Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session F10: Vortex Evolution & StabilityVortexes
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Chair: Bartosz Protas, McMaster University Room: 503 |
Monday, November 20, 2017 8:00AM - 8:13AM |
F10.00001: Stabilization of Inviscid Vortex Sheets Bartosz Protas, Takashi Sakajo In this study we investigate the problem of stabilizing inviscid vortex sheets via feedback control. Such models, expressed in terms of the Birkhoff-Rott equation, are often used to describe the Kevin-Helmholtz instability of shear layers and are known to be strongly unstable to small-scale perturbations. First, we consider the linear stability of a straight vortex sheet in the periodic setting with actuation in the form of an array of point vortices or sources located a certain distance away from the sheet. We establish conditions under which this system is controllable and observable. Next, using methods of the linear control theory, we synthesize a feedback control strategy which stabilizes a straight vortex sheet in the linear regime. Given the poor conditioning of the discretized problem, reliable solution of the resulting algebraic Riccati equation requires the use of high-precision arithmetic. Finally, we demonstrate that this control approach also succeeds in the nonlinear regime, provided the magnitude of the initial perturbation is sufficiently small. [Preview Abstract] |
Monday, November 20, 2017 8:13AM - 8:26AM |
F10.00002: Numerical simulations of vortex breakdown in low-Reynolds-number swirling flow Joseph Chung, Xiao Zhang, Ryan Houim, Elaine Oran Numerical simulations of low-Reynolds-number vortex breakdown were carried out by solving the unsteady, three-dimensional, compressible, Navier-Stokes (NS) equations on a Cartesian mesh. The flux-corrected transport algorithm was used to solve for the inviscid fluxes and high-order central differencing for the viscous terms. BoxLib, an adaptive mesh-refinement library, was used for spatial refinement near the core of the vortex. The molecular weight and temperature were scaled to relax the time-step constraints imposed by the sound speed. The results confirm three-dimensional vortex breakdown in qualitative and quantitative agreement with previous incompressible simulations. Application of the barely implicit correction (BIC) algorithm further relaxed the time-step constraint by solving for a pressure correction to the energy and momentum equations. [Preview Abstract] |
Monday, November 20, 2017 8:26AM - 8:39AM |
F10.00003: Axisymmetric contour dynamics for buoyant vortex rings Ching Chang, Stefan Llewellyn Smith Vortex rings are important in many fluid flows in engineering and environmental applications. A family of steady propagating vortex rings including thin-core rings and Hill’s spherical vortex was obtained by Norbury (1973). However, the dynamics of vortex rings in the presence of buoyancy has not been investigated yet in detail. When the core of a ring is thin, we may formulate reduced equations using momentum balance for vortex filaments, but that is not the case for “fat” rings. In our study, we use contour dynamics to study the time evolution of axisymmetric vortex rings when the density of the fluid inside the ring differs from that of the ambient. Axisymmetry leads to an almost-conserved material variable when the Boussinesq approximation is made. A set of integro-differential equations is solved numerically for these buoyant vortex rings. The same physical settings are also used to run a DNS code and compare to the results from contour dynamics. [Preview Abstract] |
Monday, November 20, 2017 8:39AM - 8:52AM |
F10.00004: Transient Growth on a High-Reynolds-number Oseen Vortex Leading to Breakup Eric Stout, Fazle Hussain Incompressible vortex-turbulence interaction and vortex perturbation transient growth are explored at Reynolds numbers (\textit{Re}$\equiv $vortex circulation/viscosity) much higher than the current computational maximum of \textit{Re}$=$10,000, via Large Eddy Simulation (LES) using the Smagorinsky model. At \textit{Re}$=$10,000, LES results agree closely with Direct Numerical Simulation (DNS) results for the perturbation energy, peak azimuthal velocity, and core radius (radius of peak azimuthal velocity) - thus validating the LES scheme. Our previous studies have shown that turbulence, strained into external spiral filaments, induces axial flow on an initially rectilinear Oseen vortex column. Axial flow comparable to the swirl destabilizes a vortex; however, at \textit{Re}$=$10000, viscous decay of the filaments limits the axial flow. We study a vortex column at \textit{Re}$=$50,000 using LES to achieve stronger axial flow, thus triggering instability and transition of the vortex into turbulence. This transition is compared with DNS of an unstable vortex at \textit{Re}$=$10000 - both simulations showing transition of the vortex column into a bundle of numerous spiraling axial vortex threads. Details of the initial transient growth, transition process and turbulence evolution will be explained. [Preview Abstract] |
Monday, November 20, 2017 8:52AM - 9:05AM |
F10.00005: The growth and breakdown of a vortex-pair in a stably stratified fluid. Advaith S, Aashay Tinaikar, Manu K V, Saptarshi Basu Vortex interaction with density stratification is ubiquitous in nature and applied to various engineering applications. Present study have characterized the spatial and temporal dynamics of the interaction between a vortex and a density stratified interface. The present work is prompted by our research on~single tank Thermal Energy Storage (TES) system used in concentrated solar power (CSP) plants where hot and cold fluids are separated by means of density stratification. Rigorous qualitative (High speed Shadowgraph) and quantitative (high speed PIV) studies enable us to have great understanding about vortex formation, propagation, interaction dynamics with density stratified interface, resulted plume characteristics and so on. We have categorized this interaction phenomena in to three different cases based on its nature as non-penetrative, partial penetrative and extensively penetrative. Along with that we have proposed a regime map consisting non-dimensional parameters like Reynolds, Richardson and Atwood numbers which predicts the occurrence above mentioned cases. [Preview Abstract] |
Monday, November 20, 2017 9:05AM - 9:18AM |
F10.00006: Abstract Withdrawn
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Monday, November 20, 2017 9:18AM - 9:31AM |
F10.00007: Swirling flow states of compressible super-critical fluids Nguyen Ly, Zvi Rusak, Shixiao Wang Steady states of axisymmetric swirling flows of a super-critical fluid in a rotating finite-length pipe are studied. The fluid thermodynamic behavior is modeled by the Van der Waals equation of state. A nonlinear partial differential equation for the solution of the flow stream function is derived in terms of the inlet flow total enthalpy, entropy, and circulation functions. This equation reflects the nonlinear thermo-physical interactions in the flows, specifically when the inlet state temperature and density vary around the thermodynamic critical point, flow compressibility is significant, and inlet swirl ratio is high. The approach is applied to an inlet flow described by a solid-body rotation with uniform profiles of the axial velocity and temperature. Bifurcation diagrams of steady compressible flows of real fluids are formed as the inlet swirl level and the centerline inlet density are increased. Focus is on fluids with low values of R/Cv. Computed results provide predictions of the critical swirl levels for the loss of stability of the columnar state and for the appearance of non-columnar states and of vortex breakdown states as a function of inlet centerline density. The difference in the dynamical behavior between that of a perfect gas and of a real gas is explored. [Preview Abstract] |
Monday, November 20, 2017 9:31AM - 9:44AM |
F10.00008: Identification of key flow for vortex generation in terms of local flow geometry Katsuyuki Nakayama The flow transition into a vortical flow in terms of the invariant local geometry (topology) specified by the velocity gradient tensor is analysed with the swirlity that is a physical quantity to represent the unidirectionality and intensity of the azimuthal flow extracted from the local flow. The velocity gradient tensor is represented in a specific coordinate system where these components are given by invariant quantities and related to the flow topology. While the swirlity specifies the transition process into a vortical flow and predicts its generation, the tensor components are traced. Then the key flow that contributes the vortex generation is identified as an invariant shear (or strain) flow, where its effect is evaluated. This analysis of the flow transition with statistical analysis in an isotropic homogeneous turbulence in a low Reynolds number shows that the key flow is the shear flow in the predicted swirl plane (after vortex transition) orthogonal to one eigenvector. This particular characteristic is similar irrespective of decomposed flow scales in this turbulence (using the band pass filter of the Fourier coefficient of the velocity), with the feature of the swirlity. [Preview Abstract] |
Monday, November 20, 2017 9:44AM - 9:57AM |
F10.00009: Effect of the local geometry on the motion of a filamentary vortex Oscar Velasco Fuentes In his seminal paper on vortex motion Helmholtz (1858) showed that a curved vortex moves within the fluid whereas a straight one remains stationary. Schwedoff (1887) later claimed that the velocity of a vortex increases with the curvature and is perpendicular to the plane of curvature. This conjecture, mathematically formalized by Da Rios (1906), is now known as the local induction approximation (LIA). Here we use a higher-order Frenet-Serret representation of the vortex centerline in order to study the effect of curvature, torsion and their derivatives on the motion of a filamentary vortex. We found that, to leading order, the curvature induces a vortex velocity in the binormal direction, the torsion induces velocity in the tangential direction and the changes in curvature and torsion along the vortex induce velocity in the normal direction. We verify these results by studying, separately, the evolution of a helical vortex and an elliptical vortex ring, whose motion is also calculated using different analytic/numerical methods. [Preview Abstract] |
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