Vortex Street Research Articles

The best whistler: A cavitating tip vortex

The discrete tone radiated from a cavitating tip vortex, known as “vortex singing,” was first recognized in 1989, but its sound generation mechanism has remained a mystery for over 30 years. In this Letter, by means of the correction for the cavitation bubble dynamics and the dispersion relation of cavity interfacial waves, we found that after the far-end disturbances propagate upstream, the whistling vortex should be triggered by near-end sound sources, the breathing mode waves. Further utilizing the theoretical solutions for singing lines and the potential singing cavitation number with frequency, we accurately identified all available tests for seeking the vortex singing over the past three decades, which not only demonstrates that the vortex singing frequency is only determined by the measurable mean cavity radius (rc), cavitation number (σ), and desinent cavitation number (σd) in experiments, but also responses to a long-standing perplexity: why such a best whistler is able to appear only within a narrow range of the cavitation number.

Lagrangian flow networks for passive dispersal: Tracers versus finite-size particles.

The transport and distribution of organisms such as larvae, seeds, or litter in the ocean as well as particles in industrial flows is often approximated by a transport of tracer particles. We present a theoretical investigation to check the accuracy of this approximation by studying the transport of inertial particles between different islands embedded in an open hydrodynamic flow aiming at the construction of a Lagrangian flow network reflecting the connectivity between the islands. To this end, we formulate a two-dimensional kinematic flow field which allows the placement of an arbitrary number of islands at arbitrary locations in a flow of prescribed direction. To account for the mixing in the flow, we include a von Kármán vortex street in the wake of each island. We demonstrate that the transport probabilities of inertial particles making up the links of the Lagrangian flow network essentially depend on the properties of the particles, i.e., their Stokes number, the properties of the flow, and the geometry of the setup of the islands. We find a strong segregation between aerosols and bubbles. Upon comparing the mobility of inertial particles to that of tracers or neutrally buoyant particles, it becomes apparent that the tracer approximation may not always accurately predict the probability of movement. This can lead to inconsistent forecasts regarding the fate of marine organisms, seeds, litter, or particles in industrial flows.

On the absence of a secondary vortex street in three-dimensional and turbulent cylinder wakes

On the absence of a secondary vortex street in three-dimensional and turbulent cylinder wakes

Exploring multiple phases and first-order phase transitions in Kármán Vortex Street

Kármán Vortex Street, a fascinating phenomenon of fluid dynamics, has intrigued the scientific community for a long time. Many researchers have dedicated their efforts to unraveling the essence of this intriguing flow pattern. Here, we apply the lattice Boltzmann method with curved boundary conditions to simulate flows around a circular cylinder and study the emergence of Kármán Vortex Street using the eigen microstate approach, which can identify phase transition and its order-parameter. At low Reynolds number, there is only one dominant eigen microstate W1 of laminar flow. At Rec1 = 53.6, there is a phase transition with the emergence of an eigen microstate pair W2,3 of pressure and velocity fields. Further at Rec2. = 56, there is another phase transition with the emergence of two eigen microstate pairs W4,5 and W6,7. Using the renormalization group theory of eigen microstate, both phase transitions are determined to be first-order. The two-dimensional energy spectrum of eigen microstate for W1, W2,3 after Rec1, W4–7 after Rec2 exhibit −5/3 power-law behavior of Kolnogorov’s K41 theory. These results reveal the complexity and provide an analysis of the Kármán Vortex Street from the perspective of phase transitions.

Stability enhancement using a new combined casing treatment strategy in an ultra-highly loaded transonic compressor rotor

Low-reaction compressors are promising for achieving high loads but face severe flow instability challenges. This study investigates a low-reaction transonic compressor rotor using casing treatment technologies to control unstable flow dynamics precisely. First, a design integrating self-recirculating and circumferential groove casing treatments near the leading edge is implemented. This design enhances flow capacity at the tip passage inlet. However, it causes a “stall transposition” phenomenon. The unstable flow structures shift from shock-tip leakage vortex interactions at the front to corner separation at the rear. Consequently, the stall mechanism transitions from an end-wall stall to a blade stall. To address this issue, a new casing treatment layout is proposed. Grooves are added after the mid-chord of the initial front casing configuration. This adaptation suppresses emerging unstable flow structures and extends the stall margin by approximately 12.07 %. Detailed flow field analysis shows that the rear grooves effectively reduced the trailing edge separation vortex. They also limit downstream corner separation and mitigate disturbances from tip leakage flows in the rear of the passage.

Experimental investigation of the Eckert-Weise effect (aerodynamic cooling) of pair side-by-side circular cylinders in a compressible cross-flow

The rear surface of a thermally insulated circular cylinder placed in a subsonic high-velocity cross-flow is significantly cooled, this phenomenon is known as aerodynamic cooling or the Eckert–Weise effect. This effect is associated with the redistribution of the stagnation temperature (energy separation) in the unsteady vortex wake. Experiments show that the effect is maximal at Mach numbers of the free-stream flow of 0.5–0.7, resulting in negative values of the temperature recovery factor (the temperature of the cylinder rear surface becomes lower than the static temperature of the free-stream flow). In this case, the cooling of the rear surface can reach tens of degrees. This effect can be utilized as the basis for a novel energy separation device, as it enables heat transfer between flows with the same stagnation temperatures. As shown in a numerical study (Aleksyuk, 2021), the effect is highly sensitive to the flow interference behind side-by-side cylinders, this is especially important for its practical application. In this study, the aerodynamic cooling of a pair identical circular cylinders in side-by-side arrangement, is experimentally investigated within the Mach and Reynolds number ranges of M = 0.34–0.58 and ReD = 1.6∙105–3.1∙105. The cylinder spacing considered in this study (P/D = 1.1; 1.5; 2.0; 3.0; and 4.0, where P is the center-to-center cylinder spacing and D is the diameter) covered the key regimes of vortex interference, that is, single, bistable, and coupled vortex streets. Also, investigations were conducted for a single circular cylinder with the same diameter within the Mach and Reynolds number ranges of M = 0.34–0.68 and ReD = 1.6∙105–3.4∙105. The channel blockage ratio was found to be 8% for a single cylinder and 16% for a pair of cylinders. Consequently, this study focuses on confined flow or flow past a confined cylinder with a uniform profile of oncoming flow velocity. It is shown that the Eckert-Weise effect for the pair of cylinders can either increase or decrease depending on the interference regimes and is sensitive to the blockage ratio value.

CFD simulation of the aerodynamic performance of co-axial multi-rotor wind turbines using the actuator line method

Multi-rotor wind turbines (MRWTs) have attracted widespread attention due to their high efficiency and large generating capacity, and they have become a potential solution for offshore wind turbines. A co-axial MRWT has the advantages of high power density and a small footprint. The actuator line method-large eddy simulation (ALM-LES) is applied to investigate the aerodynamics and near-wake characteristics of unidirectional and counter-rotating co-axial MRWTs. The influence of the blade tip vortices on rotor-to-rotor interactions, wake mixing, and recovery are analyzed. The results show that the unidirectional co-axial twin-rotor wind turbine has a good aerodynamic performance. The torque of the two rotors fluctuates significantly and periodically when the twin rotors rotate in reverse. A distance of 0.3 R between the rotors causes the front rotors to impact the aerodynamic performance of the rear rotors, whereas exceeding 0.5 R minimizes the influence of the rear rotor on the front rotor. And an appropriate azimuth angle should be selected to avoid adverse effects on aerodynamic performance.

Flow field reconstruction of trash rack based on generative adversarial networks

ABSTRACT A new model - super-resolution Wasserstein Generative Adversarial Network with Gradient Penalty (SRWgan-GP) - is developed with resolution of 512×512 to reconstruct the sliced 2D high-resolution flow field from low-resolution data. To train the SRWgan-GP model, flow field data obtained from Large Eddy Simulation (LES) behind the trash racks is utilized. A sub-pixel convolution layer is incorporated in the framework to generate higher-resolution feature maps (512 × 512), which significantly reduces the network's memory requirements under the same output resolution .The performance of the proposed model is compared with that of other commonly used generative models including u-shaped architecture model (Unet) and Convolutional Neural Network (CNN). The results reveal that the SRWgan-GP model excels in reconstructing the flow field along both the x with and y axes, demonstrating the most accurate performance with minimal error achieving an MSE of 0.001, PSNR of 46.557, and SSIM of 0.994 in depicting turbulent structures and the Kįrmįn vortex street. Power Spectral Density (PSD) analysis shows that the primary shedding frequency of the vortex street is consistent with LES at approximately 10Hz for SRWgan-GP. Additionally, the SRWgan-GP exhibits proficient accuracy in computing second-order statistics of the flow field, achieving minimal error in instantaneous Reynolds shear stresses.

Effect of wing height layout on the aerodynamic performance ofhigh-speed train

PurposeThis paper aims to investigate the effect of different wing height layouts on the aerodynamic performance and flow structure of high-speed train, in a train-wing coupling method with multiple tandem wings installed on the train roof.Design/methodology/approachThe improved delayed detached eddy simulation method based on shear stress transport k-ω turbulence model has been used to conduct computational fluid dynamics simulation on the train with three different wing height layouts, at a Reynolds number of 2.8 × 106. The accuracy of the numerical method has been validated by wind tunnel experiments.FindingsThe wing height layout has a significant effect on the lift, while its influence on the drag is weak. There are three distinctive vortex structures in the flow field: wingtip vortex, train body vortex and pillar vortex, which are influenced by the variation in wing height layout. The incremental wing layout reduces the mixing and merging between vortexes in the flow field, weakening the vorticity and turbulence intensity. This enhances the pressure difference between the upper and lower surfaces of both the train and wings, thereby increasing the overall lift. Simultaneously, it reduces the slipstream velocity at platform and trackside heights.Originality/valueThis paper contributes to understanding the aerodynamic characteristics and flow structure of a high-speed train coupled with wings. It provides a reference for the design aiming to achieve equivalent weight reduction through aerodynamic lift synergy in trains.

The effect of Reynolds number on the separated flow over a low-aspect-ratio wing

At high incidence, low-aspect-ratio wings present a unique set of aerodynamic characteristics, including flow separation, vortex shedding and unsteady force production. Furthermore, low-aspect-ratio wings exhibit a highly impactful tip vortex, which introduces strong spanwise gradients into an already complex flow. In this work, we explore the interaction between leading-edge flow separation and a strong, persistent tip vortex over a Reynolds number range of $600 \leq Re \leq 10{\,}000$ . In performing this study, we aim to bridge the insight gained from existing low-Reynolds-number studies of separated flow on finite wings ( $Re \approx 10^2$ ) and turbulent flows at higher Reynolds numbers ( $Re \approx 10^4$ ). Our study suggests two primary effects of the Reynolds number. First, we observe a break from periodicity, along with a dramatic increase in the intensity and concentration of small-scale eddies, as we shift from $Re = 600$ to $Re = 2500$ . Second, we observe that many of our flow diagnostics, including the time-averaged aerodynamic force, exhibit reduced sensitivity to Reynolds number beyond $Re = 2500$ , an observation attributed to the stabilising impact of the wing tip vortex. This latter point illustrates the manner by which the tip vortex drives flow over low-aspect-ratio wings, and provides insight into how our existing understanding of this flow field may be adjusted for higher-Reynolds-number applications.

Assessing the Environmental Impact of Aircraft/Engine Integration with Respect to Contrails

Abstract In recent years, the radiative forcing of aircraft contrails and aircraft-induced contrail cirrus have been highlighted as a serious short-term climate impact of the aviation industry. Greater understanding of factors influencing contrail properties are required if routes to mitigation are to be explored. In the current work, a parametric turbofan powered aircraft model has been created to study the impact that aircraft design, in particular the interaction between the jet and wingtip vortex, can have on ice crystal formation, growth, and dynamics within a contrail. To investigate this, a contrail microphysics module has been developed and integrated within Rolls-Royce in-house Hydra CFD code. Three-dimensional Reynolds-Averaged Navier-Stokes simulations are conducted over the jet and early vortex regime, covering an area which is often simplified in most contrail modelling approaches. It is found that the position of the engine along the wing of an aircraft can impact the formation of the wingtip vortex, altering the contrail properties and distribution downstream of the aircraft. The effect of multi-engine architecture is also assessed and shown to influence the magnitude of exhaust entrainment into the vortex.

A local and hierarchical Koopman spectral analysis of fluid dynamics

AbstractA local and hierarchical Koopman spectral analysis is proposed to extend Koopman spectral analysis typically used in a linear system or an ergodic process to its application in general nonlinear dynamics. The continuous and analytic Koopman eigenfunctions and eigenvalues, derived from operator perturbation theory, are capable of dealing with a nonlinear transition process with mathematical rigorousness. A proliferation rule is identified to derive high‐order eigenvalues and eigenfunctions from lower‐order ones, thus various spectral patterns may be generated through recursive proliferations. The locally linear map around each state constructs base local Koopman eigenvalues and eigenfunctions from an algebraic eigenvalue problem, and high‐order ones are generated via the proliferation rule to express the systematic nonlinearity. The aforementioned hierarchy simplifies the Koopman spectral analysis and is verified by studying the development of Kármán vortex streets. The triangular chain and the lattice distribution of Koopman eigenvalues confirm the critical role of the proliferation rule and the hierarchy structure of Koopman eigenvalues. The local spectral analysis on the transition process shows that the periodic flow forms as the growth rates of the critical Koopman modes reduce to zero, and meanwhile, the Koopman modes at the same frequency superpose on each other to form the well‐known Fourier or Floquet modes, where the latter are the enhanced nonlinear motions due to the alignment of Koopman eigenvalues with the critical ones.

Experimental observation of parabolic wakes in thin plates

Wakes are medium perturbations created by a moving object, such as wave patterns behind boats, or wingtip vortices following an aircraft. Here, we report about an experimental study of an uncharted form of parabolic wakes occurring in media with the group velocity twice larger than the phase velocity, as opposed to the conventional case of Kelvin wakes. They are formed by moving a laser spot on a thin plate, which excites a unique wake pattern made of confocal parabolas, due to the quadratic dispersion of the zero-order flexural Lamb mode. If the spatial dimensions are rescaled by the perturbation velocity and material constant, we obtain a single universal wake with constant parabolic focal lengths. We demonstrate an evanescent regime above the critical frequency where the wave components oscillate exclusively in the direction parallel to the perturbation path, with an opening angle of 90∘. We define a dimensionless number, analogous to Froude and Mach numbers, which determines whether or not the complete parabolic wake pattern will be excited by the moving source. Finally, we generalize the physics of wake shapes to arbitrary dispersion relations. Published by the American Physical Society 2024

Numerical simulation study of the effect of porous media passive flow control on the propulsion performance of airfoils in kármán vortex streets

This study investigates the influence of porous media on the propulsion performance of airfoils in eddy currents. The passive motion of the airfoil was simulated using overlapping grid technology and the six degrees of freedom method. Research has found that porous media reduces the traction of fixed airfoils and reduces surface turbulence intensity. In the released state, the porous airfoil horizontal movement is slower and the lateral displacement decreases. Combining the two results in a longer forward distance for the NACA0024 thick airfoil, but the effect depends on the release time. This study may inspire the design of underwater robots.

Interference mechanism of trailing edge flap shedding vortices with rotor wake and aerodynamic characteristics

A robust Reynolds-Averaged Navier-Stokes (RANS) based solver is established to predict the complex unsteady aerodynamic characteristics of the Active Flap Control (AFC) rotor. The complex motion with multiple degrees of freedom of the Trailing Edge Flap (TEF) is analyzed by employing an inverse nested overset grid method. Simulation of non-rotational and rotational modes of blade motion are carried out to investigate the formation and development of TEF shedding vortex with high-frequency deflection of TEF. Moreover, the mechanism of TEF deflection interference with blade tip vortex and overall rotor aerodynamics is also explored. In non-rotational mode, two bundles of vortices form at the gap ends of TEF and the main blade and merge into a single TEF vortex. Dynamic deflection of the TEF significantly interferes with the blade tip vortex. The position of the blade tip vortex consistently changes, and its frequency is directly related to the frequency of TEF deflection. In rotational mode, the tip vortex forms a helical structure. The end vortices at the gap sides co-swirl and subsequently merge into the concentrated beam of tip vortices, causing fluctuations in the vorticity and axial position of the tip vortex under the rotor. This research concludes with the investigation on suppression of Blade Vortex Interaction (BVI), showing an increase in miss distance and reduction in the vorticity of tip vortex through TEF phase control at a particular control frequency. Through this mechanism, a designed TEF deflection law increases the miss distance by 34.7% and reduces vorticity by 11.9% at the target position, demonstrating the effectiveness of AFC in mitigating BVI.

Two-dimensional spanwise flow regime influenced by tip vortex around a ground-mounted square cylinder in low turbulence uniform flow

The time series data of the lift force acting on a ground-mounted square cylinder in low-turbulence uniform flow reveal a distinctive pattern characterized by a predominant high-amplitude process modulated by intermittent low-amplitude fluctuations. This behavior arises from the intricate interplay between tip and Kármán vortices. However, conflicting interpretations persist, with some findings even presenting contradictory conclusions, particularly regarding the presence of symmetric shedding in the fluctuating lift force process with low amplitude. Furthermore, a clear consensus regarding the mechanism governing the interaction between the tip vortex and the spanwise vortex remains elusive. This study aims to elucidate the two-dimensional flow regime in the spanwise direction influenced by the tip vortex of a ground-mounted square cylinder in low-turbulence uniform flow through experimental investigation. Multiple-point synchronous pressure measurement and particle image velocimetry systems are utilized to measure wind pressure on the side walls and the corresponding flow field at 2/3 of the cylinder's height. The analysis confirms the presence of two distinct types of lift force coefficient behavior: low-amplitude fluctuation (LAF) characterized by longer durations and high-amplitude fluctuation (HAF) occurring in shorter intervals. Subsequently, the flow regime in the near wake corresponding to each mode of the lift force coefficient is discussed. It is observed that the LAF regime corresponds to symmetrical vortex shedding with a prolonged shear layer, maintaining nearly constant curvature. Conversely, for HAF, a pronounced Kármán vortex street is evident. This study conclusively demonstrates the existence of symmetrical vortex shedding, which predominantly contributes to the LAF component of the lift force.

Periodic Vortices Created by Plasma Actuator with Low Frequency

Dielectric barrier discharge plasma actuators, capable of creating a quasi-steady wall jet, are well suited for flow control over the microair vehicles at low Reynolds number. The plasma actuator is usually excited by a sinusoidal high-voltage power with a frequency of a few to tens of kilohertz. However, the investigations on the flowfield produced by a plasma actuator with a frequency below 200 Hz remain limited. Motivated by this demand, the formation and characterization of the vortices generated by a plasma actuator with a high-voltage frequency of 125 Hz are studied in detail. In addition to the starting vortex, it is of great importance that a train of vortices that shed periodically from the junction between the two electrodes and are quite different from the starting vortex are first observed. The shedding frequency of the periodic vortices is the same as the high-voltage frequency of 125 Hz. Combining the acoustic with the flow characteristics of the plasma actuator, the formation mechanism of these periodic vortices is discussed. Finally, a criterion for generating the periodic vortices is proposed based on the relationship between the scale of vortices and the separation distance between the two neighboring periodic vortices.

Turbulent boundary layer structures downstream of a square cylinder

Particle image velocimetry is used to investigate the coherent structures within a turbulent boundary layer (TBL) perturbed by a slender square cylinder. A moderate Reynolds number of Reτ=3691 is considered. The cylinder is immersed in different vertical regions of the TBL, from the viscous sublayer to the logarithmic layer, depending on the value of the cylinder–wall gap ratio within the range of G/D=0.0−2.0. Here, G is the distance between the wall and the lower surface of the cylinder, and D is the cross-section size of the square cylinder. The results reveal a substantial influence of the TBL statistics and structures. Utilizing velocity correlation and proper orthogonal decomposition (POD), we highlight the intriguing influence of large-/very large-scale turbulent structures induced by the cylinder. When the cylinder is positioned on or in close proximity to the wall, periodic shedding of vortices is not apparent. In the presence of a cylinder, the large-/very large-scale turbulent structures are reduced in size compared with those in the undisturbed TBL, owing to the interaction between the flow around the cylinder and the boundary layer turbulence. The lower modes of the POD in the disturbed TBL are similar to those of the undisturbed flow field. However, the large-/very large-scale turbulent structures are increasingly affected by the strengthening of the shedding vortices with increasing G/D when the cylinder is located in the logarithmic region. As a result, the Kármán vortex street becomes the dominant structure associated with the higher POD modes at sufficiently high cylinder–wall gap ratios.

Effects of turbulence on the blade root load of the tandem wind turbine in neutral atmospheric boundary layer

Abstract A model characterizing a turbulent wind field, consistent with neutral atmospheric boundary layer attributes, was developed for a field-based experimental wind turbine using stochastic processes combined with shear flow profiles. By incorporating interactions of vertical thermal exchange, terrain-induced surface roughness, and Coriolis forces, the model simulates environmental impacts. A sequence of wind turbines situated within the atmospheric wind field underwent computational analysis leveraging Large Eddy Simulation (LES) alongside an Actuator Line Model (ALM) to examine atmospheric turbulence alterations both preceding and following the turbines. Analysis of the power spectra concerning wind velocity, turbulence intensity, and components of Reynolds stress upwind and downwind demonstrated the turbines’ blade effects on surrounding turbulence patterns. The research demonstrated that turbulence kinetic energy experienced enhancement in downwind turbines as a result of the upwind turbine’s impact, particularly evident in the lower-frequency spectrum. Augmenting the distance between turbines initially aids in the wake’s turbulent structure restoration, with a marked effect on tip vortices that hold greater amounts of high-frequency energy.

Vortex-shedding modes of a pair of side-by-side thin pitching plates

We have conducted three-dimensional (3D) direct numerical simulations to analyze vortex-shedding modes past vertically arranged, side-by-side 3D pitching plates, considering cases where the plates are in the same, opposite, and different phases. The simulations are performed at a Reynolds number Re=1000, with a dimensionless pitching frequency St=1, and a maximum pitching angle θmax=15°. The vortex-shedding modes reveal horseshoe vortices transforming into distorted hairpin-like structures in the far wake for in-phase plates. Opposite phase plates exhibit helical distortion and core bifurcation, while different phase angles produce meridionally twisted, entangled hairpins. We observe a reverse von Kármán vortex street for in- and different-phase plates, while the opposite shows a reverse Kármán vortex street for the upper plate and a Kármán vortex street for the lower plate. The streakline visualizations reveal wake compression and spoke-like structures symmetrically emanating from the shear layer extremities around the plates' central region. We find leapfrog-like cross-stream vortex interaction when the plates are in phase. The line-time diagram reveals alternating patches of low-intensity cells, switching between negative and positive, alongside continuous bands of both positive and negative cells. Both plates produce similar thrust for the parameters examined in this study.