Vortex Core Research Articles

Assessment of the Vortex Feature-Based Vorticity Confinement Method Applied to Rotor Aerodynamics and Aeroacoustics

The accurate prediction of helicopter rotor aerodynamics and aeroacoustics using Computational Fluid Dynamics (CFD) techniques still remains a challenge, as the over-dissipation of numerical schemes results in a higher diffusive rate of rotor wake and vortices than what can be expected from the fluid governing equations. To alleviate this issue, a vortex feature-based vorticity confinement (FVC2-L2) method that combines the locally normalized λ2 vortex detection method with the standard second vorticity confinement (VC2) scheme is presented to counterbalance the truncation error introduced by the numerical discretization of the convective term while avoiding the over-confinement inside the boundary layer. The FVC2-L2 scheme is adopted for helicopter rotor aerodynamic and aeroacoustic predictions through its implementation in the multi-block structured grid CFD solver ROSITA and coupling with the aeroacoustic code ROCAAP based on the permeable surface Ffowcs Williams–Hawkings (PS-FWH) equation. This approach is assessed in helicopter rotor flows via three databases. Firstly, the well-documented HART-II rotor in the baseline condition is used to evaluate the capability of the presented VC scheme in blade–vortex interaction (BVI) phenomena prediction. Subsequently, the UH-1H non-lifting hovering rotor and the AH-1/OLS low-speed descending flight rotor are adopted for assessment of such a method in aeroacoustics. The benefits of the FVC2-L2 scheme in terms of aerodynamics prediction, wake preservation, and noise signal prediction are well demonstrated by comparison with the experimental data and the results obtained without VC schemes. Particularly, the FVC2-L2 scheme mainly improves the highly unsteady airloads prediction, and results in an improvement of BVI noise prediction by more than 5 dB with respect to the case without VC schemes for AH-1/OLS rotor case. Additionally, some shortcomings of the approach are noticed in engineering applications. On the basis of a simplified convective vortex, some provisional guidelines on the required εo value in terms of number of cells per vortex diameter are provided: an εo value ranging from 0.01 to 0.04 for grids which may represent the vortex core diameter with 6 to 12 cells.

Asymmetric scattering behaviors of spin wave dependent on magnetic vortex chirality

We investigate asymmetric spin wave scattering behaviors caused by vortex chirality in a cross-shaped ferromagnetic system by using the micromagnetic simulations. In the system, four scattering behaviors are found: (i) asymmetric skew scattering, depending on the polarity of vortex core, (ii) back scattering (reflection), depending on the vortex core stiffness, (iii) side deflection scattering, depending on structural symmetry of the vortex circulation, and (iv) geometrical scattering, depending on waveguide structure. The first and second scattering behaviors are attributed to nonlinear topological magnon spin Hall effect related to magnon spin-transfer torque effect, which has value for magnonic exploration and application.

Characterizing Internal Flow Field in Binary Solution Droplet Combustion with Micro-Particle Image Velocimetry

Droplet internal flow participates in liquid-phase mass transfer during multicomponent solution droplet combustion. In this work, internal flow fields in the binary droplet combustion of two polyoxymethylene dimethyl ethers (CH3O(CH2O)nCH3, n ≥ 1, abbreviated as PODEn), i.e., PODE2 and PODE4, are characterized using micro-particle image velocimetry (Micro-PIV). The buoyancy-driven upward vapor flow around the droplet is found to initiate two opposite radial flows in the droplet, which form two vortex cores near the surface, while the gravitational effect and Marangoni effect resulting from the content and temperature gradients in the binary droplets can induce disturbance to the two flows. The binary droplets have comparable spatially averaged flow velocities at the stable evaporation stage to those of pure droplets, which are around 3 mm/s. The velocity curves are more fluctuant and tend to slightly increase and reach the peak values at around 250 ms, and then decrease until droplet atomization. The flow velocities in the droplet interior are generally higher than those near the droplet surface, forming a parabolic velocity profile along the horizontal radial direction. The peak velocity first increases to 5–9 mm/s as the radial flow and vortex structure start to form and then decreases to around 3 mm/s until droplet atomization. The radial flow with a spatially averaged velocity of 3 mm/s can run around one lap during the stable evaporation stage, which implies that the convection-induced mass transfer is relatively weak, and consequently, the content gradient of the binary droplet is still mainly controlled by mass diffusion.

Microwave response of type-II superconductors at weak pinning

Theory of linear microwave response of thin films of type-II superconductors in the mixed state is developed taking into account random spatial fluctuations of the parameters of the system, such as the order parameter, diffusion coefficient, or film thickness. In the regime of collective pinning the microwave response of the system exhibits strong frequency dispersion, arising from nonequilibrium vortex core quasiparticles. The corresponding contribution to the ac conductivity is controlled by the inelastic relaxation time, and may exceed the usual Bardeen-Stephen conductivity. It is caused by the Debye-type inelastic relaxation. Debye mechanism of microwave losses may be responsible for strong effects of electromagnetic noise upon dc conductivity in the mixed state at low temperatures.

Investigation into fresh air delivery performance with vortex ring

An air supply mode based on vortex ring structures was proposed to deliver fresh air for good indoor air quality. This study focused on the influence of air supply parameters, including formation time (T*), supply air velocity (U0), and supply air temperature difference (ΔT), on the fresh air delivery performance of an air vortex ring using numerical simulations. The cross-sectional average mass fraction of fresh air (Ca) was proposed to evaluate the fresh air delivery performance of the air vortex ring supply. The results showed that the convective entrainment of the vortex ring resulted from the combined effect of the induced velocity generated by the rotational motion of the vortex core and the negative pressure zone. When the formation time T* < 3.5, Ca increases with an increase in the formation time but decreases with an increase in the formation time for T* > 3.5. The variation in Ca is insignificant for U0 < 3 m/s or U0 > 3 m/s but decreases with an increase in the supply air temperature difference (ΔT). Thus, the optimal air supply parameters for air vortex ring supply are identified as T* = 3.5, U0 = 3 m/s, ΔT = 0 °C. Compared with the traditional circular and square free air jets, within 25Ds (Ds: the diameter of air supply inlet) downstream from the air inlet, the fresh air delivery performance of the air vortex ring supply is increased by a maximum of nearly 200 %, with an average improvement of approximately 120 %.

Numerical study on prediction and discrimination methods of propeller tip vortex cavitation inception

Tip vortex cavitation is typically the first type of cavitation in real ship propellers due to the scale effect. To lessen or eliminate propeller cavitation noise, it is necessary to effectively identify and predict the tip vortex cavitation initiation of the propeller and run the propeller as far as possible in the “non-cavitation area.” However, for the current numerical computation, it is impossible to determine the minimum pressure at the vortex core directly and correctly, making it difficult to anticipate the cavitation initiation of the propeller tip vortex. In this paper, based on computational fluid dynamics (CFD) numerical calculations and the tip vortex model proposed by Xin [Proceedings of 2013 Ship Hydrodynamics Conference (2013), pp. 211–218], we propose a new prediction method for propeller tip vortex cavitation initiation—“the tip vortex model method.” The propeller tip vortex is solved by CFD calculation in this model, and the minimum pressure at the downstream vortex core is examined based on the tip vortex model to determine the initiation of propeller cavitation. We examine the cavitation inception using the tip vortex model method and compare it to the results obtained using the minimum pressure coefficient method and the minimum vapor volume method. It is discovered that the cavitation inception number obtained by the tip vortex model method is closer to the experimental results. Furthermore, the effects of different turbulence models and grid settings on the prediction of tip vortex cavitation initiation are investigated, providing an effective reference for the prediction of propeller tip vortex cavitation initiation.

On the Origins of Vorticity in a Simulated Tornado-Like Vortex

Abstract The authors explore the dynamical origins of rotation of a mature tornado-like vortex (TLV) using an idealized numerical simulation of a supercell thunderstorm. Using 30-min forward parcel trajectories that terminate at the base of the TLV, the vorticity dynamics are analyzed for n = 7 parcels. Aside from the integration of the individual terms of the traditional vorticity equation, an alternative formulation of the vorticity equation and its integral, here referred to as vorticity source decomposition, is employed. This formulation is derived on the basis of Truesdell’s “basic vorticity formula,” which is obtained by first formulating the vorticity in material (Lagrangian) coordinates, and then obtaining the components relative to the fixed spatial (Eulerian) basis by applying the vector transformation rule. The analysis highlights surface drag as the most reliable vorticity source for the rotation at the base of the vortex for the analyzed parcels. Moreover, the vorticity source decomposition exposes the importance of small amounts of vorticity produced baroclinically, which may become significant after sufficient stretching occurs. Further, it is shown that ambient vorticity, upon being rearranged as the trajectories pass through the storm, may for some parcels directly contribute to the rotation of the TLV. Finally, the role of diffusion is addressed using analytical solutions of the steady Burgers–Rott vortex, suggesting that diffusion cannot aid in maintaining the vortex core.

Quantitative experimental research on vortex generation and self-maintenance mechanisms in turbulence

Turbulence is not completely random, but contains organized and multi-scale structures. Vortices have always been recognized as the most important coherent structure in turbulent flow, playing a significant role in the generation, evolution, and maintenance of turbulence. In the present work, the vortex formation and evolution process of a fully developed turbulent boundary layer in a rectangular channel flow is experimentally studied by moving-single frame and long exposure and moving-particle image velocimetry measurements. The Rortex integral (RI) method is proposed for quantitative statistics on the critical vortex core size as well as the accurate rotation strength during the evolution process. In this paper, the vortex regeneration and self-maintenance mechanisms in near-wall turbulent flow are experimentally revealed and quantified by the RI method, to give some revelations for the future research on the turbulence theory. On the one hand, three behaviors of the hairpin vortex regeneration are discovered to play a significant role in turbulence development: (A) hairpin regeneration induced by the interaction between hairpins and packets; (B) auto-generation of multiple hairpin vortex in one packet (secondary and tertiary hairpins); and (C) the merging of hairpin vortices in the packets. On the other hand, the circulation process, which contains a mass of young vortex growth with the parent self-decaying, is verified to sustain and promote the development of turbulence. In consequence, the self-sustaining turbulence theory based on mother–child hairpins generation mechanism is supported by the experimental results.

Baroclinic Model of Jupiter’s Great Red Spot

The paper proposes a quasi-geostrophic baroclinic model of Jupiter’s Great Red Spot as a localized eddy formation in a continuously stratified rotating atmosphere under the action of a horizontal shear flow in the f-plane approximation. On the basis of the theory of ellipsoidal vortices, an analytical relationship is obtained between the geometric dimensions of the vortex, the potential vorticity of the vortex core, and the characteristics of the background flow. Measurements of a number of characteristics of both the vortex and the background current in the Voyager 1 (1979), Galileo (1996), and Cassini (2000) missions were used. Based on the theory, the vertical size of the Jupiter’s Great Red Spot was calculated, which turned out to be close to the same characteristic measured in the Voyager 1 (1979) mission. Based on the theory, an e-stimate of the vertical size of the Great Red Spot of Jupiter was obtained, which is consistent with the e-xperimental data of the Voyager 1 mission (1979).

Numerical Calculation of Heat Transfer in a Rectangular Channel with Triangular Vortex Generators in the Channel at Blade Angle 30° for Reynolds no. of 800, 1200

Abstract: The vortex generators in this study are placed at angle of 30° in a rectangular channel. These vortices create the down wash flow towards the lower channel wall while the up wash flow is away from the wall which is found in the outside region of the vortices. Along the downstream direction, the secondary velocity vectors decreases while the distance between the vortex cores increases. Thinning of the thermal boundary layer thus occurs in between the two vortices. The variation of span wise averaged Nusselt number was calculated at different values of x at Reynolds number of 800, 1200. We considered parametric studies between channel without winglet and with winglet pair. It shows that the span wise averaged Nusselt number increase with the increment of Reynolds no. at particular x. it is observed the behaviour at these Reynolds no with blade angle 30°. The increment in the span wise averaged Nusselt no. can be observed from these numerical calculations. the effect of vortex generators in the spanwise averreged nusselt number. The comparison between the plots of spanwise avereged Nusselt number with and without vortex generators shows that there is a considerable increase in Nusselt number near the vortex generator region and this effect decreases as we move far from the vortex generator region in the stream wise direction.

How tidal waves interact with convective vortices in rapidly rotating planets and stars

Context. The dissipation of tidal inertial waves in planetary and stellar convective regions is one of the key mechanisms that drive the evolution of star–planet and planet–moon systems. This dissipation is particularly efficient for young low-mass stars and gaseous giant planets, which are rapid rotators. In this context, the interaction between tidal inertial waves and turbulent convective flows must be modelled in a realistic and robust way. In the state-of-the-art simulations, the friction applied by convection on tidal waves is commonly modeled as an effective eddy viscosity. This approach may be valid when the characteristic length scales of convective eddies are smaller than those of the tidal waves. However, it becomes highly questionable in the case where tidal waves interact with potentially stable large-scale vortices such as those observed at the poles of Jupiter and Saturn. The large-scale vortices are potentially triggered by convection in rapidly-rotating bodies in which the Coriolis acceleration forms the flow in columnar vortical structures along the direction of the rotation axis. Aims. We investigate the complex interactions between a tidal inertial wave and a columnar convective vortex. Methods. We used a quasi-geostrophic semi-analytical model of a convective columnar vortex, which is validated by numerical simulations. First, we carried out linear stability analysis using both numerical and asymptotic Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) methods. We then conducted linear numerical simulations of the interactions between a convective columnar vortex and an incoming tidal inertial wave. Results. The vortex we consider is found to be centrifugally stable in the range –Ωp ≤ Ω0 ≤ 3.62Ωp and unstable outside this range, where Ω0 is the local rotation rate of the vortex at its center and Ωp is the global planetary (stellar) rotation rate. From the linear stability analysis, we find that this vortex is prone to centrifugal instability with perturbations with azimuthal wavenumbers m = {0,1, 2}, which potentially correspond to eccentricity, obliquity, and asynchronous tides, respectively. The modes with m &gt; 2 are found to be neutral or stable. The WKBJ analysis provides analytic expressions of the dispersion relations for neutral and unstable modes when the axial (vertical) wavenumber is sufficiently large. We verify that in the unstable regime, an incoming tidal inertial wave triggers the growth of the most unstable mode of the vortex. This would lead to turbulent dissipation. For stable convective columns, the wave-vortex interaction leads to the mixing of momentum for tidal inertial waves while it creates a low-velocity region around the vortex core and a new wave-like perturbation in the form of a progressive wave radiating in the far field. The emission of this secondary wave is the strongest when the wavelength of the incoming wave is close to the characteristic size (radius) of the vortex. Incoming tidal waves can also experience complex angular momentum exchanges locally at critical layers of stable vortices. Conclusions. The interaction between tidal inertial waves and large-scale coherent convective vortices in rapidly-rotating planets (stars) leads to turbulent dissipation in the unstable regime and complex behaviors such as mixing of momentum and radiation of new waves in the far field or wave-vortex angular momentum exchanges in the stable regime. These phenomena cannot be modeled using a simple effective eddy viscosity.

Majorana vortex modes in spin-singlet chiral superconductors with noncollinear spin ordering: Local density of states study

In the present study topologically nontrivial edge and vortex bound states are described in the coexistence phase of chiral spin-singlet superconductivity and noncollinear spin ordering on a triangular lattice in the presence of few (up to four) vortices. We consider the topological phase transition induced by the magnetic order between the phase hosting Majorana modes and the initial phase of the chiral d-wave superconductivity supporting non-Majorana modes which is also topologically nontrivial. The change of the excitation spectrum at the critical point is obtained in both cases of open and periodic boundary conditions in the presence of vortices. It is proved that zero energy Majorana modes localized at vortex cores are caused by noncollinear long-range magnetic ordering. Even though nearby excitation energies of subgap states including the edge-localized and vortex-localized states are very close to each other, the energy difference between different vortex bound states is an order of magnitude higher. This difference determines the energy gap for Majorana vortex modes separating them from other vortex bound states. It is found that even in the presence of noncollinear spin ordering its value can be estimated from the excitation energy of vortex bound states in the pure chiral d-wave state for the nonmagnetic case. By studying local density of states near the vortex cores the possibility to experimentally detect the described Majorana vortex modes by scanning tunneling microscopy is discussed. It is demonstrated that Majorana vortex modes and Majorana antivortex modes induced by noncollinear magnetism have different features in energy and spatially resolved density of states due to the chiral symmetry on the superconducting order parameter.

Topological Vortexes, Asymptotic Freedom, and Multifractals

In this paper, we study the Kelvinons, which are monopole ring solutions to the Euler equations, regularized as the Burgers vortex in the viscous core. There is finite anomalous dissipation in the inviscid limit. However, in the anomalous Hamiltonian, some terms are growing as logarithms of Reynolds number; these terms come from the core of the Burgers vortex. In our theory, the turbulent multifractal phenomenon is similar to asymptotic freedom in QCD, with these logarithmic terms summed up by an RG equation. The small effective coupling does not imply small velocity; on the contrary, velocity is large compared to its fluctuations, which opens the way for a quantitative theory. In the leading order in the perturbation theory in this effective coupling constant, we compute running multifractal dimensions for high moments of velocity circulation, which is in good agreement with the data for quantum Turbulence and available data for classical Turbulence. The logarithmic dependence of fractal dimensions on the loop size comes from the running coupling in anomalous dimensions. This slow logarithmic drift of fractal dimensions would be barely observable at Reynolds numbers achievable at modern DNS.

Motion of a superfluid vortex according to holographic quantum dissipation

Vortices are topological defects associated with superfluids and superconductors, which, when mobile, dissipate energy destroying the dissipationless nature of the superfluid. The nature of this ``quantum dissipation'' is rooted in the quantum physical nature of the problem, which has been the subject of an extensive literature. However, this has mostly been focused on the measures applicable in weakly interacting systems wherein they are tractable via conventional methods. Recently, it became possible to address such dynamical quantum thermalization problems in very strongly interacting systems using the holographic duality discovered in string theory, mapping the quantum problem on a gravitational problem in one higher dimension, having as benefit offering a more general view on how dissipation emerges from such intricate quantum physical circumstances. We study here the elementary problem of a single vortex in two space dimensions, set in motion by a sudden quench in the background superflow formed in a finite-density Reissner-Nordstrom holographic superfluid. This reveals a number of surprising outcomes addressing questions of principle. By fitting the trajectories unambiguously to the Hall-Vinen-Iordanskii phenomenological equation of motion we find that these are characterized by a large inertial mass at low temperature that, however, diminishes upon raising temperature. For a weak drive the drag is found to increase when temperature is lowered, which reveals a simple shear drag associated with the viscous metallic vortex cores, supplemented by a conventional normal fluid component at higher temperatures. For a strong drive we discover a unique dynamical phenomenon: the core of the vortex deforms accompanied by a large increase of the drag force.

Cone structure design for improving the separation performance of a water-only cyclone

The cone structure of a water-only cyclone is the key factor affecting its separation performance. To improve separation performance, a tri-stage curved-cone (Type Ⅲ/C) water-only cyclone was proposed and designed based on conventional cones. The flow-field characteristics and separation performance of water-only cyclones were analyzed using numerical simulation. Results indicate that the proposed Type Ⅲ/C water-only cyclone has the following superior characteristics: the pressure drop can be reduced by up to 21.43% and tangential velocity by up to 10 m/s; there are three circulating vortex cores and a thicker suspended density layer in its cone section; a continuous 0.18 mm coal particle ascent path forms; and the maximum separation distance from ash particles is 10 mm. The Type Ⅲ/C water-only cyclone had an ash content in the clean coal of 2.34% and an ash content in its underflow of 75.28%; the recovery of clean coal was 35.13%, and the recovery of clean coal combustible was 77.81%. These indicators are better than those of other conventional cyclones.

Enigma of the vortex state in a strongly correlated d -wave superconductor

We show that strong electronic repulsion transforms a vortex core from a metallic type in the overdoped regime to a Mott insulator at underdoping of a strongly correlated $d$-wave superconductor. This changeover is accompanied by an accumulation of electron density at the vortex core toward local half filling in the underdoped region, which in turn facilitates the formation of the Mott-insulating core. We find that the size of vortices evolves nonmonotonically with doping. A similar nonmonotonicity of critical field ${H}_{c2}$, as extracted from superfluid stiffness, is also found. Our results explain some recent experimental puzzles of cuprate superconductors.

Numerical study on the scale effects of two-dimensional cycloidal propellers

In this study, computational fluid dynamics (CFD) simulations were performed using commercial software StarCCM + to investigate the scale effect on the hydrodynamic performance of a single-blade cycloidal propeller.The Shear Stress Transport (SST) turbulence model was used to calculate the hydrodynamic coefficients, and a reasonable numerical scheme was determined based on the results of a convergence study with respect to the grid scale and time-step length of iterations. Accordingly, the hydrodynamic coefficients at different Reynolds numbers (Re) and scales were calculated, and the critical Reynolds number was determined. Both the distribution of vorticity and the dimensionless velocity at the vortex core were evaluated under different Re and it was found that the scale effect of cycloidal propeller differs markedly from that of conventional screw propellers. This difference leads to the invalidation of the scale effect formula recommended by the International Towing Tank Conference (ITTC). Thus, a new formula was developed based on extensive numerical simulations. The results of this study provide deeper insights into the fluid mechanism of cycloidal propeller, and can greatly accelerate their application.

Influences of microjet pressure and number of microjets on the control of shock wave/boundary layer interaction

Boundary layer separation is a common phenomenon in supersonic/hypersonic vehicles, and can adversely affect the lift coefficient. Currently, active flow control based on microjets is used to inhibit the separation of the turbulent boundary layer. The obtained results predicted by the three-dimensional Reynolds-averaged Navier–Stokes (RANS) equations and two-equation shear stress transport (SST) k-ω both with Realizable k-ε turbulence models show that the control mechanism of the microjets method is the counter-rotating vortex pair (CVP) generated by the microjet mixes the low-energy flow within the boundary layer with the high-energy flow near the boundary layer. The size of the vortex core in this CVP is the key to controlling SWBLI. The vortex nucleus that is larger and closer to the wall enables better SWBLI control. A lower or higher ratio of microjet pressure to inflow static pressure increases the total volume of the separation bubble and produces a negative gain. When the ratio of the triangular microjet hole bottom edge length to the spacing between the holes is too small, leading to a deterioration in the control effect. The addition of microjets reduces the total pressure recovery coefficient.

Interaction between spin and Abrikosov vortices in doped topological insulators

In the topological superconductor with the nematic superconductivity in $E_u$ representation, it is possible to have different types of vortices. One is associated with the vorticity in the particle-hole space and corresponds to the Abrikosov vortex. Another type corresponds to the vorticity in the spin space and is called spin vortex. We study the interaction of the Abrikosov vortex with the spin vortices. We derive the free energy of the sample with the Abrikosov and the strain-induced spin vortices using the Ginzburg-Landau approach for the two-component superconducting order parameter. We calculate the critical strain at which the spin vortex is formed. We show that the spin vortex and the Abrikosov vortex attract to each other and, as a result, they have a common core. We show that there are no zero-energy states (Majorana fermions) localized near the common vortex core of the Abrikosov vortex and the spin vortex of any type. Possible experimental realization is discussed.

Large-Eddy Simulation of Wake Vortices at Tokyo/Haneda International Airport

A large-eddy simulation (LES) of wake vortices in ground effect is conducted under the influence of airport hangar buildings to investigate the airport-specific behavior of wake vortices. We consider a landing at Tokyo/Haneda International Airport in Japan, where a wake of hangar buildings covers a landing path and touchdown zone under particular wind conditions. We combine an LES code and the Weather Research and Forecasting numerical weather prediction model to retrieve realistic wind conditions around the airport. The behavior of wake vortices is then investigated in the retrieved wind field using the adaptive mesh capability of the LES code for capturing the tiny vortex core of the wake vortex. At the crosswind on the order of a vortex descent speed, the hangar wake reduces the crosswind near the runway, enhancing the windward vortex’s rebound. The effect is alleviated by doubling the crosswind to twice the vortex descent speed. On the other hand, the wind fluctuations caused by the hangar buildings only slightly affect the wake vortex decay.