Vortex Strip Research Articles

Direct simulation of vortex dynamics of multi-cellular Taylor–Green vortex by pseudo-spectral method

This study investigates the long-time vorticity dynamics of the multi-cellular configurations of the two-dimensional (2D) Taylor–Green vortex (TGV). The pseudo-spectral method is used to solve the incompressible Navier–Stokes equation to analyze the evolution of TGV arrays. The focus is on understanding vortex interactions leading to vortex filamentation and stripping (forward cascade) during primary instability; merger and reconnection (inverse cascade) among the TGV vortical cells subsequently. Here, consideration of multiple cells avoids imposing symmetries at the smallest periodic length scale, and thereby affecting disturbance growth. The initial condition is taken from the analytic solution of the TGV, and Fourier spectral method is employed to track the interactions of the initial doubly-periodic vortices. The full sequence of evolution from one equilibrium state to another for the TGV is not addressed before, as reported here to fill this gap for multiple TGV cells in both directions. By studying various vortical interactions in the ensemble, here we report the enstrophy and energy spectra for different number of TGV cells. This is crucial in understanding the very long-time evolution process, at post-critical Reynolds numbers for the 2D TGV problem in the same physical domain, (0≤(x,y)≤4π) having (4×4) and (6×6) cells. Reported results show the evolution of these vortical cells from original configurations to finally a (1×1) vortical cells — the universal state not demonstrated before.

Undesired flows in lateral-intake multiple forebays and their hydraulic implications: case study for Asia’s largest urban water supply pumping station

Urban pumping stations often adopt the design of lateral-intake multiple forebays to accommodate multiple pump units in a limited space and to reduce interaction between the operating units. However, a full understanding of the undesired flows and hydraulic characteristics of lateral-intake multiple forebays remains limited, resulting in the design of flow-regulating measures relying on trial and error. This study numerically investigated the undesired flows in lateral-intake multiple forebays and their hydraulic implications, using Asia’s largest urban water supply pumping station as a case study. The results show that the undesired flows, including flow recirculation, helical mainstream and vortex strip, are the main reasons for the deterioration of hydraulic characteristics in the forebays. The undesired flows are more pronounced at higher inflow Froude numbers or for the forebay closer to the diversion channel inlet, resulting in lower flow uniformity and higher hydraulic loss. Further discussion shows that the flow-regulating measures improve the hydraulic characteristics by limiting the generation and development of undesired flows within the forebays. This provides references for the design of flow-regulating measures for similar forebays to reduce the cost of trial and error, which is of general value for the lateral-intake multiple forebays required for urban pumping stations.

Influence of Runner Downstream Structure on the Flow Field in the Draft Tube of a Small-Sized Water Turbine

The flow in the draft tube of the water turbine is affected by the upstream flow and the inherent structure accompanied by various undesirable characteristics, affecting the efficient and stable operation of the water turbine. Changing the flow structure downstream of the runner is an important measure to reduce hydraulic loss in the draft tube and improve stability. In this study, three downstream structures of the runner, namely, the non-locking nut, small locking nut, and extended locking nut are numerically calculated and verified using experimental results. The unstable flow characteristics of the draft tube are analyzed using variations in swirling flow, backflow, pressure gradient, and vortex strip. The results show the non-negligible effect of the locking nut, which significantly reduces the rotational momentum flux at the draft tube inlet, accelerates the decay rate of the swirling flow, and suppresses the generation of axial low pressure. The small locking nut significantly reduces the pressure gradient, shortens the backflow zone, and decreases the backflow velocity. The extended locking nut reduces the backflow zone in some sections and reduces the vortex zone of the straight section but prolongs the backflow zone and increases the backflow velocity.

How heating tracers drive self-lofting long-lived stratospheric anticyclones: simple dynamical models

Abstract. Long-lived “bubbles” of wildfire smoke or volcanic aerosol have recently been observed in the stratosphere, co-located with ozone, carbon monoxide, and water vapour anomalies. These bubbles often survive for several weeks, during which time they ascend through vertical distances of 15 km or more. Meteorological analysis data suggest that this aerosol is contained within strong, persistent anticyclonic vortices. Absorption of solar radiation by the aerosol is hypothesised to drive the ascent of the bubbles, but the dynamics of how this heating gives rise to a single-sign anticyclonic vorticity anomaly have thus far been unclear. We present a description of heating-driven stratospheric vortices, based on an axisymmetric balanced model. The simplest version of this model includes a specified localised heating moving upwards at fixed velocity and produces a steadily translating solution with a single-signed anticyclonic vortex co-located with the heating, with corresponding temperature anomalies forming a vertical dipole, matching observations. A more complex version includes the two-way interaction between a heating tracer, representing the aerosol, and the dynamics. An evolving tracer provides heating which drives a secondary circulation, and this in turn transports the tracer. Through this two-way interaction an initial distribution of tracer drives a circulation and forms a self-lofting tracer-filled anticyclonic vortex. Scaling arguments show that upward velocity is proportional to heating magnitude, but the magnitude of peak quasigeostrophic vorticity is O(f) (f is the Coriolis parameter) and independent of the heating magnitude. Estimates of vorticity from observations match our theoretical predictions. We discuss 3-D effects such as vortex stripping and dispersion of tracer outside the vortex by the large-scale flow, which cannot be captured explicitly by the axisymmetric model and are likely to be important in the real atmosphere. The large O(f) vorticity of the fully developed anticyclones explains their observed persistence and their effective confinement of tracers. To further investigate the early stages of formation of tracer-filled vortices, we consider an idealised configuration of a homogeneous tracer layer. A linearised calculation reveals that the upper part of the layer is destabilised due to the decrease in tracer concentrations with height there, which sets up a self-reinforcing effect where upward lofting of tracer results in stronger heating and hence stronger lofting. Small amplitude disturbances form isolated tracer plumes that ascend out of the initial layer, indicative of a self-organisation of the flow. The relevance of these idealised models to formation and persistence of tracer-filled vortices in the real atmosphere is discussed, and it is suggested that a key factor in their formation is the time taken to reach the fully developed stage, which is shorter for strong heating rates.

Numerical study on the hydrodynamic performance and wake dynamics of propulsive wing propulsors with different cross-flow fans

The propulsive wing propulsor (PWP), which means an underwater thruster equipped with a wing, a cross-flow fan (CFF), and a deflector, is capable of generating both horizontal thrust and vertical lift, thus enhancing the maneuverability of underwater vehicles and serving as a propulsion device. The hydrodynamic performance of the PWP is significantly influenced by the blade number it possesses. An unsteady numerical method based on the Reynolds-averaged Navier–Stokes equations was developed to examine the impact mechanism of blade number on the hydrodynamic performance, load fluctuation, and wake evolution of the PWP. The results indicate that as the blade number increases, the hydrodynamic forces, power, and propulsive efficiency of the PWP gradually increase. When the blade number exceeds 26, the performance of the PWP tends to stabilize. Insufficient blades can lead to turbulence in the internal flow of the CFF, intensifying interference between blade vortices, resulting in secondary peaks and frequency-domain bifurcations in hydrodynamics. With an increasing blade number, disturbances to the blade vortices decrease, enhancing the periodicity of PWP hydrodynamic fluctuations, but there may be an increase in high-frequency noise levels. The wake modes of the PWP undergo four transitions: double vortex pair mode, single vortex pair mode, single vortex pair + single vortex mode, and vortex strip mode. Disturbed blade vortices promote the transition of vortex pair shedding modes in the PWP wake, thereby causing variations in the periodicity of PWP hydrodynamics. Excessive amplitude and frequency may lead to structural fatigue damage in the PWP.

Mechanisms of lobed jet mixing: Comparison of bilinear, rectangular, and circular lobed mixers

In this study, bilinear lobed mixers (BLMs), rectangular lobed mixers (RLMs), and circular lobed mixers (CLMs), with two sectional area ratios of the bypass channel to the core channel, were configured while maintaining the same lobe angle, lobe height, lobed nozzle length, mixing duct length, and core sectional area. Using three-dimensional steady Reynolds-averaged Navier–Stokes equations and the SST k–ω turbulence model, numerical simulations of jet mixing in these lobed mixers at three velocity ratios of the bypass stream to the core stream were performed. The jet mixing characteristics and performances of the three types of lobed mixers were analyzed. Through a comprehensive and in-depth analysis of the jet-mixing flow fields of the three types of lobed mixers, more universal mechanisms of lobed jet mixing were revealed. Systematic and meaningful conclusions were drawn from four aspects: the formation and evolution mechanisms of the cross flow, longitudinal vortices, heat and mass convection, and orthogonal vortex strip. The findings from this study hold significant implications for the development of lobed mixers and exploration of lobed jet-mixing mechanisms.

Vortex Strips in a Two-Dimensional Ferromagnet

New magnetic structures in the Heisenberg two-dimensional classical spin model are studied. An original substitution is proposed, which allows one to reduce the equations of the model to an integrable system of nonlinear ODEs. The solution can be characterized as a “vortex strip” or an annular vortex. Its distinctiveproperties are the finite size of the existence domain, the limited total energy, and the absence of a vortex center despite the presence of a vortex structure.

ABOUT SELECTING THE VORTEX FLOWMETER OPTIMAL BLUFF BODY SHAPE

Vortex flow meters are becoming more widespread in many industries. This is due to the simplicity and reliability of the flow transducer, the scale linearity, the frequency measuring signal presence, low requirements for alignment and ensuring the straight sections length at the installation site, etc. Among the vortex measuring instruments, the most common are instruments with a bluff body. Such flow meters operation principle is based on measuring the vortex stripping frequency behind a streamlined body installed in the flow.
 In this case, the metrological characteristics are determined by the bluff body shape. Therefore, the search for the optimal sensing element shape and the hydraulic channel configuration of the flow meter as a whole remains an actual issue.
 The paper proposes an algorithm for solving this issue according to the criteria of the measured flow rates maximum range and the interaction efficiency of the bluff body with the measured medium flow. The first criterion value is determined from the condition that the Strouhal’s number remains unchanged; the second criterion is based on the estimation of the measured medium pressure drop and the measurement error.
 To realize the algorithm, simulation modeling is used in the Ansys Fluent fluid simulation software, which uses computational fluid dynamics methods. Modeling carried out for three shapes of the bluff body: a cylinder, a prism with a triangular section, a prism with a trapezoidal section, which made it possible to choose a sensitive element for further solving the multi-parameter optimization problem.
 Geometric features of the selected sensitive element shape, the limits of their change and boundary values are grounded.
 The simulation made it possible to estimate the measured flow rates range and pressure losses, as well as to determine the vortex stripping frequency, measurement error and efficiency factor for the investigated geometric model.
 To further improve the instrument metrological parameters, the authors proposed to supplement the primary transducer geometric model with gradual contraction and diffuser sections. These sections parameters are selected from the conditions of a continuous flow and the maximum measured flow rates range with a minimum pressure loss.
 The obtained results confirmed the strategy proposed by the authors. The further research prospect is to carry out simulation studies of the flow meter hydraulic channel proposed configuration for different measured media.

Optimization of impulse water turbine based on GA-BP neural network arithmetic

To develop an optimum design method for impulse water turbines with low specific speed, a representative impulse water turbine with low specific speed used in agricultural irrigation machinery was optimized with a combination of an orthogonal experimental design, a genetic algorithm, and a BP neural network in this study. Numerical calculation was applied to analyze interflow characteristics for optimized and original water turbines. Results showed that the internal flow characteristics of the optimized water turbine presented remarkable improvement compared with the original water turbine. Pressure distribution increased, the vortex strip in the draft tube was reduced remarkably, and impeller torque increased by 26 %. In addition, the optimized impeller was manufactured by 3D printing, and performance comparison was conducted between experiments of the optimized and original water turbines. The efficiency of the optimized water turbine reached 42.5 %, which exceeded the original water turbine’s of 8.5 %. With increasing rotating speed, maximum efficiency running point moved to a high flow rate, and highly efficient areas expanded. Internal characteristic analysis and a full-scale experiment for both water turbines showed that the performance of the optimized water turbine exhibited substantial improvement. The analysis and experiment also verified the theoretical correctness and feasibility of the proposed optimum design method.

Improving Hilbert–Huang transform for energy-correlation fluctuation in hydraulic engineering

Intense vibrations in hydraulic turbine generator unit draft tubes lead to a run-out of the unit shafting and threaten its safe and stable operation. Correct maintenance is therefore important for the safe operation of such units. This study involves assessing the condition of the turbine generator unit by extracting the feature information of its vibration signals. Based on previous research, we present an enhanced Hilbert–Huang transform (HHT) method with an energy-correlation fluctuation criterion to extract feature information and effectively verify the method with simulated signals. An inspection application based on the signal from a vortex strip in the draft tube of a prototype turbine under suboptimal operating conditions indicates that this method is more effective than the traditional one, with a better component identification capability and better suited to the analysis of the complex and dynamic feature information of hydro turbines.

Stability of barotropic vortex strip on a rotating sphere.

We study the stability of a barotropic vortex strip on a rotating sphere, as a simple model of jet streams. The flow is approximated by a piecewise-continuous vorticity distribution by zonal bands of uniform vorticity. The linear stability analysis shows that the vortex strip becomes stable as the strip widens or the rotation speed increases. When the vorticity constants in the upper and the lower regions of the vortex strip have the same positive value, the inner flow region of the vortex strip becomes the most unstable. However, when the upper and the lower vorticity constants in the polar regions have different signs, a complex pattern of instability is found, depending on the wavenumber of perturbations, and interestingly, a boundary far away from the vortex strip can be unstable. We also compute the nonlinear evolution of the vortex strip on the rotating sphere and compare with the linear stability analysis. When the width of the vortex strip is small, we observe a good agreement in the growth rate of perturbation at an early time, and the eigenvector corresponding to the unstable eigenvalue coincides with the most unstable part of the flow. We demonstrate that a large structure of rolling-up vortex cores appears in the vortex strip after a long-time evolution. Furthermore, the geophysical relevance of the model to jet streams of Jupiter, Saturn and Earth is examined.

Stability theory for a two-dimensional channel

A scheme for deriving conditions for the nonlinear stability of an ideal or viscous incompressible steady flow in a two-dimensional channel that is periodic in one direction is described. A lower bound for the main factor ensuring the stability of the Reynolds–Kolmogorov sinusoidal flow with no-slip conditions (short wavelength stability) is improved. A condition for the stability of a vortex strip modeling Richtmyer–Meshkov fluid vortices (long wavelength stability) is presented.

Evolution of a Vortex in a Strain Flow.

Experiments and vortex-in-cell simulations are used to study an initially axisymmetric, spatially distributed vortex subject to an externally imposed strain flow. The experiments use a magnetized pure electron plasma to model an inviscid two-dimensional fluid. The results are compared to a theory assuming an elliptical region of constant vorticity. For relatively flat vorticity profiles, the dynamics and stability threshold are in close quantitative agreement with the theory. Physics beyond the constant-vorticity model, such as vortex stripping, is investigated by studying the behavior of nonflat vorticity profiles.

Large Eddy Simulation of Francis Turbine Flow Fields under Small Opening Condition

The vibration intensity is strong in Francis turbine occurred under the small opening conditions, such as Lijia Gorges and Three Gorges project. In paper we use large eddy simulation (LES) method base on Vreman SubGrid-Scale model to study the generation and evolution process of turbulence flow, capturing the details of the flow structures and the dissipation of the turbulent kinetic energy. The SIMPIEC algorithm is applied to solve the coupled equation of velocity and pressure. The result shows that the small guide vane opening conditions deviate the optimal conditions most. So some unstable flow characters been induced. Such as the turbulent kinetic energy of fluid in guide vanes zone, the blade passage and the draft tube are very strong. The unstable flow phenomenon including the swirl, flow separation, interruption and vortex strip. It can be deduced that the vibration of unit is induced by these flow characteristic.

Large Eddy Simulation of Francis Turbine Flow Fields under Small Opening Condition

The vibration intensity is strong in Francis turbine occurred under the small opening conditions, such as Lijia Gorges and Three Gorges project. In paper we use large eddy simulation (LES) method base on Vreman SubGrid-Scale model to study the generation and evolution process of turbulence flow, capturing the details of the flow structures and the dissipation of the turbulent kinetic energy. The SIMPIEC algorithm is applied to solve the coupled equation of velocity and pressure. The result shows that the small guide vane opening conditions deviate the optimal conditions most. So some unstable flow characters been induced. Such as the turbulent kinetic energy of fluid in guide vanes zone, the blade passage and the draft tube are very strong. The unstable flow phenomenon including the swirl, flow separation, interruption and vortex strip. It can be deduced that the vibration of unit is induced by these flow characteristic.

Interaction of two unequal corotating vortices

Previous high-resolution contour dynamics calculations [Dritschel and Waugh, Phys. Fluids A 4, 1737 (1992)] have shown that in two-dimensional inviscid flow the interaction of two unequal corotating vortices with uniform vorticity is not always associated with vortex growth and may lead to vortices smaller than the original vortices. In the present study, we investigate whether these results also hold for two-dimensional vortices with continuous vorticity distributions. Similar flow regimes are found as for uniform vorticity patches, but the variation of the flow regimes with the initial vortex radii and peak vorticities is more complicated and strongly dependent on the initial shape of the vorticity profile. It is found that the “halo” of low-value vorticity, which surrounds the cores of continuous vortices, significantly increases the critical distance at which the weaker vortex is destroyed. The halo also promotes the vortex cores to merge more efficiently, since it accounts for a substantial part of the loss of circulation into filaments. Simple transformation rules and merger criteria are derived for the inviscid interaction between two Gaussian vortices. The strong dependence of the flow regimes on the initial vorticity distribution partly explains why previous laboratory experiments in an electron plasma [Mitchell and Driscoll, Phys. Fluids 8, 1828 (1996)] show complete merger of two unequal vortices in a range of parameter space where contour dynamics simulations with uniform vorticity patches predict partial merger or partial straining-out of the smaller vortex. It is shown that the measured times for complete merger are in reasonable agreement with inviscid dynamics when the vortices are very similar. For more distinct vortices the weaker vortex is often observed to be destroyed on a time scale much smaller than expected from inviscid numerical simulations. An explanation for this discrepancy is given by the combined effects of vortex stripping and viscous diffusion, which leads to an enhanced erosion of the weaker vortex. These results are verified by laboratory experiments in a conventional (rotating) fluid.

Barotropic instability in frontolytic strain

AbstractRecent observational studies have indicated that a front which is undergoing frontolytic strain may be conducive to rapid growth of waves or secondary cyclones. Previous work has shown that a frontogenetic strain flow will tend to suppress the growth of waves on a two‐dimensional vortex strip: here, the opposite case of negative strain is studied. Justification for considering a basic state which is frontolytic is presented, given the natural transience of this state. The results show that the growth is sufficiently rapid for instability to be relevant on the time‐scale of evolution of the parent front. Waves grow kinematically with the front itself, at an exponential rate. More rapid growth is possible for transient barotropically unstable modes but only for limited time. These results are discussed with a view to their impact on the understanding of atmospheric flows.

Monopolar vortices in an irrotational annular shear flow

The evolution characteristics of monopolar vortices in an irrotational annular shear flow were investigated both experimentally and theoretically. The background flow was generated in a rotating tank by an appropriate source–sink configuration, while the monopolar vortex was created by withdrawing fluid for a short time. Dye-visualization studies demonstrated the gradual destruction of the vortex through a process called ‘vortex stripping’, i.e. long filaments of passive tracers were being shed from the edge of the vortex. In contrast to uniform shear flows, these filaments were asymmetrically attached to the vortex core. Furthermore, the vortex was observed to evolve in a quasi-stationary manner until its final indefinite breaking. The asymmetric stripping process could be explained by modelling both the monopolar vortex and the ambient flow simply by point vortices, and by adopting the method of contour kinematics to trace material contours in the velocity field induced by the point vortices. Furthermore, the effect of a continuous spatial vorticity distribution was investigated by applying the contour dynamics technique, in which the vortex is represented by a stack of uniform vorticity patches. The observed vortex evolution could be well captured by this latter approach.

Isentropic Formation of the Tropopause

The existence of the extratropical tropopause, which can be defined as the sharp transition between the high potential vorticity in the stratosphere and the low potential vorticity in the troposphere, is attributed to a dynamical equilibrium of diabatic effects and vortex stripping. The process is essentially isentropic and two-dimensional. This picture is examined and confirmed in a simple one-layer quasigeostrophic model of the atmosphere. It is possibly the simplest model context where the formation of a tropopause can be found.

Vortex stripping and the erosion of coherent structures in two-dimensional flows

This paper studies the erosion of a monotonically distributed vortex by the joint action of inviscid stripping, induced by an externally imposed adverse shear, and viscous diffusion, either in the form of Newtonian viscosity or hyperviscosity. It is shown that vortex erosion is greatly amplified by the presence of diffusion; abrupt vortex breakup or gradual quasi-equilibrium evolution depend crucially on the strain to peak vorticity ratio and on the Reynolds number. Peculiar, unexpected effects are observed when hyperviscosity is used in place of Newtonian viscosity.