque and the flow field at different span‐wise sections, the J‐type blades achieve better ‎performance at mid‐spans where the effect of stall vortices is dominant. Conversely, the lower ‎performance of J‐type blades is seen at tip spans due to stronger tip vortices. Investigations also ‎reveal the criticality of the downwind region on the overall performance at high tip speed ratios. It is observed that by ‎increasing the height, the tip vortices are limited to the tip sections, and stall vortices expand further ‎along the blade. At TSR = 1, the improvement by J‐type blades rises from 10% at a height of 0.8 m to 44% ‎at 3 m. The growth in height at lower wind speeds becomes more beneficial. Compared to the straight blades, the self‐starting ‎generated torque by J‐type blades for heights of 0.8, 1.2, and 1.6 m, are improved by 15.6%, ‎‎26.9%, and 34.7%, respectively. Overall, it is concluded that by increasing the blade height, the superiority ‎of the J‐type blade becomes more noticeable as the blade mainly contributes to suppressing the stall ‎vortices effect where the tip vortices effect is not presented. ‎

Numerical investigation on the blade vortex interaction noise reduction using higher harmonic control

Accurately predicting the formation, evolution, and breakdown of helicopter blade tip vortex is crucial for simulating the Blade-Vortex Interaction (BVI) phenomenon. Firstly, the high-order Perturbed polynomial reconstructed Targeted Essentially Non-Oscillatory (TENO-P) scheme proposed by our research group is employed to improve the resolution of the helicopter rotor flowfield solver. The TENO-P scheme, building on the fifth-order TENO5 scheme, achieves one-order of accuracy improvement by adaptively adjusting the values of the free-parameter introduced by perturbed polynomial reconstruction. Subsequently, the AH-1 helicopter model rotor undergoing blade-vortex interaction is analyzed using the improved rotor flowfield solver and the Farassat-1A formula. The implementation of the TENO-P scheme notably enhances the resolution of the rotor flowfield solver in resolving the blade tip vortex structures, and the predicted noise results are in good agreement with the experimental data. Finally, the alteration of the BVI noise and its reduction mechanism of the AH-1 model rotor under different Higher Harmonic Controls (HHC) are analyzed. The findings show that the phase modulation margin increases with a decrease in harmonic order, and the noise reduction effect significantly improves as well. The negative component of the higher harmonic control is beneficial for reducing BVI noise while the positive component of the higher harmonic control exacerbates the BVI noise. The HHC reduces the collective pitch angle in the region where the tip vortex is about to be disturbed, decreasing the strength of the blade tip vortex in this region. This reduction weakens the strength of the parallel and near-parallel interaction on the advancing side, leads to the reduction of the positive peak impulsive of the BVI noise, and consequently lowers the intensity of the BVI noise.