Dataset Information

Foam-liquid front motion in Eulerian coordinates.

ABSTRACT: A mathematical model formulated as a system of Hamilton-Jacobi equations describes implicitly the propagation of a foam-liquid front in an oil reservoir, as the zero-level set of the solution variable. The conceptual model is based on the 'pressure-driven growth' model in Lagrangian coordinates. The Eulerian mathematical model is solved numerically, where the marching is done via a finite volume scheme with an upwind flux. Periodic reinitialization ensures a more accurate implicit representation of the front. The numerical level set contour values are initially formed to coincide with an early time asymptotic analytical solution of the pressure-driven growth model. Via the simulation of the Eulerian numerical model, numerical data are obtained from which graphical representations are generated for the location of the propagating front, the angle that the front normal makes with respect to the horizontal and the front curvature, all of which are compared with the Lagrangian model predictions. By making this comparison, it is possible to confirm the existence of a concavity in the front shape at small times, which physically corresponds to an abrupt reorientation of the front over a limited length scale.

SUBMITTER: Torres-Ulloa C

PROVIDER: S-EPMC6304017 | biostudies-literature | 2018 Dec

REPOSITORIES: biostudies-literature

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Publications

Foam-liquid front motion in Eulerian coordinates.

Torres-Ulloa C C Berres S S Grassia P P

Proceedings. Mathematical, physical, and engineering sciences 20181212 2220

A mathematical model formulated as a system of Hamilton-Jacobi equations describes implicitly the propagation of a foam-liquid front in an oil reservoir, as the zero-level set of the solution variable. The conceptual model is based on the 'pressure-driven growth' model in Lagrangian coordinates. The Eulerian mathematical model is solved numerically, where the marching is done via a finite volume scheme with an upwind flux. Periodic reinitialization ensures a more accurate implicit representation ...[more]

PMID: 30602926

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Project description:Rotating machinery condition monitoring and fault diagnosis are important bases for maintenance decisions, as the vibrations generated during operation are usually imperceptible to the naked eye. Eulerian video motion magnification (EVMM) can reveal subtle changes and has been widely used in various fields such as medicine, structural analysis, and fault diagnosis, etc. However, the method has a bound relationship among three parameters: spatial wavelength, amplification factor, and displacement function, so it is necessary to adjust the parameters manually in practical applications. In this paper, on the basis of the original method, an automatic solution of spatial cutoff wavelength based on brightness is proposed. First, an input video is decomposed into image sequences, their RGB color spaces are transformed into HSV color spaces, and the Value channel image representing brightness is selected to automatically calculate the spatial cutoff frequency, and then the spatial cutoff wavelength is determined, and the motion magnification video in the specified frequency band is obtained by substituting it into the original method. Then, a publicly available video is taken as an example for simulation analysis. By comparing the time-brightness curves of the three videos (original video, motion magnification video obtained by the original method and the improved method), it is apparent that the proposed method exhibits the most significant brightness variation. Finally, taking an overhung rotor-bearing test device as the object, five conditions are set, respectively: normal, rotor unbalance, loosened anchor bolt of the bearing seat, compound fault, rotor misalignment. The proposed method is adopted to magnify the motion of the characteristic frequency bands including 1X frequency and 2X frequency. The results show that no obvious displacement is found in normal working conditions, and that the rotor unbalance fault has an overall axial shaking, the bearing seat at the loose place has an obvious vertical displacement, while the compound fault combines the both fault characteristics, and the rotor misalignment fault has an obvious axial displacement of the free-end bearing seat. The method proposed in this paper can automatically obtain the space cutoff wavelength, which solves the problem of defects arising from manually adjusting the parameters in the original method, and provides a new method for rotating machinery fault diagnosis and other fields of application.

Dataset Information

Foam-liquid front motion in Eulerian coordinates.

Publications

Foam-liquid front motion in Eulerian coordinates.

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