Screening effects in flow through rough channels

A surprising similarity is found between the distribution of hydrodynamic stress on the wall of an irregular channel and the distribution of flux from a purely Laplacian field on the same geometry. This finding is a direct outcome from numerical simulations of the Navier-Stokes equations for flow at low Reynolds numbers in two-dimensional channels with rough walls presenting either deterministic or random self-similar geometries. For high Reynolds numbers, when inertial effects become relevant, the distribution of wall stresses on deterministic and random fractal rough channels becomes substantially dependent on the microscopic details of the walls geometry. In addition, we find that, while the permeability of the random channel follows the usual decrease with Reynolds, our results indicate an unexpected permeability increase for the deterministic case, i.e., ``the rougher the better''. We show that this complex behavior is closely related with the presence and relative intensity of recirculation zones in the reentrant regions of the rough channel.Comment: 4 pages, 5 figure

Analysis of plasma instabilities and verification of the BOUT code for the Large Plasma Device

The properties of linear instabilities in the Large Plasma Device [W. Gekelman et al., Rev. Sci. Inst., 62, 2875 (1991)] are studied both through analytic calculations and solving numerically a system of linearized collisional plasma fluid equations using the 3D fluid code BOUT [M. Umansky et al., Contrib. Plasma Phys. 180, 887 (2009)], which has been successfully modified to treat cylindrical geometry. Instability drive from plasma pressure gradients and flows is considered, focusing on resistive drift waves, the Kelvin-Helmholtz and rotational interchange instabilities. A general linear dispersion relation for partially ionized collisional plasmas including these modes is derived and analyzed. For LAPD relevant profiles including strongly driven flows it is found that all three modes can have comparable growth rates and frequencies. Detailed comparison with solutions of the analytic dispersion relation demonstrates that BOUT accurately reproduces all characteristics of linear modes in this system.Comment: Published in Physics of Plasmas, 17, 102107 (2010

A Method for Thermal Performance Characterization of Ultra-Thin Vapor Chambers Cooled by Natural Convection

Vapor chamber technologies offer an attractive approach for passive cooling in portable electronic devices. Due to the market trends in device power consumption and thickness, vapor chamber effectiveness must be compared with alternative heat spreading materials at ultrathin form factors and low heat dissipation rates. A test facility is developed to experimentally characterize performance and analyze the behavior of ultrathin vapor chambers that must reject heat to the ambient via natural convection. The evaporatorside and ambient temperatures are measured directly; the condenser-side surface temperature distribution, which has critical ergonomics implications, is measured using an infrared (IR) camera calibrated pixel-by-pixel over the field of view and operating temperature range. The high thermal resistance imposed by natural convection in the vapor chamber heat dissipation pathway requires accurate prediction of the parasitic heat losses from the test facility using a combined experimental and numerical calibration procedure. Solid metal heat spreaders of known thermal conductivity are first tested, and the temperature distribution is reproduced using a numerical model for conduction in the heat spreader and thermal insulation by iteratively adjusting the external boundary conditions. A regression expression for the heat loss is developed as a function of measured operating conditions using the numerical model. A sample vapor chamber is tested for heat inputs below 2.5 W. Performance metrics are developed to characterize heat spreader performance in terms of the effective thermal resistance and the condenser-side temperature uniformity. The study offers a rigorous approach for testing and analysis of new vapor chamber designs, with accurate characterization of their performance relative to other heat spreaders

Mathematical modelling of the spread of contamination during fires in forests exposed to radioactive contamination

The paper suggested in the context of the general mathematical model of forest fires [1] gives a new mathematical setting and method of numerical solution of a problem of a radioactive spread above the forest region. Numerical solution of problems of radioactive smoke spread during crown fire in exemplified heat energy release in the forest fire front was found. Heat energy release in the forest fire front was found to cause further radioactive particles spread by the action of wind. In the absence of wind, radioactive smoke particles deposit again on the underlying surface after a time. As a wind velocity increases, these particles are transferred in the ground layer over distances proportional to a wind velocity

Non-Newtonian fluid flow through three-dimensional disordered porous media

We investigate the flow of various non-Newtonian fluids through three-dimensional disordered porous media by direct numerical simulation of momentum transport and continuity equations. Remarkably, our results for power-law (PL) fluids indicate that the flow, when quantified in terms of a properly modified permeability-like index and Reynolds number, can be successfully described by a single (universal) curve over a broad range of Reynolds conditions and power-law exponents. We also study the flow behavior of Bingham fluids described in terms of the Herschel-Bulkley model. In this case, our simulations reveal that the interplay of ({\it i}) the disordered geometry of the pore space, ({\it ii}) the fluid rheological properties, and ({\it iii}) the inertial effects on the flow is responsible for a substantial enhancement of the macroscopic hydraulic conductance of the system at intermediate Reynolds conditions. This anomalous condition of ``enhanced transport'' represents a novel feature for flow in porous materials.Comment: 5 pages, 5 figures. This article appears also in Physical Review Letters 103 194502 (2009

Axisymmetric viscous gravity currents flowing over a porous medium

We study the axisymmetric propagation of a viscous gravity current over a deep porous medium into which it also drains. A model for the propagation and drainage of the current is developed and solved numerically in the case of constant input from a point source. In this case, a steady state is possible in which drainage balances the input, and we present analytical expressions for the resulting steady profile and radial extent. We demonstrate good agreement between our experiments, which use a bed of vertically aligned tubes as the porous medium, and the theoretically predicted evolution and steady state. However, analogous experiments using glass beads as the porous medium exhibit a variety of unexpected behaviours, including overshoot of the steady-state radius and subsequent retreat, thus highlighting the importance of the porous medium geometry and permeability structure in these systems.Comment: 11 pages, 6 figures, 1 tabl

Fluctuating hydrodynamic modelling of fluids at the nanoscale

A good representation of mesoscopic fluids is required to combine with molecular simulations at larger length and time scales (De Fabritiis {\it et. al}, Phys. Rev. Lett. 97, 134501 (2006)). However, accurate computational models of the hydrodynamics of nanoscale molecular assemblies are lacking, at least in part because of the stochastic character of the underlying fluctuating hydrodynamic equations. Here we derive a finite volume discretization of the compressible isothermal fluctuating hydrodynamic equations over a regular grid in the Eulerian reference system. We apply it to fluids such as argon at arbitrary densities and water under ambient conditions. To that end, molecular dynamics simulations are used to derive the required fluid properties. The equilibrium state of the model is shown to be thermodynamically consistent and correctly reproduces linear hydrodynamics including relaxation of sound and shear modes. We also consider non-equilibrium states involving diffusion and convection in cavities with no-slip boundary conditions