Session L3: Vortex Dynamics: Mixed Applications

Application of Biot-Savart Solver to Predict Axis Switching Phenomena in Finite-Span Vortices Expelled from a Synthetic Jet

The Biot-Savart law is a simple yet powerful inviscid and incompressible relationship between the velocity induced at a point and the circulation, orientation and distance of separation of a vortex line. The authors have developed an algorithm for obtaining numerical solutions of the Biot-Savart relationship to predict the self-induced velocity on a vortex line of arbitrary shape. In this work the Biot-Savart solver was used to predict the self-induced propagation of non-circular, finite-span vortex rings expelled from synthetic jets with rectangular orifices of varying aspect ratios. The solver's prediction of the time varying shape of the vortex ring and frequency of axis switching was then compared with Particle Image Velocimetry (PIV) data from a synthetic jet expelled into a quiescent flow i.e. zero cross flow condition. Conclusions about the effectiveness and limitations of this simple, inviscid relationship are drawn from this experimental data.   

Enhancement of heat transfer by clamped flags in a Poiseuille channel flow.

A pair of flexible flags clamped vertically in a heated channel was numerically modeled to study an enhancement of heat transfer by the clamped flags in a Poiseuille channel flow. The penalty immersed boundary method was adopted to analyze the fluid--structure--thermal interaction between the surrounding fluid and the clamped flags. The dynamics of the clamped flags was categorized into three distinctive modes: a flapping mode, a fully deflected mode, and an irregular mode. The distinctive modes that depended on the relationship between the hydrodynamic force and the restoring force displayed different movement patterns. The flapping mode provided superior thermal performance to the other modes. Vortices generated from the flapping flags swept out the thermal boundary layer and entrained the fluid near channel walls into the channel core flow while passing through the wake periodically. Compared to rigid flags, the flapping flags significantly improved the thermal efficiency. In addition, the effects of channel height and Reynolds number on the thermal efficiency were explored to obtain an optimal parameter set, which presented the highest thermal performance in present study. The flexible flags regarding the optimal parameter set showed an increase of up to 230{\%} in net heat flux, compared to the baseline flow. Dynamic modes decomposition (DMD) method was adopted to examine the correlation between the vorticity and temperature fields.   

Rotation-triggered path instabilities of rising spheres and cylinder

Path-instabilities are a common observation in the dynamics of buoyant particles in flows. However, the factors leading to the onset of oscillatory motion have remained difficult to predict even for simple bodies such as bubbles, spheres and cylinders. In literature, two quantities are considered to control the buoyancy-driven dynamics for isotropic bodies (spheres and cylinders); they are the particle's density relative to the fluid ($\Gamma \equiv \rho _{\mathrm{p}}$/$\rho_{\mathrm{f}})$ and its Galileo number (Ga). In contrast to this picture, we show that buoyant spheres (as well as cylinders) can exhibit dramatically \quad different modes of vibration and wake-shedding patterns under seemingly identical conditions ($\Gamma $ and Ga fixed). These effects stem from the simplest of changes in the mass distribution of the particle (hollow to solid sphere), which changes its rotational inertia. We show that rotation can couple with the particle's translational motion and trigger distinctly different wake-induced oscillatory motions. The present findings also provide an explanation for the wide variation that is witnessed in the dynamics of buoyant isotropic bodies.   

Particle motion in a periodic driving flow. The role of added mass force and the finite size of particles.

The motion of particles in a fluid is an open problem. The main difficulty arises from the fact that hydrodynamical forces acting on a particle depend on the flow properties. In addition, the form and the size of particles must be taken into account. In this work we present numerical results of the particle transport in a periodic driving flow in a channel flushing into an open domain. To study the transport of particles we solve the equation of motion for a spherical particle in which we include the drag, the gravity, the buoyancy, the added mass and the history force. Additionally we include the corrections for a particle of finite size. For solving this equation a knowledge of the velocity field is required. To obtain the velocity field we solve the Navier Stokes and the continuity equations with a finite volume method. In the flow under study a vorticity dipole and a spanwise vortex are present, both have an important influence on the motion of particles. The dipole enhances displacement of particles because flow between vortices behaves like a jet and the spanwise vortex produces the lifting and deposition of particles from/to the bottom. We observe clustering of particles both into the channel and in the open domain as observed in coastal systems.   

Stability and dynamics of electron plasma vortex under external strain

The behavior of two-dimensional vortex structures is of key interest in a number of important physical systems, including geophysical fluids\footnote{\small D.~G.~Dritschel and B.~Legras, {\it Phys. Today} {\bf 46}, 44 (1993).} and strongly magnetized plasmas.\footnote{\small P.~W.~Terry, {\it Rev. Mod. Phys.} {\bf 72}, 1 (2000).} Studied here is the case of an initially axisymmetric vortex subjected to a simple strain flow. Experiments are performed using pure electron plasmas confined in a Penning-Malmberg trap to model the dynamics of an ideal two-dimensional fluid.\footnote{\small C.~F.~Driscoll \textit{et. al.}, {\it Physica C} {\bf 369}, 21 (2002)} Vortex-In-Cell simulations are also conducted to complement the laboratory results. The dynamical behavior and stability threshold of the strained vortex are measured, showing good agreement with Kida's elliptical patch model for relatively flat vorticity profiles\footnote{S.~Kida, {\it J. Phys. Soc. Japan} {\bf 50}, 3517 (1981).}. However, non-flat profiles feature a reduced stability threshold, apparently due to filamentation at the vortex periphery.   

Rotating Wheel Wake

For open wheel race-cars, such as Formula One, or IndyCar, the wheels are responsible for $40\%$ of the total drag. For road cars, drag associated to the wheels and under-carriage can represent $20-60\%$ of total drag at highway cruise speeds. Experimental observations have reported two, three or more pairs of counter rotating vortices, the relative strength of which still remains an open question. The near wake of an unsteady rotating wheel. The numerical investigation by means of direct numerical simulation at $Re_D$=400-1000  is presented here to further the understanding of bifurcations the flow undergoes as the Reynolds number is increased.  Direct numerical simulation is performed using Nektar++, the results of which are compared to those of Pirozzoli et al. (2012). Both proper orthogonal decomposition and dynamic mode decomposition, as well as spectral analysis are leveraged to gain unprecedented insight into the bifurcations and subsequent topological differences of the wake as the Reynolds number is increased.   

Physics of rowing

Synchronization in rowing seems like a crucial condition for those who aim at winning top-level rowing races. However, in nature, one can observe animals with many legs, such as krill, swimming in a desynchronized manner which is nearly metachronal. From a physicist point of view, rowing by following a metachronal wave also seems like a great idea because, at high Reynolds number, the metachronal gait has one big advantage over the synchronized gait: it reduces the fluctuations of speed and thus the drag on the body. In this experimental study, we have built a scale model of a rowing boat to deal with the question of the effect of synchronization on the boat performance.