Enhanced, passive transport is studied numerically in an oscillating vortex chain with stress-free boundary conditions. The long-range transport is found to be diffusive in the long-time limit with an effective diffusion coefficient D * that peaks dramatically in the vicinity of a few, well-defined resonant frequencies. Superdiffusive transients are also observed for frequencies near these resonant frequencies, with the duration of the transients diverging at the resonant frequencies. Standard analytical techniques based on the Melnikov approximation and on lobe dynamics fail to explain the behavior in the vicinity of these resonant peaks. An alternate explanation is provided, based on flights that have power-law scaling up to a maximum length that also diverges at the resonant frequencies. The long flights for frequencies near the resonant peaks occur because tracers in a lobe return (after an integer number of oscillation periods) to almost precisely the same location in the lobe of another vortex. These periodic orbits correspond to the formation -only at the resonant frequencies -of "tangle islands" within the chaotic region.
Long-range transport is studied numerically in a time-independent, three-dimensional (3D) fluid flow composed of the superposition of two chains of alternating vortices, one horizontal and the other vertical. Tracers in this flow follow chaotic trajectories composed of correlated Lévy flights with varying velocities. Locations of the chaotic regimes in the flow are compared with recent theories of chaos in non-Beltrami 3D flows. Growth of the variance of a distribution of tracers is divided into transient and long-term regimes, each with different growth exponents.
We propose here an experimental investigation of a vortex submitted to a radial perturbation while being compressed. This experiment reproduces a model situation of the complex flows that take place in a real engine cylinder. An isolated tumbling flow is first submitted to an injection of fluid and then compressed and measurements are realised by Particle Image Velocimetry (PIV). The Proper Orthogonal Decomposition is known to be an unbiased method to identify the coherent structures of turbulent flows. It is possible to make this decomposition for a given phase or to create a set of basis functions with the whole set of compression stroke velocity fields. First, the experimental set-up will be presented, then the second part provides the POD principle. Results of phased POD decomposition of the compression of the unperturbated vortex will be presented. Finally results from the time invariant POD will be discussed to study the influence of the jet perturbation in the compression of a vortex.
Both time-dependent and time-invariant Proper Orthogonal Decompositions are performed on LES and PIV data as an initial step in a study of tumble breakdown in in-cylinder flows. Evidence of tumble instability during compression is found in the time-dependent POD of both data sets. Time-invariant POD modes are presented which will be used later in low-dimensional models of these systems.
The objective of this project is to analyze the instability associated with the breakdown of tumble during compression of an internal combustion engine flow. It has been observed that the tumble vortex (a vortex whose axis is perpendicular to the cylinder axis which is produced during intake by an asymmetry of the .alve(s)) becomes unstable during compression and ultimately leads to turbulence near the end of compression. This turbulence leads directly to better engine performance and the possible use of leaner fuel mixtures via faster burning rates.We are using data from two cases of a coarse-meshed LES performed by Dr.Haworth [l] as well as 2D PIV data of a simplified model provided to us by Dr. Boree [Z]. The LES is a motored flow (no combustion) in a cylinder with a single valve and shrouds to induce tumble. The two LES cases correspond to an axisymmetric valve case with shroud and an offset valve case to generate higher tumble during intake. The PIV model consists of a compressible box with an offset rectangular slit giving very high tumble levels. The plane of velocity measurements is in the plane of tumble.Our goal is to use the POD to identify the instability and breakdown of tumble during compression from this data. We expect this instability to resemble that found by Obukhov's group in a rotating tri-axial ellipsoid which is suddenly stopped [3]. Namely, the main vortex rotates to a perpendicular plane from its original location and begins to break up. This system is analogous to our Row in that the order of the length of the axes changes as the piston moves upwards during compression. As the axis of the cylinder becomes smaller than its diameter we expect the main vortex to become unstable and break up into smaller vortices orthogonal to the tumble vortex and to the cylinder axis. As the aspect ratio becomes larger there is not enough room for the vortices, and they break up into even smaller vortices.The time-varying domain of the Row does not allow for the usual POD approach. Instead two different POD methods are used here. The first is a "phase-dependent" POD where the POD is performed at various phases (crank angles) of the flow over all of the cycles. This method gives basis functions
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