Bulletin of the American Physical Society
74th Annual Meeting of the APS Division of Fluid Dynamics
Volume 66, Number 17
Sunday–Tuesday, November 21–23, 2021; Phoenix Convention Center, Phoenix, Arizona
Session H24: Vortex Dynamics and Vortex Flows: Theory, Simulations and Astro/Geophysical |
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Chair: Stefan Llewellyn Smith, UCSD Room: North 224 B |
Monday, November 22, 2021 8:00AM - 8:13AM |
H24.00001: Aysmptotic equations for thin dipole layers Gregory Baker, Ching Chang, Stefan G Llewellyn Smith, Dale I Pullin We develop asymptotic, thin-layer equations that describe the evolution of two adjacent, semi-infinite material fluid strips, each with spatially uniform but generally differing vorticity. This diplole layer moves in an otherwise irrotational, unbounded inviscid incompressible fluid. The configuration is viewed as a simple model for the wake formed by two boundary layers separating from a splitter plate. At leading order, the closed initial-value, nonlinear, long-wavelength equations describe the dipole layer center line motion together with functions representing both the local thickness-weighted mean velocity and velocity difference. For unequal far-field velocities, stability analysis of the linearized equations reveals Kelvin-Helmholz instability. Equal velocities gives a pure dipole layer where solution of the initial-value problem shows a double pole in Laplace transform space leading to linear algebraic growth. This agrees with the long wavelength limit of the full linearized, three-curve stability equations for sinuous modes. |
Monday, November 22, 2021 8:13AM - 8:26AM |
H24.00002: Demonstration of finite-time singularity for an inviscid vortex ring model Philip J Morrison, Yoshifumi Kimura The recently proposed low degree-of-freedom model of Moffat and Kimura [1] for describing the approach to finite-time singularity of the incompressible Euler fluid equations is investigated. The model assumes an initial finite-energy configuration of two vortex rings placed symmetrically on two tilted planes. The Hamiltonian structure of the inviscid limit of the model is obtained. The associated noncanonical Poisson bracket [3] and two invariants, one that serves as the Hamiltonian and the other a Casimir invariant, are discovered. It is shown that the system is integrable with a solution that lies on the intersection for the two invariants, just as for the free rigid body of mechanics whose solution lies on the intersection of the kinetic energy and angular momentum surfaces. Also, a direct quadrature is given and used to demonstrate the Leray form for finite-time singularity in the model. To the extent the Moffat and Kimura model accurately represents Euler's ideal fluid equations of motion, we have shown the existence of finite-time singularity. Talk based on [3]. |
Monday, November 22, 2021 8:26AM - 8:39AM |
H24.00003: A generalized Karman-like drag law for exotic vortex street equilibria Mark A Stremler, Emad Masroor Th. von Karman showed that the time-averaged drag force on a submerged body producing a 2S vortex wake can be estimated by the features of a representative point vortex model. We generalize this approach, giving drag forces estimates for bluff bodies producing exotic wakes with N>2 vortices per period. The analysis consists primarily of a linear momentum balance applied to spatially periodic point vortex systems moving in relative equilibrium. Linear stability of some exotic vortex street equilibria help justify this approach. Drag force estimates are presented for 'P+S' (N=3) and '2P' (N=4) vortex wakes, and comparisons are made with the classic '2S' drag estimate. |
Monday, November 22, 2021 8:39AM - 8:52AM |
H24.00004: Aggregated Lifting-line Vortex Modeling for Unsteady Aerodynamics Diederik Beckers, Jeff D Eldredge Lightweight aircraft are vulnerable to flow separation induced by gusts. For purposes of regulating flight in the presence of such gusts, it is important to estimate the flow behavior and the instantaneous aerodynamic forces. Our objective is to predict the aerodynamic response of a finite wing in a free stream to a gust in a robust, but computationally cheap way. For this purpose, we propose an aggregated lifting-line vortex model and explore its validity. The model consists of three parts: a steady lifting line model, a collection of unsteady vortex filament loops, denoted as the outer model, and a series of two-dimensional unsteady potential flow models, distributed over the span of the wing and denoted as the inner models. The gust response of the wake behind a finite wing in a free stream is then modeled as a perturbation to the steady wake, where the steady wake is represented by the lifting line model vortex filaments and the perturbation is represented by the inner model point vortices and the outer model vortex filaments. |
Monday, November 22, 2021 8:52AM - 9:05AM |
H24.00005: A new quadrature for vortex sheet evolution Adam C DeVoria The motion of a vortex sheet can be effectively computed using trapezoidal integration combined with a blob regularization. Such a method experiences competing trade-offs between the blob parameter and the resolvable spatial scales and simulation run time. Here, a different method is proposed that eliminates the blob parameter by utilizing the evolution of the vortex sheet strength. This addresses the effects of curvature and sheet deformation with momentum conservation. The quadrature expression is obtained with two assumptions. First, a linear variation of the vortex sheet strength is used rather than a linear variation of the complete integrand (strength and kernel) as in the trapezoid rule. Second, the sheet is taken to be comprised of straight panels. A Kutta condition removes the logarithmic singularities in the local contribution to the principal value (i.e. self-induced velocity) as would be the case for an infinitely-resolved smooth sheet. It is hoped that this method will allow more detailed study of the small-scale structure of vortex cores. |
Monday, November 22, 2021 9:05AM - 9:18AM |
H24.00006: Three-dimensional numerical simulations of a Ranque-Hilsch vortex tube working with subcritical carbon dioxide Raphaël OBERTI, Junior LAGRANDEUR, Sébastien PONCET Numerical simulations of a Ranque-Hilsch vortex tube working with subcritical carbon dioxide (CO2) are performed using different modeling approaches assessed in terms of accuracy and computational cost. Three different fluid properties models and two turbulence models in both high and low Reynolds number formulations are compared to experimental data available in the literature. The ability of the models to predict the cold mass fraction as well as the temperature separation is discussed. A deep insight into the internal flow characteristics is then carried out to assess the assumptions made by one-dimensional thermodynamic models. For the range of operating conditions, results show a fairly good agreement in terms of cold mass fraction, cold and hot outlet temperatures, and hot outlet pressure with high Reynolds approaches, while the k-ω SST model performs better to predict the internal flow characteristics in conjunction with the Span-Wagner equation of state. To the best of the author's knowledge, the similarity between the Bödewadt flow and the boundary layer flow along the wall facing the hot exit is confirmed for the first time in a Ranque-Hilsch vortex tube working with subcritical CO2. |
Monday, November 22, 2021 9:18AM - 9:31AM Not Participating |
H24.00007: Two-dimensional viscous coupled interactions of a symmetric vortex pair and a neutrally buoyant cylinder Banavara Shashikanth, Yanxing Wang Numerical simulations using the Lattice Boltzmann Method are presented of the following two-dimensional incompressible flow problem. Starting from configurations corresponding to translating inviscid equilibria, namely, the translating Föppl equilibria (counter-rotating point vortex pair and a circular cylinder) and the translating Hill equilibria (counter-rotating point vortex pair and an elliptic cylinder), viscosity is turned on for t>0 and the subsequent viscous interaction is simulated. The interaction is in a dynamically coupled setting where the neutrally buoyant cylinder is free to move along the symmetry axis under the action of the instantaneous fluid stresses on its surface. It is observed that for starting configurations in which the vortex pair trails the cylinder, the viscous evolution stays close to the inviscid equilibrium. However, for starting configurations in which the vortex pair leads the cylinder, there is significant deviation from the inviscid equilibrium. In such cases, the vortices either accelerate and leave the cylinder behind or, more interestingly, leave their leading positions and are attracted towards the trailing positions. In other words, the cylinder in such cases threads through the leading vortices, overtakes them and the vortices are observed to trail the cylinder again. |
Monday, November 22, 2021 9:31AM - 9:44AM |
H24.00008: Kinetic Energy Transport in the neighborhood of a counter-rotating vortex pair in a stratified and turbulent environment Xiang Yang, Yuanwei Bin, Rui Ni, Yantao Yang, Robert F Kunz We conduct direct numerical simulations (DNSs) of a counter-rotating vortex pair in a stratified, turbulent environment to study the kinetic energy transport in the flow. Special attention is given to how the vortices decay. Two "cascade" processes are identified at moderate and strong flow stratification conditions that quickly destroy the vortex pair. With moderate flow stratification and moderate background turbulence, crow instability leads to vortex reconnection, as suggested by the literature. In an unstratified environment, a vortex ring would form and remain in the flow for a long period of time. At stratified flow conditions, however, a series of subsequent vortex reconnections take place, breaking large vortices into smaller ones. This "cascade" process quickly dissipates the vortices. With strong flow stratification, crow instability cannot cause vortex reconnection, but baroclinic production in the vicinity of the primary vortices gives rise to secondary vortices, and secondary vortices to tertiary vortices, leading to another "cascade" process that quickly dissipates the kinetic energy. |
Monday, November 22, 2021 9:44AM - 9:57AM |
H24.00009: Vertical Aspect Ratios and Longevities of Complex Vortices and the Application to GFD Flows and Astrophysical Vortices Philip S Marcus, Aidi Zhang Theoretical scaling, numerical simulations, and laboratory experiments all show that there is well-defined ratio of the vertical length scale to the horizontal length scale of Gaussian vortices in a rotating, stratified fluid. However, many vortices of interest, especially in GFD, have multiple length scales, e.g., the horizontal major diameter of the Great Red Spot of Jupiter is 10 times greater than its Rossby deformation radius, which sets the horizontal width of its high-speed ring. We examine how theses multiple scales change the aspect ratio and the longevities of vortices, and, in particular, relate these findings to recent Juno satellite observations, which may show that the vertical thickness of the Jovian vortices is significantly greater than a few pressure scale-heights. |
Monday, November 22, 2021 9:57AM - 10:10AM |
H24.00010: Vorticity Dynamics on a Sphere with Discrete Exterior Calculus Pankaj Jagad, Ravi Samtaney Geophysical flows, such as atmospheric flows on planets, are generally approximated as incompressible, inviscid surface flows, and characterized by two-dimensional (2D) turbulence. Evaluating the effect of rotation, in terms of the non-dimensional Rossby number, is important because the planetary rotation forms large scale structures (such as Rossby waves), which affects the direct enstrophy and inverse energy cascades in 2D turbulence. Exterior calculus deals with the calculus on differential geometries, hence differential forms, and provides an alternative to the vector calculus. Discrete exterior calculus (DEC) is numerical exterior calculus and deals with the discrete differential forms. DEC-based discretization methods satisfy discrete analogues of continuous operations of interest, and conservation of key physical quantities such as vorticity is a well-known feature of DEC-base methods. These positive attributes makes DEC an excellent choice for investigating vorticity dynamics. Moreover, the DEC discretization is independent of the coordinate system, and therefore suitable for investigating flows over curved surfaces. Presently, we investigate the effect of rotation on the vorticity dynamics of flows on a unit sphere with a DEC scheme (Jagad et al. Phys. Fluids 2021). We vary the Rossby number from infinity (non-rotating) to 1.30x10-3. Our investigations reveal that rotation diminishes the 2D turbulence cascades although it does not cease the cascade completely, and the zonalization of structures with decreasing Ro is non-monotonic depending on the choice of initial conditions. |
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