Formation number of confined vortex rings

This paper investigates the formation number of vortex rings generated by a piston-cylinder mechanism in a confined tube. We use Direct Numerical Simulations (DNS) of axisymmetric confined vortex rings to study the influence of different parameters on the separation (or pinch-off) of the vortex ring from the trailing jet. It is shown that the structure of the vortex ring at pinch-off depends on the type of injection program (pulse dominated by either positive or negative acceleration ramps) and the confinement ratio D w /D , where D w is the inner diameter of the tube and D the diameter of the cylinder). For low confinement ratios ( D w /D ≤ 2), a vortex of opposite sign generated at the lateral wall strongly interacts with the vortex ring and the pinch-off is not clearly observed. The pinch-off is observed and analysed for confinement ratios D w /D ≥ 2 . 5. DNS data are used to estimate the value of the formation time, which is the time necessary for the vortex generator to inject the same amount of circulation as carried by the detached vortex ring. The confined vortex ring at pinch-off is described by the model suggested by Danaila, Kaplanski and Sazhin [A model for confined vortex rings with elliptical core vorticity distribution, Journal of Fluid Mechanics, 811 :67-94, 2017]. This model allows us to take into account the influence of the lateral wall and the elliptical shape of the vortex core. The value of the formation time is predicted using this model and the slug-flow model

Modelling of confined vortex rings

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A model for confined vortex rings with elliptical-core vorticity distribution

We present a new model for an axisymmetric vortex ring confined in a tube. The model takes into account the elliptical (elongated) shape of the vortex ring core and thus extends our previous model [Danaila, Kaplanski and Sazhin, J. of Fluid Mechanics, 774, 2015] derived for vortex rings with quasi-circular cores. The new model offers a more accurate description of the deformation of the vortex ring core, induced by the lateral wall, and a better approximation of the translational velocity of the vortex ring, compared with the previous model. The main ingredients of the model are the following: the description of the vorticity distribution in the vortex ring is based on the previous model of unconfined elliptical-core vortex rings [Kaplanski, Fukumoto and Rudi, Physics of Fluids, 24, 2012]; Brasseur's approach [Brasseur, PhD Thesis, 1979] is then applied to derive a wall-induced correction for the Stokes stream function of the confined vortex ring flow. We derive closed formulae for the flow stream function and vorticity distribution. An asymptotic expression for the long time evolution of the drift velocity of the vortex ring as a function of the ellipticity parameter is also derived. The predictions of the model are shown to be in agreement with direct numerical simulations of confined vortex rings generated by a piston-cylinder mechanism. The predictions of the model support the recently suggested heuristic relation [Krieg andMohseni, J. Fluid Engineering, 135, 2013] between the energy and circulation of vortex rings with converging radial velocity. A new procedure for fitting experimental and numerical data with the predictions of the model is described. This opens the way for applying the model to realistic confined vortex rings in various applications including those in internal combustion engines

The differential-algebraic and bi-Hamiltonian integrability analysis of the Riemann type hierarchy revisited

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic hierarchy is revisited, its new Lax type representation and Poisson structures constructed in exact form. The related bi-Hamiltonian integrability and compatible Poissonian structures of the generalized Riemann type hierarchy are also discussed.Comment: 18 page

Modelling of a two-phase vortex-ring flow using an analytical solution for the carrier phase

A transient axially symmetric two-phase vortex-ring flow is investigated using the one-way coupled, two-fluid approach. The carrier phase parameters are calculated using the approximate analytical solution suggested by Kaplanski and Rudi (Phys. Fluids vol. 17 (2005) 087101-087107). Due to the vortical nature of the flow, the mixing of inertial admixture can be accompanied by crossing particle trajectories. The admixture parameters are calculated using the Fully Lagrangian Approach (FLA). According to FLA, all of the dispersed phase parameters, including the particle/droplet concentration, are calculated from the solution to the system of ordinary differential equations along chosen particle trajectories; FLA provides high-accuracy particle number calculations even in the case of crossing particle trajectories (multi-valued fields of the dispersed media). Two flow regimes corresponding to two different initial conditions are investigated: (i) injection of a two-phase jet; and (ii) propagation of a vortex ring through a cloud of particles. It was shown that the dispersed media may form folds and caustics in these flows. In both cases, the ranges of governing parameters leading to the formation of mushroom-like clouds of particles are identified. The caps of the mushrooms contain caustics or edges of folds of the dispersed media, which correspond to particle accumulation zones

Differential-Algebraic Integrability Analysis of the Generalized Riemann Type and Korteweg-de Vries Hydrodynamical Equations

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic equations at N = 3; 4 is devised. The approach is also applied to studying the Lax type integrability of the well known Korteweg-de Vries dynamical system.Comment: 11 page

Ligand-Receptor Interactions

The formation and dissociation of specific noncovalent interactions between a variety of macromolecules play a crucial role in the function of biological systems. During the last few years, three main lines of research led to a dramatic improvement of our understanding of these important phenomena. First, combination of genetic engineering and X ray cristallography made available a simultaneous knowledg of the precise structure and affinity of series or related ligand-receptor systems differing by a few well-defined atoms. Second, improvement of computer power and simulation techniques allowed extended exploration of the interaction of realistic macromolecules. Third, simultaneous development of a variety of techniques based on atomic force microscopy, hydrodynamic flow, biomembrane probes, optical tweezers, magnetic fields or flexible transducers yielded direct experimental information of the behavior of single ligand receptor bonds. At the same time, investigation of well defined cellular models raised the interest of biologists to the kinetic and mechanical properties of cell membrane receptors. The aim of this review is to give a description of these advances that benefitted from a largely multidisciplinar approach