Session G10: Vortex Dynamics and Vortex Flows III

Machine learning for classification of vortex patterns generated by pitching and plunging plates

The motion of a flat plate in an oncoming flow can generate a number of different vortex patterns. These include the familiar 2S, P+S, and 2P vortex streets, among others. Such flows are often used as models for studying how fish or other animals swim. Because the particular shape and kinematics of a moving body lead to subtle differences in the vortical structures observed downstream, there is great interest in being able to accurately classify different vortex patterns. In this work, we use machine learning techniques to distinguish between similar vortex patterns generated by different flat plate motions. Specifically, we numerically simulate 2S vortex streets generated by pitching and plunging plates, respectively, at low Reynolds numbers. We look to identify downstream features of the vortex patterns that encode the upstream flat plate motions. Initial results show that using only point measurements of velocity, standard methods such as linear discriminant analysis can accurately distinguish a 2S vortex street generated by a pitching plate from a 2S vortex street generated by a plunging plate.   

Effect of particle moment of inertia on the dynamics and wakes of freely rising cylinders

We perform a numerical study on the two-dimensional motions and wakes of freely rising and falling circular cylinders in quiescent fluid. We show that the amplitude of oscillation and the overall system-dynamics are intricately linked to two parameters: the particle's mass-density relative to the fluid $m^* \equiv \rho_p/\rho_f$, and its relative moment-of-inertia $I^* \equiv {I}_p/{I}_f$. Using over 144 combinations of ${m}^*$ and $I^*$, we comprehensively map out the parameter space covering very heavy ($m^* > 10$) to very buoyant ($m^* < 0.1$) particles at fixed Galileo number (Ga = 500). The entire data collapses into two scaling regimes demarcated by a transitional Strouhal number, $St_t \approx 0.17$. $St_t$ separates a mass-dominated regime from a regime dominated by the particle's moment of inertia. A shift from one regime to the other also marks a gradual transition in the wake-shedding pattern: from the classical $2S$ (2-Single) vortex mode to a $2P$ (2-Pairs) mode of wake vortices. Thus, autorotation, triggered by moment of inertia reduction, can significantly enhance the translational oscillations of freely rising isotropic bodies.   

Permeable disks at low Reynolds numbers

The wake of a permeable disk can be rather exceptional: a toroidal vortex can form and remains stably at a fixed distance from the disk. The streamwise length of the vortex depends on the Reynolds and Darcy numbers. We investigate this fascinating flow for Reynolds numbers from 10 to 130 and Darcy numbers ($Da$) from $10^{-9}$ to $1$. Direct numerical simulations are performed on a 2D grid with axisymmetric boundary conditions. Three flow regimes are observed: for low $Da$ (effectively impervious), the wake is characterized by the presence of a toroidal vortex whose length is approximately equal to that of an impervious disk. For $10^{-6} [Preview Abstract]

Vortex dipole as a mechanism of shedding for inviscid methods

For a sharp edge of arbitrary interior angle it is shown that the physical mechanism of vortex shedding is the existence of a vortex dipole/doublet at the edge. This is obtained by applying the limit of a point vortex approaching the shedding edge while its circulation increases. Then the vortex merges with its image to create the dipole. In the case of a finite body (doubly-connected fluid region), such as an airfoil, this dipole establishes an equivalent bound circulation round the body. However, the complex potential is not actually constructed with a dipole at the trailing edge, but that this hypothetical potential determines the strength of an equivalent bound vortex that represents the effect of the formation of vorticity to be shed. The mechanism of vortex shedding can then be interpreted as a finite portion of the infinite vorticity/circulation of the dipole being ``torn apart,'' with the latter then regenerating with a new strength to instantaneously satisfy the regularized flow condition at the next instance of time. When done in a continuous manner, the result is a shed vortex sheet.   

Tomo-PIV measurements of the flow field in the wake of a sphere

A sphere can be considered as a prototypical 3D bluff body. In order to improve our understanding of its 3D wake flow, a combination of time-resolved planar particle image velocimetry (PIV) and tomographic PIV (tomo-PIV) was implemented. Experiments were performed in a closed-loop water channel facility and sphere Reynolds numbers Re$_{D}$ = UD/$\nu $ = 400, 800, 1200 and 2000, where $U$ is the free-stream velocity, $\nu $ the kinematic viscosity and $D$ the sphere diameter. The measurement volume (Height x Length x Width, 5 x 5 x 1.5 $D^{\mathrm{3}})$ comprised the sphere and the downstream wake. Tomo-PIV snap-shots were correlated with the time-resolved PIV such that the 3D temporal evolution of the shed vortices became clear. At Re$_{D} \quad =$ 400, this procedure revealed shed hairpin vortices having a vertical plane of symmetry in agreement with many dye visualization studies. However, the measurements also revealed weaker induced hairpins resulting from the interaction of the near-wake flow and the surrounding free stream. These induced vortices were not visible in previous dye and smoke visualizations and have only been observed in simulations. Data processing of the data at higher Re$_{D}$ is currently ongoing.   

The leading-edge vortex of swift-wing shaped delta wings

Recent investigations on the aerodynamics of natural fliers have illuminated the significance of the Leading-Edge Vortex (LEV) for lift generation in a variety of flight conditions. In this investigation, a model non-slender delta shaped wing with a sharp leading-edge is tested at low Reynolds Number, along with a delta wing of the same design, but with a modified trailing edge inspired by the wing of a common swift \textit{Apus apus}. The effect of the tapering swift wing on LEV development and stability is compared with the flow structure over the un-modified delta wing model through particle image velocimetry. For the first time, a leading-edge vortex system consisting of a dual or triple LEV is recorded on a swift-wing shaped delta wing, where such a system is found across all tested conditions. It is shown that the spanwise location of LEV breakdown is governed by the local chord rather than Reynolds Number or angle of attack. These findings suggest that the trailing-edge geometry of the swift wing alone does not prevent the common swift from generating an LEV system comparable with that of a delta shaped wing.   

Computational Fluid Dynamics (CFD) simulations of a Heisenberg Vortex Tube

A 3D Computational Fluid Dynamics (CFD) simulation of a Heisenberg Vortex Tube (HVT) is performed to estimate cooling potential with cryogenic hydrogen. The main mechanism driving operation of the vortex tube is the use of fluid power for enthalpy streaming in a highly turbulent swirl in a dual-outlet tube. This enthalpy streaming creates a temperature separation between the outer and inner regions of the flow. Use of a catalyst on the peripheral wall of the centrifuge enables endothermic conversion of para-ortho hydrogen to aid primary cooling. A $\kappa $-$\varepsilon $ turbulence model is used with a cryogenic, non-ideal equation of state, and para-orthohydrogen species evolution. The simulations are validated with experiments and strategies for parametric optimization of this device are presented.   

A regularized vortex-particle mesh method for large eddy simulation

We present recent developments of the remeshed vortex particle-mesh method for simulating incompressible fluid flow. The presented method relies on a parallel higher-order FFT based solver for the Poisson equation. Arbitrary high order is achieved through regularization of singular Green's function solutions to the Poisson equation and recently we have derived novel high order solutions for a mixture of open and periodic domains. With this approach the simulated variables may formally be viewed as the approximate solution to the filtered Navier Stokes equations, hence we use the method for Large Eddy Simulation by including a dynamic subfilter-scale model based on test-filters compatible with the aforementioned regularization functions. Further the subfilter-scale model uses Lagrangian averaging, which is a natural candidate in light of the Lagrangian nature of vortex particle methods. A multiresolution variation of the method is applied to simulate the benchmark problem of the flow past a square cylinder at $\mathrm{Re}=22000$ and the obtained results are compared to results from the literature.   

Viscous-enstrophy scaling law for Navier-Stokes reconnection

Simulations of perturbed, helical trefoil vortex knots and anti-parallel vortices find $\nu$-independent collapse of temporally scaled $(\sqrt{\nu}Z)^{-1/2}$, $Z$ enstrophy, between when the loops first touch at $t_\Gamma$, and when reconnection ends at $t_x$ for the viscosity $\nu$ varying by 256. Due to mathematical bounds upon higher-order norms, this collapse requires that the domain increase as $\nu$ decreases, possibly to allow large-scale negative helicity to grow as compensation for small-scale positive helicity and enstrophy growth. This mechanism could be a step towards explaining how smooth solutions of the Navier-Stokes can generate finite-energy dissipation in a finite time as $\nu\to0$.