We're sorry but this page doesn't work properly without JavaScript enabled. Please enable it to continue.
Feedback

A numerical study of the Navier–Stokes transport coefficients for two-dimensional granular hydrodynamics

00:00

Formal Metadata

Title
A numerical study of the Navier–Stokes transport coefficients for two-dimensional granular hydrodynamics
Title of Series
Number of Parts
63
Author
License
CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
Identifiers
Publisher
Release Date
Language

Content Metadata

Subject Area
Genre
Abstract
A numerical study that aims to analyze the thermal mechanisms of unsteady, supersonic granular flow by means of hydrodynamic simulations of the Navier–Stokes granular equation is reported in this paper. For this purpose, a paradigmatic problem in granular dynamics such as the Faraday instability is selected. Two different approaches for the Navier–Stokes transport coefficients for granular materials are considered, namely the traditional Jenkins–Richman theory for moderately dense quasi-elastic grains and the improved Garzó–Dufty–Lutsko theory for arbitrary inelasticity, which we also present here. Both the solutions are compared with event-driven simulations of the same system under the same conditions, by analyzing the density, temperature and velocity field. Important differences are found between the two approaches, leading to interesting implications. In particular, the heat transfer mechanism coupled to the density gradient, which is a distinctive feature of inelastic granular gases, is responsible for a major discrepancy in the temperature field and hence in the diffusion mechanisms.
Electric power distributionPlain bearingParticle physicsVideoComputer animation
GasMechanical fanLecture/Conference
AerodynamicsCoarse grainingDensityComputer animation
DensityCoarse grainingAerodynamicsEffects unit
DensityPlain bearingPaperOrbital periodCaudill, Rowlett, ScottEffects unitAtomismFlight simulatorForceDensityVideoVolumetric flow rateCut (gems)BauxitbergbauMechanicVertical integrationShake (shingle)Pattern (sewing)Apparent magnitude
TemperatureVertical integrationElectronic componentCocktail party effectPistonHeatParticleParking meterWärmestromdichteTemperatureDiffusionComputer animation
PistonDensityAmplitudePlatingPistonThermodynamic equilibriumImpact eventComputer animation
TemperatureWärmestromdichteNatürliche RadioaktivitätStriking clockDensityTemperatureHeatComputer animation
Scale (map)KümpelnTemperaturePaperVolumetric flow rateTypesettingLecture/ConferenceMeeting/Interview
Transcript: English(auto-generated)
Hello, my name is Lydia Almatan and I'm going to introduce the article called a numerical study of the Navier-Stokes transport coefficient for a two-dimensional granular gas and my co-authors are Professor Jose Antonio Carrillo, Professor Clara Salvena, Professor Vicente Gartho and Professor Torsten Poitian.
In this article we present a numerical study of a two-dimensional granular system comparing the well-known event driven molecular dynamic simulation with two different approaches for the Navier-Stokes transport coefficient for the hydrodynamic simulation. These two approaches are Jenkin-Ritzmann theory, which is considered for moderately
dense quasi-elastic grains and the improved Gartho-Duvty-Lutsko theory, which includes the effect of the inelasticity on the transport coefficient. Previous studies of the Farada instability for inelastic hard disk compared molecular dynamic simulation with the Jenkin-Ritzmann hydrodynamic
simulation, finding a good description of the rapid granular flow. Our aim is to check if one can get a better agreement using improved transport coefficient. This instability appears when a fluid is shaking in vertical direction considering an external force like gravity and
in this video we can see the density field for the three different simulation. MD Jenkin-Ritzmann hydrodynamics and GDL hydrodynamics. When the Farada instability has already formed, this happens after about 50 periods of shaking. We observe a supermonic period dynamics where the period is twice the period of forcing.
We study different quantities to analyze the mechanism of unsteady supersonic granular flow. We are representing a vertical cut of different flow magnitudes as a function of the height in the diameters at a position where the maximum height of the pattern is achieved.
From left to right and from top to bottom, we have represented packing fraction, internal energy, temperature, vertical component heat flux, cooling coefficient and kinetic energy. All of them are scattered with gravity and particles diameters.
Let us draw the attention to the packing fraction and the temperature field. At T0 the piston is going down through the equilibrium position. From that point the GDL prediction is denser than JR in height between 10 and 20 diameters. Then we have the dissolution of the peak and the valley appears.
After that, we have another impact with the plate forming again a peak. The maximum density in MD is smaller than in hydrodynamics. The most striking difference between GDL and JR solution is the temperature. Where at large height the difference is about one order of magnitude.
This is related with the extra term that appears in the heat flux related with the gradient of the density. All these fields are explained in detail and discussed along the paper. The perspective is to understand the role of the extra term that appears in the temperature equation and in other setups as such a
shear flow. Enjoy the reading.