Vorticity Distribution Research Articles

Influence of pinning centers of different natures on surrounding vortices

Studies involving vortex dynamics and their interaction with pinning centers are an important issue to reach higher critical currents in superconducting materials. The vortex distribution around arrays of engineered defects, such as blind and through holes, may help to improve the superconducting properties. Thus, in this work, we used the time-dependent Ginzburg-Landau theory to investigate the vortex dynamics in superconductors of mesoscopic dimensions with a large central square defect with three different configurations: (i) a hole which passes through the sample (interface with the vacuum); (ii) a superconducting region with lower critical temperature Tc; and (iii) a region with a more robust superconductivity, i.e., with a higher Tc. Such systems can be envisaged as elementary building blocks of a macroscopic decorated specimen. Therefore, we evaluated the influence of different interfaces on the vortex dynamics and their effects in the field-dependent magnetization and time-dependent induced electric potential variation. The results show that the superheating field is independent from the nature of the defect. However, the currents crowd at the vertices of the through hole producing a lower degradation of the local superconductivity, which may increase the upper critical field. On the other hand, the last type of defect can be used to control the vortex dynamics in the main superconducting region around the defect with more accuracy. While the first two defects are attractive for the vortices, the third type is repulsive, being needed several penetrated vortices in the superconducting matrix to allow penetration of vortices into the higher Tc domain.

Froude Number Effects on Two-Dimensional Hydrofoils

The performance of a two-dimensional hydrofoil of arbitrary camber, moving at arbitrary Froude number at a constant depth below a free surface, is considered. The treatment is based upon the use of singularity distributions and thin foil theory. By assuming an appropriate series form for the vortex distribution representing the hydrofoil, it is shown that the problem can be reduced to the solution of a set of linear algebraic equations. These are solved by a collocation procedure. Numerical results for the performance characteristics are then given for several hydrofoil configurations, submergence depths, and Froude numbers. These indicate that operation at Froude numbers greater than about ten is practically equivalent to operation at infinite Froude number. However, at lower values of the Froude number and for all the configurations considered, Froude number effects are important, even at submergence depths of several chord lengths.

On Loops in Water Wave Branches and Monotonicity of Water Waves

We give a quite simple approach how to prove the absence of loops in bifurcation branches of water waves in rotational case with arbitrary vorticity distribution. The supporting flow may contain stagnation points and critical layers and water surface is allowed to be overhanging. Monotonicity properties of the free surface are presented. Especially simple criterium of absence of loops is given for bifurcation branches when the bifurcation parameter is the water wave period. We show that there are no loops if you start from a water wave with a positive/negative vertical component of velocity on the positive half period.

Influence of incoming flow parameters on the flow field in a trapped vortex cavity with radial bluff-body

The study focuses on a novel trapped vortex pilot flameholder (TVPF) design, which combines a pilot cavity that has individual air inlets, with a V-shaped radial bluff body. The flow field under sub-atmospheric pressure was investigated using particle image velocimetry (PIV) systems, obtaining the velocity distribution, vortex position, and vorticity distribution for different inlet parameters. Corresponding analysis revealed the overall flow structure of the cavity-flameholder combination, together with the different flow fields under various positions, total pressure, and inlet Mach number. The results show that from the central plane towards the side of the cavity, a no/single vortex to double vortex structure is observed inside the cavity. The three typical flow patterns are radial flameholder entrainment dominated, transition state and high-speed mainstream dominated, each has different velocity distribution and vortex structure. High vorticity mainly exists on both sides of the inlet air and the shear layer between the cavity and mainstream. The alteration of inlet parameters will lead to the change in the cavity jet's momentum, affect the self-sustaining capacity of the cavity vortex system under the influence of mainstream flow, and further lead to different changes in the flow field under the three flow patterns.

Hydrodynamic characteristics of liquid–liquid–liquid three-phase flow in a confined microchannel

Numerical simulations have been performed to reveal the hydrodynamic characteristics of liquid–liquid–liquid three-phase flow in a confined microchannel via a VOF-CSF model. Further the effects of outer phase flowrate, dimensions, the viscosities of all three phases as well as the interfacial tensions of both inner and outer interfaces are systematically investigated. It is found that the shear stress and pressure gradient together determine the formation and disappearance of vortices inside the compound droplets. The internal fluid velocity of compound droplets is significantly altered by the flowrate and viscosity, while the effect of interfacial tension can be ignored. As for the vorticity distribution inside the compound droplets, it exhibits a positive correlation with the capillary number of outer phase. Besides, a prediction correlation for the average velocity of compound droplets with several dimensionless numbers is also established with good precision. The results obtained in this study could provide meaningful theoretical guidance for rational design and regulation of transport behaviors with liquid–liquid–liquid three-phase flow in a confined microchannel.

Assessment of the design influence of the vortex generator on the performance of the solar vortex engine

• Three different design configurations of the solar vortex engine are evaluated. • CFD simulation approach is used for the evaluation of the three SVE designs. • Vortex generator with transparent cover operates as a heat trap and enhances vortex. • Cone structure increases the air vorticity, temperature and buoyancy forces in the vortex. • A hole in the engine’s base produces high velocity with the least vortex stability. The vortex generator is an essential segment in the solar vortex engine (SVE). Its design could be modified to strengthen the generated air vortex and enhance the system's performance. This work aims to investigate the vortex generator design's influence on the SVE's performance. Three different vortex generator designs are studied employing three-dimensional CFD simulations. Experimental investigations have been utilised to support the CFD simulation. The considered designs are Case-1: basic design, Case-2: with a cone structure inside the arena and Case-3: with a hole at the bottom of the vortex generator. The cone structure increases the heat transfer area, increasing the vortex generator's air temperature and producing higher buoyancy forces for the flow field. Cases 1 and 2 produced the best vortex stability as the air vortex shape, pressure and vorticity distributions are uniform. The highest static pressure drop is achieved with the basic design. The basic design, Case-1, produces 1.0% and 5.0% higher static pressure drop than Case-2 and Case-3, respectively. The lower hole affected the air vortex stability negatively.

Effects of the parameters of inner air cylinder on evolution of annular SF6 cylinder accelerated by a planar shock wave

Based on the compressible Navier–Stokes equations combined with the fifth-order weighted essentially non-oscillatory scheme, this paper discusses the interaction of a planar shock wave with an annular SF6 cylinder. The influence of the position and radius of inner cylinder on the evolution of the annular cylinder is examined in detail. Numerical schlieren results clearly show the evolution of the inner and outer interfaces induced by the Richtmyer–Meshkov instability and reveal the evolution of complex shock wave structures as the incident planar shock interacts with the annular cylinder. Shock transformation from the free precursor refraction pattern to the free precursor von Neumann refraction pattern occurs when the inner cylinder position shifts forward, while the shock transformation from the twin von Neumann refraction pattern to the free precursor refraction pattern and the shock transformation from free precursor refraction pattern to the free precursor von Neumann refraction pattern occur when the radius of the inner cylinder gradually becomes larger. The generation and transportation of vorticity on the interfaces are also analyzed, revealing that changes to the inner cylinder play a significant role. The distribution and evolution of vorticity on the interfaces influence the formation of the primary vortex structure at later stages. Quantitative analysis of the circulation and enstrophy indicates that the smaller the inner radius, the larger the value of circulation and enstrophy at the later stage.

Hydraulic loss analysis in a pump-turbine with special emphasis on local rigid vortex and shear

Since the pump as turbine is increasingly employed in energy storage, improving efficiency in both pump and turbine modes is required for economic benefits. This study aims to analyze vortex flow characteristics and vortex control methods in both modes to reduce hydraulic loss. In this paper, a delayed detached eddy simulation was applied in a low specific speed pump-turbine. Based on the entropy production analysis and vorticity binary decomposition in the local vortices, the results show that the local shear is the leading cause of hydraulic loss instead of the existence of vortices. The average wake loss can be 1.6 times higher than the loss in jet regions in pump mode, but there is little difference in the distribution of shear and vortices in the wake flow in turbine mode. The local loss caused by the rotor–stator interaction with a tongue effect at blade passing frequency is up to threefold over the loss without a tongue effect in both modes. Reducing shear and ratio of shear to rigid vorticity of the local vortices via modification in the volute tongue angle to suppress the tongue effect can be an effective way to decrease hydraulic loss in both modes.

Trailing Horizontal Vortices in Observed and Numerically Simulated Tornadoes

Abstract High-resolution numerical simulations of supercell storms reveal complex distributions of vorticity in the vicinity of tornadoes, especially when visualized in three dimensions. As in the simulations, quasi-horizontal vortices (HVs) are occasionally observed near tornadoes, as condensation tubes wrapping around the tornadoes. In this study, visual observations of a violent tornado and visualizations of a high-resolution simulation based on the same tornado case are combined to document distinct HV structures, which trail the tornado very close to the ground toward its right flank (with respect to the tornado’s forward motion), hereafter referred to as “trailing HVs.” The analysis shows that trailing HVs are larger and stronger than HVs typically observed around tornadoes. Still, their sense of rotation matches that of other documented HVs, which is consistent with vorticity generation by surface drag and/or baroclinic torques along internal boundaries of relatively warm rear-flank downdrafts. Interestingly, trailing HVs may display smaller spiral vortices circulating their periphery, which can evolve into more complex structures. Visualizations of three-dimensional vorticity show that the trailing HVs are organized through entanglement of large and small HVs along nearby rear-flank internal boundaries. The internal boundaries also serve as focus for along-boundary stretching of vorticity that becomes mostly streamwise at the location of the trailing HV, resulting in HV strengthening. The spiral vortices are associated with the same entangling processes responsible for the parent (larger) trailing HV structure. Moreover, the analysis suggests that trailing HVs may reinforce the surface wind speeds on the right flank of the tornado.

Frequency-Domain Lifting-Line Aerodynamic Modelling for Wing Aeroelasticity

A frequency-domain lifting-line solution algorithm for the prediction of the unsteady aerodynamics of wings is presented. The Biot–Savart law is applied to determine the normalwash generated by the wake vorticity distribution, whereas steady and unsteady airfoil theories (Glauert’s and Theodorsen’s, respectively) are used to evaluate the sectional aerodynamic loads, namely the lift and pitching moment. The wake vorticity released at the trailing edge derives from the bound circulation through the Kutta condition and is convected downstream with the velocity of the undisturbed flow. The local bound circulation is obtained by the application of the Kutta–Joukowski theorem, extended to unsteady flows. Assuming a bending and torsion wing, this paper provides the aerodynamic matrix of the transfer functions, relating the generalised aerodynamic loads to the Lagrangian coordinates of the elastic deformation. Its rational approximation yields a reduced-order state-space aerodynamic model suitable for an aeroelastic stability analysis and control purposes. The numerical investigation examines the influence of both the wake shed/trailed vorticity modelling and different approximations of the Kutta–Joukowski theorem for unsteady flows on the aerodynamic transfer functions given by the developed frequency-domain lifting-line solver. The accuracy of the solver is assessed by comparison with the predictions obtained by a three-dimensional boundary-element-method solver for potential flows. It is shown that, at least for the frequency range considered, regardless of the approximation of the Kutta–Joukowski theorem applied, the formulation based on the Theodorsen theory provides predictions that are in very good agreement with the results from the boundary element method for a slender wing. This agreement worsens as the wing aspect ratio decreases. A lower level of accuracy is obtained by the application of the sectional loads given by the Glauert theory. In this case, the predictions are more sensitive to the approximation used to express the Kutta–Joukowski theorem for unsteady flows.

Large-Eddy Simulation of Hydrodynamic Structure in a Strongly Curved Bank

Advances in computer technology have facilitated the use of large-eddy simulation (LES) as a numerical simulation method in fluid mechanics. In this study, LES was used for the numerical simulation of curved water flow with a large curvature. The simulation results show that water separation occurs near the convex bank of the bend transverse section while the separation area increases and then decreases along the water depth direction, where the peak is at half-depth. As the water surface is affected by air shear stress, the velocity decreases. However, as the gradient increases, the vorticity is larger and the vorticity distribution is more even. Reflux occurs in the inlet and outlet sections of the bend but does not occur on the surfaces of z/H = 0.5 and z/H = 0.2, where the vorticity distribution is uneven. In the narrow corridor of the concave and convex banks, notably near the curved top, vorticity distribution is concentrated with a high intensity. At the center of the curve, the vorticity intensity is weak but 10 times higher at the concave and convex banks. A strong correlation exists between circulation structure and vorticity distribution: the vorticity is large where the circulation is intense and the structure is complex.

Structure transitions in arrays of point-vortices upon free space propagation

We study the free space propagation of arrays of N × N point vortices with equal unitary topological charge embedded in a Gaussian beam, initially distributed into either a square lattice or a disordered array with the same mean vortex density and separation. The far-field patterns and the near-field evolution are analyzed as a function of different control parameters, such as the size of the carrier beam, the number of vortices, the mean separation distance among them P, and a geometrical parameter S p , defined as the ratio of the size of the array to the size of the host beam. The value of S p turns out to be determinant for the final spatial distribution of the optical vortices in the far-field pattern and also plays a very relevant role in the near-field evolution. While the initial array structure is basically preserved, rotated and scaled up when , the vortices redistribute forming a circumference around the propagation axis for , depleting most of the central intensity, even if the vortex density is far lower than the previously predicted limit for depletion. In the near field, we find an expression for the rotation angle of the whole structure when preserved, as a function of the propagation distance, which depends on P, but it is around eight-fold larger than the Gouy phase shift of the host. Also, we observe the formation of a high intensity ring pattern, whose radius is independent of the size of the carrier and the initial distribution of vortices, but it is only determined by the number of vortices. We verified our numerical results with experiments, finding a very good agreement between them.

An extended and improved particle‐spectral method for analysis of unsteady inviscid incompressible flows through a channel of finite length

AbstractThis paper addresses the development of a method to simulate and analyze unsteady flows of incompressible and inviscid fluids in rectangular channels. Mathematically, the flow problem formulates as Euler equations in terms of the stream function and vorticity. The normal velocity and the vorticity are given at the inlet of the channel, and only the normal velocity is specified at the outlet. The particle‐spectral method describes the vorticity field change in a Lagrangian sense by dynamics of marker particles and an Eulerian description of the velocity field using the global Galerkin approximation. The method involves the subdivision of flow domain on rectangular cells; the approximation of vorticity distribution in cells by least‐squares method; Galerkin coefficients calculation using analytical integration on space variables. For time integration, the five‐stage Runge‐Kutta method of the third accuracy order and the sixth one of symplecticity with adaptive step size control uses. The extension of the particle‐spectral approach comprises algorithms for fluid flows qualitative analysis jointly with the time simulation of unsteady flows. This includes the trajectories of marker particles calculation, computing the particle's residence time in the channel, kinetic energy dynamics, and algorithms for analyzing the dynamics and mixing of vortex patches. Test calculations based on reference solutions showed the effectiveness and good accuracy of the particle‐spectral approach. Using the developed method the dynamics of one and two initial vortex patches in the channel were investigated. We found the final state of their long‐time dynamics is time‐periodic or quasi‐periodic movements. The application of qualitative analysis algorithms demonstrates these final states produce a chaotic scattering of fluid particles in the flow‐through zone of the channel.

Wavy Whiskers in Wakes: Explaining the Trail-Tracking Capabilities of Whisker Arrays on Seal Muzzles.

Seals can detect prey up to 180 m away using only their flow-sensing whiskers. The unique undulating morphology of Phocid seal whiskers reduces vortex-induced vibrations (VIVs), rendering seals highly sensitive to biologically relevant flow stimuli. In this work, digital models of harbor and grey seal whiskers are extracted using 3D scanning and a mathematical framework that accurately recreates their undulating geometry is proposed. Through fluid-structure interaction studies and experimental investigations involving a whisker array mounted on 3D-printed microelectromechanical systems sensors, the vibration characteristics of the whisker array and the interaction between neighboring whiskers in steady flows and fish-wake-like vortices are explained for the first time. Results reveal that the downstream vortices intensity and resulting VIVs are consistently lower for grey than harbor seal whiskers and a smooth cylinder, suggesting that the grey seal whisker geometry can be an ideal template for the biomimetic design of VIV-resistant underwater structures. In addition, neighboring whiskers in an array influence one another by resulting in greater flow vorticity fluctuation and distribution area, thus causing increased vibrations than an isolated whisker, which indicates the possibility of a signal-strengthening effect in whisker arrays.

Vortex-Pressure Fluctuation Interaction in the Outlet Duct of Centrifugal Pump as Turbines (PATs)

The outlet duct is the only outlet flow component of the pump as turbines (PATs). The flow state within it not only affects its operation stability but also influences the safe operation of downstream process equipment. The undesirable flow phenomenon of the vortex is the main reason for pressure pulsations and vibrations; therefore, it is important to adopt simulation and experimental methods to reveal the vortex-pressure fluctuation interaction characteristics in the outlet duct of PATs. Firstly, the spatial and temporal evolution of the vortex in the outlet duct under different operation conditions were compared based on the Q-vortex identification criterion. Subsequently, the frequency components corresponding to local high amplitude vorticity and pressure pulsations were clarified. Finally, the relationship between vortex evolution and the pressure pulsations in the outlet duct was established. The results showed that the flow rates of the turbine significantly affected the spatial and temporal evolution of the vortex rope in the outlet duct. The front chamber leakage flow and vortex shedding from the blade trailing edge also influenced the vortex distribution characteristics in the outlet duct. The dominant frequency of the pressure pulsation in the outlet duct was 6 fn under different operating conditions, and the amplitude of the pressure pulsation increased with the flow rates. The effect of vortex evolution on the local pressure pulsation characteristics decreased with increasing flow rates. The results can be used to improve and stabilize the operation and further optimization of PATs.

Analyticity of rotational traveling capillary–gravity waves with critical layers

We establish real analyticity of the free surface of a two-dimensional steady rotational flow of water with critical layers. The flow is acted upon by gravity and surface tension. We show that any Wloc2,∞-regular free surface is analytic provided the vorticity distribution is analytic. In particular, the surface of a water flow with constant vorticity is analytic.

Influence of coupling schemes of radial and circumferential flame stabilization modes on flow and combustion characteristics of compact combustion for gas turbine

The combination of the strut and cavity is a common structural configuration for ultra-compact combustor in the gas turbine. The streamwise vortices inside the cavity play the role of stabilizing the flame and mass exchange in the spanwise direction, which is very important for the compactness and ignition performance. In this paper, the numerical simulations and the experiments were performed to study the influence of the combustor strut blocking ratio, cavity length-to-depth ratio, and strut inclination angle on the flow, the streamwise vortices distribution, as well as the combustion characteristics. We also discussed the generation of streamwise vortices and the effects of streamwise vortices on the flow and combustion performance. The results showed that the strut blocking ratio and cavity length-to-depth ratio mainly affect the strut recirculation zone and the cavity recirculation zone, the interaction of which is the key to the generation of the streamwise vortices. The reasonable distribution of the streamwise vortices promotes the mass exchange and the uniformity of the temperature distribution. In addition, the strut inclination angle has a great influence on the flow characteristics, and the forward-inclined strut is more conducive to combustion. Based on the obtained conclusions, a new design of ultra-compact integrated combustor is proposed, and it has improved flow and combustion performance.

Natural convection analysis of copper–alumina/water hybrid nanofluids in a U-shaped cavity with adiabatic wavy walls

ABSTRACT The numerical analysis of natural convection heat transfer of copper–alumina hybrid nanofluid inside a U-shaped enclosure with adiabatic wavy walls is presented in this manuscript. The Boussinesq approximation is employed in the governing equation of the model. Dimensionless variables are used to transform the governing equation into a dimensionless form. The domain is discretized into a finite number of three-node triangular elements. The weighted residual Galerkin finite element method is used to solve the model numerically. To ensure numerical stability, a damped Newton–Raphson algorithm is employed after each finite element iteration. The analysis of the influence of the nanoparticle volume fraction of 0–0.1, nanoparticle ratio of copper: alumina from 0:1 to 1:0, the Rayleigh number from to , and the amplitude and undulation of the wavy walls of 0.05−0.15 and 1−5 respectively are extensively discussed in this paper. The streamlines, isotherms, and vorticity distribution along with the average and local Nusselt number to investigate the effect of various parameters on the fluid flow and heat transfer. It is observed that the hybrid nanofluid increases the thermal performance within the wavy U-shaped cavity by 7% and 12% for one and two adiabatic wavy walls correspondingly compared to its mono nanofluid components and pure water.

Optimal performance of actuator disc models for horizontal-axis turbines

This study analyzes actuator disc (AD) models of horizontal-axis turbines to determine optimal performance, defined as the maximum power extracted at any tip speed ratio. We use the calculus of variations to maximize rotor torque relative to the thrust without making any assumptions about the rotor loading. The torque was obtained from the angular momentum equation and the thrust from the Kutta-Joukowsky equation which depends on the circumferential velocity and tip speed ratio. The optimality requirement is that the pitch of the vorticity exiting the rotor must be constant across the wake and equal to the ratio of torque to thrust. This result generalizes the classical finding of Betz and Goldstein that optimal lightly-loaded ADs have constant pitch. Optimizing the torque in the far-wake, well downstream of the rotor, leads to the same requirement of constant pitch. This implies that the pitch of an optimal rotor is constant everywhere in the wake at all tip speed ratios. We show that it is not possible for the pitch to reach its optimal value because of the vorticity distribution in the wake, and propose modifications to the pitch at the rotor and in the far-wake. The axial and circumferential velocities in the far-wake, which are easily determined, were used to find those at the rotor from the “disc loading equation” for the angular momentum which is also the normalized bound circulation at the rotor. For the simplest case of a lightly-loaded rotor at zero tip speed ratio, the induced circumferential velocity is linear in radius and the axial component is quadratic, As the tip speed ratio increases, the optimal power and thrust asymptote to the familiar Betz-Joukowsky values, and the induced axial velocity and rotor bound circulation become constant. At low tip speed ratios, the optimal wakes are constrained by the need to avoid breakdown of the flow at high swirl, and the conventional thrust equation, involving the axial velocity only, is inaccurate. As found in previous studies, the power coefficient increases monotonically with tip speed ratio, but the thrust coefficient reaches a maximum value slightly above the Betz-Joukowsky limit at a tip speed ratio of two, before decreasing towards the limit.

Pressure Fluctuation–Vorticity Interaction in the Volute of Centrifugal Pump as Hydraulic Turbines (PATs)

The pump as turbines (PATs) has been widely used in the petrochemical, seawater desalination, and mining industries. Volutes are critical components for flow guidance and energy conversion in the PATs. Therefore, its inner flow characteristic could significantly influence the hydraulic turbine system stability. To reveal the vortex evolution, pressure pulsation characteristics, and the interaction between the two in the volute of PATs, a single-stage cantilever hydraulic turbine is investigated by the numerical and experiment method. The effect of impeller rotation on vorticity distribution and pressure fluctuation intensity in volute is analyzed based on the numerical simulation results. By clarifying the frequency components corresponding to local high amplitude vorticity and pressure pulsations, the relationship between vortex evolution and pressure pulsations is established. The results showed that the dominant frequency of pressure pulsation in the circumferential direction of the volute is 6fn under different operating conditions, and the pressure pulsation characteristics in the inlet section of the volute were less affected by the rotor–stator interaction. Under Qb and 1.3Qb conditions, the vorticity pulsation near the walls in the circumferential direction of the volute had less effect on local pressure pulsation characteristics. The evolution of vorticity at the leading edge of the volute tongue intensified the local pressure pulsations as the flow rate increased. Under 0.7Qb conditions, the vorticity pulsation characteristics in the volute are complex and have a relatively significant influence on local pressure pulsation.