Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session P12: Vortex Dynamics and Vortex Flows: Structures/Interactions |
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Chair: Kamran Mohseni, U. Florida Room: 303 |
Monday, November 25, 2019 5:16PM - 5:29PM |
P12.00001: Angular momentum in vortex sheets Adam DeVoria, Kamran Mohseni The conservation of angular momentum in vortex sheets in considered. When the integrity of the vortex sheet as a mathematically continuous object is maintained, the angular momentum is automatically conserved by virtue of linear momentum conservation. However, the practical computation of the dynamics of a complete vortex sheet is a numerically intractable problem. The common method of replacing the inner spiral core of a rolled-up sheet by an isolated point vortex requires the conservation of circulation and linear momentum. However, since a finite portion of the fluid domain occupied by the sheet has been removed and replaced by a single point, the angular momentum of that finite portion must be explicitly considered and conserved. The time rate-of-change of angular momentum in the core is represented by a moment/torque on the vortex and the corresponding conservation is ensured by the appropriate vorticity flux into the core and throughout the sheet. The effect of this constraint on the total circulation in the sheet and the location of the vortex are presented for the roll-up of self-similar vortex sheets. [Preview Abstract] |
Monday, November 25, 2019 5:29PM - 5:42PM |
P12.00002: Three-dimensional Vortical Structures in a Curved Pipe under Fully Developed Pulsatile Inflow Christopher Cox, Michael W. Plesniak We numerically investigate spatial and temporal evolution of multiple three-dimensional vortices under a fully developed cardiac physiological (pulsatile) inflow of a Newtonian fluid in a 180 degree curved rigid pipe with circular cross-section, without taper or torsion. We identify vortical structures using vortex identification methods and characterize their evolution throughout the deceleration phase, capturing both Dean- and Lyne-type vortices for which the planes of rotation are different. We track trajectories of Dean-type vortices and find agreement with experimental results. We also show the connection along the axial direction between regions of organized vorticity observed at various cross-sections, which previous 2-D analysis could not provide, and demonstrate that the combined effect of geometry curvature and deceleration produces a strong helical flow that is conducive to the formation of a single pair of Dean-type counter-rotating vortices that is connected to the classical Dean vortex pair near the entrance to the curve. Understanding the formation of these vortical structures is necessary to draw any correlation between the flow and wall shear stress distributions produced under physiological conditions. [Preview Abstract] |
Monday, November 25, 2019 5:42PM - 5:55PM |
P12.00003: Self-similar Turbulent Vortex Rings: Interaction of Propellant Gases with Blood Backspatter and the Transport of Gunshot Residue Alexander Yarin, Patrick Comiskey Self-similar turbulent vortex rings are investigated theoretically in the framework of the semi-empirical turbulence theory for the modified Helmholtz equation. The velocity and vorticity fields are established, as well as the transport of passive admixture by turbulent vortex rings. Turbulent vortex rings of propellant gases originating from the muzzle of a gun after a gunshot are an important phenomenon to consider in crime scene reconstruction. It is shown that this has a significant repercussion on the outcome of backward blood spatter resulting from a gunshot. Turbulent vortex rings of propellant gases skew the distribution of blood stains on the ground and can either propel blood drops further from the target, or even turn them backwards toward the target. An image of the propagating muzzle gases after bullet ejection is overlaid with the predicted flow field which reveals satisfactory agreement. Gunshot residue is an important factor in determining the events of a violent crime due to a gunshot and are considered to be entrained and transported by the propellant gases. The self-similar solutions for the flow, vorticity, and concentration of gunpowder particles are predicted and the results are shown to be consistent with the experimental data. [Preview Abstract] |
Monday, November 25, 2019 5:55PM - 6:08PM |
P12.00004: Formation number, pinch-off time and ‘optimal formation time’ of orifice-generated vortex rings Raphael Limbourg, Jovan Nedic Vortex rings are generated experimentally by impulsively discharging fluid through a sharp-edge nozzle or orifice. As the actuator pushes the flow through the tube, the shear layer at the outlet rolls-up, detaches and propagates downstream in one or several vortices from which we can define the pinch-off time, the formation number and an ‘optimal formation time’. The radial component of velocity at the exhaust of an orifice results in a significant increase in the final circulation, the kinetic energy and the hydrodynamic impulse (Krieg \& Mohseni, 2013). Measurements show a 140\% increase in the total circulation compared to a nozzle. In the case of orifice-generated vortex rings, the formation number has been found to range between 1.0 to 2.0. Furthermore, the radial component of velocity drastically destabilises the flow which results in an earlier pinch-off of the primary ring. Trailing vortices merge with the primary ring to grow into a well-formed ring at an ‘optimal formation time’. Energy consideration based on the Fraenkel-Norbury family of vortex rings accurately predicts the formation number for orifice-generated vortex rings. [Preview Abstract] |
Monday, November 25, 2019 6:08PM - 6:21PM |
P12.00005: Accurate and efficient coupling of a near-wall Eulerian solver with a Vortex Particle-Mesh method for aerodynamics and wakes Philippe Billuart, Philippe Chatelain, Gregoire Winckelmans We present and illustrate a new hybrid Eulerian-Lagrangian approach for aerodynamics: the near-wall region is resolved using an Eulerian solver (here finite differences) while the vortex-particle-mesh (VPM) method, supplemented by an immersed interface method (IIM), is used for capturing the wake region. Indeed, the isotropic elements of the VPM-IMM do not permit to resolve accurately and efficiently the boundary layer but perform very well in the wake region thanks to their negligible dispersion and diffusion. The grid-based solver is well suited for resolving the boundary layers. With such coupling, the advantages of both solvers are kept whereas their respective drawbacks are eliminated, permitting to simulate efficiently high Reynolds number flows. The key feature of the approach also lies in the way both methods are coupled: accurately and without Schwarz iteration. The approach is tested and analysed/validated on the flow past a cylinder. It is then applied to the flow past a regularized Joukowski airfoil. [Preview Abstract] |
Monday, November 25, 2019 6:21PM - 6:34PM |
P12.00006: Investigating the Van der Pol analogy in vortex shedding using Pade approximants and compact finite differences Daniel Johnston, Mohammed Afsar, Adrian Sescu, Ioannis Kokkinakis The Van der Pol (VDP) oscillator serves as an analogy for vortex shedding in the near-wake region of doubly infinite (i.e. spanwise homogeneous) slender bluff bodies. In this work, approximate solutions to the VDP equation are investigated using Pade approximants and compact finite difference schemes. The Pade approximant formulae are found using expansions of the well-known asymptotic solution. We compare this to the corresponding Taylor series and the classical 4th order Runge-Kutta solution. The Pade approximant solutions consistently show closer agreement to the numerical solution over their corresponding Taylor series, especially at $O(1)$ values of the small parameter in the VDP equation, for a longer interval in time. We then asses the accuracy of the numerical solution using compact difference schemes. We find that the spectral-like schemes introduced by Lele (J. Comp. Phys. 103, p.16, 1992) show closer agreement with the VDP analogy, when compared with conventional schemes, as the initial rate of growth of the oscillations in the near-wake is increased. Finally, we consider this analogy as a model of the Von-Karman vortex street in the wake behind a cylinder, validate the results using CFD simulations, and discuss conditions for which its applicability may break down. [Preview Abstract] |
Monday, November 25, 2019 6:34PM - 6:47PM |
P12.00007: Numerical investigation of the model on vortex reconnection Yoshifumi Kimura, Keith Moffatt Recently we have developed an analytical model for the finite singularity problem for the Naiver-Stokes equations [1],[2]. In this model, two circular vortex rings of circulation $\pm \Gamma$ and radius $R=1/\kappa$ are symmetrically placed on two planes inclined to the plane $x=0$ at angles $\pm\alpha$. Under an assumption that the vortex Reynolds number, $R_{\Gamma}=\Gamma/\nu$, is very large, we have derived a nonlinear dynamical system for the local behavior near the points of closest approach of the vortices. Careful numerical investigation of the dynamical system reveals that the magnitude of vorticity could take any large value for small viscosity but remains finite since the minimum core radius never becomes zero. The assumptions for this analysis are far beyond the ones that the current DNS could attain, but we are curious whether and how much DNS can verify the tendency of the analysis. We are going to show some preliminary results of DNS. [1] Towards a finite-time singularity of the Naiver-Stokes equations Part 1. Derivation and analysis of dynamical system, H.K.M. \& Y.K. JFM (2019) {\bf 861} 930—967. [2] Towards a finite-time singularity of the Naiver-Stokes equations Part 2. Vortex reconnection and singularity evasion, H.K.M. \& Y.K. JFM (2019) {\bf 870}, R1. [Preview Abstract] |
Monday, November 25, 2019 6:47PM - 7:00PM |
P12.00008: Interaction of Tubular Vortices as a Function of Contact Angle Oscar Velasco Fuentes We study the evolution of two equal tubular vortices, which initially touch each other, as a function of the angle formed by their centerlines at the point of contact. To this end we solve the vorticity equation in a triple-periodic domain with a vortex-in-cell method, using as initial conditions two helical vortices of equal circulation $\Gamma$, pitch $L$, radius $R$ and core radius $a$. The axes of the helices are parallel lines separated by a distance $2R+2a$, so that the vortices touch each other at a single point within the numerical domain. At this point the vortices centerlines make an angle $\alpha=180^\circ-2 \tan^{-1}(L/2\pi R)$. We analyzed the flow evolution by monitoring the position and topology of iso-surfaces of vorticity magnitude as well as the distribution of fluid particles initially located within the vortices. Both methods yield the same results in the identification of the following regimes: for small angles ($\alpha \rightarrow 0^\circ$) the vortices merge in a time that increases with the angle, for large angles ($\alpha \rightarrow 90^\circ$) the vortices reconnect in a time that decreases with the angle, for intermediate angles the vortices exchange mass but keep their identity during the whole simulation. [Preview Abstract] |
Monday, November 25, 2019 7:00PM - 7:13PM |
P12.00009: Point vortices with dynamic circulation Philip J. Morrison The intimate connection between scalar vorticity dynamics and point vortex dynamics is well known. Because of Kirchhoff, Kida, and many others, Hamiltonian point vortex dynamics has been widely studied in a variety of contexts. In this talk I will discuss a generalization: a new conservative system of point vortex dynamics that allows for dynamic circulations. [Preview Abstract] |
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