Turbulent vortex rings in weakly turbulent and in turbulent ambient flow

Turbulent vortex rings were investigated in weakly turbulent flow and in three different grid generated turbulent flows to clarify the reciprocal action of the vortex ring with defined external turbulence. Assuming self-similarity and turbulent viscosity as proportional to V₀D₀ the equations for the ring diameter D(t) and the velocity of propagation V(t) were derived. The time difference Δt between the virtual origins of 1/V(t) respectively D²(t) led to an invariant term. The equation of momentum is fulfilled. – Position and diameter of the vortex rings were determined till their decay by means of an optical system, which did not disturb the vortex rings. The experimental results in weakly turbulent ambient flow obtained by the author and by others confirm the theory very well. The ambient turbulence was nearly constant in the measuring region; its effect could be described by simply adding its viscosity to the vortex ring’s internal turbulent viscosity. The results could be represented in unified non-dimensional diagrams. Moreover, an explanation was found as to why the mean internal turbulent viscosity is constant.     

Decay of quantized vorticity in superfluid He at mK temperatures

An experimental investigation of the free decay of quantized turbulence in isotopically pure superfluid ⁴He at mK temperatures is discussed. Vortices are created by a vibrating grid, and detected by their trapping of negative ions. Preliminary results suggest the existence of a temperature-independent vortex decay mechanism below T70 mK.     

Phase and vortex dynamics in Josephson junction arrays with percolative disorder

The AC conductance G of site-diluted Josephson junction arrays close to the percolation threshold was studied over a broad frequency range. As a function of frequency, G exhibits a crossover from a low-frequency Euclidean to a high-frequency fractal regime. At low-frequency the response is dominated by vortices and its temperature dependence is well-described by dynamical extensions of the Kosterlitz–Thouless theory for two-dimensional systems.     

Numerical simulation of unsteady interaction of centrifugal impeller with its diffuser using Lagrangian discrete vortex method

In this study, an advanced Lagrangian vortex- boundary element method is applied to simulate the unsteady impeller-diffuser interactions in a diffuser pump not only for design but also for off-design considerations. In velocity calculations based on the Biot-Savart law we do not have to grid large portions of the flow field and the calculation points are concentrated in the regions where vorticity is present. Lagrangian representation of the evolving vorticity field is well suited to moving boundaries. An integral pressure equation shows that the pressure distribution can be estimated directly from the instantaneous velocity and vorticity field. The numerical results are compared with the experimental data and the comparisons show that the method used in this study can provide us insight into the complicated unsteady impeller-diffuser interaction phenomena in a diffuser pump.     

Exotic vortex structures of the dipolar Bose–Einstein condensates trapped in harmonic-like and toroidal potential

Based on the tunable intensity and waist of Gaussian laser, harmonic-like and toroidal potentials can be achieved and the ground-state properties of the dipolar Bose–Einstein condensate (BEC) trapped in such potentials are investigated. It is found that, in the harmonic-like potential, the singly and doubly quantized vortices can exist in the scale condensate and translate respectively into vortex pairs and triangular vortex lattice with increasing dipole–dipole interaction (DDI). Especially, the sandwich-like structure can be observed in the ground-state density profiles by tuning the direction and strength of DDI for some rotating frequency. In the toroidal potential, the competition between the inter-component interaction and DDI can induce the transition between immiscible and miscible states, and results in the structures of a doubly quantized vortex surrounded by a vortex ring. It is worth emphasizing that, with the increasing of DDI, the doubly quantized vortex in the harmonic-like potential becomes two singly quantized vortices, while in the toroidal potential it is no happen due to the presence of Gaussian barrier.     

A three-dimensional numerical study on instability of sinusoidal flame induced by multiple shock waves

The instabilities of a three-dimensional sinusoidally premixed flame induced by an incident shock wave with Mach = 1.7 and its reshock waves were studied by using the Navier–Stokes(NS) equations with a single-step chemical reaction and a high resolution, 9th-order weighted essentially non-oscillatory scheme. The computational results were validated by the grid independence test and the experimental results in the literature. The computational results show that after the passage of incident shock wave the flame interface develops in symmetric structure accompanied by large-scale transverse vortex structures. After the interactions by successive reshock waves, the flame interface is gradually destabilized and broken up, and the large-scale vortex structures are gradually transformed into small-scale vortex structures. The small-scale vortices tend to be isotropic later.The results also reveal that the evolution of the flame interface is affected by both mixing process and chemical reaction. In order to identify the relationship between the mixing and the chemical reaction, a dimensionless parameter, η, that is defined as the ratio of mixing time scale to chemical reaction time scale, is introduced. It is found that at each interaction stage the effect of chemical reaction is enhanced with time.The enhanced effect of chemical reaction at the interaction stage by incident shock wave is greater than that at the interaction stages by reshock waves. The result suggests that the parameter η can reasonably character the features of flame interface development induced by the multiple shock waves.     

Vortex shedding around a near-wall circular cylinder induced by a solitary wave

This study developed a two-dimensional generalized vortex method to analyze the shedding of vortices and the hydrodynamic forces resulting from a solitary wave passing over a submerged circular cylinder placed near a flat seabed. Numerical results for validation are compared with other numerical and experimental results, and satisfactory agreement is found. A series of simulations were performed to study the effects of gap-to-diameter ratio and incident wave height on vorticity pattern as well as the forces exerted on the cylinder. The range of the heights of incident waves is from 0.3h to 0.7h, where h is the still water depth. The range of the gap-to-diameter ratios is from 0.1 to 0.8. The results indicate that the flow pattern and the pressure distribution change significantly because of the close proximity of the seabed where the vorticity flux on the seabed-side surface of the cylinder is suppressed. Placing the cylinder nearer the seabed increases the drag and the positive lift on the cylinder. When the gap-to-diameter ratio increases, the pattern of vortices changes because of the interaction between the main recirculation zone and the shear layers separated from the gap. The maxima of drag, lift and total force increase linearly with the height of the incident wave.     

Numerical investigations of the vortex interactions for a flow over a pitching foil at different stages

The fluid–structure interaction is investigated numerically for a two-dimensional flow (Re=2.5·10⁶) over a sinusoid-pitching foil by the SST (Shear Stress Transport) k–ω model. Although discrepancies in the downstroke phase, which are also documented in other numerical studies, are observed by comparing with experimental results, our current numerical results are sufficient to predict the mean features and qualitative tendencies of the dynamic stall phenomenon. These discrepancies are evaluated carefully from the numerical and experimental viewpoints.In this study, we have utilized Λ, which is the normalized second invariant of the velocity gradient tensor, to present the evolution of the Leading Edge Vortex (LEV) and Trailing Edge Vortex (TEV). The convective, pressure, and diffusion terms during the dynamic stall process are discussed based on the transport equation of Λ. It is found that the pressure term dominates the rate of the change of the rotation strength inside the LEV. This trend can hardly be observed directly by using the vorticity transport equation due to the zero baroclinic term for the incompressible flow.The mechanisms to delay the stall are categorized based on the formation of the LEV. At the first stage before the formation of the LEV in the upper surface, the pitching foil provides extra momentum into the fluid flows to resist the flow separation, and hence the stall is delayed. At the second stage, a low-pressure area travels with the evolution of the LEV such that the lift still can be maintained. Three short periods at the second stage corresponds to different flow patterns during the dynamic stall, and these short periods can be distinguished according to the trend of the pressure variation inside the LEV. The lift stall occurs when a reverse flow from the lower surface is triggered during the shedding of the LEV. For a reduced frequency k_f=0.15, the formation of the TEV happens right after the lift stall, and the lift can drop dramatically. With a faster reduced frequency k_f=0.25, the shedding of the LEV is postponed into the downstroke, and the interaction between the LEV and TEV becomes weaker correspondingly. Thus, the lift drops more gently after the stall. In order to acquire more reliable numerical results within the downstroke phase, the Large Eddy Simulation (LES), which is capable of better predictions for the laminar-to-turbulent transition and flow reattachment process, will be considered as the future work.     

Direct numerical simulation of free and forced square jets

Direct numerical simulation (DNS) of incompressible, spatially developing square jets in the Reynolds number range of 500–2000 is reported. The three-dimensional unsteady Navier–Stokes equations are solved using high order spatial and temporal discretization. The objective of the present work is to understand the evolution of free and forced square jets by examining the formation of large-scale structures. Coherent structures and related interactions of free jets suggest control strategies that can be used to achieve enhanced spreading and mixing of the jet with the surrounding fluid. The critical Reynolds number for the onset on unsteadiness in an unperturbed free square jet is found to be 875–900 while it reduces to the range 500–525 in the presence of small-scale perturbations. Disturbances applied at the flow inlet cause saturation of KH-instability and early transition to turbulence. Forced jet calculations have been carried out using varicose perturbation with amplitude of 15%, while frequency is independently varied. Simulations show that the initial development of the square jet is influenced by the four corners leading to the appearance hairpin structures along with the formation of vortex rings. Farther downstream, adjacent vortices strongly interact leading to their rapid breakup. Excitation frequencies in the range 0.4–0.6 cause axis-switching of the jet cross-section. Results show that square jets achieve greater spreading but are less controllable in comparison to the circular ones.