dem simulation of flow of granular particles on an inclined plane in liggghts

7/25/2019 DEM Simulation of Flow of Granular Particles on an Inclined Plane in LIGGGHTS

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DEM simulation of

Flow of Granular Particleson an Inclined plane

in LIGGGHTS

EN 649

Mohit PrateekRoll No. 09D02017

Project Guide: Manaswita Bose



Results and Discussions

Post processing

Simulation

Introduction to geometry and pre simulation values

Introduction to simulation software



LAMMPS is a classical molecular dynamics code,and an acronym for Large-scaleAtomic/Molecular Massively Parallel Simulator.

LAMMPS has potentials for soft materials

(biomolecules, polymers) and solid-statematerials (metals, semiconductors) and coarse-grained or mesoscopic systems. It can be used tomodel atoms or, more generically, as a parallelparticle simulator at the atomic, meso, orcontinuum scale.

LAMMPS also offers a "GRANULAR" package forDEM simulations.

LAMMPS



LIGGGHTS stands for LAMMPS Improved for General Granular

and Granular Heat Transfer Simulations.

As this name implies, it is based on the Open Source MD codeLAMMPS.

LIGGGHTS now brings these DEM features to a new level. Thefollowing features have been implemented on top of theLAMMPS "GRANULAR" features:

A re-write of the contact formulations, including thepossibility to define macroscopic particle cohesion

Import and handling of triangular meshes from CAD A moving mesh feature

Improved particle insertion A model for heat generation and conduction between

particles in contact

LIGGGHTS



Steady flows are obtained in a narrow range ofangles (13 - 14.5 degrees); lower angles result instopping of the flow and higher angles incontinuous acceleration. The flow is relativelydense with the solids volume fraction 0.5 and

significant layering of particles is observed.

The value of stiffness constant for which results forhard and soft particles are identical is found to

be k = 2×

1000000 x mg/d where m is the mass ofa particle, g is the acceleration due to gravityand d is the particle diameter.

Reference: Rheology and Segregation of Granular Mixtures

Anurag Tripathi



Due to a strong analogy between the random motionof the granular particles and the thermal motion ofmolecules in the kinetic-theory picture of gases,fluidized phase of grains is commonly called as a“granular gas” and the mean-squared average valueof the random velocities is commonly referred to as

the “granular temperature”

Simple kinetic theories for rapid granular flows,however had the restriction of small dissipationassumption which stems from the common assumptionthat the granular temperature, T, (isotropic measure of

the velocity fluctuations) is sufficient to completelycharacterize the fluctuation through out the flow(Chou (2000)).

Literature Review



Louge et al. (1990) have performed computer simulationsof rapid granular shear flow between parallel bumpyboundaries and compared their results with theoreticalpredictions of kinetic theory and found that the kinetictheory applies to gaps as small as three particlediameters.

Babic (1993) studied steady gravity driven flow betweenparallel bumpy boundaries and found that the particleflux from theory compared favorably with simulationresults and earlier experiments.

Hsiau and Hunt (1993) performed kinetic theory analysisof flow induced particle diffusion and thermalconduction in granular materials and found differencebetween the theoretical predictions and experimentalmeasurements. Savage and Dai (1993) studied shearflows and found wall layering at higher concentrations.

Literature Review



To account for the frictional interaction between theparticles, Jenkins and Richman (1985) used additionalequation for the conservation of spin energy involvingthe flux of spin energy and couple stress equations, otherthan the mass, linear momentum and translationalenergy balance as in the case of frictionless particles.

Lun and Savage (1987) developed a kinetic theoryformulation for rough particles in the dense limit, wherethe collisional stress is large compared to the kineticstress.

Xu et al. (2003) compared numerical solutions of thekinetic theory with simulations and microgravityexperiments and found that, at least in fully developed,collisional, steady flows with relatively small collisionaldissipation, the solutions of the kinetic theory, subject tothe appropriate boundary conditions, agree well withboth simulations and experimental data.

Literature Review



Pouliquen and Renaut (1996) determined thecritical angle at which particles start to flow downan incline. The critical angle was found toincrease with decrease in initial layer thickness.

Non-dimensional mean velocity (um/gh) was

found to be proportional to the layer thickness (h),when scaled with hstop. Experimentalmeasurements of this critical curve hstop carriedout for different materials and rough bottomsgive the same shape, which can be fitted by anequation

Literature Review



The computational results of Hirshfeld and Rapaport(1997) for a binary mixture of particles with differentsizes in a two-dimensional chute flow under gravityshowed that large particles rise to the top of the layer.

Dury and Ristow (1997) performed soft particle DEMsimulations of a binary mixture of different size disks in ahalf filled two-dimensional rotating drum andinvestigated effect of rotational speed of the drum onthe dynamics of the segregation process.

Rice and Hrenya (2010) studied clusteringphenomenon in mixtures in two-dimensional simple

shear flows using molecular dynamic simulations

Bidisperse spherical particles in a rotating horizontaldrum were studied using Discrete Element Method(DEM) simulations by Arntz et al. (2008).

Literature Review – Simulation Studies



Geometrical Representation*.STL File; Viewed by Paraview



Region of Simulation: 10 cm x 4 cm x 4 cm

SI units

Inclined Plane:Base : 5 cm

Angle: 13.92 degrees

Gravity: 9.81 m/s/s

Pre-Simulation Values



Insertion of 5000 atoms

Diameter: 0.5 mm

Volume Fraction: 0.7Density: 2500

Initial velocity: 0,0,0

Coefficient of Restitution: 0.9

Young's Modulus: 5E6

Poisson's ratio: 0.45

Granular Particle Properties:



• ITEM: ATOMS id type type x y z vx vy vz fx fy fz tqx tqy tqz omegax omegay omegaz radius

First Timestep

254 1 1 -0.0455105 -0.0194732 0.0172402 0 0 -0.271634 0 0 -1.60516e-06 0 0 0 0 0 0 0.00025

346 1 1 -0.0449629 -0.0188075 0.016992 0 0 -0.280454 0 0 -1.60516e-06 0 0 0 0 0 0 0.00025

… … …. … … … … …. … … … … …. … … … …. … … … … …. … … … … …. … … … 0.00025

…. … … … … …. … … … … …. … … … … …. … … … … …. … … … … …. … … … … …. …

Next Timestep

2141 1 1 -0.0435509 -0.018768 0.01721 0 0 -0.272721 0 0 -1.60516e-06 0 0 0 0 0 0 0.00025

4889 1 1 -0.0431077 -0.0196025 0.0169182 0 0 -0.283023 0 0 -1.60516e-06 0 0 0 0 0 0 0.00025

… … …. … … … … …. … … … … …. … … … …. … … … … …. … … … … …. … … … 0.00025

…. … … … … …. … … … … …. … … … … …. … … … … …. … … … … …. … … … … …. …

Simulation*.DUMP File; Viewed by VMD



Simulation Video*.DUMP File; Viewed by VMD

• The video file can be viewed at the given link:

https://dl.dropbox.com/u/19552558/Video_EN_649_Mohit_Prateek.avi





Post

Processing

SCILAB



L E V E L 2L E V E L 1

FUNCTIONS

MAKE3D.SCI

REMOVEX.SCI

SORTBYCOLUMN.SCI



MAKE3D.SCI

function [M2]=make3d(M,division_size) [rows, column] =size(M);

ds = division_size;

M2 = M(1:ds,:,:);

for i = 2:(rows/ds)

M2(:,:,i) = M(((i*ds)-(ds-1)):(i*ds),:,:);

end

returnendfunction

function [Mx2]=removex(Mx)len = length(Mx(:,4));

for i = 10:10:len

if Mx(i,4) > 0.05 then

Mx = Mx(i:len,:);

i = i - 10;else break;

end

len = length(Mx(:,4));

end Mx2 = Mx;

returnendfunction

REMOVEX.SCI

Function Description



SORT_COLUMN_ROWWISE2D.SCI

function [A,k ]=sort_column_rowwise2d(a,column_number)

cs = column_number;

[B,k ]=gsort(a(:,cs),'g');

[r,c] = size(a);A = rand(r,c);

for i = 1:r

A(i,:) = a (k (i),:);

end

returnendfunction

function mohitplot()a=gca();

a.font_size=2;

poly1= a.children.children(1);

poly1.thickness = 3;a.title.font_size = 5;a.x_label.font_size = 3.5;a.y_label.font_size = 3.5;

xgrid

endfunction

MOHITPLOT.SCI

Function Description



Read File using fscanfMat()

• Convert it into a hypermatrix

• Extract different values from the matrix like id, velocity, omega

Calculate Quantities required

• V = sqrt(vx.*vx + vy.*vy + vz.*vz);

• F_atom = sqrt(fx.*fx + fy.*fy + fz.*fz);• T_atom = sqrt(tx.*tx + ty.*ty + tz.*tz);

• KE_atom = (1/2)*2500*(4/3*%pi*(0.00025^3))*(vx.*vx + vy.*vy + vz.*vz);

• RE_atom = (1/2)*(2/5)*2500*(4/3*%pi*(0.00025^3))*(0.00025^2)*(ox.*ox + oy.*

• KE_RE_atom = KE_atom + RE_atom



READING FILE

stacksize('max'); // To increasethe limit in Scilab !

M_raw =fscanfMat('Default_edited.flow');

M_raw = M_raw(:,1:18); //Removing radius column !

M = make3d(M_raw,5000); //There is a loss of data after ifthe division size is not a multipleof division size !

[row, column, rc] = size(M);

// Reading file and naming it !id = M(:,1,:);

x = M(:,4,:);y = M(:,5,:);z = M(:,6,:);

vx = M(:,7,:);vy = M(:,8,:);vz = M(:,9,:);fx = M(:,10,:);fy = M(:,11,:);fz = M(:,12,:);tx = M(:,13,:);ty = M(:,14,:);tz = M(:,15,:);ox = M(:,16,:);oy = M(:,17,:);oz = M(:,18,:);// File reading done !

EXTRACTING VALUES

Code Description



FOR SINGLE PARTICLE

// Calculations start !

v = sqrt(vx.*vx + vy.*vy + vz.*vz);

F_atom = sqrt(fx.*fx + fy.*fy + fz.*fz);

T_atom = sqrt(tx.*tx + ty.*ty + tz.*tz);

KE_atom =

(1/2)*2500*(4/3*%pi*(0.00025^3))*(v x.*vx + vy.*vy + vz.*vz);

RE_atom =(1/2)*(2/5)*2500*(4/3*%pi*(0.00025^3))*(0.00025^2)*(ox.*ox + oy.*oy +oz.*oz);

KE_RE_atom = KE_atom + RE_atom;

for i =1:rc

vtotal(i) = sum(v(:,:,i));

KE(i) = sum(KE_atom(:,:,i));

RE(i) = sum(RE_atom(:,:,i));KE_RE(i) =sum(KE_RE_atom(:,:,i));

F(i) = sum(F_atom(:,:,i));

T(i) = sum(T_atom(:,:,i));

end

FOR ALL PARTICLES

Code Description



Graphs

SCILAB

All the graphs are self explanatory,although a few lines have been

included wherever necessary.



L E V E L 4L E V E L 3L E V E L 2L E V E L 1

GRAPHS

WRT TIME

FOR ANGLE 13

FOR ANGLE 20

WRT AXIS

FOR Z’-AXIS

FOR ANGLE 13

FOR ANGLE 20

FOR X’-AXIS

FOR ANGLE 13

FOR ANGLE 20



SAMPLE CODE FOR GENERATING A GRAPH

t = 1:1:rc;

l = 1100;

b = 750;

scf(1);

f=gcf(); // Create a figure

f.figure_size= [l,b];

plot(t,vtotal);

mohitplot();

xtitle("Variation of Velocity with Time", "Time (s)", "Velocity (m/s)");

Code Description



Variation of Velocity with time

The velocity increases with time as expected



Variation of Translational Kinetic Energywith time

The energy increases with time as expected



Variation of Rotational Kinetic Energywith time



Variation of Total Kinetic Energywith time

Here we have shown the variation of Total Kinetic Energy with time which has more orless the same variation as velocity



Variation of Force with timeThere is a huge force initially which is due to the granular particles striking the plane. Afterwards the

force decreases. The peaks in the graph denote the collison with the incline.



Variation of Energy with timeThe below graph shows the variation of all the energies with time for two angles.



Rotate axis using the rotation matrix

• Sort it in increasing or decreasing order of X’ or Z’ axis

• Add these coordinates to the hypermatrix

• Group it into bins of 1000 and calculate a mean for each of them

Calculate Quantities required

• v_mean_x = sqrt(vx_x.*vx_x + vy_x.*vy_x + vz_x.*vz_x);

• F_mean_x = sqrt(fx_x.*fx_x + fy_x.*fy_x + fz_x.*fz_x);

• T_mean_x = sqrt(tx_x.*tx_x + ty_x.*ty_x + tz_x.*tz_x);

• KE_mean_x = (1/2)*2500*(4/3*%pi*(0.00025^3))*(vx_x.*vx_x + vy_x.*vy_x + v

• RE_mean_x = (1/2)*(2/5)*2500*(4/3*%pi*(0.00025^3))*(0.00025^2)*(ox_x.*ox_

oy_x.*oy_x + oz_x.*oz_x);

• KE_RE_mean_x = KE_mean_x + RE_mean_x;



ROTATING AND ADDING TO THE

HYPERMATRIX

// Rotating the axis !theta = 13.93*%pi/180;

x1 = x*cos(theta) - z*sin(theta);y1 = y;

z1 = x*sin(theta) + z*cos(theta);// Done rotating

M(:,19,:) = x1;M(:,20,:) = y1;M(:,21,:) = z1;M_raw(:,19) = x1;M_raw(:,20) = y1;M_raw(:,21) = z1;

[Mx, sort_index] = sort_column_rowwise2d(M_raw, 19); //Sorting in decreasing oreder of x' coordinate

for i = 1:279 xmean(i) = mean(Mx(((i-1)*500+1):(i*500),19));

vx_x(i) = mean(Mx(((i-1)*500+1):(i*500),7));vy_x(i) = mean(Mx(((i-1)*500+1):(i*500),8));vz_x(i) = mean(Mx(((i-1)*500+1):(i*500),9));fx_x(i) = mean(Mx(((i-1)*500+1):(i*500),10));fy_x(i) = mean(Mx(((i-1)*500+1):(i*500),11));fz_x(i) = mean(Mx(((i-1)*500+1):(i*500),12));tx_x(i) = mean(Mx(((i-1)*500+1):(i*500),13));ty_x(i) = mean(Mx(((i-1)*500+1):(i*500),14));tz_x(i) = mean(Mx(((i-1)*500+1):(i*500),15));ox_x(i) = mean(Mx(((i-1)*500+1):(i*500),16));oy_x(i) = mean(Mx(((i-1)*500+1):(i*500),17));oz_x(i) = mean(Mx(((i-1)*500+1):(i*500),18));

End

v_mean_x = sqrt(vx_x.*vx_x + vy_x.*vy_x + vz_x.*vz_x);F_mean_x = sqrt(fx_x.*fx_x + fy_x.*fy_x + fz_x.*fz_x);T_mean_x = sqrt(tx_x.*tx_x + ty_x.*ty_x + tz_x.*tz_x);KE_mean_x =

(1/2)*2500*(4/3*%pi*(0.00025^3))*(vx_x.*vx_x +vy_x.*vy_x + vz_x.*vz_x);

RE_mean_x =(1/2)*(2/5)*2500*(4/3*%pi*(0.00025^3))*(0.00025^2)*(ox

_x.*ox_x + oy_x.*oy_x + oz_x.*oz_x);

KE_RE_mean_x = KE_mean_x + RE_mean_x;

GROUPING AND CALCULATING

Code Description



L E V E L 4L E V E L 3L E V E L 2L E V E L 1

GRAPHS

WRT TIME

FOR ANGLE 13

FOR ANGLE 20

WRT AXIS

FOR Z’-AXIS

FOR ANGLE 13

FOR ANGLE 20

FOR X’-AXIS

FOR ANGLE 13

FOR ANGLE 20



Variation of Velocity along the inclineThe velocity increases continuously. There is a slight downfall at 0.05 which is due to the

particles striking the ground and hence the removal of acceleration.

V i ti f T l ti l Ki ti E



Variation of Translational Kinetic Energyalong the incline

It varies almost same as the velocity.

V i ti f R t ti l Ki ti E



Variation of Rotational Kinetic Energyalong the incline

As we can see, Rotational energy increases along the inclinewith a sudden increase at0.05 m due to the collision with the ground

V i ti f T t l Ki ti E



Variation of Total Kinetic Energyalong the incline

Here we have shown the variation of Total Kinetic Energy which has more or less the same variation as velocity



Variation of Force along the inclineThe huge peak that we see at 0.01 is the point at which the incline ends and particles strike the ground, which explains

why the huge force. Apart from that, the force reamins constant along the inlcine since there is no interaction withthe incline.



Variation of Energy along the incline

Variation of Velocity normal to the



Variation of Velocity normal to theincline

Variation of Translational Kinetic Energy



Variation of Translational Kinetic Energynormal to the incline

Variation of Rotational Kinetic Energy



Variation of Rotational Kinetic Energynormal to the incline

Variation of Total Kinetic Energy normal



Variation of Total Kinetic Energy normalto the incline

The energy increases since the partciles at top are more free to move compared tothe particles at the bottom of the pile.



Variation of Force normal to the inclineThe huge peak that we see at 0.01 is the point at which the incline ends and particles strike the ground, which explains

why the huge force. Apart from that, the force reamins constant along the inlcine since there is no interaction withthe incline.



Variation of Energy normal to the inclineThe below graph shows the variation of all the energies with time for two angles.



Rheology and Segregation of Granular Mixtures –

Anurag Tripathi, 2010

Velocity correlations in dense gravity-driven granularchute flow - Oleh Baran, Deniz Ertas, and Thomas C.Halsey, 2006

Flow rule of dense granular flows down a rough incline- Tamás Börzsönyi and Robert E. Ecke, 2007

Transition in a dense granular flow - V. Kumaran and S.Maheshwari

Discrete Element Modelling Of Granular Snow Particlesusing LIGGGHTS - Vinodh Vedachalam, 2011

References



Special Thanks To

Prateek MaheshwariAditya TelangChaitanya Wadi



Thank You ! :)

Mohit Prateek

Roll No. 09D02017

dem simulation of flow of granular particles on an inclined plane in liggghts

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