atomistic molecular simulations for engineering...

Atomistic molecular simulations

for engineering applications:

methods, tools and results

Jadran Vrabec

Motivation

Simulation methods vary

in their level of detail

The more detail,

the more predictive power

Quantum chemical

methods scale with

O(M3) ─ O(M7)

[M: basis functions]

Force field methods are

favorable with respect to

scaling and thermodynamics

Force fields ─ Thermodynamics

Contain all thermodynamic properties

Static: thermal, caloric, entropic

Dynamic: viscosity, diffusion, thermal conductivity, …

Surface properties, e.g. surface tension

Straightforwardly applicable to mixtures

Excellent predictive power

Technical accuracy

Classical models for molecular interactions

Parameters have a physical interpretation

in geometries, e.g. wetting, adsorption, zeolites, …

in processes, e.g. condensation, flow, …

Directly applicable for the study of fluids

Iso-Butane

Sampling force fields

Molecular dynamics Monte Carlo

ms2: simulation tool for thermodynamic properties

Molecular dynamics / Monte Carlo

Arbitrary mixtures of rigid molecules

Grand equilibrium method (for VLE)

Several classical ensembles

Consistent FORTRAN90 code

Object oriented

All loops vectorized

MD and MC parallelized

3D visualization interface

All static properties (thermal, caloric, entropic)

Gradual insertion for entropic properties

Transport properties (Green-Kubo)

Deublein et al., Comp. Phys. Commun. 182 (2011) 2350

Equation of state for CO2 (Span and Wagner, 1996)

0 ResF, , ,

R T

7

0 0 0 0 0

1 2 3 i i

i 4

, ln a a a ln a ln 1 exp n

i i i i i

7 34t d t d cRes

i i

i 1 i 8

, a a exp

i i

39t d 2 2

i i i i i

i 35

a exp ( ) ( )

Ideal part:

Residual part:

T = 216 … 1100 K, p = 0 … 800 MPa

i

42b 2 2

i i i

i 40

a exp C ( 1) D ( 1)

τ =Tc / T δ = ρ / ρc

Derivatives of the Massieu-Planck potential

)/(RTF mn

nm

nmT

/1 NVT

10

01

20. . .

Any equilibrium thermodynamic property = combination of ´s nm

A total of nine independent

properties sampled per

NVT simulation with ms2

Cyclohexane

Density / mol m-3

Rigid 6CLJ united-atom model by Merker et al., Fluid Phase Equilib. 315 (2012) 77

Cyclohexane

Present simulation data

Span and Wagner, Int. J. Thermophys. 24 (2003) 41

Penoncello et. al., Int. J. Thermophys. 16 (1995) 519

Density / mol m-3

„potential energy“

Cyclohexane

Density / mol m-3

„pressure“




Cyclohexane

Density / mol m-3

„isochoric heat capacity“




Ongoing project with ms2

9 independent thermodynamic data types from one NVT simulation

Generation of an extensive dataset in an automatized fashion

• Parallel execution of (~80 simulation runs) x (9 data points)

Fit of a fundamental EOS in terms of Fres to these data

• EOS may serve for the optimization of the force field

• EOS may be the starting point for technical EOS fitting

Poster T21: Thol, Rutkai, Span, Vrabec:

Molecular simulation of thermodynamic properties and

an equation of state for the Lennard-Jones model fluid

Present status and outlook for ms2

An efficient molecular simulation tool for

thermodynamic properties of homogeneous fluids

New features

Ewald summation for ionic systems

Pair correlations functions

MPI/OpenMP hybrid parallelization

Next development steps

Integer arithmetics

Internal molecular degrees of freedom

Execution on graphics processing units (GPUs)

r / mol/l

0 10 20 30

T / K

300

400

500

600

Dimethyl-hydrazin

Monomethyl- hydrazin

Hydrazin

Force fields for Hydrazine and two derivates

Simulation, this work

Experimental data from the literature +

Simulation, Gutowski et al. 2009

Hydrazine

Monomethyl-

hydrazine

Dimethyl-

hydrazine

e

e

e

Hi /

MP

a

0

500

1000

1500

N2

Ar

Hi /

MP

a

0

5000

10000

15000

20000

T / K

260 280 300

Hi /

MP

a

0

100

200

300

Stickstoff

Argon

Stickstoff

Argon

Stickstoff

Argon

Kohlenstoffmonoxid

Hydrazin

Monomethylhydrazin

Dimethylhydrazine

x,yH2O

/ mol/mol

0.0 0.2 0.4 0.6 0.8 1.0

T / K

370

380

390

VLE and gas solubility of

systems containing Hydrazine,

Monomethylhydrazine

and Dimethylhydrazine

Water + Hydrazine @ 1 bar

Nitrogen

Nitrogen

Nitrogen

e

e

e

Carbon monoxide

Elts et al., Fluid Phase Equilib. 322-323 (2012) 79


Experimental data (literature) +

Peng-Robinson EOS

Poster T37: Merker, Hsieh, Lin, Hasse, Vrabec:

Fluid phase equilibria for the oxidation of cyclohexane in carbon dioxide expanded

liquids from experiment, molecular simulation, Peng-Robinson EOS and COSMO-SAC

VLE and gas solubility of CO2-expanded liqiuds

Cyclohexane (C6H12)

6 LJ sites

Cyclohexanol

(C6H12O)

7 LJ sites +

3 point charges +

H

-

O

+

CH

Cyclohexanol (C6H10O)

7 LJ sites +

point dipole

Oxygen (O2)

2 LJ sites +

point quadrupole

Carbon dioxide (CO2)

3 LJ sites +

point quadrupole

0 5 10 15

devi

ation [%

]

-5

0

5

10

15

20

Poster T12: Dubberke, Vrabec:

Speed of sound of siloxanes as workings fluids in Organic Rankine Cycles

Speed of sound of Hexamethylsiloxane (MM)

365 K

pressure [MPa]

EOS: Colonna et al., 2006

xN2

/ mol/mol

0.00 0.02 0.04 0.06

p /

MP

a

0

4

8

12 30°C

70°C

90°C

126.85°C

50°C

0°C

-30°C-50°C

Acetone

Acetone in N2 and O2 under extreme conditions

Presentation Wed 10:40: Windmann, Köster, Vra.:

Study on vapor-liquid equilibria of nitrogen +

acetone and oxygen + acetone with a focus on the

extended critical region

Massively parallel molecular dynamics code: ls1

Flow

Nucleation

Identical force field types as with ms2

Additionally, Tersoff potential for solids

„Large“ systems, „long“ time scales

Concurrency in space, not in time

Scaling tests on Cray XE6 (Hermit)

Peak performance: 1.045 Pflops 1015 operations / s

Racks: 38 with 96 nodes each

Nodes: 3552

Cores: 113.664 (2 sockets each with 16 cores / node)

Processor: AMD Interlagos @ 2.3 GHz

#12

(November 2011)

Molekülzahl

105 106 107 108

Rechenzeit / s

10

100

1000

Computational effort ~ O(N1)

4.096 cores

1.000 time steps

Scaling of ls1 on Cray XE6 (Hermit)

Molecule number

Execution t

ime /

s

Octree load balancing strategy of ls1

Hierarchical subdivision of the simulation volume through recursive bisection

Choice of planes for bisection that lead to an equal load in the subvolumes

Designed for strongly inhomogeneous molecular systems

Capable to deal with rapidly changing inhomogeneity

Scenarios for scaling tests of ls1

Bulk Droplet Slab

Bulk: homogeneous liquid (Ethylene oxide)

Domain decomposition trivial

Slab: liquid slab surrounded by vapor in equilibrium (Argon)

Topology for domain decomposition simple

Droplet: liquid droplet surrounded by vapor in equilibrium (Argon)

Topology for domain decomposition more complex

Cores

102 103 104 105

Exe

cu

tio

n t

ime

/ s

10

100

1000 Bulk

Film

Tropfen

Strong Scaling

222 = 4.194.304 molecules

Droplet

Slab

1.000 time steps


Cores

102 103 104 105

Exe

cu

tio

n t

ime

/ s

10

100

1000

Bulk

Film

Tropfen

Strong scaling

226 = 67.108.864 molecules

Bulk


1.000 time steps

Droplet

Slab

mole fraction (N2)

0.0 0.2 0.4 0.6 0.8 1.0

pre

ssure

[M

Pa]

0

5

10

15

simulation

equation of state

experimental data

200 K

290 K

ξ = 0.974

VLE of Nitrogen + Ethane

Simulation

Peng-Robinson

Experiment (lit.)

Stoll et al., AIChE J. 49 (2003) 2187

Direct simulation of the LLE

• Mixture of 60 mol-% Nitrogen and 40 mol-% Ethane

• Identical molecular model as before

• 20,000 molecules

• Molecular dynamics with ls1

• Canonical ensemble (NVT)

• Initial configuration with randomly dispersed components

box length [nm]

0 2 4 6 8 10 12 14 16 18

mole

fra

ction

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

N2

C2H6

LLE of N2 + C2H6 after 48 ns

Temperature: 128 K

Pressure: 11.0 MPa

Average over

500,000 time steps

mole fraction of N2 [mol/mol]

0.0 0.2 0.4 0.6 0.8 1.0

tem

pe

ratu

re [

K]

115

120

125

130

135

p = 1.8 to 4.0 MPa,

depending on exp. data

LLE temperature dependence of N2 + C2H6


Experimental data, literature +

mole fraction of N2 [mol/mol]

0.0 0.2 0.4 0.6 0.8 1.0

pre

ssure

[M

Pa

]

0

5

10

15

20

LLE pressure dependence of N2 + C2H6


Experimental data, literature +

T = 127 to 129 K,

depending on exp. data

Poster T25:

Eckelsbach,

Vrabec:

Prediction of

liquid-liquid

equilibria of

nitrogen +

ethane with a

molecular model

that was

adjusted to

vapor-liquid

equilibria

Summary

The computational effort of classical force field methods scales

linearly with the molecule number

Classical force fields contain the thermodynamic properties adequately

Molecular dynamics simulations of inhomogeneous fluids

may efficiently use Petaflop machines

The spectrum of possible applications is very wide

atomistic molecular simulations for engineering...

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