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 L25: Vortex Dynamics and Vortex Flow: Theory |
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Chair: Arman Hemmati, Imperial College London Room: 607 |
Monday, November 25, 2019 1:45PM - 1:58PM |
L25.00001: The motion of buoyant point vortices Anirban Guha, Jeff Carpenter A general formulation is presented for studying the motion of buoyant vortices. It extends the well-known Hamiltonian framework for interacting homogeneous point vortices to include buoyancy effects acting on the vortices. This is then used to systematically examine the buoyant 1-, 2-, and 3-vortex problems. In doing so we find that 2 buoyant vortices may either evolve as a pair in bounded circular orbits, or as two independent unbounded vortices that drift apart, and a criteria is found to distinguish these cases. Special attention is given to the buoyant vortex couple, consisting of two vortices of equal and opposite circulation, and equal buoyancy anomaly. We show that a theoretical maximum height is generally possible for the rise (or fall) of such couples against buoyancy forces. Finally, the possibility and onset of chaotic motions in the buoyant 3-vortex problem is addressed. In contrast to the homogeneous 3-vortex problem, the buoyant vortex system shows evidence that chaos is present. We also demonstrate the chaotic advection of tracer parcels arising from the flow field induced by just 2 buoyant vortices. [Preview Abstract] |
Monday, November 25, 2019 1:58PM - 2:11PM |
L25.00002: Performance of Overset Mesh in Modeling Generic Wakes for Underwater Swimming Suyash Verma, Arman Hemmati The wakes of generic stationary, and oscillating square panels are examined using Overset Grid Assembly (OGA), implemented in OpenFOAM. Using Direct Numerical Simulation (DNS), this study focused on the accuracy and effectiveness of OGA in simulating wake, through combination of multiple meshes for domain and bodies respectively. First, the wake of a stationary square panel is considered at angles of attack between 0$^{\mathrm{o}}$ and 60$^{\mathrm{\thinspace o}}$. The results are compared with the numerical study of Taira et al. (2009) based on Immersed Boundary Method. Then, the wake of a pitching panel is examined at Re$=$2000 and St$=$0.2. Comparing the results with previous numerical (Senturk et al. 2018), and experimental (Buchholz, et.al. 2006) studies, show that the mean drag coefficient are in good agreement, and wake features were captured accurately. This provides sufficient evidence for the high capabilities of overset methodology in analyzing wake physics of sharp-edge bodies in oscillatory, and mixed motion. Future studies on complex shaped bodies are examined by combining fluid structure interaction with OGA, which also enables studying the effect of flexibility on hydrodynamic performance of propulsors. [Preview Abstract] |
Monday, November 25, 2019 2:11PM - 2:24PM |
L25.00003: Evolution of Vortex Dipole Disturbances in Channel Flow Anthony Leonard The initial-value problem for the linearized Navier-Stokes equations for channel flow with mean velocity and mean vorticity given by $\mathbf{U} = (U(y),0,0)$ and $\boldmath{\Omega} = (0,0, -dU(y)/dy)$ is investigated for initial disturbances consisting of vortex dipoles. Approximate analytical solutions to the resulting Orr-Sommerfeld (OS)/ Squire equations are found in terms of special functions, thus avoiding the need of large-scale computation. Under the assumption of linearity, the initial vortex dipole merely travels downstream with the local mean velocity $U(y) $ as a diffusive scalar. However, additional disturbances are produced continually because the quantity $ U''(y) \partial v/\partial x $ appears in the OS equation as a source for transported quantity $ \nabla^2 v$. In turn, $ - U'(y) \partial v/\partial z $ is the source term in the Squire equation for the transported quantity $\omega_y$. We find it particularly effective to represent this additional $v$ field as an expansion in terms of eigenfunctions of the OS equation with complex values of $k_\perp$ ($k_\perp^2 = k_x^2 + k_z^2$). For the inviscid case, e.g., these solutions satisfy \begin{equation} \frac{d^2 v_j}{dy^2} - \frac{U^{\prime \prime}(y) v_j}{U(y) - c} = k^2_ {\perp j}v_j \end{equation} [Preview Abstract] |
Monday, November 25, 2019 2:24PM - 2:37PM |
L25.00004: Tomo-PIV measurements of tethered sphere VIV onset while crossing the Hopf bifurcation Rene van Hout, Lior Eshbal, Daniel Kovalev, David Greenblatt Here, for the first time we examine the transient evolution of the vortical structures in the wake of a tethered sphere as the uniform upstream velocity is slowly increased and the tethered sphere (diameter $D$) dynamics passes through the Hopf bifurcation. Tomo-PIV experiments (at 15Hz) were performed in a closed-loop water tunnel. The volume of interest ($4.5\times6.5\times2.5 D^3$) was located immediately downstream of the sphere. The reduced velocity, $U^* = U/(f_ND$), was stepwise raised from 2.2 to 4.5 in 100s (d$U$/d$t = 4.36\times10^{-4}$m/s), where $U$ is the free-stream velocity, and $f_N$ is the natural frequency of the tethered sphere. Large coherent structures resembling two streamwise oriented, longitudinal ``legs" were observed at $U^*$ = 2.5 while the sphere was stationary. Approaching $U^*$ = 3, hairpin vortices, having a vertical plane of symmetry, were shed, alongside weaker induced hairpins that strengthened with increasing $U^*$. While vertical symmetry was sporadically disturbed, the onset of VIV occurred around $U^*$ = 3.7, peaking at $U^*$ = 4.4, as the plane of symmetry was shifted to the horizontal. [Preview Abstract] |
Monday, November 25, 2019 2:37PM - 2:50PM |
L25.00005: Compressible swirling flow states in diverging or contracting pipes Yuxin Zhang, Noah Cyr, Zvi Rusak, Shixiao Wang The dynamics of inviscid, compressible and axisymmetric swirling flow of a perfect gas in diverging or contracting circular pipes is studied by global analysis techniques and numerical simulations. Inlet flow is described by profiles of circumferential and axial velocities and temperature with a fixed azimuthal vorticity. Outlet flow is a non-reflective zero radial-velocity state. We first solve the columnar flow ODE problem developed by Rusak et al. (2015) for the outlet state as a function of inlet swirl ratio, Mach number and pipe geometry. Several steady states are possible including centerline decelerated velocity states, centerline accelerated velocity, vortex breakdown states and wall-separation states. Numerical simulations using the unsteady and axisymmetric Euler equations are also conducted. They are based on Steger \& Warming (1979) flux-splitting, finite-difference method. Simulations shed light on the stability of the various steady states and their domain of attraction in terms of initial conditions. Results show that increasing inlet Mach number with a fixed geometry delays the appearance of vortex breakdown and wall-separation states to higher swirl levels. Pipe divergence at a fixed Mach number promotes breakdown while pipe contraction induces wall-separation. [Preview Abstract] |
Monday, November 25, 2019 2:50PM - 3:03PM |
L25.00006: New exact solutions of the Euler equation: hybrid equilibria of Stuart vortices and point vortices Vikas Krishnamurthy, Miles Wheeler, Darren Crowdy, Adrian Constantin We present a large class of exact solutions to the planar, steady, incompressible Euler equation. These solutions combine the celebrated Stuart vortices with point vortices to form stationary 'hybrid' equilibria. These equilibria consist of a set of point vortices otherwise surrounded by a sea of everywhere smooth Stuart vorticity. The solutions can be deformed continuously and non-trivially by varying a parameter which appears as a simple integration constant in the theory. Various limits of these solutions result in purely point vortex equilibria in otherwise irrotational flow. It is also possible to construct an infinite sequence of such solutions, with increasing numbers of point vortices. In this talk, we will present several examples as well as a brief outline of the general theory. [Preview Abstract] |
Monday, November 25, 2019 3:03PM - 3:16PM |
L25.00007: The three-dimensional stability of Lamb-Oseen vortex flows in a finite-length pipe Weimin Yuan, Shixiao Wang, Zvi Rusak The 3D viscous flow instability modes that appear on a Lamb-Oseen voretx flow in a finite-length straight, circular pipe are analyzed. This study extends the previous stability analysis of a solid-body rotation flow. Neutral stability lines of the axisymmetric ($m=0$) and spiral ($m=1$) modes are presented in a Reynolds number ($Re$) versus inlet swirl ratio ($\omega$) operational diagrams for various vortex core sizes of Lamb-Oseen vortex flow. The analysis reveals the significant role of the vortex core size on the onset of the dominant flow instability. The vortex is dominated by $m=1$ (spiral) modes for a relatively large vortex core size. This behavior shifts to dominant $m=0$ (axisymmetric) modes for smaller vortex core sizes. The Reynolds-Orr equation is then used to analyze the various production terms of the perturbation's kinetic energy in the vortex core as well as on the pipe boundaries. It is found that for a medium or small core size of the vortex the base flow in the core is actively involved with the perturbation's kinetic energy production in the bulk and onset of axisymmetric instability, while for a large core size the core is much less active. This phenomenon is related to the observed core size effect on the onset of various types of instability modes. [Preview Abstract] |
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