Rankine Vortex Research Articles

Instability of a dusty vortex

We investigate the effect of inertial particles dispersed in a circular patch of finite radius on the stability of a two-dimensional Rankine vortex in semi-dilute dusty flows. Unlike the particle-free case where no unstable modes exist, we show that the feedback force from the particles triggers a novel instability. The mechanisms driving the instability are characterized using linear stability analysis for weakly inertial particles and further validated against Eulerian–Lagrangian simulations. We show that the particle-laden vortex is always unstable if the mass loading $M>0$ . Surprisingly, even non-inertial particles destabilize the vortex by a mechanism analogous to the centrifugal Rayleigh–Taylor instability in radially stratified vortex with density jump. We identify a critical mass loading above which an eigenmode $m$ becomes unstable. This critical mass loading drops to zero as $m$ increases. When particles are inertial, modes that fall below the critical mass loading become unstable, whereas modes above it remain unstable but with lower growth rates compared with the non-inertial case. Comparison with Eulerian–Lagrangian simulations shows that growth rates computed from simulations match well the theoretical predictions. Past the linear stage, we observe the emergence of high-wavenumber modes that turn into spiralling arms of concentrated particles emanating out of the core, while regions of particle-free flow are sucked inward. The vorticity field displays a similar pattern which leads to the breakdown of the initial Rankine structure. This novel instability for a dusty vortex highlights how the feedback force from the disperse phase can induce the breakdown of an otherwise resilient vortical structure.

Characterizing Continental US Hurricane Risk: Which Intensity Metric Is Best?

AbstractThe damage potential of a hurricane is widely considered to depend more strongly on an integrated measure of the hurricane wind field, such as integrated kinetic energy (IKE), than a point‐based wind measure, such as maximum sustained wind speed (Vmax). Recent work has demonstrated that minimum sea level pressure (MSLP) is also an integrated measure of the wind field. This study investigates how well historical continental US hurricane damage is predicted by MSLP compared to both Vmax and IKE for continental United States hurricane landfalls for the period 1988–2021. We first show for the entire North Atlantic basin that MSLP is much better correlated with IKE (rrank = 0.50) than Vmax (rrank = 0.26). We then show that continental US hurricane normalized damage is better predicted by MSLP (rrank = 0.83) than either Vmax (rrank = 0.67) or IKE (rrank = 0.65). For Georgia to Maine hurricane landfalls specifically, MSLP and IKE show similar levels of skill at predicting damage, whereas Vmax provides effectively no predictive power. Conclusions for IKE extend to power dissipation as well, as the two quantities are highly correlated because wind radii closely follow a Modified Rankine vortex. The physical relationship of MSLP to IKE and power dissipation is discussed. In addition to better representing damage, MSLP is also much easier to measure via aircraft or surface observations than either Vmax or IKE, and it is already routinely estimated operationally. We conclude that MSLP is an ideal metric for characterizing hurricane damage risk.

Assessment of turbulence and cavitation models in prediction of vortex induced cavitating flow in fuel injector nozzles

Vortex-induced cavitation develops in high pressure fuel injector equipment in areas where despite the very high surrounding pressures (>100 MPa), the rotational motion of the fluid causes large pressure drops in the core of a well-organized longitudinal vortex structure leading to cavitation with normally string type correspondingly also called string cavitation ; typically, the size of the string cavitation is small compared to the overall dimensions while they develop in a transient mode linked with the local flow turbulence. To address these complex interaction processes, some turbulence models have been tested in a diesel injector nozzle for which quantitative experimental data are available and are utilized to assess the predictive capability of relevant models; the flow has been considered compressible, turbulent and isothermal. The closure models considered include the RNG k−ε, SST k−ω, RSM, WALE LES as well as a developed very-large eddy simulation model (VLES). The employed mass-transfer cavitation models are the Schnerr and Sauer (SS), Zwart-Gerber-Belamri (ZGB), HEM and a modified ZGB model with a self-adaptive adjustment of condensation coefficient. The results indicate that the RNG k−ε model and SST k−ω model fail to predict the string cavitation induced by vortex flow in the nozzle due to the drawback of the isotropic vortex-viscosity hypothesis. The RSM model could capture an acceptable string cavitation morphology. The numerical results utilizing the VLES model and LES model are in considerably good agreement with the experimental data, while the VLES model can provide the predictions of cavitating flow as precise as that using the LES model but on a much coarser mesh. The distributions of tangential velocity are similar to the velocity characteristics of Rankin vortex or Taylor vortex, which can help understand the coherent vortex structures in string cavitating flow. It is also shown that the RSM turbulence model with modified ZGB cavitation model improves the accuracy of prediction in the vortex-induced cavitation compared to the other three cavitation models.

Turbulence Structure and Dynamics Investigation of Turbulent Swirl Flow in Pipe Using High-Speed Stereo PIV Data

Turbulent swirl flow, which exists in numerous turbomachinery systems, is the focus of this paper. It consumes a significant amount of energy, so it is a subject of investigation for many researchers. It is even more present in ventilation systems, as numerous axial fans are still installed without guide vanes. The experimental investigation of the turbulent swirl flow behind an axial fan in a pipe, installed in a test rig with a free inlet and ducted outlet, as defined in the international standard ISO 5801, is presented in this paper. Moreover, in this paper, the axially restricted case is studied. A designed axial fan generates a Rankine vortex with a complex structure, and research on the vortex turbulence structure and dynamics is presented. On the basis of the HSS PIV (high-speed stereo particle image velocimetry), measurement results are calculated using invariant maps. All states of turbulence anisotropy are thoroughly analyzed by applying the invariant theory on HSS PIV results. Vortex dynamics is observed on the basis of the total velocity minima positions and their repetitions. Both methods are correlated, and important conclusions regarding vortex behavior are deduced.

Viscous Rankine vortices

A generalized version of the Rankine vortex is taken as initial state in an infinite fluid domain in two dimensions. The inner rigid-body motion of the Rankine vortex is surrounded by an outer irrotational vortex, where the inner flow and outer flow are allowed to have different amplitudes. We study the time evolution in a viscous fluid, where the kinematic viscosity scales the unit of dimensionless time. By an inverse Hankel transform, the Rankine vortex appears as an integrated continuous spectrum of axisymmetric Fourier–Bessel modes with radial wave numbers k. Each of these velocity modes is represented by a Bessel function J1(kr) where r is the radial distance from the vortex center. The amplitude of each individual mode will decay exponentially at a rate of νk2, where ν is the kinematic viscosity. The decaying continuous Fourier–Bessel spectrum is calculated analytically, while the evolution of the flow field is found by numerical evaluation of an inverse Hankel transform. We also consider the presence of a free surface in the gravity field, where pressure distribution in the vertical direction is hydrostatic. The far field remains irrotational during the viscous decay.

Flow characteristics of a tangential vortex intake with steep-slope tapering section

Abstract Tangential vortex intakes are compact hydraulic structures commonly used in water supply, drainage and sewerage systems to convey water from high to low elevations efficiently. For certain intake design, due to the complex three-dimensional (3D) flow transition, hydraulic jump and shock waves may form. This paper presents an experimental and 3D computational fluid dynamics (CFD) modeling of the flow in a tangential vortex intake with a steep-slope (sloping angle = 45°) tapering section. Swirling velocity field was measured using laser Doppler anemometry (LDA) for discharges with typical flow features. CFD predictions were most encouraging in the good agreement with measured head-discharge relationship, air core size and velocity. It was found that the flow regimes are determined by the hydraulic controls at different sections under different discharges, forming a complex flow transition with an inclined hydraulic jump at the tapering section. While the swirling flow in the dropshaft is highly asymmetrical, the local tangential velocity is similar to that of a stable tangential intake with Rankine vortex behaviour. Flow energy dissipation is caused by the hydraulic jump at the tapering section and the friction loss at the dropshaft. The present study offers comprehensive insights to the design of tangential vortex intake structures. HIGHLIGHTS Tangential vortex intake flow with steep-slope tapering section elucidated first time. Comprehensive flow profiles and velocity field measured for a range of discharges. 3D CFD predictions are in good agreement with the measurements. Flow regimes are determined by the hydraulic controls at different sections. Flow energy dissipation is caused by hydraulic jump and dropshaft friction loss.

Effects of key structure parameters on flow field and sensitivity analysis for a bubble separator in MSR

In order to investigate the separation mechanism and provide some guidance for the separator design, the single-phase flow field of the bubble separator for the Molten Salt Reactor is simulated numerically by Reynolds Stress Model. The results show that a low-pressure and high-velocity region is induced under the obstruction of the guiding vanes in the flowing channel and the tangential velocity distribution resembles the Rankine vortex. Besides, the swirl number along the axial position increases first and then decreases due to the improvement of the first light phase outlet. Moreover, the effects of the key structure parameter of the generating swirler including deflection angle, the guiding vane number and the hub ratio on the flow field are investigated and their sensitivity analyses are conducted at the same time. It demonstrates that the deflection has the largest influence on the flow field and the hub ratio is the second.

Fluid vortex mapping using the rotational Doppler effect

The light from a twisted laser beam, scattered at an air/water interface, experiences a rotational Doppler shift. We use a superposition of two beams with different topological charges to measure the beat frequency of the scattered light by a Rankine type vortex at different positions from its center. We show that the angular velocity decreases with the distance in total agreement with a Rankine vortex model. Several extensions are then considered, including the detection of turbulences generated in the wake of airplanes.

Aircraft and Satellite Observations of Vortex Evolution and Surface Wind Asymmetry of Concentric Eyewalls in Hurricane Irma

We compare the vortex evolutions of eyewall replacement cycles (ERCs) between the sea-surface and the free-atmosphere levels and investigate the asymmetric structure of concentric eyewalls (CEs) by examining a combination of aircraft observations and surface wind fields derived from C-band spaceborne synthetic aperture radar (SAR) images during Hurricane Irma (2017) from 4 September 2017 to 8 September 2017. A total of 116 radial wind profiles measured by an aircraft were collected and showed that ERCs occur at both the sea-surface and the free-atmosphere levels. The outer eyewall was shown to form at the free atmospheric level (~3 km) with a narrow structure at the sea-surface level and an outward tilt with height in the cross-section. In our study, four ERC events were determined from wind profile parameters fitted by a modified Rankine vortex model, which was validated by 328 radial legs collected from six hurricanes. The outer eyewall did not replace the inner eyewall at the sea-surface level in the third ERC, due to the maintenance of a short duration and intense original eyewall. Additionally, Irma’s intensity weakened during the fourth ERC rather than re-intensified, because of the generation of a third wind maximum outside the secondary eyewall. Comparisons of five SAR-derived surface wind fields in Irma and another two hurricane cases illustrated that the location of the secondary eyewall generation is a key point in the interpretation of anomaly intensity changes in the fourth ERC.

Study of aerodynamic characteristics of an aircraft during approach to landing in a disturbed atmosphere

An approximate method is proposed for determining the aerodynamic effect of coherent vortex structures (CVS) of atmospheric turbulence on an aircraft. As a source of the CVS the vortex wind wakes arising when the atmospheric wind flows around the mountain massif of the Son Tra peninsula, located near the Da Nang airport, and the vortex wake behind the Su-27 type aircraft in the landing configuration are considered. Modeling the formation of a vortex structure is carried out by the grid method within the framework of the boundary value problem for the Reynolds-averaged Navier—Stokes equations. The evolution and stochastics of the far wake are modeled in a two-dimensional approximation by discrete Rankine vortices. The assessment of the increment of forces and moments from the effect of the vortex system on the aircraft was carried out within the framework of the panel method. The situation is considered when a light transport aircraft gets into a vortex wake behind an aircraft with a swept wing and a passenger aircraft of the MS-21 type, approaching for landing at the CVS from a mountainous terrain.

Dispersion of particles in two-dimensional monopolar and dipolar vortices using a Lagrangian stochastic model

The dispersion of particles in two-dimensional vortices, two circular monopoles, and the Chaplygin–Lamb dipole is studied numerically with a Lagrangian stochastic model. The monopoles are the Rankine and the steady Oseen vortex, whose azimuthal velocity profile is irrotational at a long radial distance. The total velocity of each particle is divided into two parts: the deterministic field due to the vortex plus a stochastic velocity representing homogeneous turbulence. The experiments are carried out with thousands of particles to calculate the dispersion as a function of time. The dispersion in the monopoles grows rapidly and then increases at a lower rate as the particles transit toward the potential region. This transition occurs more quickly in the Rankine vortex, so the Oseen vortex has a wider time-lapse to generate a more significant dispersion. In the case of the Chaplygin–Lamb dipole, having an internal and external flow, the dispersion has different behavior depending on which region the particles depart. The dispersion curves describe the exchange of particles between the poles and the outer flow as the dipole drifts. We discuss the capacity of the dipole to transport particles through long distances.

Kinetic modeling of fractal aggregate mobility

Although the mobility or transport parameters, such as lift drag and pitching moments for regular-shaped particulates, are widely studied, the mobility of irregular fractal-like aggregates generated by the aggregation of monomers is not well understood. These particulates which are ubiquitous in nature, and industries have very different transport mechanisms as compared to their spherical counterpart. A high-fidelity direct simulation Monte Carlo (DSMC) study of two fractal aggregates of different shapes or dimensions is undertaken in the slip and transitional gas regime to understand the underlying mechanism of gas-particle momentum transfer that manifests as the orientation-averaged mobility parameters of the particulates. The study specifically focuses on the viscous contribution of these parameters and develops a non-linear correlation for drag and lift parameters p and q obtained from DSMC by normalizing the axial and lateral forces. The drag parameter p predicted a monotonic increase in fractal particulate drag with respect to a spherical monomer while the lift parameter q shows an initial increasing trend but a decreasing tendency toward the high Mach number or high compressibility regime. The approximate model that captures the compressibility and rarefaction effects of the fractal mobility is used to study the evolution of these particulates in a canonical Rankine vortex to illustrate the wide disparity in the trajectories of the fractal aggregate vs a spherical geometry approximation generally found in the literature.

Operational performance characteristics of an axial double baffles three channels classifier for coarse pulverized coal

In order to obtain the working principle of the axial direction classifier and raise its separation efficiency, the flow field and classification performance of the classifier was investigated by numerical simulation and experimental measurement. The particle size distribution at inlet, outlet and return pipe was measured by laser particle size analyzer and coupled with Rosin-Rammler model. The particle trajectory was analyzed using the discrete phase model. The tangential velocities played a dominant role in particles radial distribution mainly in the form of Rankine vortex. The axial velocities determine the vertical distribution of particles. The velocity distributions and turbulence influence the cutting particle size and separation efficiency mostly. The most suitable condition is baffles angle of 20° and inlet velocity of 19.3 m/s considering the load of the mill and the fineness of the pulverized coal at the inlet of the classifier.

Separation efficiency theoretical model of swirl-vane separator based on bidirectional vortex

Swirl vane separator is a vital component to separate liquid water from gas to provide high quality steam to turbines in liquid water reactors. The gas rotating flow in the riser of a swirl vane separator is a bidirectional vortex. Its tangential velocity is similar with Rankine vortex. Its axial velocity is bidirectional. The gas bidirectional vortex is solved by constructing a Bragg-Hawthorne equation for the stream function. The gas flow velocity predicted by new method agrees quite well with CFD. The maximum velocity differences in axial direction are 6.2%. Based on this model, the droplet trajectory is obtained and a new separation efficiency model has been developed. The average difference between experiment results and the predicted separation efficiency is reduced from 14.7% to 3.1%. Moreover, parametric analysis using new model has been carried out to discuss the effect of inlet velocity, droplet diameter, swirl vane angle and hub diameter.

Аtmospheric wind flow around the mountain landscape in the vicinity of Danang airport and flight safety issues

Wind boundary layer flow over the mountain landscape and large structures located around runways (RWs) creates coherent vortex structures (CVSs) that can cross a glideslope and airspace in the vicinity of an airport. The aircraft, encountering a vortex structure, experiences significant changes of the aerodynamic forces and moments, what is especially hazardous due to proximity to terrain. From a mathematical point of view, the solution of this problem presents a challenge due to extremely large space – time scale of the phenomenon, the lack of relevant atmospheric models, as well as comprehensive initial – boundary conditions in numerical modeling. In this paper, a composite solution is constructed: the CVSs area generation is computed in sufficient details within the framework of the grid method. Based on the data obtained in the approximation of analytical functions, an initial vortex structure is formed, the evolution and stochastics of which are modeled within the potential approximation by means of Rankine vortices. The evaluation of the forces and moments increment from the impact of vortex structures on the aircraft was carried out by the panel method using the engineering approach. As an example, the CVSs, resulting from wind flow around the mountainous area of the Son Tra Peninsula, that is located short of RWs 35R-17L and 35L-17R of Da Nang airport, are investigated. To improve the computational grids quality and verify the method of solving the boundary value problem for the Reynolds-averaged Navier-Stokes equations, we used the criteria based on the principle of maximum pressure, requiring Q-parameter positivity property in the vortices cores and flow separation regions. A CVS related aviation event, involving a passenger aircraft MC-21, is studied. The aircraft, after takeoff from RW 35R-17L setting the course close to the direction of the vortex wind structure axis from the Son Tra Peninsula, encountered the mountainous area CVS.

Analysis and prediction models of flow field in mountain tunnels under strong canyon wind

Flow field in mountain tunnels induced by canyon wind, which has significant references for the desirable environment creation in tunnels, has not been fully revealed. In order to investigate the influence of tunnel length on the flow structure and the vortex dynamics in tunnels under strong canyon wind, a series of numerical simulations were performed by using ANSYS Fluent. Numerical models, including the canyon wind domain and the tunnel domain, were established, and the Reynolds-averaged Navier-Stokes (RANS) equations along with the standard k-ε model were validated by model experiments. Nine tunnel lengths (50–2000 m) and six canyon wind velocities (5–30 m/s) were considered. The formation mechanism of the flow structure in tunnels with different lengths was revealed and compared with that in street canyons. Meanwhile, velocity and pressure distributions in the whole tunnel were analyzed based on the Rankine vortex model, the boundary-layer separation and the mass flow rate at tunnel exits. Besides, quantitative models for the flow field in tunnels, which are applicable for typical tunnels with two lanes, were established. This study can be considered as a reference for the pollutant purification and the ventilation system design in mountain tunnels.

Reliability of electric power grids under tornadoes

Strong wind disasters, especially tornadoes with high damage scales, constantly cause huge damage to electric power grids (EPGs). In this paper, a concept is presented to quantify the connectivity reliability of EPGs under tornadoes. First, a tornado wind field is established using a modified Rankine vortex model, which is a representative 2D tornado wind field model. Second, fragility models of grid components, including transmission substations, transmission support structures, distribution poles, distribution conductors, and local circuits, are introduced. Third, a Monte Carlo simulation is presented to evaluate the connectivity reliability of EPGs under tornadoes. Finally, the connectivity reliability is verified under different scales and propagation angles of tornadoes by taking an actual EPG in China as a case study. Results show that the connectivity reliability directly correlates with the maximum wind speed and the propagation angle of the tornado, and the EPG experiences severe damage when the tornado exceeds the Enhanced Fujita 3 scale.

On the relationships between different vortex identification methods based on local trace criterion

Vortical flow is generally considered to be a flow with a rotational trend, but vortex regions vary depending on the vortex identification methods by which they are extracted. In this paper, theoretical relationships between commonly used Q series vortex criteria, eigenvalue-based vortex criteria, and the Rortex method are analytically derived and built based on the local trace (LT) criterion (LTcri). The projections of vortex regions extracted by different vortex criteria onto the LT-plane constructed by LTcri are presented to graphically discuss their physical meanings and interrelations. The LTcri-based method reflects the local swirling patterns of flow and provides new interpretations of various vortex criteria in terms of local flow patterns. The simple vortex models, including Rankin vortex and Burgers' vortex, forced isotropic turbulence flow, and a compressor corner separation flow case with a practical Mach number, are tested and analyzed. The potential of the LTcri-based method is shown both by analyzing vortex dynamic properties and by distinguishing the different swirling patterns of complex vortices in tangle. This contributes to the exploration of flow mechanisms and furthers investigations into vortex dynamics.

Flame whirling characteristics of fire in a room with vent

SummaryVelocity distribution and motion of a whirling flame in a room fire with vent were studied analytically in this article. Using Rankine vortex model, whirling flame models with and without decay of the rotation velocity were established. The whirling flame model and the cross‐wind velocity boundary conditions were used to study the velocity distribution of the rotating flame under the action of side wind. When there is a linear velocity gradient in the lateral wind, the whirling flame still revolves around the same axis at different heights in the model without attenuation of rotation velocity, but the axis becomes tilted. In the rotation velocity attenuation model, the axis of the whirling flame changes from a straight line to a curve, and the change of the shape of the whirling flame is related to the flame height, the rotation angular velocity, and the maximum wind velocity. Under the assumption of Rankine vortex model with the same rotation angular velocity, the uniform lateral wind and lateral wind with linear velocity gradient can only affect the position and shape of the whirling flame axis but not change the rotation angular velocity.

Application of SAR Data for Tropical Cyclone Intensity Parameters Retrieval and Symmetric Wind Field Model Development

The spaceborne synthetic aperture radar (SAR) is an effective tool to observe tropical cyclone (TC) wind fields at very high spatial resolutions. TC wind speeds can be retrieved from cross-polarization signals without wind direction inputs. This paper proposed methodologies to retrieve TC intensity parameters; for example, surface maximum wind speed, TC fullness (TCF) and central surface pressure from the European Space Agency Sentinel-1 Extra Wide swath mode cross-polarization data. First, the MS1A geophysical model function was modified from 6 to 69 m/s, based on three TC samples’ SAR images and the collocated National Oceanic and Atmospheric Administration stepped frequency microwave radiometer wind speed measurements. Second, we retrieved the wind fields and maximum wind speeds of 42 TC samples up to category 5 acquired in the last five years, using the modified MS1A model. Third, the TCF values and central surface pressures were calculated from the 1-km wind retrievals, according to the radial curve fitting of wind speeds and two hurricane wind-pressure models. Three intensity parameters were found to be dependent upon each other. Compared with the best-track data, the averaged bias, correlation coefficient (Cor) and root mean-square error (RMSE) of the SAR-retrieved maximum wind speeds were –3.91 m/s, 0.88 and 7.99 m/s respectively, showing a better result than the retrievals before modification. For central pressure, the averaged bias, Cor and RMSE were 1.17 mb, 0.77 and 21.29 mb and respectively, indicating the accuracy of the proposed methodology for pressure retrieval. Finally, a new symmetric TC wind field model was developed with the fitting function of the TCF values and maximum wind speeds, radial wind curve and the Rankine Vortex model. By this model, TC wind field can be simulated just using the maximum wind speed and the radius of maximum wind speed. Compared with wind retrievals, averaged absolute bias and averaged RMSE of all samples’ wind fields simulated by the new model were smaller than those of the Rankine Vortex model.