Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session L16: Vortex Simulation and Theory |
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Chair: Robert Krasny, University of Michigan Room: Georgia World Congress Center B303 |
Monday, November 19, 2018 4:05PM - 4:18PM |
L16.00001: Interaction of two axially-symmetric helical vortices Alejandro Espinosa Ramirez, Oscar Velasco Fuentes We studied the evolution of two equal, coaxial, symmetrically located helical vortices in an unbounded, inviscid, incompressible fluid. We computed the evolution with a triple-periodic vortex-in-cell method and found four main regimes of behavior: 1) Thin vortices translate and rotate uniformly while preserving their form, as predicted by Joukowsky (1912), and their velocities agree with those obtained by Velasco Fuentes (2018), 2) Thicker vortices behave as predicted by Joukowsky (1912) but they move with smaller velocities than the thin vortices studied by Velasco Fuentes (2018), 3) Fat, large-pitch vortices merge to form a single cylindrical column with mainly axial vorticity. This process is analogous to the merger of two Rankine vortices (which correspond to helical vortices of infinite pitch) but the vortices approach each other faster and merge even from relatively large distances (where Rankine vortices would not merge). 4) Small-pitch vortices merge to form a single cylindrical shell with mainly azimuthal vorticity. This occurs even for thin vortices if the pitch is sufficiently small. |
Monday, November 19, 2018 4:18PM - 4:31PM |
L16.00002: A New Implementation of the Vortex Method for Elliptical Vortex Evolution Ling Xu, Robert Krasny We discuss a new implementation of the vortex method for the incompressible Euler equations. This work focuses on smooth vorticity distributions as opposed to vortex sheets. As usual the vorticity is carried by Lagrangian particles and the velocity is recovered by the Biot-Savart law. The new implementation combines remeshing, adaptive refinement, and treecode acceleration to resolve complex features of the flow. Applications are given to vortex dynamics in two-dimensional free-space. |
Monday, November 19, 2018 4:31PM - 4:44PM |
L16.00003: Numerical Study of the Viscous Lamb Dipole Robert Krasny, Ling Xu The Lamb dipole is a steady propagating solution of the inviscid fluid equations with opposite-signed vorticity in a circular disk. As known from previous studies, in the presence of viscosity the dipole grows in size, the propagation velocity decreases, and a thin tail of low-level vorticity is left behind as the head propagates forward. To clarify the roles of convection and diffusion, we compare finite-difference solutions of the Navier-Stokes equation (NSE) and the linear diffusion equation (LDE) using the inviscid Lamb dipole as the initial condition. We find that the maximum core vorticity decreases at the same rate for the NSE and LDE, for Reynolds numbers in the range from 125 to 1000. However as the Reynolds number increases, the total positive circulation decreases slightly faster for the NSE than the LDE, showing that convection enhances the cancellation of opposite-signed vorticity in the dipole. Other details of the flow are examined including the structure of the tail and entrainment of initially irrotational fluid in the head. |
Monday, November 19, 2018 4:44PM - 4:57PM |
L16.00004: Simulation of a vortex ring of significant core thickness John M Russell Consider axisymmetric, solenoidal motion of an inviscid uniform density fluid in which the region of rotational motion is interior to a torus. Let the fluid at remote distances from the torus be at rest and let the motion be steady relative to an observer moving with the torus. The simulation assumes that the azimuthal vorticity is directly proportional to the distance from the axis of symmetry (an assumption consistent with the fact that material lines, and hence vortex lines, undergo stretching and compression as they convect from one position to another in the core). The simulation assumes unit value of the centroidal radius---i.e. the distance from the centroid of a typical meridional cross section to the axis of symmetry---as well as unit value of the total dipole strength of the motion. The minor radius---i.e. the radius of a circular disk whose area is that of a typical meridional section the core---is one half the centroidal radius. The results show that if the core cross section is circular there is a non-physical slip between the fluid inside and outside the core. One may eliminate the slip by optimizing the cross sectional shape. The radius of curvature of the optimum shape is largest at the inner equator and smallest at the leading and trailing extremities. |
Monday, November 19, 2018 4:57PM - 5:10PM |
L16.00005: Numerical simulation and modal analysis of vortices in a pump sump Byungjin An, Qiong Liu, Motohiko Nohmi, Masashi Obuchi, Kunihiko Taira Pump sumps are settling chambers for incoming flows prior to their removal by pumps. These pump sumps are widely used for drainage in pumping stations and power plants. During off-design operations, free surface and sub-surface vortices can appear in pump sumps, causing significant pump performance degradation and system vibrations. The present study is performed to obtain insights to develop an effective and highly robust vortex suppressing device for pump sumps. Large eddy simulations are conducted on a scaled model pump sump to reproduce the vortex flow field with free surface and sub-surface vortices. The vortical flow is investigated by proper orthogonal decomposition (POD) based on the velocity field to extract the key energetic features. The dominant POD modes near the suction pipe provide insights for understanding the complex vortex dynamics and developing a novel control device for the suppression of vortex appearances. |
Monday, November 19, 2018 5:10PM - 5:23PM |
L16.00006: A new type of axisymmetric vortex shedding from a sphere moving vertically in a stratified fluid Hideshi Hanazaki, Tatsuya Yasuda, Shinya Okino A numerical study is described of the flow past a sphere moving vertically at constant speed in a stratified fluid. It is found that the flow under moderate or strong stratification (Fr=W/Na ≤14, W: sphere velocity, N: buoyancy frequency and a: sphere radius) remains axisymmetric even at Re=500, unlike the flow of a homogeneous fluid which becomes asymmetric for Re>200. A striking feature is that this axisymmetric flow gives, under moderate stratification (7≤Fr≤14), an axisymmetric vortex or 'vorticity' shedding, which has never been observed in the wake of an axisymmetric bluff body. The 'vorticity' shedding occurs even when the familiar vortex shedding can not be identified in the streamlines. The phenomenon corresponds to the observation in previous shadowgraph experiments (e.g. Hanazaki 2009), which showed a periodic generation of knots in the jet downstream of a sphere. |
Monday, November 19, 2018 5:23PM - 5:36PM |
L16.00007: A non-Boussinesq vortex ring Ching Chang, Stefan Gregory Llewellyn Smith The motion of an axisymmetric buoyant vortex ring is calculated using contour dynamics. An evolution equation for vortex sheet on the interface is obtained to account for additional physics such as buoyancy. In this talk, we will first review the Boussinesq limit. Then an equation for vortex sheet in the non-Boussinesq regime is derived. The evolution of rings using both approaches are compared for Atwood numbers. In the non-Boussinesq case, surface tension can also be introduced through a pressure jump on the interface. We also discuss the relevant dimensionless numbers and explore the dynamics of buoyant vortex rings in parameter space. |
Monday, November 19, 2018 5:36PM - 5:49PM |
L16.00008: Tracking vortex surfaces frozen in the virtual velocity in non-ideal flows Jinhua Hao, Shiying Xiong, Yue Yang The vorticity-related conservation theorems for ideal flows, such as Helmholtz's theorem, break down in non-ideal flows which can be viscous or with non-conservative body forces. On the other hand, the vorticity-related quantities within a carrier convected by a virtual circulation-preserving velocity can still be conserved in some non-ideal flows. We provide the conditions for the existence and uniqueness of a globally smooth virtual velocity with several explicit examples. By incorporating the virtual velocity into the vortex-surface field (VSF), we can track vortex surfaces in some non-ideal flows. If a flow has a viscous-like diffusion term which is orthogonal to the vorticity without singularity, we obtain an explicit virtual velocity to accurately track vortex surfaces in time. This modified flow is dissipative but prohibits reconnection of vortex lines. If a globally smooth virtual velocity does not exist, an approximate virtual velocity is still useful. We use the approximate virtual velocity to track vortex surfaces in a magnetohydrodynamic flow. Compared with the VSF evolution convected by the physical velocity, the conservation of vorticity flux is significantly improved, and the spurious vortex deformation induced by the Lorentz force is eliminated. |
Monday, November 19, 2018 5:49PM - 6:02PM |
L16.00009: Unsteady vortex interactions with Joukowski airfoils on elastic supports Huansheng Chen, Justin Jaworski Coherent vortices present in the atmosphere or that are generated by aircraft create a gust field that exerts unsteady aerodynamic forces on the wings and appendages of downstream aircraft. In particular, the unsteady aerodynamic forces resulting from spanwise-oriented gust encounters produce an unsteady vortex wake that is also coupled to the motion of the incident vortex and to the wing shape and position. These coupled interactions between an incident line vortex, a Joukowski airfoil on elastic supports, and its wake are formulated analytically and computed numerically. The vortex motion and the fluid forces on the airfoil are derived from inviscid potential flow, and the continuous shedding of vorticity from the trailing edge is modeled by the emended Brown and Michael equation. Special attention is paid to the limiting cases of flat-plate airfoils that are either stationary or under prescribed motions for which validation data exist. The present effort extends beyond these restrictions to include the geometrical effects of the Joukowski airfoil profile and its aeroelastic influence on the incoming vortex path and the unsteady fluid loading. |
Monday, November 19, 2018 6:02PM - 6:15PM |
L16.00010: The vortex-entrainment sheet Adam C DeVoria, Kamran Mohseni A vortex sheet is a well-known inviscid model of high Reynolds number viscous boundary and shear layers. The circulation in the layer is preserved via a jump in the harmonic potential across the sheet; there is also a jump in the tangential velocity that defines the vortex sheet strength. However, viscous layers necessarily contain mass and momentum, in addition to vorticity, which are entrained by a normal velocity at the edge of the layer. Hence, a more complete model of a viscous layer or wake that is collapsed to an infinitely thin sheet should account for the entrainment as well as the vorticity. We propose such a model, termed a vortex-entrainment sheet, which is characterized by jumps in the harmonic potential and the stream function or, equivalently, by jumps in both the tangential and normal components of velocity. For separation at a sharp edge, the singular pressure gradient is neutralized, in accordance with the normal momentum balance, by delivering an instantaneous impulse to the fluid. A non-tangential shedding angle of the sheet from the sharp edge necessarily requires non-zero entrainment. |
Monday, November 19, 2018 6:15PM - 6:28PM |
L16.00011: Helical contour dynamics Stefan Llewellyn Smith, Tianyi Chu, Ching Chang Contour dynamics simulates the evolution of vortices by following the evolution of their boundaries. In its two-dimensional version, the vorticity inside vortices is constant, while in its axisymmetric version, the vorticity is proportional to distance from the axis of symmetry. We investigate helical contour dynamics, for which the flow is invariant along a helical vector. The nonlinear inviscid equations of motion reduce to two advection equations with forcing on the right-hand sides. However, this forcing is only non-zero along the boundaries of vortices for appropriate chosen velocity distributions. This leads to time-dependent vortex sheets on the boundary. The resulting contour dynamics equations are derived and some example cases are studied. |
Monday, November 19, 2018 6:28PM - 6:41PM |
L16.00012: Hollow vortex in a corner straining flow Todd Christopher, Stefan Gregory Llewellyn Smith A hollow vortex is a solution to the 2D Euler equations with a finite-area region of constant pressure and nonzero circulation. Hollow vortices in straining flow have been previously treated, but the influence of boundaries has not yet been investigated. Equilibrium solutions for a hollow vortex in straining flow in a right-angled corner are found in terms of the Schottky-Klein prime function. Using complex-variable techniques and the prime function, the vortex boundary is constructed as a conformal map from the canonical doubly-connected domain of the concentric annulus to the physical domain of the hollow vortex in a corner. Comparison with the limiting case of a point vortex in a corner is made, and extensions to corners of arbitrary angle and non-equilibrium cases are discussed. Motivation includes regions of high nutrient or pollution density in the ocean, which can be formed in coastal regions from rivers or runoffs; the advection and mixing of the regions depend in part on the local flow and shoreline geometry, and a hollow vortex in straining flow is a possible model for this process. |
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