Progess iv nov 5

Microstructure-Property

Relationship in Randomly

Packed Mono-sized Structures

ME-8883

TEAM MEMBER: Mahdi Roozbahani, Jie(Jessie) Cao

Nov 5, 2014

STRUCTURE DATASETS

Full Datasets --- Gravitational Sphere Packing Simulation

Samples --- 200 Non-overlapping Random Volumes of 60×60×60 Voxels

TWO POINT STATISTICS

Visualization 2-point Statistics in 2D

2-point statistics of void phase – central slice

(N0. 200 Volume)

TWO POINT STATISTICS

2-point statistics of particle phase – central slice

(N0. 200 Volume)

Visualization 2-point Statistics in 2D

TWO POINT STATISTICS

Visualization 2-point Statistics

Void Phase

(N0. 200 Volume)

TWO POINT STATISTICS

Visualization 2-point Statistics

Solid Phase

(N0. 200 Volume)

PCA ANALYSIS

Evaluate Eigenvalue Results

Cumulative Eigenvalue Explanation

95%

PCA ANALYSIS

Two Point Statistics in PCA Space

First 2 components

First 3 components

STRUCTURE PROPERTY DATA

Permeability --- Transport Property

Permeability Datasets --- Computed using FVM in MATLAB (Ahmet)

Pre

ssu

re

G

ra

die

nt fo

r S

im

ulatio

n

STRUCTURE PROPERTY DATA

Permeability k --- Transport Property

Hydraulic Conductivity K --- K = kρg/μ, assume fluid is water

(m/s)

MICROSTRUCTURE - PROPERTY CORRELATION

Property --- Hydraulic Conductivity K, assume fluid is water

Microstructure --- Randomly Packed Mono-sized Structure (loose)

Hyd

raulic C

onductivity (m

/s)

PC1

Linear model: f(x,y) = p00 + p10*PC1 + p01*PC2

Coefficients (with 95% confidence bounds):

p00 = 0.2595 (0.2583, 0.2606)

p10 = 0.002132 (0.001976, 0.002287)

p01 = 0.0002297 (-0.0002588, 0.0007181)

Goodness of fit

SSE: 0.01297

R-square: 0.788

Adjusted R-square: 0.7858

RMSE: 0.008114

PROBLEMS

1. PCA Analysis

2. Additional Analysis on Binary-sized Structure ?

Cumulative Eigenvalue Explanation

95%

REAL MICRO-STRUCTURE

STRUCTURE PROPERTY DATA

STRUCTURE PROPERTY DATA

REFERENCES

• Roozbahani, M. M., Graham‐Brady, L., & Frost, J. D. (2014). Mechanical trapping

of fine particles in a medium of mono‐sized randomly packed spheres.

International Journal for Numerical and Analytical Methods in Geomechanics.

• Çeçen, A., Fast, T., Kumbur, E. C., & Kalidindi, S. R. (2014). A data-driven

approach to establishing microstructure–property relationships in porous

transport layers of polymer electrolyte fuel cells. Journal of Power Sources,

245, 144-153.

• Mönkeberg, F., & Hiptmair, R. (2012). Finite volume methods for fluid flow in

porous media.

• Aarnes, J. E., Gimse, T., & Lie, K. A. (2007). An introduction to the numerics of

flow in porous media using Matlab. In Geometric Modelling, Numerical

Simulation, and Optimization (pp. 265-306). Springer Berlin Heidelberg.

• Santamarina, J. C., Klein, A., & Fam, M. A. (2001). Soils and Waves: Particulate

Materials Behavior, Characterization and Process Monitoring.

• Spatial Statistics Code From Tony.

• FVM Code From Ahmet.