Vortex Ring Research Articles

Improving depth uncertainty in plenoptic camera-based velocimetry

This work describes the development of a particle tracking velocimetry (PTV) algorithm designed to improve three-dimensional (3D), three-component velocity field measurements using a single plenoptic camera. Particular focus is on mitigating the longstanding depth uncertainty issues that have traditionally plagued plenoptic particle image velocimetry (PIV) experiments by leveraging the camera’s ability to generate multiple perspective views of a scene in order to assist both particle triangulation and tracking. 3D positions are first estimated via light field ray bundling (LFRB) whereby particle rays are projected into the measurement volume using image-to-object space mapping. Tracking is subsequently performed independently within each perspective view, providing a statistical amalgamation of each particle’s predicted motion through time in order to help guide 3D trajectory estimation while simultaneously protecting the tracking algorithm from physically unreasonable fluctuations in particle depth positions. A synthetic performance assessment revealed a reduction in the average depth errors obtained by LFRB as compared to the conventional multiplicative algebraic reconstruction technique when estimating particle locations. Further analysis using a synthetic vortex ring at a magnification of − 0.6 demonstrated plenoptic-PIV capable of maintaining the equivalent of 0.1–0.15 voxel accuracy in the depth domain at a spacing to displacement ratio of 5.3–10.5, an improvement of 84–89% compared to plenoptic-PIV. Experiments were conducted at a spacing to displacement ratio of approximately 5.8 to capture the 3D flow field around a rotor within the rotating reference frame. The resulting plenoptic-PIV/PTV vector fields were evaluated with reference to a fixed frame stereoscopic-PIV (stereo-PIV) validation experiment. A systematic depth-wise (radial) component of velocity directed toward the wingtip, consistent with observations from prior literature and stereo-PIV experiments, was captured by plenoptic-PTV at magnitudes similar to the validation data. In contrast, the plenoptic-PIV did not discern any coherent indication of radial motion. Our algorithm constitutes a significant advancement in enhancing the functionality and versatility of single-plenoptic camera flow diagnostics by directly addressing the primary limitation associated with plenoptic imaging.Graphical abstract

Numerical analysis of aero-hydrodynamic wake flows of a floating offshore wind turbine subjected to atmospheric turbulence inflows

The influence of atmospheric turbulence inflow on coupled dynamic behaviors and wakes of floating offshore wind turbine (FOWT) is pronounced, especially as blade size increases. In this study, we explore the effects of atmospheric inflow on aero-hydrodynamics and wake characteristics of a spar-type FOWT. A well-validated in-house computational fluid dynamic (CFD) solver, FOWT-UALM-SJTU, is utilized to conduct the numerical simulations. To generate the realistic atmospheric inflow condition, the large eddy simulation (LES) with long-duration is employed. Two other cases involving uniform inflow and shear inflow are conducted to provide some comparable results. Compared to uniform inflow and shear inflow, the power and thrust of FOWT under atmospheric inflow display greater instability, with their power spectrums exhibiting higher intensity in high frequency region. The variation of yaw moment in atmospheric scenario is significantly drastic, leading to a remarkable response in platform yaw motion. Notably, the dominant frequency in this scenario is the blade passage frequency, as opposed to the incident wave frequency observed in the uniform and shear scenarios. The atmospheric inflow promotes the manifestation of wake breakdown and wake meandering, resulting in the faster wake recovery of FOWT. Besides, the meandering in the far wake is more significant compared to uniform and shear scenarios. The absence of vortex rings in atmospheric scenario is observed, along with the presence of more complex and smaller vortices in far wake. Our findings highlight the remarkable impacts of atmospheric inflow on dynamic responses and wake evolution of FOWT, and it is recommended that the atmospheric inflow be taken into account when assessing wake interactions between multiple FOWTs.

Monge–Ampère geometry and vortices

We introduce a new approach to Monge–Ampère geometry based on techniques from higher symplectic geometry. Our work is motivated by the application of Monge–Ampère geometry to the Poisson equation for the pressure that arises for incompressible Navier–Stokes flows. Whilst this equation constitutes an elliptic problem for the pressure, it can also be viewed as a non-linear partial differential equation connecting the pressure, the vorticity, and the rate-of-strain. As such, it is a key diagnostic relation in the quest to understand the formation of vortices in turbulent flows. We study this equation via an associated (higher) Lagrangian submanifold in the cotangent bundle to the configuration space of the fluid. Using our definition of a (higher) Monge–Ampère structure, we study an associated metric on the cotangent bundle together with its pull-back to the (higher) Lagrangian submanifold. The signatures of these metrics are dictated by the relationship between vorticity and rate-of-strain, and their scalar curvatures can be interpreted in a physical context in terms of the accumulation of vorticity, strain, and their gradients. We show explicity, in the case of two-dimensional flows, how topological information can be derived from the Monge–Ampère geometry of the Lagrangian submanifold. We also demonstrate how certain solutions to the three-dimensional incompressible Navier–Stokes equations, such as Hill’s spherical vortex and an integrable case of Arnol’d–Beltrami–Childress flow, have symmetries that facilitate a formulation of these solutions from the perspective of (higher) symplectic reduction.

An investigation of flow regimes and mixing in a novel arrow-shaped jet reactor

Fluid mixing plays a vital role in the industry of chemical engineering. In this work, a novel arrow-shaped jet reactor by varying the angle of fluid impingement in the inlet channel was investigated. Flow field visualization experiments using Planar Laser-Induced Fluorescence (PLIF) technique were carried out to study various flow regimes and mixing performance. Results show that differentiated flow patterns of engulfment flow regimes appear within the arrow-shaped jet reactor. Particularly, vortex ring shedding was found in the unsteady engulfing flow regime, which promoted the mixing significantly. Besides, the mechanism of the variation of fluid impinging angle on mixing in an arrow-shaped jet reactor was investigated by numerical simulation. The results indicate that the transformation from double-leg vortex to single-leg vortex and the increase of the volume of vortex clusters caused by vortex ring shedding are the main reasons for the improvement of the mixing of engulfment flow regime.

Velocity gradient analysis of a head-on vortex ring collision

We simulate the head-on collision between vortex rings with circulation Reynolds numbers of 4000 using an adaptive, multiresolution solver based on the lattice Green's function. The simulation fidelity is established with integral metrics representing symmetries and discretization errors. Using the velocity gradient tensor and structural features of local streamlines, we characterize the evolution of the flow with a particular focus on its transition and turbulent decay. Transition is excited by the development of the elliptic instability, which grows during the mutual interaction of the rings as they expand radially at the collision plane. The development of antiparallel secondary vortex filaments along the circumference mediates the proliferation of small-scale turbulence. During turbulent decay, the partitioning of the velocity gradients approaches an equilibrium that is dominated by shearing and agrees well with previous results for forced isotropic turbulence. We also introduce new phase spaces for the velocity gradients that reflect the interplay between shearing and rigid rotation and highlight geometric features of local streamlines. In conjunction with our other analyses, these phase spaces suggest that, while the elliptic instability is the predominant mechanism driving the initial transition, its interplay with other mechanisms, e.g. the Crow instability, becomes more important during turbulent decay. Our analysis also suggests that the geometry-based phase space may be promising for identifying the effects of the elliptic instability and other mechanisms using the structure of local streamlines. Moving forward, characterizing the organization of these mechanisms within vortices and universal features of velocity gradients may aid in modelling turbulent flows.

Fluid–acoustic interactions around an expanding pipe with orifice plates

Expanding pipes with orifice plates are often utilized as silencers for fluid machinery. However, intense tonal sounds can be generated from a flow through such expanding pipes. To clarify the mechanism of tonal sound from a flow through a circular expanding pipe with two orifice plates and the conditions for intense acoustic radiation, the flow and acoustic fields are directly solved based on the compressible Navier–Stokes equations. Phase-averaged flow fields indicate the occurrence of periodic vortex shedding in the free shear layers of the expanding pipe, resulting in acoustic radiation. The effects of the orifice radius and freestream Mach number on the acoustic radiation are focused on. The computational results demonstrate that vortex rings or spiral vortices are generated in the cavities formed by the orifice plates, where the primary vortical shape changes, depending on the freestream Mach number and orifice radius. The collision of the vortex ring and spiral vortex with the orifice plate or downstream edge of the expanding pipe leads to the occurrence of circumferentially in-phase and one-wavelength-mode pressure fluctuations, respectively. The orifice radius also affects the convective velocity of vortices and the position of the acoustic source, varying the frequency of the acoustic radiation. The findings of this research provide the first clarifications of fluid–acoustic interactions in an expanding pipe with orifice plates.

Variational construction of tubular and toroidal streamsurfaces for flow visualization

Approximate streamsurfaces of a three-dimensional velocity field have recently been constructed as isosurfaces of the closest first integral of the velocity field. Such approximate streamsurfaces enable effective and efficient visualization of vortical regions in three-dimensional flows. Here we propose a variational construction of these approximate streamsurfaces to remove the limitation of Fourier series representation of the first integral in earlier work. Specifically, we use finite-element methods to solve a partial differential equation that describes the best approximate first integral for a given velocity field. We use several examples to demonstrate the power of our approach for three-dimensional flows in domains with arbitrary geometries and boundary conditions. These include generalized axisymmetric flows in the domains of a sphere (spherical vortex), a cylinder (cylindrical vortex) and a hollow cylinder (Taylor–Couette flow) as benchmark studies for various computational domains, non-integrable periodic flows (ABC and Euler flows) and Rayleigh–Bénard convection flows. We also illustrate the use of the variational construction in extracting momentum barriers in Rayleigh–Bénard convection.

Effect of surface roughness on large-scale downburst-like impinging jets

Downbursts are cold descending winds that develop from thunderstorm clouds and, after impingement on the ground, produce an intense low-level horizontal front characterized by an axisymmetric toroidal vortex structure. Surface roughness is a key factor in the characterization of mean and turbulent wind speed features of synoptic-scale stationary atmospheric boundary layer winds. The goal of the present research is to physically assess whether the same can apply to the surface layer produced during thunderstorms, which are non-stationary, highly time-transient, and spatially limited phenomena. Downburst-like flows were produced through the impinging jet technique at the WindEEE Dome, at Western University in Canada. Three different surfaces were tested, and an equivalent full-scale roughness length (z0,eq) was determined. Experimental records are made publicly available. The large geometric and kinematic scales produced high Reynolds numbers, which enabled us to classify the flow as “fully turbulent” and therefore representative of full-scale downbursts. Results indicate a weak dependency on the Reynolds number, which suggests no relevant flaws in extending the results to the natural environment. The overall wind speed maxima weakly depend on z0, whereas a sharp velocity decrease is observed beyond the radial position of the maxima with increasing z0. Surface roughness enhances the boundary layer separation and consequently elevates the height of maximum wind speed above the surface. Vertical profiles of the horizontal velocity return a quite clear nose shape. Turbulence intensity shows a C-like shape with maxima in the near proximity of the ground that increase with z0.

Effects of increasing orbital number on the field transformation in focused vortex beams

Acoustic vortex beams possess helical wavefronts characterized by an orbital number n. In the presence of focusing, the toroidal vortex ring for n = 1 moves out of the focal plane z = d and toward the source with increasing n, accompanied by a departure from its toroidal shape. In this talk, ray theory is developed to explain this field transformation. An expression is derived for the radius and cross-sectional area of the annular channel formed by the family of rays emanating from a thin circular ring centered at the origin in the source plane z = 0. This expression leads to explicit results for the field amplitude and caustic coordinates due to a focused vortex source with an arbitrary axisymmetric amplitude distribution. Comparison with field calculations in which diffraction is included demonstrate that the caustics describe the redistribution of the global maximum and its shift toward the source plane with increasing n. For moderate focusing gains (of order 10 or 20), a toroidal vortex ring for n = 1 transforms with increasing n into a spheroidal surface in the prefocal region 0 < z < d having volume nλd 2/6, where λ is the wavelength, inside of which exists a shadow zone. [C.A.G. was supported by the ARL:UT McKinney Fellowship in Acoustics.]

Probing dynamics of elliptical vortex rings via direct vorticity measurements with digital inline holography

Probing dynamics of elliptical vortex rings via direct vorticity measurements with digital inline holography

Influence of Dispersed Particles on Structure of a Vortex Ring and Its Propagation

Influence of Dispersed Particles on Structure of a Vortex Ring and Its Propagation

Formation and propagation characteristics of a weak shock wave in maglev tube

The propagation of the weak shock wave (WSW) to the tunnel exits and their radiation as micro-pressure waves (MPWs) may cause sonic booms or structural resonance of buildings, posing potential hazards to humans, animals, and buildings in the exit's environment. The characteristics of the WSW and sonic booms of a maglev train/tube coupling model were studied based on the two-dimensional axisymmetric unsteady Reynolds average Navier–Stokes turbulence model. In the later stage of a MPW, the formation mechanism, geometry, and kinematic characteristics of compressible vortex rings (CVRs) were systematically analyzed. The inertial effect causes the initial wavefront to gradually transition from a Gaussian-shape waveform to a triangular waveform during its propagation, eventually coalescing into a WSW. The overpressure, density jump, and shock Mach number at the WSW location all increase with the increasing train speed, while the WSW thickness decreases accordingly. The formation distance of the WSW is inversely proportional to the amplitude of the initial wavefront gradient, and the WSW directly causes the occurrence of the exit sonic boom. The MPW amplitude has significant directionality with a largest value in the axial direction. Within the speed range of 450–700 km/h, the sound pressure level of the MPW exceeds the hearing threshold and even reaches the feeling threshold. The evolution of CVRs includes primary CVR, secondary CVR, and Kelvin–Helmholtz vortices. Primary CVR has the greatest impact on the axial MPW among them. The occurrence of CVRs will cause a second small noise level other than the sonic boom.

Numerical study of a laminar vortex ring of a polymer solution

Numerical study of a laminar vortex ring of a polymer solution

A Novel Unsteady Vortex Ring Method for Aerodynamic Calculations of a Flapping Wing Rotor

A Novel Unsteady Vortex Ring Method for Aerodynamic Calculations of a Flapping Wing Rotor

Functional bio-inspired hybrid fliers with separated ring and leading edge vortices.

Recent advances in passive flying systems inspired by wind-dispersed seeds contribute to increasing interest in their use for remote sensing applications across large spatial domains in the Lagrangian frame of reference. These concepts create possibilities for developing and studying structures with performance characteristics and operating mechanisms that lie beyond those found in nature. Here, we demonstrate a hybrid flier system, fabricated through a process of controlled buckling, to yield unusual geometries optimized for flight. Specifically, these constructs simultaneously exploit distinct fluid phenomena, including separated vortex rings from features that resemble those of dandelion seeds and the leading-edge vortices derived from behaviors of maple seeds. Advanced experimental measurements and computational simulations of the aerodynamics and induced flow physics of these hybrid fliers establish a concise, scalable analytical framework for understanding their flight mechanisms. Demonstrations with functional payloads in various forms, including bioresorbable, colorimetric, gas-sensing, and light-emitting platforms, illustrate examples with diverse capabilities in sensing and tracking.

A Study of Shock-Induced Transient Jets: The Impact of Exit Conditions on Mach Disk and Vortex Ring

Abstract We investigate the effect of exit pressure history on the flow characteristics of underexpanded transient jets. Using both experiments and numerical simulations, we study the dynamics of shock-cell and vortex structures within these jets. A shock tube with an open-ended configuration allows us to generate transient jets by adjusting the diaphragm pressure ratio and the length of the driver section. Our results indicate that when the shock Mach number exceeds 1.6, a Mach disk forms, indicating a highly underexpanded transient jet at the exit of the shock tube. A distinguishing feature of this jet is the emergence of counter-rotating vortex rings (CRVRs) alongside the initial primary vortex ring. Our findings reveal a substantial influence of both the amplitude and duration of the peak exit pressure on the characteristics of the Mach disk and vortex ring. Notably, the characteristics of the primary vortex ring exhibit significant sensitivity to the formation and evolution of CRVRs. In cases of continuously decreasing exit pressure, the Mach disk follows a consistent self-similar decay pattern, regardless of the peak exit pressure magnitude. Finally, we present an empirical relationship between exit pressure and the characteristics of the Mach disk. In summary, this research provides insight into the complex interaction between the exit pressure history and the flow characteristics in underexpanded transient jets.

Laminar to turbulent transitions of pipe flows by resonances of natural frequencies of components of test sections

This investigation analyses special papers and doctoral theses that treat transitions of pipe flows as a resonance phenomenon of wave frequencies. These frequencies are natural frequencies of pipe flows, of components of the test section and of vortex ring formations. Resonance conditions are derived that show how the critical Reynolds number, Rec , depends on the volume of the plenum chamber, the pipe diameter, the pipe length, etc. The derived resonance relations were verified experimentally using the experimental data of the third author, yielding R e c ∼ 1 / V ple , R e c ∼ 1 / ( L D ) and other interesting results. These findings suggest that the laminar-to-turbulent transition has various modes and transitive dependences. To understand this fully, it is necessary to take all components of the test section involved into account. The test section considered in this paper consists of a mass flow controller to supply the airflow and a plenum chamber, followed by the actual pipe of interest. It is shown that all the components can contribute to the measured value of the critical Reynolds number of pipe flow transition.

Propulsion curve analysis and optimisation of biomimetic pectoral fin with three degree of freedom based on multi-layer perception

This paper aims to improve the swimming efficiency of biomimetic robotic fish by optimising its propulsion curve with three degree of freedom (DOF), in which the key is to minimise the resistance during swing backstroke of the pectoral fin. For this purpose, a reference point on the pectoral fin is first selected, and then an 8-shaped propulsion curve is constructed to coordinate rowing and flapping motions. Meanwhile, a propulsion curve of feathering motion is also given correspondingly. On this basis, the overall curvature and curve offset are proposed as measurement parameters for the deformation of the propulsion curve and the proportion of abdominal/dorsal circles in the propulsion curve, respectively. As the motion law of feathering is given in a sinusoidal pattern, a data set of hydrodynamic parameters is obtained for pectoral fin propulsion under different motion parameter conditions by computational fluid dynamics(CFD) numerical simulation. Once again, a propulsion curve optimisation model is established based on multi-layer perception(MLP), which uses the hydrodynamic parameters data set as input. The results show that the resistance of swing backstroke reached the minimum when overall curvature is π/10 and curve offset is 0.4, which is enhanced by 30.13% and 33.33% at thrust and lift direction compared to the existing design, respectively. Furthermore, the flow field structure and hydrodynamic parameters around the robotic fish are calculated by CFD. The results show that two sets of vortex rings are generated around the fish body during a propulsion cycle. The vortex rings detached towards the lower and upper sides of the fish body such that the lift is minimal, the thrust direction is relatively stable, and the resistance is minimal during the swing backstroke. The experimental results indicate that it can raise propulsion efficiency during the pectoral fin propulsion process, verifying the effectiveness of this method.

Vorticity dynamics at partial-slip boundaries

In this paper we discuss the dynamics of vorticity at partial-slip boundaries. We consider the total vector circulation, which includes both the total vorticity of the fluid and the slip velocity at the boundary (the interface vortex sheet). The generation of vector circulation is an inviscid process, which does not depend on either viscosity or the slip length at the boundary. Vector circulation is generated by the inviscid relative acceleration between the fluid and the solid, due to either tangential pressure gradients or tangential acceleration of the partial-slip wall. While the slip length does not affect the creation of vector circulation, it governs how vector circulation is distributed between the total vorticity of the fluid and the interface vortex sheet. Specifically, the partial-slip boundary condition prescribes the ratio between boundary vorticity and the strength of the interface vortex sheet, and the viscous boundary flux transfers vector circulation between the interface vortex sheet and the fluid interior to maintain this condition. The interaction between a vortex ring and a partial-slip wall is examined to highlight various aspects of this formulation. For the head-on collision, the quantity of vector circulation diffused into the fluid as secondary vorticity increases as the slip length is decreased, resulting in a stronger secondary vortex and increased rebound of the vortex ring. For the oblique interaction, the extent to which the vortex ring connects to the boundary increases as the slip length is increased.

Reconstruction and prediction of the rotor wake flow field in hovering state

A clear understanding of the flow structure and evolution of the rotor wake flow field is one of the key problems to be solved in the development of rotor aerodynamics. The tip vortices are the primary structure of the rotor wake flow field. A theoretical model of the vortex ring was established to verify the feasibility of flow field reconstruction. Particle image velocimetry (PIV) is used to measure the two-dimensional velocity field in the rotor wake. Because of the wandering motion of tip vortices, a new conditional average algorithm is proposed to deal with the flow field. On this basis, it is proposed that the plane interval of the rotor wake flow field reconstructed by interpolation should be less than 20 deg. The vortex core radius is obtained by the analysis method based on the circulation. A Back Propagation (BP) neural network was established to predict the axial and radial positions of the tip vortices and the radius of the vortex core. The inputs are the vortex ages measured by the experiment, and the outputs are the position and radius of the vortex core under any vortex ages. The predicted values were in good agreement with the experimental results. The study provides further analytical methods and new insights for the characteristics and evolution of tip vortices.