Kinematic and mixing characteristics of vortex interaction induced by a vortex generator model:a numerical study

The underlying effect of vortex interaction characterized by the merging and non-merging on mixing enhancement is of fundamental significance to understand the flow dynamics of strut injectors in scramjets.Starting from a simplified configuration of a vortex generator,this study focuses on the influence of geometric parameters on vortex structures and fluid mixing through compressible Navier-Stokes(NS)simulations.By adjusting the induction of outer vortices,the inner co-rotating vortex pair exhibits two modes of interaction(merging/separation regime)reflected by closer/farther vortex centers.Defined by the zero variation rate of the inner vortex spacing,the critical state of equilibrium is determined.The critical condition is well predicted by a theoretical model based on the Biot-Savart law.Through the introduction of mixedness and mixing time,the intrinsic impact of interaction modes on fluid mixing is revealed.Compared with the vortex dynamics in the merging regime,the one in the separation regime is more effective for passive scalar mixing augmentation.With efficient material stretching characterized by the higher interface stretching factor and averaging finite-time Lyapunov exponent(FTLE),the mixing time is shortened by as much as 2.5 times in the separation regime.The implication of the present two interaction regimes in mixing enhancement physically reflected by the averaging FTLE has the potential to improve the combustion performance and shorten the combustor chamber.

High-fidelity simulation of blade vortex interaction of helicopter rotor based upon TENO scheme

Numerical simulation methods for unsteady vortex field of helicopter rotor with high resolution and low dissipation TENO8-AA primitive variables reconstruction schemes are established based on moving-embedded grid and Navier-Stokes equations.Firstly,the Targeted Essentially Non-Oscillatory(TENO)scheme are developed by employing ENO-like candidate stencil selection strategy,and the candidate stencil is adopted with optimal weight in smooth region while it is discarded completely in discontinuous region,which reduces the dissipation and dispersion errors and approaches better spectral properties.Then,the aerodynamic characteristics of Helishape-7A model rotor in Blade Vortex Interaction(BVI)state and the flowfield of Lynx rotor in hover are simulated,which validates that the blade tip vortex trajectory with larger wake age and more details of vortex can be captured by TENO8-AA scheme with only a quarter of grid points and half time comparing to WENO-JS scheme.Moreover,the simulation accuracy of thrust coefficient is improved by up to 36%.Finally,the analyses for BVI and aeroacoustic characteristics of Operational Loads Survey(OLS)rotor are conducted,and the different forms of interaction mechanism are explored,such as oblique and parallel interactions.The results indicate that TENO scheme not only ensures the resolution of simulation in discontinuous region,but also minimizes the numerical dissipation in smooth region dominated by blade tip vortex.Therefore,the acoustic pressure peak prediction error of rotor in BVI state is significantly reduced to 5.6%and 0.8%at two microphone locations,respectively.

Numerical Study of Vortex Interactions in Bose-Einstein Condensation

The dynamics and interaction of quantized vortices in Bose-Einstein condensates(BECs)are investigated by using the two-dimensional Gross-Pitaevskii equation(GPE)with/without an angular momentum rotation term.If all vortices have the same winding number,they would rotate around the trap center but never collide.In contrast,if the winding numbers are different,their interaction highly depends on the initial distance between vortex centers.The analytical results are presented to describe the dynamics of the vortex centers when β=0.While if β≠0,there is no analytical result but some conclusive numerical findings are provided for the further understanding of vortex interaction in BECs.Finally,the dynamic laws describing the relation of vortex interaction in nonrotating and rotating BECs are presented.

The Dynamics of Barotropic Vortex Merging

The merging of multiple vortices is a fundamental process of the dynamics of Earth＇s atmosphere and oceans. In this study, the interaction of like-signed vortices is analytically and numerically examined in a framework of two-dimensional inviscid barotropic flows. It is shown that barotropic vortex interaction turns out to be more intricate than simple merging scenarios often assumed in previous studies. Some particular configurations exist in which the vortex merging process is never complete despite strong interaction of like-signed vortices, regardless of the strengths or distances between the vortices.While the conditions for a complete vortex merging process introduced in this study appear to be too strict for most practical applications, this study suggests that careful criteria for vortex mergers should be properly defined when simulating the interaction of vortices, because the merging may not always result in a final enhanced circulation at the end of the interaction,as usually assumed in the literature.

Evolution of the vortex state in the BCS-BEC crossover of a quasi two-dimensional superfluid Fermi gas

We use the path-integral formalism to investigate the vortex properties of a quasi-two dimensional（2D） Fermi superfluid system trapped in an optical lattice potential.Within the framework of mean-field theory,the cooper pair density,the atom number density,and the vortex core size are calculated from weakly interacting BCS regime to strongly coupled while weakly interacting BEC regime.Numerical results show that the atoms gradually penetrate into the vortex core as the system evolves from BEC to BCS regime.Meanwhile,the presence of the optical lattice allows us to analyze the vortex properties in the crossover from three-dimensional（3D） to 2D case.Furthermore,using a simple re-normalization procedure,we find that the two-body bound state exists only when the interaction is stronger than a critical one denoted by G_c which is obtained as a function of the lattice potential＇s parameter.Finally,we investigate the vortex core size and find that it grows with increasing interaction strength.In particular,by analyzing the behavior of the vortex core size in both BCS and BEC regimes,we find that the vortex core size behaves quite differently for positive and negative chemical potentials.

Lattice Boltzmann Study of a Vortex Ring Impacting Spheroidal Particles

Interaction of vortex rings with solid is an important research topic of hydrodynamic.In this study,a multiple-relaxation time(MRT)lattice Boltzmann method(LBM)is used to investigate the flow of a vortex ring impacting spheroidal particles.The MRT-LBM is validated through the cases of vortex ring impacting a flat wall.The vortex evolution due to particle size,the aspect ratio of a prolate particle,as well as Reynolds(Re)number are discussed in detail.When the vortex ring impacting a stationary sphere,the primary and secondary vortex rings wrap around each other,which is different from the situation of the vortex ring impacting a plate.For the vortex ring impacting with a prolate spheroid,the secondary vortex ring stretches mainly along the long axis of the ellipsoid particle.However,it is found that after the vortex wrapping stage,the primary vortex recovers along the short axis of the particle faster than that in the long axis,i.e.,the primary vortex ring stretches mainly along the short axis of the particle.That has never been address in the literature.

Effects of Vortex Generator on Cylindrical Protrusion Aerodynamics

Experimental and numerical studies were carried out to evaluate the effect of vortex generator on a small cylindrical protrusion at Mach number 2.0. The experiments were performed using the supersonic blow down wind tunnel on different heights of cylindrical protrusion with vortex generator placed ahead of them. The upstream and downstream flow around the cylindrical protrusion is influenced by vortex generator as is observed using both visualization and pressure measurement techniques. Numerical studies using three dimensional steady implicit formulations with standard k-ω turbulence model was performed. Results obtained through the present computation are compared with the experimental results at Mach 2.0. Good agreements between computation and experimental results have been achieved. The results indicate that the aerodynamic drag acting on cylindrical protrusion can be reduced by adopting vortex generator.

A numerical study of tadpole swimming in the wake of a D-section cylinder

The vortex structure and the hydrodynamic performance of a tadpole undulating in the wake of a D-section cylinder are studied by solving the Navier-Stokes equations for the unsteady incompressible viscous flow. A dynamic mesh fitting the tadpole＇s deforming body surface is used in the simulation. It is found that three main factors can contribute to the thrust of the tadpole behind a D-cylinder： the backward jet in the wake, the local reverse flows on the tadpole surface and the suction force caused by the passing vortices. The tadpole？s relative undulating frequency and the distance between the D-cylinder and the tadpole have a great influence on both the vortex structure and the hydrodynamic performance. At some undulating frequency, a tadpole may break or dodge vortices from the D-cylinder. When the vortices are broken, the tadpole can gain a great thrust but will consume much energy to maintain its undulation. When the vortices are dodged, the tadpole is subject to a small thrust or even a drag. However, it is an effective way to save much energy in the undulating swimming, as the Kármán gait does. As the tadpole is located behind the D-cylinder at different distances, three typical kinds of wake are observed. When an incomplete Kármán vortex street forms between the D-cylinder and the tadpole, the tadpole is subject to the highest thrust.

Effect of Rotational Speed on the Stability of Two Rotating Side-by-side Circular Cylinders at Low Reynolds Number

Flow around two rotating side-by-side circular cylinders of equal diameter D is numerically studied at the Rey- nolds number 40〈 Re 〈200 and various rotation rate 8i. The incoming flow is assumed to be two-dimensional laminar flow. The governing equations are the incompressible Navier-Stokes equations and solved by the finite volume method （FVM）. The ratio of the center-to-center spacing to the cylinder diameter is T/D=2. The objective of the present work is to investigate the effect of rotational speed and Reynolds number on the stability of the flow. The simulation results are compared with the experimental data and a good agreement is achieved. The stability of the flow is analyzed by using the energy gradient theory, which produces the energy gradient function K to identify the region where the flow is the most prone to be destabilized and the degree of the destabilization. Numerical results reveal that K is the most significant at the separated shear layers of the cylinder pair. With Re in- creases, the length of the wake is shorter and the vortex shedding generally exhibits a symmetrical distribution for θi〈θcrit. It is also shown that the unsteady vortex shedding can be suppressed by rotating the cylinders in the counter-rotating mode.

Aeroacoustic prediction based on large-eddy simulation and the Ffowcs Williams-Hawkings equation

A hybrid noise computation method is presented in this paper.Large-eddy simulation with wall-model equation is proposed to compute the flow field.With a stress-balanced wall-model equation,the near-wall computation cost of large eddy simulation was effectively reduced.The instantaneous flow variables obtained by the large-eddy simulation were used to compute the noise source terms of the Ffowcs Williams-Hawkings equation.The present method was investigated with two test cases:a single cylinder at Re=10,000 and a rod-airfoil at Re=480,000.The flow quantities and aeroacoustic characteristics were compared with the reference data.The mean velocity profiles and spectra of the flow fluctuations were consistent with data from the literature.When compared with the reference data,the noise computation error was less than 3 dB.The computation results demonstrate the present wall-modeled large eddy simulation is efficient for the noise computation of complex vortex shedding flows.

Unsteady Behavior and Control of Vortices in Centrifugal Compressor

Two examples of the use of vortex control to reduce noise and enhance the stable operating range of a centrifugal compressor are presented in this paper.In the case of high-flow operation of a centrifugal compressor with a vaned diffuser,a discrete frequency noise induced by interaction between the impeller-discharge flow and the diffuser vane,which appears most notably in the power spectra of the radiated noise,can be reduced using a tapered diffuser vane(TDV) without affecting the performance of the compressor.Twin longitudinal vortices produced by leakage flow passing through the tapered portion of the diffuser vane induce secondary flow in the direction of the blade surface and prevent flow separation from the leading edge of the diffuser.The use of a TDV can effectively reduce both the discrete frequency noise generated by the interaction between the impeller-discharge flow and the diffuser surface and the broadband turbulent noise component.In the case of low-flow operation,a leading-edge vortex(LEV) that forms on the shroud side of the suction surface near the leading edge of the diffuser increases significantly in size and blocks flow in the diffuser passage.The formation of an LEV may adversely affect the performance of the compressor and may cause the diffuser to stall.Using a one-side tapered diffuser vane to suppress the evolution of an LEV,the stable operating range of the compressor can be increased by more than 12 percent,and the pressure-rise characteristics of the compressor can be improved.The results of a supplementary examination of the structure and unsteady behavior of LEVs,conducted by means of detailed numerical simulations,are also presented.