Rankine Vortex Research Articles

Wall contact effects of particle-wall collision process in a two-phase particle fluid

Particle-wall collision is a complex liquid-solid coupling matter approximating to a chaotic state. Previous research mainly focused on the issues of particle trajectory and near-wall flow field, but the particle-wall collision mechanism and contact effects are unclear. To address this, a coupled computational fluid dynamics and discrete element method (CFD-DEM) modeling method is proposed. Firstly, flow field profiles are acquired by the CFD method as the initial motion conditions. Then, the particles are regarded as rigid bodies, and the data interactions between CFD and DEM are implemented by calculating for interaction force and void fraction. The results show that there are radial texture phenomena on the particle trajectories caused by the flowing interference; the central region has the lowest velocity and can be regarded as the rigid core of a Rankine vortex; if inlet diameter is 20 mm, the contacting distribution with rotating superposition can reach the best uniformity; the higher viscosity can carry more particles, and the transporting ability of the fluid medium is improved; the uniform contact effects can be more easily performed by the low viscosity fluid. This research can offer theoretical relevance to the modeling for multi-phase particle fluid, and provide technical support for flow regulation in the areas of fluid-based processing, turbine blade erosion, and reactor wall abrasion.

Novel scaling law for estimating propeller tip vortex cavitation noise from model experiment

The tip vortex cavitation (TVC) noise of marine propellers is of interest due to the environmental impacts from commercial ships as well as for the survivability of naval ships. Due to complicated flow and noise field around a marine propeller, a theoretical approach to the estimation of TVC noise is practically unrealizable. Thus, estimation of prototype TVC noise level is realized through extrapolation of the model TVC noise level measured in a cavitation tunnel. In this study, for the prediction of prototype TVC noise level from a model test, a novel scaling law reflecting the physical basis of TVC is derived from the Rayleigh-Plesset equation, the Rankine vortex model, the lifting surface theory, and other physical assumptions. Model and prototype noise data were provided by Samsung Heavy Industries (SHI) for verification. In applying the novel scaling law, similitude of the spectra of nuclei is applied to assume the same nuclei distribution in the tip vortex line of the model and the prototype. It was found that the prototype TVC noise level predicted by the novel scaling law has better agreement with the prototype TVC noise measurement than the prototype TVC noise level predicted by the modified ITTC noise estimation rule.

Instability and acoustic fields of the Rankine vortex as seen from long-term calculations with the tenth-order multioperators-based scheme

The instability of the compressible Rankine vortex is investigated using a multioperators-based scheme with the tenth-order approximation to the convection terms of the fluid dynamics equations supplied by the ninth-order dissipation mechanism. The scheme was optimized for high resolution of small scales by choosing its free parameters. The results of long-term calculations with several meshes allowed to reproduce the general scenario of the instability development with self-excitations of different modes and the final stage of rotating quadrupole sound radiation. The calculated frequencies and sound pressure levels are presented for several Mach numbers.

To the theory of particle lifting by terrestrial and Martian dust devils

The combined Rankine vortex model is applied to describe the radial profile of azimuthal velocity in atmospheric dust devils, and a simplified model version is proposed of the turbulent surface boundary layer beneath the Rankine vortex periphery that corresponds to the potential vortex. Based on the results by Burggraf et al. (1971), it is accepted that the radial velocity near the ground in the potential vortex greatly exceeds the azimuthal velocity, which makes tractable the problem of the surface shear stress determination, including the case of the turbulent surface boundary layer. The constructed model explains exceeding the threshold shear velocity for aeolian transport in typical dust-devil vortices both on Earth and on Mars.

Characteristics and evolution of an Agulhas ring

AbstractA South Atlantic ring is studied through remote sensing altimetry, hydrographic stations, and drifters' trajectories. The ring's core was characterized by warmer and saltier Indian Ocean waters. At the time of the cruise, the ring's signature extended radially out to 124 km and vertically down to 2000 m, and its core absolute dynamic topography (ADT) exceeded the surrounding Atlantic Ocean waters in 0.4 m. The geostrophic velocities were anticyclonic with maximum speeds about 35 cm s−1 at 100 m and reaching negligible values near 4500 m. The rotational transport inside the ring was 33 Sv in the thermocline and intermediate layers. The drifters' data distinguish a 30‐km core revolving as a solid body with periodicity near 5 days and a transitional band that revolves with constant tangential velocity, resembling a Rankine vortex. The ADT data identify the ring's track, showing that it was shed by the Agulhas Current retroflection in November 2009 and propagated northwest rapidly during the first 2 months (mean speed of about 10 cm s−1) but slowed down substantially (3–4 cm s−1) between March and July 2010, when it was last detected. The altimetry data also outlines the evolution of the ring's core ADT, radius, vorticity, and, through a simple calibration with the cruise data, rotational transport. In particular, the ring surface and vertical‐mean vorticity decay with time scales of 373 and 230 days, respectively, indicating that most of the property anomalies contained by the ring are diffused out to the subtropical gyre before it reaches the western boundary current system.

The stability of swirling flows with a heat source

The absolute instability of a Rankine vortex with an axial flow and paraxial heat source is investigated. The dispersion relation for vortex modes is derived analytically. The dependence of dispersion properties of the media on control parameters such as swirl parameter S, velocity a, and heat source power (density parameter Q) is studied. The frequency of helical waves increases and the increment decreases with increasing heat source power, accompanied by a decrease in the width of the neutral stability region. Numerical analysis also suggests that one of the dispersion curve branches could include an instability region of a parametric nature.

Vortex merger near a topographic slope in a homogeneous rotating fluid

The effect of a bottom slope on the merger of two identical Rankine vortices is investigated in a two-dimensional, quasi-geostrophic, incompressible fluid. When two cyclones initially lie parallel to the slope, and more than two vortex diameters away from the slope, the critical merger distance is unchanged. When the cyclones are closer to the slope, they can merge at larger distances, but they lose more mass into filaments, thus weakening the efficiency of merger. Several effects account for this: the topographic Rossby wave advects the cyclones, reduces their mutual distance and deforms them. This alongshelf wave breaks into filaments and into secondary vortices which shear out the initial cyclones. The global motion of fluid towards the shallow domain and the erosion of the two cyclones are confirmed by the evolution of particles seeded both in the cyclones and near the topographic slope. The addition of tracer to the flow indicates that diffusion is ballistic at early times. For two anticyclones, merger is also facilitated because one vortex is ejected offshore towards the other, via coupling with a topographic cyclone. Again two anticyclones can merge at large distance but they are eroded in the process. Finally, for taller topographies, the critical merger distance is again increased and the topographic influence can scatter or completely erode one of the two initial cyclones. Conclusions are drawn on possible improvements of the model configuration for an application to the ocean.

The slip effect of micro-droplets in Rankine vortex

The method of moments with interphase slip is simplified to numerically study the interaction between nanoscale droplets and gas flow in a Rankine vortex. In the method, the flow of gas phase and the moments of the droplets size distribution are calculated respectively and the transfers of momentum and heat between the gas and the droplets which are expressed by the moments are introduced into the governing equations as the source terms. In this way, the velocity slip between the gas phase and the droplet phase is captured by the present method. Then, the method is used to simulate the flow of Rankine vortex where the water droplets with constant radius are injected into the vortex core. The results show that the vortex is disturbed and the droplets move outward due to the effect of the velocity slip between the phases. The larger the droplet radius, the stronger the velocity slip effect. When the radius of the injected droplets is small, the vortex keeps stable and the droplets aggregate as a ring outside the core of the vortex. When the droplets radii are large enough, the vortex is not stable any more due to the strong slip effect and negative vorticity is induced in the core of the vortex. The droplets form a swing arm and spiral out of the vortex. At last, the effects of the growth of droplets on the vortex evolution and interphase slip are also investigated. The grown droplets spiral out and the position of maximum mean radius also moves outward with time. In the vortex core, condensation stops after a short time because no more vapor is supplied. With the growing process, more momentum is transferred from the gas phase to the droplets and the slip velocity between droplets and gas vanishes more quickly.

Tornado community-level spatial damage prediction including pressure deficit modeling

Based on the observation of damage from past tornadoes, tornado intensity is frequently the highest at the center and gradually decreases outward, which is consistent with a Rankine vortex model. In this study, the Rankine vortex model was applied to model the pressure deficit resulting from a tornado, and then combined with pressures resulting from wind velocity to develop fragility surfaces for buildings representative of the typical residential building stock in a community. In the absence of data, an additional coefficient is used herein to consider different amount of pressure deficit participating in wind loads on buildings to enable community resilience studies. However, it is duly noted that at the individual building level the internal pressure coefficient used in ASCE-7 should be adjusted based on data to be consistent with current wind engineering methods in the United States. Moreover, a scenario tornado path was modeled based on historical statistics of U.S. tornadoes over almost four decades using mean values, and spatial damage to a cluster of wood-frame buildings representative of a residential subdivision of a community was investigated. The methodology presented herein can provide damage information spatially over a community which is a key to studying resilience at the community-level.

Doppler radar-derived wind field of five tornado events with application to engineering simulations

Doppler radar data corresponding to five tornado events are analyzed using the Ground-Based Velocity Track Display method and the three-dimensional velocity field of nine volumetric samples is extracted. These samples are selected to cover a range of wind speeds (between 36m/s and 64m/s) and vortex structures representative of EF0 to EF3 tornadoes in a first attempt to generate a tornado wind field database. Tangential velocity profiles, swirl ratios and vortex structures, i.e. single-celled or two-celled vortex, are determined for each of these volumetric samples.Among the nine volumetric samples, two show single-celled characteristics, vortex breakdown bubble is evident in one and four demonstrate two-celled vortex characteristics. The radial profiles of the tangential velocity are in good agreement with a modified Rankine vortex model. The variation of maximum tangential velocities with height is very different when compared to the velocity variation in typical atmospheric boundary layer flows. The swirl ratios of the tornado volumetric samples are computed using the flow rate through the updrafts and the maximum circulation in the flows.

Characteristics and possible formation mechanisms of severe storms in the outer rainbands of Typhoon Mujiga (1522)

To better understand how severe storms form and evolve in the outer rainbands of typhoons, in this study, we investigate the evolutionary characteristics and possible formation mechanisms for severe storms in the rainbands of Typhoon Mujigae, which occurred during 2–5 October 2015, based on the NCEP–NCAR reanalysis data, conventional observations, and Doppler radar data. For the rainbands far from the inner core (eye and eyewall) of Mujigae (distance of approximately 70–800 km), wind speed first increased with the radius expanding from the inner core, and then decreased as the radius continued to expand. The Rankine Vortex Model was used to explore such variations in wind speed. The areas of strong stormy rainbands were mainly located in the northeast quadrant of Mujigae, and overlapped with the areas of high winds within approximately 300–550 km away from the inner core, where the strong winds were conducive to the development of strong storms. A severe convective cell in the rainbands developed into waterspout at approximately 500 km to the northeast of the inner core, when Mujigae was strengthening before it made landfall. Two severe convective cells in the rainbands developed into two tornadoes at approximately 350 km to the northeast of the inner core after Mujigae made landfall. The radar echo bands enhanced to 60 dBZ when mesocyclones occurred in the rainbands and induced tornadoes. The radar echoes gradually weakened after the mesocyclones weakened. The tops of parent clouds of the mesocyclones elevated at first, and then suddenly dropped about 20 min before the tornadoes appeared. Thereby, the cloud top variation has the potential to be used as an early warning of tornado occurrence.

Experimental Study on the Effect of Number of Bubble Occurrences on Tip Vortex Cavitation Noise Scaling Law

A novel scaling law for the tip vortex cavitation (TVC) noise was determined, employing the Rankine vortex model, the Rayleigh–Plesset equation, the lifting surface theory, the boundary layer effect, and the number of bubbles generated per unit time (N0). All terms appearing in the final derived scaling law are well known three-dimensional (3D) lifting surface parameters, except for N0. In this study, the dependence of N0 with inflow velocity and hydrofoil dimension is investigated experimentally while trying to retain the same TVC patterns among different experimental conditions. Afterward, the effect of N0 on the TVC noise is analyzed. Optimal TVC observation conditions are determined from consideration of cavitation number and Reynolds number of two comparable conditions. Two geometrically scaled hydrofoils are concurrently placed in a cavitation tunnel for the hydrofoil size variation experiment. Wall effects and flow field interaction are prevented with the aid of computational fluid dynamics. Images taken with a high‐speed camera are used to count N0 by visual inspection. The noise signals at all conditions are measured and an acoustic bubble counting technique, to supplement visual counting, is devised to determine N0 acoustically from the measured noise data. The broad-band noise scaling law incorporating N0 and the International Towing Tank Conference (ITTC) cavitation noise estimation rule for hydrofoil are both applied to estimate the TVC noise level for comparison with the measured noise level. The noise level estimated by the broad-band noise scaling law accounting for the acoustically estimated N0 gives the best agreement with the measured noise level.

CFD simulation and optimization of the flow field in horizontal turbo air classifiers

This paper mainly presents a numerical study of the gas flow in horizontal turbo air classifiers. The effect of the air-inlet direction on the performance of classifier was also investigated through powder classification experiments. The simulated results show that the vertical vortex is the dominant flow in conical part of the classifier and there exists the horizontal vortex in the classifying chamber. The tangential velocity profile resembles a Rankine vortex inside the rotor cage. The vertical vortex intensity increases with increasing the inlet air velocity, while the rotor cage speed has limited effect on the control of gas pathlines in the classifying chamber. Horizontal turbo air classifiers are divided into four quadrants according to the air-inlet direction. For classifiers in quadrants I and III, a double-layer flow with opposite directions generates around the rotor cage which causes a secondary vortex. The secondary vortex is eliminated and the airflow becomes uniform in the classifier that belongs to quadrant Π or IV. The experimental results with fluidized catalytic cracking catalysts and fly ash demonstrate that cut sizes of this classifier decrease averagely by 5μm and 2.2μm respectively, and the classification accuracy increases by 7.5–10.3%.

Curvature instability of a curved Batchelor vortex

In this paper, we analyse the curvature instability of a curved Batchelor vortex. We consider this short-wavelength instability when the radius of curvature of the vortex centreline is large compared with the vortex core size. In this limit, the curvature instability can be interpreted as a resonant phenomenon. It results from the resonant coupling of two Kelvin modes of the underlying Batchelor vortex with the dipolar correction induced by curvature. The condition of resonance of the two modes is analysed in detail as a function of the axial jet strength of the Batchelor vortex. In contrast to the Rankine vortex, only a few configurations involving $m=0$ and $m=1$ modes are found to become the most unstable. The growth rate of the resonant configurations is systematically computed and used to determine the characteristics of the most unstable mode as a function of the curvature ratio, the Reynolds number and the axial flow parameter. The competition of the curvature instability with another short-wavelength instability, which was considered in a companion paper (Blanco-Rodríguez & Le Dizès, J. Fluid Mech., vol. 804, 2016, pp. 224–247), is analysed for a vortex ring. A numerical error found in this paper, which affects the relative strength of the elliptic instability, is also corrected. We show that the curvature instability becomes the dominant instability in large rings as soon as axial flow is present (vortex ring with swirl).

Estudio de un vórtice de Rankine con velocidad axial discontinua en un tubo infinito

Estudio de un vórtice de Rankine con velocidad axial discontinua en un tubo infinito

FSWツールを用いたAl合金回転ツール点接合におよぼすツールサイズの影響

The properties of rotating tool spot joining joints with different rotating tools by the combination between the shoulder diameter and the probe length were investigated in this study. The shoulder diameter of rotating tool affects the tensile strength of the joint significantly. An oversize shoulder diameter decreased the joint strength. The probe length affects more the fracture mode than the joint strength. Interface fracture mode occurred with a rotating tool of short probe length. Plug fracture occurred with a rotating tool of long probe length. Rotary motion of restricted area in the joining interface by the rotating tool was confirmed by displacements of the joining interfaces. Rankin vortex was observed on the joining interface by velocity distribution of rotary motion of joining interface. Al oxide film layers were formed spirally on upper joining interfaces

Direct numerical simulation analysis of spanwise oscillating Lorentz force in turbulent channel flow at low Reynolds number

Direct numerical simulations of a turbulent channel flow at low Reynolds number (Re_{tau } = 180, based on the driving pressure gradient and channel half width) are performed. Some results are also presented for Re_{tau } = 400. In this work we apply an idealized spanwise Lorentz force near the lower wall of the channel and compare the results for the applied force and no-force cases in both the upper half and the lower half of the channel. We have studied two-point correlations to explain the effect of the Lorentz force on streamwise vortices and streaky structures. Despite the observation of clear stabilization of the streaky structures in the vicinity of the wall, the existence of the streamwise vortices is explained by the well-known turbulence regeneration cycle, which improves the understanding of streaky and streamwise vortex structure formation on turbulence generation. Spanwise oscillating Lorentz force effects on the Rankine vortex structures are investigated. Our results lead us to establish an explanation on the effect of sweep and ejection events on the mean vortex structures in the flow field. A mean vortex structure is defined by the time-averaged location of the local minimum and maximum of the streamwise r.m.s. vorticity. We also depict turbulence production rates for both cases and compared the lower and upper half of the channel.

The migration and growth of nuclei in an ideal vortex flow

Tip vortex cavitation occurs on ship propellers which can cause significant noise compared to the wet flow. In order to predict the inception of tip vortex cavitation, numerous researches have been investigated about the detailed flow field around the tip. According to informed studies, the inception of tip vortex cavitation is affected by many factors. To understand the effect of water quality on cavitation inception, the motion of nuclei in an ideal vortex flow, i.e., the Rankine vortex flow, was investigated. The one-way coupling point-particle tracking model was employed to simulate the trajectory of nuclei. Meanwhile, Rayleigh-Plesset equation was introduced to describe the growth of nuclei. The results show that the nucleus size has a significant effect on nucleus’ trajectory. The capture time of a nucleus is approximately inversely proportional to its radius. The growth of nucleus accelerates its migration in the vortex flow and shortens its capture time, especially for the case of explosive growth.

The transition from a coherent optical vortex to a Rankine vortex: beam contrast dependence on topological charge

Spatially coherent helically phased light beams carry orbital angular momentum (OAM) and contain phase singularities at their centre. Destructive interference at the position of the phase singularity means the intensity at this point is necessarily zero, which results in a high contrast between the centre and the surrounding annular intensity distribution. Beams of reduced spatial coherence yet still carrying OAM have previously been referred to as Rankine vortices. Such beams no longer possess zero intensity at their centre, exhibiting a contrast that decreases as their spatial coherence is reduced. In this work, we study the contrast of a vortex beam as a function of its spatial coherence and topological charge. We show that beams carrying higher values of topological charge display a radial intensity contrast that is more resilient to a reduction in spatial coherence of the source.

CFD Simulation of Air Cyclone Separator

A computational fluid dynamics model was developed for air cyclone separator in order to predict the flow pattern inside the cyclone using an Eulerian approach, three dimensions Reynolds-Average Navier-Stokes equations, closed via the Reynolds Stress model as a turbulence model for air flow. The particles were modeled as a discrete phase model using the Lagrangian transport model with turbulent particle dispersion. Computational fluid dynamics modeling was employed to investigate fluid flow patterns and particle trajectories at steady state operating conditions of Stairmand cyclone. Analysis of a computational fluid dynamics simulation accurately revealed that the air flow behavior in cyclone separator consists of two vortexes : an outer vortex with a downwardly directed axial flow and an inner vortex with an upwardly directed flow, this flow profile known as Rankine vortex. A low-pressure zone appeared in the center line of the cyclone due to high swirling velocity. The results showed that the pressure drop increased with increasing the inlet air velocity. The results of the collection efficiency showed that the efficiency increased as the particles diameter increased. A good agreement achieved between the simulation results and published experimental results. The computational fluid dynamics code (ANSYS FLUENT 14.5) with the Reynolds Stress model as the turbulence model, predicted very well the flow field parameters of cyclones and can be used in cyclone design for any dimensions.