Vorticity Field Research Articles

Study on Aerodynamic Interference of Tilt-rotor Aircraft at Different Rotor Deflection Angles

This paper presents a numerical simulation of a tiltrotor aircraft developed in the United States, examining the aerodynamic interference between the rotors, wings, and fuselage in three flight conditions: forward flight, transition mode, and hover. The study investigates the distribution of the velocity field, pressure field, vorticity field, and streamlines around the aircraft at different rotor tilt angles.

Generalized Brenier Principle and the Closure Problem of Landgren–Monin–Novikov Hierarchy for Vorticity Field

Brenier’s concept – a representation of solutions to the equations of ideal incompressible fluids in terms of probability measures on the set of Lagrangian trajectories in the case of their stochasticity, is a generalization of Arnold’s principle of least action of finding smooth solutions of Euler’s equations. In this work, the variational generalized Brenier principle (Brenier, J. Am. Math. Soc. 1989) is used to close the infinite chain of Landgren–Monin–Novikov equations for the n-point probability density functions fn of the vortex field of two-dimensional turbulence. In addition, within the framework of the statistical approach, an approximation of the variational problem with conditions at the ends posed by Shnirelman (Mat. Sat. 1985) for the Euler equation is proposed.

Analyzing the inspiratory airflow unsteadiness in the respiratory tract using dynamic mode decomposition method

To enhance the understanding of airflow characteristics in the human respiratory tract, the inspiratory airflow field was simulated under both tidal and quasi-steady inspiratory flow rates at the mouth inlet using the large eddy simulation method. Special attention was paid on analyzing the inspiratory airflow unsteadiness using the dynamics mode decomposition (DMD) method based on the vorticity field and comparing it with the proper orthogonal decomposition (POD) method. The following novel findings were obtained. (1) Power spectral density indicates that the inspiratory airflow is highly turbulent in the pharynx–larynx region. The vorticity field in the upper airway is more affected by inspiratory patterns compared to turbulence fluctuations. (2) The DMD results indicate that the shear flow in the pharynx–larynx region is mainly caused by flow under low-frequency modes, while the disturbances of the jet flow are caused by flow under multiple frequency modes. Steady-state inspiratory pattern demonstrates the decay characteristics different from the tidal inspiratory pattern. (3) Compared to the POD method, which may contain multiple frequency components, the DMD decomposition yields modes with a single frequency, enabling a more accurate capture of the frequency and decay characteristics of the respiratory flow under each mode. In conclusion, this study demonstrates that the DMD method is more suitable for studying the respiratory airflow unsteadiness and further confirms the necessity of adopting clinically measured inspiratory data to investigate airflow unsteadiness.

Flow around triangular prisms with varying vertex angle at low Reynolds numbers

The present work investigates the unsteady flow around triangular prisms with vertex angles of 30°,45°,60°, and 90° for shedding Reynolds number between 50 and 150. The numerical simulations of flow around triangular prisms at different vertex angles and Reynolds number has been carried out using the open-source code OpenFOAM. The wake of the prisms in different cases has been examined using instantaneous and time-averaged velocity and vorticity fields. The energy dynamics in the wake are demonstrated using enstrophy. The paper explains the shedding around a prism and reports the differences in the wake due to the different vertex angles of the prisms employed in the present work. Strouhal number and force coefficients have been obtained and compared for different prisms. The coefficient of lift and drag phase plot indicates a higher spread for prisms with larger vertex angles at higher Reynolds number. The shedding frequency has a linear variation with Reynolds numbers for the prisms. The obtained results were compared with earlier works on square cylinders and 45° oriented square cylinder.

Time-Resolved Flowfield and Acoustic Measurements of a Ducted and Unducted Rotor

The impact of adding a duct to an 18.5″ diameter, triple-bladed, electrically driven rotor operating up to Mtip=0.5 at static conditions is investigated experimentally to identify the source mechanisms governing the measured acoustic differences. An unducted rotor is characterized by strong, coherent tip vorticity that interacts with each blade passing, generating high-amplitude harmonic tones. The addition of the duct results in tonal broadening and an increase of the primary and harmonic tone amplitudes. Up to a 15 dB increase in broadband noise across the entire frequency range is measured. High-speed particle imaging velocimetry up to 6.4 kHz is employed to acquire phase-locked and ensemble-averaged measurements of the velocity, vorticity, and turbulence fields. While it is often theorized that a duct can shield lateral acoustic radiation, this study finds that the ducted rotor is louder across all operating regimes, and the noise increases with tip Mach number. The ducted rotor dissipates the coherent tip vorticity into incoherent turbulence intensity due to the interaction of the vortices with the duct internal walls, contributing to a strong broadband noise increase and tonal broadening. The ducted rotor broadband noise increase is due to the rotor interacting with a more turbulent inflow condition and increased turbulence intensity throughout the plume shear layer.

Study on suction effect of water jet propulsion pump based on entropy weight theory

Water jet propulsion pumps start at special stages such as mooring and sailing, the ship is in shallow water, and the underwater keen clearance (UKC) is relatively small, which is easy to induce underwater suction vortex near the inlet position and cause violent vibration of the pumping unit. The powerful suction effect of the water-jet propulsion pump can draw in debris from the bottom of the riverbed, causing damage to the propulsion pump. This research investigated the suction effect of water jet propulsion pump under different UKC conditions. A flow field analysis method based on the entropy weight theory was constructed to reveal the flow characteristics of the flow field where the underwater suction vortex occurs. The research found that the suction effect on the flow field tends to stabilize under the condition of UKC greater than 2.5D0. After UKC reaches 4.2D0, suction effects essentially cease to create large-scale shear stresses near the riverbed. In addition, this research analyzes the vorticity field using vorticity and net circulation to elucidate the vortex strength within the flow field under different UKC conditions. The probability of generation of underwater suction vortices will be greatly reduced when the UKC is greater than 0.83D0.

Super-resolution reconstruction of turbulence for Newtonian and viscoelastic fluids with a physical constraint

Super-resolution reconstruction (SR) of turbulent flow fields with high physical fidelity from low-resolution turbulence data is a novel and cost-effective way in a turbulence study. However, some naive image-to-image machine learning methods often produce nonphysical features inconsistent with the physical characteristics of turbulence. The present work proposes, respectively, convolutional neural network and generative adversarial network-based turbulence SR models using the kinetic energy spectra of turbulence flow as a physical constraint. The models have been validated in turbulence SR reconstruction for a Newtonian fluid under the flow condition of homogeneous isotropic turbulence at Reynolds number, Re=3140 and 4710 and viscoelastic fluid at the same Re numbers and Weisenberg number, Wi=0.796 and 1.194 (the elasticity number El=Wi/Re=0.000 254), respectively. The results show that with the energy spectra constraint (ESC), not only the nonphysical features occurred in the energy spectra of velocity field could be eliminated by the SR models, the errors of their reconstructed vorticity fields in comparison with the results of direct numerical simulation are also significantly smaller than those of the SR models without ESC. Therefore, incorporation of physical constraints is vital in preserving physical characteristics in SR of turbulent flow.

The study of propagation characteristics of the millimeter-wave vortex in magnetized plasma by using the FDTD method

It is pointed out that the millimeter-wave vortex may contribute to an efficient method of plasma heating since it was found that the millimeter-wave vortex can propagate in magnetized plasma even in which the normal plane wave is in cut-off condition. Then, it was assumed that the vortex field was the Laguerre–Gaussian (L–G) mode which is a free-space solution, but the generation and stable propagation of the L–G mode vortex are not easy in the millimeter frequency range. On the other hand, it is known that the millimeter-wave hybrid mode of the cylindrical corrugated waveguide also has vortex properties. In this paper, we investigate the propagation characteristics of a millimeter-wave vortex of a hybrid mode of a cylindrical corrugated waveguide in the magnetized plasma by using three-dimensional numerical simulations with the finite-difference time-domain (FDTD) method. It is found that the millimeter-wave vortex of hybrid mode also can propagate in the magnetized plasma even in a condition in which the normal plane wave is in cut-off condition, and the propagation power in the plasma is highly dependent on the topological charge l.

Slip velocity and field information of two-phase cavitating flows

In this work, laser-induced florescent particle image velocimetry was performed to measure simultaneously the liquid and vapor velocity fields at the mid-span of a small-scale Venturi type section to determine the presence of a slip velocity between the phases. Various dynamic behavior and Kelvin–Helmholtz (K-H) instability involved in the cloud cavity shedding regime are discussed at four different cavitation numbers. The velocity, vorticity, and turbulence field information of the two phases are analyzed. The liquid–vapor mixture in a cavitating flow is usually considered a homogeneous medium in currently used computational models, but it is shown in this study that the two phases have very different dynamics. The measurements of the time-averaged velocities highlight the existence of a noteworthy slippage between the liquid and the vapor phases, especially in the upstream part of the cavitation region, where the slippage between the two phases can reach about 50% of the liquid velocity. Using phase-locked average, it is shown that the slip velocity in the upstream region is mainly located at the upper liquid–vapor interface, while the slip velocity in the closure area is near the bottom wall, due to the reentrant jet. These results contradict a primary assumption of the current models, where the medium is usually considered as a homogeneous mixture with a unique velocity field, thus providing a reference for future computational model improvement.

Controlling factors of Riedel shear spacing in the simple shear mode of strike-slip fault: Insights from sandbox models

Strike-slip faults generally develop Riedel shears (R-shears), which exhibit parallel and evenly-spaced distribution characteristics. However, the factors controlling the R-shear spacing in strike-slip faults are still unclear. The influence of material properties such as internal friction angle and cohesion, basal friction, and the thickness of brittle layers (T) on the R-shear spacing (S) are investigated using analogue models in this paper. Research findings indicate that the internal friction angle of the material and the thickness of the brittle layer have a significant impact on the R-shear spacing, with the thickness of the brittle layer directly determining the R-shear spacing as evidenced by their linear correlation. In comparison, cohesion and basal friction have insignificant effects on R-shear spacing. Based on this, experiments were carried out using various thicknesses of brittle layers (specified materials) to investigate the impact of the brittle layer thickness on the R-shear spacing, and Particle Image Velocimetry (PIV) is used to analyze the distribution pattern of R-shear development at each stage. The results indicate that fractures occur in regions where the vorticity field alternates between positive and negative values, and as the evolution progresses, the maximum strain gradually converges towards the center of the deformation zone, leading to a reduction in the activity of the R-shear, while the spacing of the R-shear remains unaltered. The normalized (S/T) results indicate that the experimental value of 1.32 aligns with natural laws and is very close to the normalized value of the natural faults, which is 1.24. It can be inferred that the thickness of the seismogenic crust within the range of the Altyn Tagh Fault is 40.9–43.5 km.

Characteristic analysis of the vortex excited using the photoacoustic transducer with a spiral light absorption surface

Abstract It is proved that the vortex acoustic field can be excited with laser by designing the photoacoustic transducer with a spiral light absorption surface. The generated acoustic field has a spiral phase wavefront, and the pressure on the central axis along its propagation direction is zero. The orbital angular momentum that can be used for positioning and manipulation of particles is formed by the vortex. The characteristics of the generated acoustic vortex at different frequency and detection position are analyzed for 1-5 topological charge. And the influence of the geometric configurations such as the width and size of logarithmic spiral slot are also studied for the achieving the desired vortex field with focused intensity.

Efficient approach for generating vortex sources with arbitrary orbital angular momentum in acoustic experiments

Abstract In theoretical research framework of acoustics or optics, how to provide stable and efficient experimental vortex sources with arbitrary orbital angular momentum (OAM) (especially with larger OAM) is a highly challenging research topic. Here, we propose and demonstrate the general principle of two different methods to generate vortex sources with arbitrary OAM, based on the point-sources array and acoustic metamaterials, respectively. Specifically, the general synthetic law is summarized from the analytical perspective behind generating two-dimensional vortex waves using different point sources with different phases, and the design flexibility of acoustic metamaterials is also utilized to provide an ideal solution for generating vortex sources with larger OAM. Besides, we qualitatively and quantitatively determine the OAM of generated vortex waves through simple formulas, and briefly discuss the applicability and stability of two different methods with complementary advantages. The principles of vortex sources generation revealed in this work provide direct theoretical support for the experimental exploration of interactions between multiphysics fields and complex media, with potential applications in vortex fields manipulation and OAM detection.

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Investigation of the Coupling Between the Dynamics of Vortical Structures and Flame Stability in Bluff-Body Premixed Combustion Using Extended Spectral Proper Orthogonal Decomposition

Abstract Large eddy simulation data of a bluff-body stabilized flame are analyzed using spectral proper orthogonal decomposition (SPOD) to investigate: (i) the role of flame-vortex interactions in the dominant flow dynamics, and (ii) how the proper choice of the cross-spectral density (CSD) defining SPOD can assist in identifying the underlying dynamics. Bluff-body flame holders aim to achieve stable flames under lean premixed conditions to minimize pollutant emissions. The recirculation region induced by the body promotes the mixing of hot combustion products with unburnt gases, preventing the global blowoff. However, the coupling between the shear layers and flame-induced vorticity sources can result in large flow structures that either contribute to increased flame stability or exhibit features typical of the early stages of flame blowout. SPOD is a data-driven technique remarkably powerful in extracting low-dimensional models. For each frequency, it computes a basis of orthogonal modes that maximizes the content of a predefined CSD in the leading modes. By choosing physically-relevant variables to construct the CSD, different physics can be explored, which is used here to investigate the coupled dynamics between the flame-induced baroclinic torque, vortical structures, and the temperature field. The results show that the vorticity and temperature fields exhibit low-dimensional dynamics characterized by a narrowband frequency and its harmonics; these dynamics are varicose oscillations of the flame region, governed by the baroclinic torque. Sinuous oscillations typical of wake instability for non-reactive flows are also present, suggesting a competition between them.

Dumbbell-shaped piezoelectric energy harvesting from coupled vibrations

This paper presents a novel dumbbell-shaped piezoelectric energy harvesting from vortex-induced vibration (VIV) and galloping. The designed harvester system leverages the coupled vibrations to improve the output performance. The conceptual design of the dumbbell-shaped harvester system is first developed, the theoretical model of the harvester is then established, three-dimensional simulation analyses are conducted, and the prototypes of the harvester that combines a cylinder and a cuboid are finally manufactured. The effect of the cylinder lengths and airflow velocity on the harvesting characteristics is explored. The results demonstrate the derived mathematical model is fully verified through experimental method. VIV occurs in the 0.5D and 1D dumbbell-shaped harvester systems at lower airflow velocities, while galloping takes place at higher velocities, both of which contribute to increase the output performance. In contrast, the 1D - 3D dumbbell-shaped harvesters demonstrate a VIV behavior only and suppress vibration. The maximum voltage generated by the 0.5D harvester is 12.03 V at 4.29 m s-1, which is 11.18 % higher than that of a single cuboid harvester. The vorticity fields illustrate the vortex shedding mode and intensity, as well as reveal the underlying influence mechanism.

Vorticity and magnetic dynamo from subsonic expansion waves. II. Dependence on the magnetic Prandtl number, forcing scale, and cooling time

The amplification of astrophysical magnetic fields takes place via dynamo instability in turbulent environments. Vorticity is usually present in any dynamo, but its role is not yet fully understood. This work is an extension of previous research on the effect of an irrotational subsonic forcing on a magnetized medium in the presence of rotation or a differential velocity profile. We aim to explore a wider parameter space in terms of Reynolds numbers, the magnetic Prandtl number, the forcing scale, and the cooling timescale in a Newtonian cooling. We studied the effect of imposing that either the acceleration or the velocity forcing function be curl-free and evaluated the terms responsible for the evolution vorticity. We used direct numerical simulations to solve the fully compressible, resistive magnetohydrodynamic equations with the Pencil Code. We studied both isothermal and non-isothermal regimes and addressed the relative importance of different vorticity source terms. We report no small-scale dynamo for the models that do not include shear. We find a hydro instability, followed by a magnetic one, when a shearing velocity profile is applied. The vorticity production is found to be numerical in the purely irrotational acceleration case. Non-isothermality, rotation, shear, and density-dependent forcing, when included, contribute to increasing the vorticity. As in our previous study, we find that turbulence driven by subsonic expansion waves can amplify the vorticity and magnetic field only in the presence of a background shearing profile. The presence of a cooling function makes the instability occur on a shorter timescale. We estimate critical Reynolds and magnetic Reynolds numbers of 40 and 20, respectively.

Research on the Flow-Induced Vibration of Cylindrical Structures Using Lagrangian-Based Dynamic Mode Decomposition

An oscillating flow past a structure represents a complex, high-dimensional, and nonlinear flow phenomenon, which can lead to the failure of structures due to material fatigue or constraint relaxation. In order to better understand flow-induced vibration (FIV) and coupled flow fields, a numerical simulation of a two-degrees-of-freedom FIV in a cylinder was conducted. Based on the Lagrangian-based dynamic mode decomposition (L-DMD) method, the vorticity field and motion characteristics of a cylinder were decomposed, reconstructed, and predicted. A comparison was made to the traditional Eulerian-based dynamic mode decomposition (E-DMD) method. The research results show that the first-order mode in the stable phase represents the mean flow field, showcasing the slander tail vortex structure during the vortex-shedding period and the average displacement in the in-line direction. The second mode predominantly captures the crossflow displacement, with a frequency of approximately 0.43 Hz, closely matching the corresponding frequency observed in the CFD results. The higher dominant modes mainly capture outward-spreading, smaller-scale vortex structures with detail displacement characteristics. The motion of the cylinder in the in-line direction was accompanied by symmetric vortex structures, while the motion of the cylinder in the crossflow direction was associated with anti-symmetric vortex structures. Additionally, crossflow displacement will cause a symmetrical vortex structure that spreads laterally along the axis behind the cylinder. Finally, when compared with E-DMD, the L-DMD method demonstrates a notable advantage in analyzing the nonlinear characteristics of FIV.

Analysis of vapor bubble diameter, departure frequency and dynamics in a single cavity

The ongoing quest for methods that enhance the efficiency of heat transfer processes, particularly those involving phase change, underscores the importance of comprehending the dynamics of vapor bubbles during boiling. This study investigates heat transfer mechanisms and the dynamics of vapor bubbles within the nucleate boiling regime. Experimental tests were conducted on a flat copper surface featuring a single cavity, focusing on analyzing vapor bubble growth and departure stages. The working fluid examined was HFE-7100 under saturated conditions. The formation and growth aspects of vapor bubbles, including their diameter (Dd) and departure frequency (f), were investigated through experimental data obtained by two different techniques: by an optical sensor of variable resistance capable of generating an analog signal from a voltage change and by a high-speed camera that captures images immediately after the instant that the bubble detached from the surface. Both techniques provide visual insights into the boiling phenomenon. An escalation in heat flux and, consequently, wall superheat resulted in an increased bubble departure frequency. Furthermore, the optical flow analysis successfully identified velocity and vorticity fields induced by micro convection, the prevailing heat transfer mode in nucleated boiling. A slight horizontal displacement trend over time was observed, which may be caused by the asymmetry in the velocity profile, confirmed by velocity peaks tending toward one direction. Vortex analysis reveals rotational motion concentrated in specific regions, with noticeable deformation near the bottom of the bubble and asymmetric movement contributing to vorticity. These findings provide insights into the vapor bubble dynamics, which is important for understanding the cavity rewetting phenomena.

Numerical simulation of the influence of wave parameters on the horizontal cylinder in the nonlinear coupling of the wave–current

Considering that marine structures are frequently subjected to the combined effects of waves and currents, the wave–current coupling environment largely determines the structural load and the surrounding water–air mixed flow, which is a typical feature of offshore structures, such as ships and offshore platforms. This study focuses on the interaction between a horizontal cylinder and a free surface in a wave–current nonlinear coupled environment using numerical simulations. The numerical method is based on the incompressible Navier–Stokes equation, with the volume-of-fluid method used to capture the free surface. Based on the second-order Stokes wave theory, we studied the impact of wave height and steepness on the cylinder force, vorticity field, free-surface deformation, and spatial–temporal distribution characteristics of entrainment bubbles. The results showed that the wave height and wave steepness have opposite effects on the root mean square (RMS) value of the force and influence the amplitude and period of the force curve. The stretching of the negative vortex led to varying degrees of double-frequency oscillation modes in the force curves. The main sources of bubbles in the wake are the breaking of the free surface and the entrainment caused by the cylinder vortex, and the bubbles caused by the former account for the majority. Compared with the wave height, an increase in wave steepness can cause a more severe interface breaking, resulting in more entrainment bubbles.

MMS Observations of Electron Vorticity in the Earth’s Magnetosheath

The Earth’s magnetosheath serves as a natural laboratory to study the transition of highly turbulent fluctuations. The fundamental information about plasma turbulences can be examined observationally with the help of electron vorticity measurements. This study presents the first statistics of the electron vorticity field in the magnetosheath by utilizing 4 yr data from NASA’s Magnetospheric Multiscale mission. In this study, the magnetosheath vorticity has a dominant perpendicular anisotropy. The vorticity field in the subsolar region is much stronger than that of magnetosheath flanks. Clear dusk-favored asymmetry for large vorticity is identified in the subsolar region. We examine that the electron flow vorticity in the turbulent magnetosheath is well anticorrelated with the electron density. The vorticity is of great importance in energy dissipation and electron heating in the magnetosheath flanks. This study can improve the current understanding of electron vorticity due to its ubiquitous role in space plasma turbulences.