A mechanical model of normal and anomalous diffusion

The overdamped dynamics of a charged particle driven by an uniform electric field through a random sequence of scatterers in one dimension is investigated. Analytic expressions of the mean velocity and of the velocity power spectrum are presented. These show that above a threshold value of the field normal diffusion is superimposed to ballistic motion. The diffusion constant can be given explicitly. At the threshold field the transition between conduction and localization is accompanied by an anomalous diffusion. Our results exemplify that, even in the absence of time-dependent stochastic forces, a purely mechanical model equipped with a quenched disorder can exhibit normal as well as anomalous diffusion, the latter emerging as a critical property.Comment: 16 pages, no figure

Prediction and Measurement of the local extinction coefficient in sprays for 3D simulation/experiment data comparison

AbstractIn the recent years, large progresses in laser imaging techniques have allowed to extract spatially resolved 2D and 3D quantitative spray information even in optically dense situations. The main breakthrough of these techniques is the possibility of suppressing unwanted effects from multiple light scattering using Structured Illumination. Thanks to this new feature, effects due to light extinction can also be corrected allowing the measurement of the local extinction coefficient. These quantitative information which is available even in challenging conditions, where Phase Doppler does not work anymore, can be used for data comparison between experiment and simulation. The local extinction coefficient is particularly valuable for the description of the droplet field, defined as the “spray region”, as it contains information related to both droplets size and concentration. In this article we detail, then, the procedure enabling the modelers to obtain numerically this local extinction coefficient over the full 3D spray system. Following this procedure, results can now be adequately compared between simulation and experiment. The proposed comparison approach can better guide model adjustments in situation where the initial droplet size distribution is unknown or approximated and presents a step towards future validations of spray simulations, especially those based on Lagrangian Particle Tracking. The approach is exemplified here for the case of a Diesel-type spray. The results reveal at which specific spray locations discrepancies occur, and highlight the sensitivity of the initial droplet size distribution on the resulting extinction coefficient

Sensitivity of VOF simulations of the liquid jet breakup to physical and numerical parameters

AbstractIn this paper the characteristics of the primary breakup of a liquid jet is analyzed numerically. We applied the Volumes of Fluids (VOF) approach utilizing the Direction Averaged Curvature (DAC) model, to estimate the interface curvature, and the Direction Averaged Normal (DAN) model, to propagate the interface. While being used for the first time to predict liquid atomization, this methodology showed a high accuracy. The influence of varying the fluid properties, namely liquid-gas density and viscosity ratio, and injection conditions is discussed related to the required grid resolution. Resulting droplet sizes are compared to distributions obtained through the One-Dimensional Turbulence (ODT) model