Contour line | EPFL Graph Search

A contour line (also isoline, isopleth, isoquant or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. It is a plane section of the three-dimensional graph of the function f(x,y) parallel to the (x,y)-plane. More generally, a contour line for a function of two variables is a curve connecting points where the function has the same particular value. In cartography, a contour line (often just called a "contour") joins points of equal elevation (height) above a given level, such as mean sea level. A contour map is a map illustrated with contour lines, for example a topographic map, which thus shows valleys and hills, and the steepness or gentleness of slopes. The contour interval of a contour map is the difference in elevation between successive contour lines. The gradient of the function is always perpendicular to the contour lines. When the l

Large Eddy Simulations of sediment entrainment induced by a lock-exchange gravity current

Carmelo Juez Jiménez, Foteini Kyrousi, Alessandro Leonardi, Jessica Zordan

Large Eddy simulations of lock-exchange gravity currents propagating over a mobile reach are presented. The numerical setting allows to investigate the sediment pick up induced by the currents and to study the underlying mechanisms leading to sediment entrainment for different Grashof numbers and grain sizes. First, the velocity field and the bed shear-stress distribution are investigated, along with turbulent structures formed in the flow, before the current reaches the mobile bed. Then, during the propagation of the current above the erodible section of the bed the contour plots of the entrained material are pre- sented as well as the time evolution of the areas covered by the current and by the sediment at this section. The numerical outcomes are compared with experimental data showing a very good agreement. Overall, the study confirms that sediment pick up is prevalent at the head of the current where the strongest turbulence occurs. Further, above the mobile reach of the bed, settling process seems to be of minor importance, with the entrained material being advected downstream by the current. Additionally, the study shows that, although shear stress is the main mechanism that sets particles in motion, turbu- lent bursts as well as vertical velocity fluctuations are also necessary to counteract the falling velocity of the particles and maintain them into suspension. Finally, the analysis of the stability conditions of the current shows that, from one side, sediment concentration gives a negligible contribution to the stability of the front of the current and from the other side, the stability conditions provided by the current do not allow sediments to move into the ambient fluid.

2018

Endoscopic low coherence interferometry applied to tri-dimensional contouring of upper airways

Yves Delacrétaz

This thesis presents a novel approach for optical tri-dimensional contouring, requiring only one acquisition to extract a contour depth. It is based on an interferometric setup, using a reduced coherence light source, and is fully adaptable to endoscopic procedure commonly in used in ear-nose-throat (ENT) medicine. It has been demonstrated that the method can be successfully applied to imaging of porcine upper airways. Although this method uses interferometry to obtain depth range measurement, the phase signal is not directly evaluated, rather the location of the coherent superposition of two waves is extracted, and thus provides a robust technique even in harsh environment. The key feature is to extract the coherent area on the image by locating intentionally induced fringes created by off-axis superposition of a smooth reference wave and an object wave coming from a rough or diffusing sample through an optical system with limited aperture. A model for the propagation of the light through the optical system has been developed. It takes into account the broadened emission spectrum of the light source, as well as the statistical speckle effect induced by the illumination of a rough surface with partially coherent light. Simulated results have been carefully compared with measurements, both in the spatial domain and in the Fourier domain (spatial frequencies response), which has permitted to better understand the processes involved in the creation of the interference fringes, and improve the design of the device. Different filters have been investigated in order to extract the depth information from acquired interferograms. By using Gabor filterbanks, which do not need any a priori knowledge of the signal, selectivity of the extracted signal has been enhanced by a factor of 1.3 compared to a simple local Fourier spectrum evaluation, and time of the extraction procedure divided by 6, even when compared to fast iterative calculation in the Fourier spectrum. Moreover, by imposing the frequency and/or orientation of the signal to detect, which can be known by a simple calibration procedure, it has been proved that the selectivity can be further enhanced by a factor of 2.5, keeping the calculation time as short or even shorter. A compact prototype has been designed and built, with a specific multiple fibers arrangement for illumination. The system is separated in two parts: the first one is directly attached to the rigid endoscope, and contains imaging as well as recombining object/reference wave optics, and the detector. It fits into a box with overall dimensions of 115 × 83 × 94 mm. The second part contains the laser source, the scanning arm and the injection optics for the fibered system. It is designed to be left on a small cart. This device can potentially be brought to the bedside, and used during routine endoscopic check-up. Associated with the device, a complete framework has been elaborated in order to simplify the acquisition procedure as well as the signal processing. This results in a fully automated environment taking in charge hardware control, data storage and signal processing, up to the tri-dimensional scene rendering.

EPFL2009

Evolution of the vorticity distribution in vortex rings

Guillaume de Guyon-Crozier

Vortex rings are very efficient at transporting fluid on long distances and can generate large forces, either thrust or drag. These abilities are influenced by the vorticity distribution within the vortex. Previous work on vortices produced by piston-cylinders showed that the vorticity distribution reaches a steady state when the vortex separates from the apparatus. First, we experimentally investigate the evolution of the vorticity distribution independently of the vortex separation. The vortices are created by impulsively accelerating cones immersed in water. In this configuration, the self-induced velocity of the vortex is directed towards the cone and there is no separation. Particle image velocimetry is carried on at Reynolds numbers around 30000. The vorticity distribution is quantified using the non-dimensional energy of the vortex, which is the energy with respect to the impulse and circulation. After three convective times, the volume of fluid recirculating within the vortex ring is filled with vortical fluid and the non-dimensional energy to a value around 0.3. The vorticity produced on the cone circumvents the vortex and a portion of the vortex volume is lost via tail-shedding. The translational velocity of the vortex ring linearly depends on its circulation and non-dimensional energy. This velocity, relative to the cone, also converges after three convective times and is found to be a more reliable scaling parameter than energy or circulation. It consistently reaches values around 0.9. In a second part, we present models to predict the vortex growth in the wake of disks and cones. Two models are developed. The first model reduces the vortex ring to a core of constant vorticity density. The translational velocity of the vortex is deduced and its trajectory integrated. The model accurately predicts the maximum circulation of the vortex. A second model, based on axisymmetric discrete vortex methods, predicts the growth, vorticity distribution and tail-shedding of the vortex. A third model is developed to explain why the non-dimensional energy consistently converges to values around 0.3. Based on the self similar roll-up of inviscid shear layers, a non-dimensional energy of 0.33 is computed for vortices formed by impulsively accelerated disks or pistons. The model also predicts that a linear acceleration profile leads to a more uniform vorticity distribution, decreasing the non-dimensional energy to 0.18. This result indicates that the vorticity distribution can be controlled by varying the velocity profile of the vortex generator. Another control option is to use permeable disks. We impulsively accelerated perforated disks and observed the vortex formation. A portion of the incoming flow bleeds through the disk and does not circulate around the disk edge, resulting in a lower vorticity maximum. The vortex ring has a more uniform vorticity distribution, as well as a more elongated shape. The non-dimensional energy is brought down to 0.14. Finally, vortex rings have a great potential to transport fluid on long distances, such as extinguishing powder. Their resilience to vortical perturbations is critical for the transport and depends on the vorticity distribution within the vortex. Simulations with nested contour methods are performed to assess that resilience. Vortices with lower non-dimensional energy shed less vortical volume when facing perturbations and qualify as better candidates for fluid transport.

EPFL2021