Philip Yecko

Viscous modes in two-phase mixing layers

The temporal instability of parallel viscous two-phase mixing layers is studied by adopting a composite error function flow profile such that boundary layers in each fluid sandwich the interface. Linear spectra and neutral stability curves are calculated numerically and the effects of varying the density ratio, viscosity ratio and Weber number are presented. In addition to the interfacial mode two Tollmien–Schlichting type modes are found and attributed to the presence of the two viscous boundary layers. This is important because it is shown that any of these three modes may be the most unstable, depending on parameter values. Mode multiplicity and competition has not yet been thoroughly explored for this problem even though it is essential to the analysis of experiments and to further stability study of flows relevant to breaking up of interfaces.

Transient growth in two-phase mixing layers

Transient growth properties are computed for a two-phase temporal mixing layer of immiscible fluids with interfacial tension. Large transient growth factors are found to occur at short times in parameter regimes characteristic of the primary breakup of a liquid. Optimal growth factors scale with the square of the Reynolds number, as for single-phase flow

Modeling bubbles and droplets in magnetic fluids

We develop, test and apply a volume of fluid (VOF) type code for the direct numerical simulation of two-fluid configurations of magnetic fluids with dynamic interfaces. Equilibrium magnetization and linear magnetic material are assumed and uniform imposed magnetic fields are considered, although extensions to nonlinear materials and to fields with spatio-temporal variability are possible. Models are computed for configurations of bubbles of non-magnetic fluid rising in ferrofluid and droplets of ferrofluid falling through non-magnetic fluid. Bubbles and droplets exhibit similar changes of shape in the presence of vertical fields, due to a combination of elongation along the field lines and the fluid dynamics of ordinary rising or falling at small Bond number. Bubbles become more prolate than droplets under the same parameters and are accordingly found to break up more readily than droplets in stronger fields. Indirect effects are observed, such as the change in rise time and the consequent changes in the flow due to increased Reynolds number.

Set-based corral control in stochastic dynamical systems: Making almost invariant sets more invariant

We consider the problem of stochastic prediction and control in a time-dependent stochastic environment, such as the ocean, where escape from an almost invariant region occurs due to random fluctuations. We determine high-probability control-actuation sets by computing regions of uncertainty, almost invariant sets, and Lagrangian coherent structures. The combination of geometric and probabilistic methods allows us to design regions of control, which provide an increase in loitering time while minimizing the amount of control actuation. We show how the loitering time in almost invariant sets scales exponentially with respect to the control actuation, causing an exponential increase in loitering times with only small changes in actuation force. The result is that the control actuation makes almost invariant sets more invariant.

Stability of layered channel flow of magnetic fluids

The stability of a sheared interface separating a viscous magnetic fluid (ferrofluid) and an ordinary viscous fluid is examined for arbitrary wavelength disturbances using three dimensional linear perturbation theory. The unperturbed state corresponds to a two-layer Poiseuille profile in which a uniform magnetic field of arbitrary orientation is imposed. Coupling between the field and fluid occurs via the magnetic Maxwell stress tensor, formulated here for nonlinear magnetic material, expanding the scope of previous studies of linear media. Neutral curves and stability characteristics at low Reynolds number are presented and analyzed, and are found to depend sensitively on the linear and nonlinear magnetic properties of the material. The stability properties of the flow are shaped by a small set of the least stable modes of the spectrum, a result that evades single mode or potential flow analyses. The gravest modes can be of different character, resembling either interfacial or shear modes, modified by ma...

Two‐phase Shear Instability: Waves, Fingers, and Drops

Abstract: We examine the development of instability for a shear flow made up of two distinct immiscible fluids, taking into account their disparate densities, viscosities, and the possibility of tension acting on the interface that separates them. Linear theory leads to a pair of coupled Orr‐Sommerfeld equations supplemented by the required matching conditions at the interface. The most unstable mode found here is believed to explain the nature of the instability essential to breakup at its onset. In addition, we find a second mode, which can be most unstable in certain situations of interest. Direct numerical simulations are performed for a range of parameter values. At early times, the simulations reveal the linear and nonlinear amplitude growth, verifying the applicability and accuracy of the numerical method over a range of density and viscosity ratios. At later times, the simulations show the development of elongated structures and the subsequent breakup of the heavier fluid into drops.

An Experimental Testbed for Multi-Robot Tracking of Manifolds and Coherent Structures in Flows

In this paper, we describe the development of an experimental testbed capable of producing controllable ocean-like flows in a laboratory setting. The objective is to develop a testbed to evaluate multi-robot strategies for tracking manifolds and Lagrangian coherent structures (LCS) in the ocean. Recent theoretical results have shown that LCS coincide with minimum energy and minimum time optimal paths for autonomous vehicles in the ocean. Furthermore, knowledge of these structures enables the prediction and estimation of the underlying fluid dynamics. The testbed is a scaled flow tank capable of generating complex and controlled quasi-2D flow fields that exhibit wind-driven double-gyre flows. Particle image velocimetry (PIV) is used to extract the 2D surface velocities and the data is then processed to verify the existence of manifolds and Lagrangian coherent structures in the flow. The velocity data is then used to evaluate our previously proposed multi-robot LCS tracking strategy in simulation.Copyright

Vofi — A library to initialize the volume fraction scalar field

Abstract The Vofi library has been developed to accurately calculate the volume fraction field demarcated by implicitly-defined fluid interfaces in Cartesian grids with cubic cells. The method enlists a number of algorithms to compute the integration limits and the local height function, that is the integrand of a double Gauss–Legendre integration with a variable number of nodes. Tests in two and three dimensions are presented to demonstrate the accuracy of the method and are provided in the software distribution with C/C++ and FORTRAN interfaces. Program summary Program title: Vofi Catalogue identifier: AEYT_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEYT_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 94963 No. of bytes in distributed program, including test data, etc.: 1679223 Distribution format: tar.gz Programming language: C, with C++ and FORTRAN interfaces. Computer: Any computer with a C compiler. Operating system: Tested on x86 with Linux (openSUSE 13.1, Ubuntu 12.04) and Mac OS X. Has the code been vectorized or parallelized?: The code does not need any change to be used in parallel with domain decomposition, as done for example in the Paris-Simulator code, http://parissimulator.sf.net , that is massively parallel and uses the Vofi library. Word size: 64 bits Classification: 4.11. Nature of problem: The library computes the volume fraction of a cubic grid cell cut by an interface described by an implicit function. Solution method: The library computes the integration limits along two coordinate directions and the local height function, that is the integrand of a double Gauss–Legendre integration with a variable number of nodes. Restrictions: Cartesian grids with cubic cells. Running time: Fractions of a second for a grid cell cut by the interface.

Small and Adrift with Self-Control: Using the Environment to Improve Autonomy

We present information theoretic search strategies for single and multi-robot teams to localize the source of a chemical spill in turbulent flows. In this work, robots rely on sporadic and intermittent sensor readings to synthesize information maximizing exploration strategies. Using the spatial distribution of the sensor readings, robots construct a belief distribution for the source location. Motion strategies are designed to maximize the change in entropy of this belief distribution. In addition, we show how a geophysical description of the environmental dynamics can improve existing motion control strategies. This is especially true when process and vehicle dynamics are intricately coupled with the environmental dynamics. We conclude with a summary of current efforts in robotic tracking of coherent structures in geophysical flows. Since coherent structures enables the prediction and estimation of the environmental dynamics, we discuss how this geophysical perspective can result in improved control strategies for autonomous systems.

Linear and Nonlinear Incompressible Waves

Waves in fluids are ubiquitous, from the outward propagation of pond ripples, ocean waves crashing ashore, sound and shocks in the air, and so many others that to list them all would be impossible.