Scale Vortices Research Articles

Numerical simulation of two-dimensional turbulence based on Immersed Boundary Lattice Boltzmann method

The two-dimensional turbulence is numerically investigated using Immersed Boundary Lattice Boltzmann Method. The 2D turbulence should be considered as 2D channel flow where the flow is forced by the arrays of cylinders vertically placed in the inlet of 2D channel. The inverse cascade in two cases, the normal wall boundary case and rough wall boundary case, is obtained in the inertial range. The scaling behavior of energy spectrum in the inverse cascade is k−5/3, which is according with the Kraichnan theory of 2D turbulence. It is found that the time-evolving vortex number density distribution n(A)∼t−1A−1, based on the Rortex vortex definition criterion, which is in fair agreement with the theory of Burgess and Scott at intermediate scales sufficiently far from the forcing and the largest vortex scale. The energy flux of the normal wall boundary case cascades to the large scale. The energy flux of the rough wall boundary case cascades to large scale when the scale l < D. The energy flux at l > D cascades to the small scale. The energy dissipation filed εl coarse grained at the scale l has the pow-law behaviors with the scale. The intermittency measured by PDF exists in the inverse inertial range of 2D turbulence. On the basis of the vortex scaling law of Burgess and Scott and our simulation results, the universal scaling law of velocity structure function in the inverse cascade is obtained by extending the 3D turbulent S-L intermittency model to the inverse inertial range of 2D turbulence.

Magnetic Recording of Superconducting States

Local polarization of magnetic materials has become a well-known and widely used method for storing binary information. Numerous applications in our daily life such as credit cards, computer hard drives, and the popular magnetic drawing board toy, rely on this principle. In this work, we review the recent advances on the magnetic recording of inhomogeneous magnetic landscapes produced by superconducting films. We summarize the current compelling experimental evidence showing that magnetic recording can be applied for imprinting in a soft magnetic layer the flux trajectory taking place in a superconducting layer at cryogenic temperatures. This approach enables the ex situ observation at room temperature of the imprinted magnetic flux landscape obtained below the critical temperature of the superconducting state. The undeniable appeal of the proposed technique lies in its simplicity and the potential to improve the spatial resolution, possibly down to the scale of a few vortices.

On wake vortex encounter of axial-symmetric projectiles launched successively underwater

To understand the potential hazard and mechanism of wake vortex encounter underwater, we perform a numerical simulation on two successively launched projectiles with 6 degrees of freedom. The evolution of wake vortices and their interaction with projectiles are studied under various launcher transport speed and launch sequences. Two major wake vortex structures are discovered: the vortex ring and the counter-rotating vortex pair. As the projectile angle of attack increases, the dominant vortex inside the wake transforms from vortex rings to hairpin vortices, then counter-rotating vortex pairs. The large scale vortices in the wake are highly directional before breaking up, and the counter-rotating vortex pairs can impose significant influence on projectile attitude upon wake vortex encounter. In contrast, minor influence can be done by vortex rings under the same situation. Projectiles launched with higher platform transport speed tend to be more affected by wake vortices due to the strong counter-rotating vortex pairs generated with a high angle of attack.

Pseudoentropic derivation of the regularized lattice Boltzmann method.

The lattice Boltzmann method (LBM) facilitates efficient simulations of fluid turbulence based on advection and collision of local particle distribution functions. To ensure stable simulations on underresolved grids, the collision operator must prevent drastic deviations from local equilibrium. This can be achieved by various methods, such as the multirelaxation time, entropic, quasiequilibrium, regularized, and cumulant schemes. Complementing a part of a unified theoretical framework of these schemes, the present work presents a derivation of the regularized lattice Boltzmann method (RLBM), which follows a recently introduced entropic multirelaxation time LBM by Karlin, Bösch, and Chikatamarla (KBC). It is shown that both methods can be derived by locally maximizing a quadratic Taylor expansion of the entropy function. While KBC expands around the local equilibrium distribution, the RLBM is recovered by expanding entropy around a global equilibrium. Numerical tests were performed to elucidate the role of pseudoentropy maximization in these models. Simulations of a two-dimensional shear layer show that the RLBM successfully reproduces the largest eddies even on a 16×16 grid, while the conventional LBM becomes unstable for grid resolutions of 128×128 and lower. The RLBM suppresses spurious vortices more effectively than KBC. In contrast, simulations of the three-dimensional Taylor-Green and Kida vortices show that KBC performs better in resolving small scale vortices, outperforming the RLBM by a factor of 1.8 in terms of the effective Reynolds number.

Effects of heat transfer on separated boundary layer behavior under adverse pressure gradients

Separated boundary layers in a converging-diverging channel under two different wall heat transfer conditions, including the adiabatic wall and the cooled isothermal wall, have been investigated by using a large eddy simulation (LES) code coupled with a wall heat transfer module. The wall temperature of the cooled isothermal wall is 0.8 times of the inflow temperature, which is a typical value in a low-pressure turbine. The pressure distribution of the converging-diverging channel bottom wall is similar to that of a typical low-pressure turbine blade suction surface. The flow conditions are set as the exit isentropic Reynolds number (Re = 60,154) and the exit isentropic Mach number (Ma = 0.402). The results show that the cooled isothermal wall condition can increase the static pressure rise coefficient significantly, accelerate the transition process of the separation boundary layer, and suppress the separation. Furthermore, the cooled isothermal wall condition can decrease the frequency of the large-scale spanwise vortex rolled-up, reducing the influence of the spanwise vortex on the separated shear layer and decreasing the scales of the downstream hairpin vortex. In addition, the instability of the separated shear layer can be regarded as the superposition result of both the Tollmien-Schlichting (T-S) instability mechanism and the Kelvin-Helmholtz (K-H) instability mechanism, while the K-H instability mechanism on the whole is slightly more dominant in the presence of separation and reattachment. This trend is more obvious under the cooled isothermal wall condition.

Objective Center-Finding Algorithm for Tropical Cyclones in Numerical Models

Precise center-detection of tropical cyclones (TCs) is critical for dynamic analysis in high resolution model data. The existence of both smaller scale perturbations and larger scale circulations could reduce the accuracy of center positioning. In this study, an objective center-finding algorithm is developed based on a two-dimensional Fourier filter and a vorticity centroid algorithm. This proposed algorithm is able to automatically adjust its parameters according to the scale of the target vortex instead of using artificially prescribed parameters in previous research. What’s more, this new algorithm has been optimized and validated by a hundred idealized vortexes with different sizes and small-scale perturbations. A high-resolution simulation of Typhoon Soudelor (2015) was used to evaluate the performance of the new algorithm, and the proposed objective center-finding algorithm was found able to detect a precise and reliable center.

Analysis of vortices formed in flow passage of a five-bladed centrifugal water pump by means of PIV method

Detailed optical measurements for the flow inside rotating passages of a five-bladed centrifugal impeller were performed by particle image velocimetry (PIV). The flow in mid-plane perpendicular to the pump axis was measured at 1400 r/min rotation speed. Seven flow rates, namely, 1.2, 1.0, 0.8, 0.6, 0.4, 0.2, and 0 Qd, were surveyed. The averaged PIV velocity maps and streamline were analyzed. Results show that when flow rate decreases to 0.8 Qd, the flow separation forms initially at the blade suction side in passage 1. With decreasing of flow rate, the flow separation appears in much more passage, the separation region enlarges, and the flow at the pressure side begins to form flow separation. All passages are gradually occupied by the vortices generated by flow separation, until the passages are finally blocked. The scale of vortex along the stream-wise direction at the suction side is larger than that at the pressure side, whereas the scale of vortex along the span-wise direction is smaller than that at the pressure side. With the decrease in flow rate, the scales of vortices at the suction and pressure sides increase, and the vortices at both sides move toward the inlet and outlet, respectively. Moreover, the effect of vortices on the tangential and radial components of the absolute velocity was analyzed.

Simulation of Dipole Vorticity Dynamics Colliding Viscous Boundary Layer at High Reynolds Numbers

The vorticity dynamics of a Lamb-like dipole colliding with flat boundaries are investigated for high Reynolds number flows by implementation of the lattice Boltzmann method (LBM). The standard LBM based on the single-relaxation-time collision model suffers from numerical instabilities at high Reynolds numbers. Herein, a regularized collision model is employed for the LBM to preserve the stability and accuracy of the numerical solutions at such flow conditions. The computations are performed for the normal collision of the dipole with the no-slip boundary for several Reynolds numbers in the range of . The results obtained based on the regularized lattice Boltzmann (RLB) method for the statistical flow characteristics like the vorticity field and enstrophy quantity of the dipole-wall collision problem are investigated. The present study demonstrates that the shear-layer instabilities near the wall are responsible for rolling-up of the boundary layer before it is detached from the surface for high Reynolds numbers. This detachment mechanism leads to a viscous rebound and formation of small scale vortices. The shear-layer vortices formed dramatically influence the flow evolution after the collision and result strong enhancement of the total enstrophy of the flow field. By comparing the present results with those of provided by other numerical solutions, it is also concluded that the RLB scheme implemented is robust and sufficiently accurate numerical technique in comparison with the flow solvers based on the Navier-Stokes equations for predicting the statistical features of separated fluid flows even at high Reynolds numbers.

The effect of bogie fairings on the slipstream and wake flow of a high-speed train. An IDDES study

In this study, an improved delayed detached eddy simulation (IDDES) method based on shear-stress transport k-ω turbulence model has been used to investigate the slipstream and wake flow around a high-speed train with different bogie fairings at Re = 1.85 × 106. The accuracy of the numerical method has been validated by wind tunnel experiments and full-scale field tests. Further, the train slipstream, underbody flow and wake structures are compared for three cases. The results show that the bogies covered by full size bogie fairings significantly decrease the train slipstream velocity and weaken the pressure fluctuation around the high-speed train, especially near the bogie regions. Compared to the maximum slipstream velocity at trackside position in Case 2 (half size fairings), it increases by 15.2% in Case 1 (no fairing) and decreases by 16.1% in Case 3 (full size fairings), respectively. The larger size fairings are found to reduce the scale of longitudinal vortices and decrease the streamwise vorticity level in the wake region, thereby lowering the slipstream velocity distribution in the wake. Finally, the larger bogie fairings are recommended to improve the train aerodynamic performance as well as to improve the safety of trackside workers and passengers standing on the platform.

Large Eddy Simulation of Self-Excited Oscillation Pulsed Jet (SEOPJ) Induced by a Helmholtz Oscillator in Underground Mining

Pulsed waterjet can break rocks effectively by taking advantage of the water hammer effect, and is thus widely used in mining, petroleum, and natural gas fields. With the aim to further clarify the flow field characteristics of pulsed jets induced by a Helmholtz oscillator, large eddy simulation was conducted under different operating pressures. The velocity distribution, mean flow field, and the coherent structure were examined using the oscillators of different cavity lengths and diameters. The results clearly showed that the major frequency of jet pulsation gradually increased with the increase of operating pressure. A stable periodic velocity core was formed at the outlet of the Helmholtz oscillator, while the external flow field was subjected to periodic impact. As a result, the ambient fluid was strongly entrained into the jet beam. With the increase of the cavity length, the length of the core segment decreased while the energy loss caused by the cavity increased, which was also accompanied by a rapid attenuation of the axial velocity at the jet outlet. The coherent structure of the jet in the oscillator with small cavity diameter was more disordered near the nozzle outlet, and the vortex scale was larger. The effect of cavity diameter can be reflected in the feedback modulation of the jet in the cavity. Compared with the conical nozzle, the length of the core section of the jet was shorter, but the jet had better bunching, a smaller diffusion angle, and better mixing performance. These results provide a further understanding of the characteristics of pulsed water jet for better utilizations in the fields of energy exploitation.

Effect of drag reducing riblet surface on coherent structure in turbulent boundary layer

The characteristics of turbulent boundary layer over streamwise aligned drag reducing riblet surface under zero-pressure gradient are investigated using particle image velocimetry. The formation and distribution of large-scale coherent structures and their effect on momentum partition are analyzed using two-point correlation and probability density function. Compared with smooth surface, the streamwise riblets reduce the friction velocity and Reynolds stress in the turbulent boundary layer, indicating the drag reduction effect. Strong correlation has been found between the occurrence of hairpin vortices and the momentum distribution. The number and streamwise length scale of hairpin vortices decrease over streamwise riblet surface. The correlation between number of uniform momentum zones and Reynolds number remains the same as smooth surface.

Study of the effects of walls on vortex formation and liquid maldistribution with two-phase flow around a spherical particle via numerical simulation

With the ever-increasing dependency on the activity of industrial catalysis in fixed bed reactors (FBRs), recent microscale studies based on liquid film spreading behavior on particle surfaces using numerical methods have attracted much attention. However, most studies have investigated one particle separately, and the effects of vessel walls or other particles are not considered. In our preceding study, we found that liquid spreading behavior and flow patterns are strongly related to the gas vortex and its shape under the particle. Therefore, in this work, the formation and scale of the gas vortex, as well as its generation and breakdown during the flow process, are considered as the parameters in the simulation. Two geometries named the near-wall configuration and the normal configuration were assumed and fully investigated using ANSYS FLUENT v15.0 with different operating parameters. As a result, both the size and the formation of the gas vortex without wall effects are larger and steadier than those with wall effects, and correspondingly, the liquid film is well distributed on the surface regardless of the gas and liquid (G/L) velocity because of the equivalent velocity of the gas trace near the particle. In contrast, in the near-wall configuration, when the flat wall approaches the particle, two vortexes under the particle probably break down and further merge into one larger vortex and cause liquid maldistribution on the particle surface during the development of the flow process. The velocities of the gas traces are inequivalent, even causing a reversed flow and thus trapping the liquid phase inside the interstices, which can be alleviated by increasing the rate of G/L velocity and setting a larger interstice between the particle and the flat wall. The newly uncovered information will enhance the understanding of liquid spreading behavior on particle surfaces and thus be applicable to the performance of FBRs.

Self-Organization, Structures, and Anomalous Transport in Turbulent Partially Magnetized Plasmas with Crossed Electric and Magnetic Fields.

Self-organization and anomalous transport in gradient-drift driven turbulence in partially magnetized plasmas with crossed electric and magnetic fields is demonstrated in two-dimensional fluid simulations. The development of large scale structures and flows is shown to occur as a result of the inverse energy cascade from short wavelength instabilities. The turbulence shows complex interaction of small scale modes with large scale zonal flow modes, vortices, and streamers resulting in strongly intermittent anomalous transport that significantly exceeds the classical collisional values. The turbulence driven secondary instabilities and large scale structures are shown to dominate the anomalous electron current. Such anomalous transport and structures are consistent with a number of experimental observations in laboratory plasmas.

Numerical Study on Tone Noise of Different Thickness Airfoils

Based on the Lattice Boltzmann Method(LBM)-Large Eddy Simulation(LES), a direct numerical calculation is presented of tone noise generated by flow past symmetric NACA airfoils with different thickness and at a Reynolds number based on chord of Re = 2.0 × 105. The computation results indicate that the acoustic source of the airfoil mainly at region of trailing edge and the flow separation. For NACA series airfoils with different thicknesses of the same curvature, the increase of thickness could enlarge pressure fluctuation and produce larger scale of vortices. Noise sources are identified in the region of trailing edge and the flow separation. The sound pressure level spectrum analysis shows that the tone noise gradually disappears and the noise spectrum displays broadband features with the increases of airfoil thickness. The noise directivity shows that the sound pressure radiation around the airfoil characteristic the dipole acoustic field. In addition, data analysis shows that the generation of tone noise is closely related to the vortex shedding of the trailing edge of the airfoil.

Heat transfer and flow characteristics in a rectangular channel with small scale vortex generators

This article puts forward a novel idea which can be used to control the turbulent coherent structures and make the turbulence more steady by using a “wake blocking wall”. The “wake blocking wall” is induced by small scale vortex generators (miniature cuboids). The flow and heat transfer characteristics in a rectangular channel with a range of miniature cuboid vortex generators (MCVGs) are numerically investigated by large eddy simulation (LES) with ANSYS FLUENT. The height of miniature cuboid is far less than the boundary layer thickness, which means that the cuboids are embed in fully-developed turbulent boundary layer. Furthermore, the spacing between two adjacent cuboids is about one hundred times wall units. The Reynolds number, based on the bulk velocity and channel half-height, is 3745. The influence of the cuboid wake on the turbulent boundary layer is probed. The result indicates that the “wake blocking wall” can alter the coherent structures in turbulent boundary layer, especially the velocity streaky structures. The variation of velocity in viscous sub-layer is mostly suppressed. However, in the logarithmic law region, velocity and temperature gradients are both mostly increased. The overall heat transfer enhancement efficiency is characterized by the synthesis performance coefficient, which includes Nusselt number and skin friction coefficient. The result shows that the wake and vortices induced by cuboids can restrict turbulent movement in spanwise direction, which results in enhancement of the heat transfer performance as well as reduction of the skin-friction in the channel. The Nusselt number and the synthesis performance coefficient increases by 5.17% and 8.15%, respectively.

Continuum mechanics with torsion

This paper is an attempt to introduce methods and concepts of the Riemann-Cartan geometry largely used in such physical theories as general relativity, gauge theories, solid dynamics, etc. to fluid dynamics in general and to studying and modeling turbulence in particular. Thus, in order to account for the rotational degrees of freedom of the irregular dynamics of small scale vortexes, we further generalize our unified first-order hyperbolic formulation of continuum fluid and solid mechanics which treats the flowing medium as a Riemann-Cartan manifold with zero curvature but non-vanishing torsion. We associate the rotational degrees of freedom of the main field of our theory, the distortion field, to the dynamics of microscopic (unresolved) vortexes. The distortion field characterizes the deformation and rotation of the material elements and can be viewed as anholonomic basis triad with non-vanishing torsion. The torsion tensor is then used to characterize distortion's spin and is treated as an independent field with its own time evolution equation. This new governing equation has essentially the structure of the non-linear electrodynamics in a moving medium and can be viewed as a Yang-Mills-type gauge theory. The system is closed by providing an example of the total energy potential. The extended system describes not only irreversible dynamics (which raises the entropy) due to the viscosity or plasticity effect but it also has dispersive features which are due to the reversible energy exchange (which conserves the entropy) between micro and macro scales. Both the irreversible and dispersive processes are represented by relaxation-type algebraic source terms so that the overall system remains first-order hyperbolic. The turbulent state is then treated as an excitation of the equilibrium laminar state due to the non-linear interplay between dissipation and dispersion.

Decay of a vortex lattice formed by gravity waves on the water surface

Abstract The generation and decay of a vortex lattice formed by standing gravity waves of 3 Hz frequency on the water surface have been studied experimentally using the particle image velocimetry technique. During the process of excitation the formation of large-scale vortices as a result of interaction of eddies from a vortex lattice is observed. Immediately after the pumping had been turned off in the initial time interval of about 30 s, the time dependence of vortex motion energy E vort close to an exponential decrease was observed with a characteristic time of τ w ≈ 7 s , which is mainly due to the viscous losses of the surface waves. A decrease in wave amplitude leads to reduction in the Stokes drift of floating particles. In the second time interval from 30 to 200 s there is no exponential dependence E vort ( t ) , that is related, apparently, to an energy relaxation of different vortex scales: from the bath size to the pumping wavelength. In this time interval the vortex interaction is also recorded leading to redistribution of energy from the pumping region to large scales. It should be emphasized that the vortex motion generated by the interaction of nonlinear waves is conserved after the complete decay of the wave motion on the water surface, and there is a transfer of energy from small scales to large ones as a result of the process of unification of several lattice vortices into a large-scaled vortex – reverse energy flow. In the time interval above 200 s there is an exponential energy relaxation of vortices of the maximum scale because of the viscous bath bottom and sides friction.

Turbulence structure in open channel flow with partially covered artificial emergent vegetation

An innovative approach was recently proposed to increase water depth and improve navigation in rivers by increasing overall roughness through an adaptive placement of artificial vegetation. In this approach, a section of the river width is covered with artificial vegetation constructed from an array of dampers that can be added or removed while maintaining sufficient width for navigational purposes. The goal of the work here is to explore the mean flow and turbulent momentum transport properties of such flow in a controlled flume setting, where the flow rate is steady, the vegetation placement is uniform, and the Froude number is maintained at sub-critical conditions. The focus is on vegetation-induced roughness alterations to the bulk flow statistics as well as the structure of turbulence impacted by the presence of such artificially engineered vegetation. The canopy flow experimentally explored here differs from the well-studied planar uniform emergent canopy flow because the interface between the vegetation and non-vegetation areas occurs along a lateral direction instead of the vertical direction. The flume experiments were conducted by partially covering the channel width with emergent artificial vegetation that is flexible and can interact with the flow. The quantities studied are the equilibration distance of the flow statistics from the leading vegetation edge as such distance is essential to any engineering design. Moreover, the mean flow and turbulence regimes at several longitudinal sections were analyzed using spectral analysis and conditional sampling to identify the main vortical structures and their contribution to momentum transport. Spectral analysis demonstrated that the sizes of the dominant vortices can be classified into stem-scale (small-scale) and shear-scale (larger scale) vortices as conventional in canonical canopy flows. The shear layer formed in the planar direction and its associated coherent vortices are spawned near the edge of the vegetated area in a manner analogous to a plane mixing layer. Quadrant analysis showed two contributions to the overall shear stress and lateral momentum exchange between the vegetated and non-vegetated zone, namely, ejections and sweeps. The measured ejection-sweep contributions are short-lived but significant to the overall turbulent momentum transport consistent with other canopy flow studies. Approximately 80% of the turbulent stress contributions at the interface occur within 30% of the time. Because the flume experiments were conducted at sufficiently high Reynolds number and sufficiently low Froude number, the scalability of the experimental findings here to much larger settings encountered in engineering practice are briefly discussed.

Study on vortex shedding mode on the wake of horn/ridge ice contamination under high-Reynolds conditions

This paper studied the unsteadiness of vortex motion produced by a three-dimensional wing section with horn/ridge ice contamination. Using improved delayed detached eddy simulation method, multi-scale vortex and their associated flow structures were successfully captured. Results have shown a diversity of unsteadiness scales at different time series, including shear layer instability, vortex pairing, co-rotating and breaking up. Proper orthogonal decomposition was then introduced to extract the characteristic vortex shedding modes with scheduling the eigenvalues λi from large to small. The dominate and secondary proper orthogonal decomposition modes under horn ice condition were displayed, which could be illustrated as fluctuations near recirculation zone, and large-scale vortex shedding/reattaching motion, respectively. The proper orthogonal decomposition modal characteristics for ridge ice showed that vortex scales varied from large to small. The trajectory of large-scale vortex reattaching and co-rotating exist simultaneously with the pressure peak and recover, which also verified the association of proper orthogonal decomposition modes with different scales of vortices. Future works would be presented on demonstration of the complex structures and the dynamic features in such flow.

Long frontal waves and dynamic scaling in freely evolving equivalent barotropic flow

We present a scaling theory that links the frequency of long frontal waves to the kinetic energy decay rate and inverse transfer of potential energy in freely evolving equivalent barotropic turbulence. The flow energy is predominantly potential, and the streamfunction makes the dominant contribution to potential vorticity (PV) over most of the domain, except near PV fronts of width $O(L_{D})$, where $L_{D}$ is the Rossby deformation length. These fronts bound large vortices within which PV is well-mixed and arranged into a staircase structure. The jets collocated with the fronts support long-wave undulations, which facilitate collisions and mergers between the mixed regions, implicating the frontal dynamics in the growth of potential-energy-containing flow features. Assuming the mixed regions grow self-similarly in time and using the dispersion relation for long frontal waves (Nycander et al., Phys. Fluids A, vol. 5, 1993, pp. 1089–1091) we predict that the total frontal length and kinetic energy decay like $t^{-1/3}$, while the length scale of the staircase vortices grows like $t^{1/3}$. High-resolution simulations confirm our predictions.