Density functional theory modeling of vortex shedding in superfluid He-4

Formation of vortex rings around moving spherical objects in superfluid He-4 at 0 K is modeled by time-dependent density functional theory. The simulations provide detailed information of the microscopic events that lead to vortex ring emission through characteristic observables such as liquid current circulation, drag force, and hydrodynamic mass. A series of simulations were performed to determine velocity thresholds for the onset of dissipation as a function of the sphere radius up to 1.8 nm and at external pressures of zero and 1 bar. The threshold was observed to decrease with the sphere radius and increase with pressure thus showing that the onset of dissipation does not involve roton emission events (Landau critical velocity), but rather vortex emission (Feynman critical velocity), which is also confirmed by the observed periodic response of the hydrodynamic observables as well as visualization of the liquid current circulation. An empirical model, which considers the ratio between the boundary layer kinetic and vortex ring formation energies, is presented for extrapolating the current results to larger length scales. The calculated critical velocity value at zero pressure for a sphere that mimics an electron bubble is in good agreement with the previous experimental observations at low temperatures. The stability of the system against symmetry breaking was linked to its ability to excite quantized Kelvin waves around the vortex rings during the vortex shedding process. At high vortex ring emission rates, the downstream dynamics showed complex vortex ring fission and reconnection events that appear similar to those seen in previous Gross-Pitaevskii theory-based calculations, and which mark the onset of turbulent behavior.Comment: 23 pages, 7 figure

Visualization of intricate flow structures for vortex breakdown analysis

Journal ArticleVortex breakdowns and flow recirculation are essential phenomena in aeronautics where they appear as a limiting factor in the design of modern aircrafts. Because of the inherent intricacy of these features, standard flow visualization techniques typically yield cluttered depictions. The paper addresses the challenges raised by the visual exploration and validation of two CFD simulations involving vortex breakdown. To permit accurate and insightful visualization we propose a new approach that unfolds the geometry of the breakdown region by letting a plane travel through the structure along a curve. We track the continuous evolution of the associated projected vector field using the theoretical framework of parametric topology. To improve the understanding of the spatial relationship between the resulting curves and lines we use direct volume rendering and multi-dimensional transfer functions for the display of flow-derived scalar quantities. This enriches the visualization and provides an intuitive context for the extracted topological information. Our results offer clear, synthetic depictions that permit new insight into the structural properties of vortex breakdowns

Lagrangian analysis of fluid transport in empirical vortex ring flows

In this paper we apply dynamical systems analyses and computational tools to fluid transport in empirically measured vortex ring flows. Measurements of quasisteadily propagating vortex rings generated by a mechanical piston-cylinder apparatus reveal lobe dynamics during entrainment and detrainment that are consistent with previous theoretical and numerical studies. In addition, the vortex ring wake of a free-swimming Aurelia aurita jellyfish is measured and analyzed in the framework of dynamical systems to elucidate similar lobe dynamics in a naturally occurring biological flow. For the mechanically generated rings, a comparison of the net entrainment rate based on the present methods with a previous Eulerian analysis shows good correspondence. However, the current Lagrangian framework is more effective than previous analyses in capturing the transport geometry, especially when the flow becomes more unsteady, as in the case of the free-swimming jellyfish. Extensions of these results to more complex flow geometries is suggested

Comparison of moving and stationary clapping bodies

We report differences in the flow dynamics and in the body kinematics between a clapping body that is allowed to propel forward freely (Dynamic) and one that is constrained from moving forward (Stationary). The experiments were done in quiescent water. The body consists of two interconnected plates hinged at one end with a 'torsion' spring. Initially, a thread loop holds the plates apart at an interplate angle of 60 degrees. Cutting of the thread initiates the clapping motion, and if allowed, the body propels forward a certain distance. Experiments have been performed for three values of $d^*$(= depth/length): 1.5, 1.0, and 0.5. In both cases, vortex loops initially develop along the three edges of each plate, which reconnect by the end of the clapping motion resulting in the formation of an elliptical vortex loop in the wake for $d^*$ = 1.5, 1.0 bodies, and multiple connected rings for $d^*$ = 0.5 bodies. Three main and unexpected differences are observed between the 'Dynamic' and 'Stationary' bodies. In the dynamic case, the clapping action is faster compared to the stationary case, with the maximum angular plate velocity being twice as high. The mean thrust coefficient, $\overline{C_T}$, based on plate tip velocity, is higher for the stationary. The value of $\overline{C_T}$ and the circulation in the starting vortices is almost independent of $d^*$ for the dynamic case, whereas it increases with $d^*$ for the stationary case. The core separation of starting vortices closely matches in both stationary and dynamic cases although circulation varies

Kinematics and dynamics of vortex rings in a tube

Kinematic theory and flow visualization experiments were combined to examine the dynamic processes which control the evolution of vortex rings from very low to very high Reynolds numbers, and to assess the effects of the wall as a vortex ring travels up a tube. The kinematic relationships among the size, shape, speed, and strength of vortex rings in a tube were computed from the theory. Relatively simple flow visualization measurements were used to calculate the total circulation of a vortex rings at a given time. Using this method, the strength was computated and plotted as a function of time for experimentally produced vortex rings. Reynolds number relationships are established and quantitative differences among the three Reynolds number groups are discussed

Preliminary design of an intermittent smoke flow visualization system

A prototype intermittent flow visualization system that was designed to study vortex flow field dynamics has been constructed and tested through its ground test phase. It produces discrete pulses of dense white smoke consisting of particles of terephthalic acid by the pulsing action of a fast-acting three-way valve. The trajectories of the smoke pulses can be tracked by a video imaging system without intruding in the flow around in flight. Two methods of pulsing the smoke were examined. The simplest and safest approach is to simply divert the smoke between the two outlet ports on the valve; this approach should be particularly effective if it were desired to inject smoke at two locations during the same test event. The second approach involves closing off one of the outlet ports to momentarily block the flow. The second approach requires careful control of valve dwell times to avoid excessive pressure buildup within the cartridge container. This method also increases the velocity of the smoke injected into the flow. The flow of the smoke has been blocked for periods ranging from 30 to 80 milliseconds, depending on the system volume and the length of time the valve is allowed to remain open between valve closings

Navier-Stokes Simulation of Quasi-Axisymmetric and Three-Dimensional Supersonic Vortex Breakdown

Computational simulation of supersonic vortex breakdown is considered for internal and external flow applications. The interaction of a supersonic swirling flow with a shock wave in bounded and unbounded domains is studied. The problem is formulated using the unsteady, compressible, full Navier-Stokes equations which are solved using an implicit, flux-difference splitting, finite-volume scheme. Solutions are obtained for quasi-axisymmetric and three-dimensional flows. The quasi-axisymmetric solutions are obtained by forcing the components of the flowfield vector to be equal on two axial planes, which are in close proximity to each other. For the flow in a bounded domain, a supersonic swirling flow is introduced into a configured circular duct. The duct is designed such that a shock wave intersects with the incoming swirling flow in the inlet portion. For the quasi-axisymmetric flow problem, a parametric study is performed which includes the effects of the Reynolds number, Mach number, swirl ratio and the type of exit-boundary conditions on the development and behavior of vortex breakdown. The effect of the duct wall boundary-layer flow on the vortex breakdown is also investigated. For the same duct geometry, three-dimensional effects are studied along with the effect of the duct wall boundary-layer flow. For the external flow application, a supersonic swirling jet is issued from a nozzle into a uniform supersonic flow of lower Mach number. For the quasi-axisymmetric flow problem, the effects of the Reynolds number and the type of downstream-boundary conditions are studied. For the three-dimensional flow problem, the effects of the grid fineness, grid-point distribution, grid shape and swirl ratio on the vortex breakdown are studied. The results show several modes of vortex breakdown such as no-breakdown, transient single-bubble breakdown, transient multi-bubble breakdown, periodic multi-bubble multi-frequency breakdown and helical spiral breakdown. In another application, a subsonic steady quasi-axisymmetric flow of an isolated slender vortex core is considered. The solution is obtained using a simple set of parabolic equations. The results are in excellent agreement with those of the full Navier-Stokes equations

On viscoelastic cavitating flows: A numerical study

The effect of viscoelasticity on turbulent cavitating flow inside a nozzle is simulated for Phan-Thien-Tanner (PTT) fluids. Two different flow configurations are used to show the effect of viscoelasticity on different cavitation mechanisms, namely, cloud cavitation inside a step nozzle and string cavitation in an injector nozzle. In incipient cavitation condition in the step nozzle, small-scale flow features including cavitating microvortices in the shear layer are suppressed by viscoelasticity. Flow turbulence and mixing are weaker compared to the Newtonian fluid, resulting in suppression of microcavities shedding from the cavitation cloud. Moreover, mass flow rate fluctuations and cavity shedding frequency are reduced by the stabilizing effect of viscoelasticity. Time averaged values of the liquid volume fraction show that cavitation formation is strongly suppressed in the PTT viscoelastic fluid, and the cavity cloud is pushed away from the nozzle wall. In the injector nozzle, a developed cloud cavity covers the nozzle top surface, while a vortex-induced string cavity emerges from the turbulent flow inside the sac volume. Similar to the step nozzle case, viscoelasticity reduces the vapor volume fraction in the cloud region. However, formation of the streamwise string cavity is stimulated as turbulence is suppressed inside the sac volume and the nozzle orifice. Vortical perturbations in the vicinity of the vortex are damped, allowing more vapor to develop in the string cavity region. The results indicate that the effect of viscoelasticity on cavitation depends on the alignment of the cavitating vortices with respect to the main flow direction