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PROF. DR.-ING. HABIL. JADRAN VRABEC THERMODYNAMIK UND ENERGIETECHNIK INSTITUT FÜR VERFAHRENSTECHNIK ThEt VI. International Conference on Computational Fluid Dynamics Molecular simulation of fluid dynamics on the nanoscale St. Petersburg, July 16, 2010 M. Horsch, Y.-Tz. Hsiang, Z. Liu, S. K. Miroshnichenko, J. Zhai, J. Vrabec Universität Paderborn (IVT) Universität Stuttgart (ITT), National Cheng Kung University (國立成功大學)

Molecular simulation of fluid dynamics on the nanoscalehorsch/pdt/slides/2010_ICCFD2.pdf · PROF.DR.-ING.HABIL. JADRAN VRABEC THERMODYNAMIK UND ENERGIETECHNIK INSTITUT FÜR VERFAHRENSTECHNIK

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Page 1: Molecular simulation of fluid dynamics on the nanoscalehorsch/pdt/slides/2010_ICCFD2.pdf · PROF.DR.-ING.HABIL. JADRAN VRABEC THERMODYNAMIK UND ENERGIETECHNIK INSTITUT FÜR VERFAHRENSTECHNIK

PROF. DR.-ING. HABIL. JADRAN VRABECTHERMODYNAMIK UND ENERGIETECHNIK

INSTITUT FÜRVERFAHRENSTECHNIK

ThEt

VI. International Conference on Computational Fluid Dynamics

Molecular simulation of fluid dynamics

on the nanoscale

St. Petersburg, July 16, 2010

M. Horsch, Y.-Tz. Hsiang, Z. Liu, S. K. Miroshnichenko, J. Zhai, J. Vrabec

Universität Paderborn (IVT)

Universität Stuttgart (ITT), National Cheng Kung University (國立成功大學)

Page 2: Molecular simulation of fluid dynamics on the nanoscalehorsch/pdt/slides/2010_ICCFD2.pdf · PROF.DR.-ING.HABIL. JADRAN VRABEC THERMODYNAMIK UND ENERGIETECHNIK INSTITUT FÜR VERFAHRENSTECHNIK

PROF. DR.-ING. HABIL. JADRAN VRABECTHERMODYNAMIK UND ENERGIETECHNIK

INSTITUT FÜRVERFAHRENSTECHNIK

ThEt

Simulation scenario: Poiseuille flow

Poiseuille flow:

The fluid and a

single wall are

accelerated in

opposite directions

Couette flow:

Two walls are

accelerated in

opposite directions

z

z

-z

Page 3: Molecular simulation of fluid dynamics on the nanoscalehorsch/pdt/slides/2010_ICCFD2.pdf · PROF.DR.-ING.HABIL. JADRAN VRABEC THERMODYNAMIK UND ENERGIETECHNIK INSTITUT FÜR VERFAHRENSTECHNIK

PROF. DR.-ING. HABIL. JADRAN VRABECTHERMODYNAMIK UND ENERGIETECHNIK

INSTITUT FÜRVERFAHRENSTECHNIK

ThEt

Simulation scenario: Couette flow

z

-z

Poiseuille flow:

The fluid and a

single wall are

accelerated in

opposite directions

Couette flow:

Two walls are

accelerated in

opposite directions

Page 4: Molecular simulation of fluid dynamics on the nanoscalehorsch/pdt/slides/2010_ICCFD2.pdf · PROF.DR.-ING.HABIL. JADRAN VRABEC THERMODYNAMIK UND ENERGIETECHNIK INSTITUT FÜR VERFAHRENSTECHNIK

PROF. DR.-ING. HABIL. JADRAN VRABECTHERMODYNAMIK UND ENERGIETECHNIK

INSTITUT FÜRVERFAHRENSTECHNIK

ThEt

y coordinate in units of nm2 4 6

fluid

density in u

nits o

f m

ol/l

0

10

20

30 0.42 - 0.48 ns0.06 - 0.12 ns

T = 175 K; r = 18.4 mol/l; h = 3 nm; W = 0.353; d = 0.947

Short-range ordering in a nanochannel

LJTS (CH4)

Page 5: Molecular simulation of fluid dynamics on the nanoscalehorsch/pdt/slides/2010_ICCFD2.pdf · PROF.DR.-ING.HABIL. JADRAN VRABEC THERMODYNAMIK UND ENERGIETECHNIK INSTITUT FÜR VERFAHRENSTECHNIK

PROF. DR.-ING. HABIL. JADRAN VRABECTHERMODYNAMIK UND ENERGIETECHNIK

INSTITUT FÜRVERFAHRENSTECHNIK

ThEt

Flow regulation

1000000 2000000 3000000

flu

id a

cce

lera

tio

n in

LJ u

nits

-0.0005

0.0000

0.0005

0.0010

Poiseuille flow of LJTS (Argon) in a graphite slit pore, T = 0.85 /k, h = 24 , = s

da/dt = -2

[U + v(t-t´) - 2v(t)]; t´ = 61.2

d /dt = 1/2

; = 0.00361

simulation time step (corresponding to 1.0 fs)

1000000 2000000 3000000ave

rage

flu

id v

elo

city in

LJ u

nits

-0.05

0.00

0.05

0.10

1/32

Page 6: Molecular simulation of fluid dynamics on the nanoscalehorsch/pdt/slides/2010_ICCFD2.pdf · PROF.DR.-ING.HABIL. JADRAN VRABEC THERMODYNAMIK UND ENERGIETECHNIK INSTITUT FÜR VERFAHRENSTECHNIK

PROF. DR.-ING. HABIL. JADRAN VRABECTHERMODYNAMIK UND ENERGIETECHNIK

INSTITUT FÜRVERFAHRENSTECHNIK

ThEt

Poiseuille flow of methane in a graphite channel

Page 7: Molecular simulation of fluid dynamics on the nanoscalehorsch/pdt/slides/2010_ICCFD2.pdf · PROF.DR.-ING.HABIL. JADRAN VRABEC THERMODYNAMIK UND ENERGIETECHNIK INSTITUT FÜR VERFAHRENSTECHNIK

PROF. DR.-ING. HABIL. JADRAN VRABECTHERMODYNAMIK UND ENERGIETECHNIK

INSTITUT FÜRVERFAHRENSTECHNIK

ThEt

y coordinate in units of nm0 2 4 6 8

density

in u

nits o

f m

ol/l

0

10

20

30

40

50

60

0

10

20

30

40

50

60

velo

city in

units

of m

/s

center walld

Poiseuille flow: Velocity profile

Page 8: Molecular simulation of fluid dynamics on the nanoscalehorsch/pdt/slides/2010_ICCFD2.pdf · PROF.DR.-ING.HABIL. JADRAN VRABEC THERMODYNAMIK UND ENERGIETECHNIK INSTITUT FÜR VERFAHRENSTECHNIK

PROF. DR.-ING. HABIL. JADRAN VRABECTHERMODYNAMIK UND ENERGIETECHNIK

INSTITUT FÜRVERFAHRENSTECHNIK

ThEt

y coordinate in units of nm-4 -2 0 2 4 6 8

density in u

nits o

f m

ol/l

0

10

20

30

40

50

60

0

10

20

30

40

50

60

velo

city

in u

nits

of m

/s

wall center walld

Poiseuille flow: Velocity profile

Page 9: Molecular simulation of fluid dynamics on the nanoscalehorsch/pdt/slides/2010_ICCFD2.pdf · PROF.DR.-ING.HABIL. JADRAN VRABEC THERMODYNAMIK UND ENERGIETECHNIK INSTITUT FÜR VERFAHRENSTECHNIK

PROF. DR.-ING. HABIL. JADRAN VRABECTHERMODYNAMIK UND ENERGIETECHNIK

INSTITUT FÜRVERFAHRENSTECHNIK

ThEt

y coordinate in units of nm-4 -2 0 2 4 6 8

velo

city

in u

nits o

f m

/s

0

10

20

30

40

50

60wall wall

vslip = 40 m/s

rslip = 3.7 nm

d

Poiseuille flow: Velocity profile

Page 10: Molecular simulation of fluid dynamics on the nanoscalehorsch/pdt/slides/2010_ICCFD2.pdf · PROF.DR.-ING.HABIL. JADRAN VRABEC THERMODYNAMIK UND ENERGIETECHNIK INSTITUT FÜR VERFAHRENSTECHNIK

PROF. DR.-ING. HABIL. JADRAN VRABECTHERMODYNAMIK UND ENERGIETECHNIK

INSTITUT FÜRVERFAHRENSTECHNIK

ThEt

y coordinate in units of 20 30 40 50 60

velo

city

in u

nits o

f m

1/2-1

/2

0.00

0.05

0.10

0.15

0.20

0.25wallwall

vslip = 0.091 m1/2-1/2

rslip = 23

d

Couette flow: Velocity profile

Argon (LJTS)

T = 0.85 ε

μ = μs(T)

Page 11: Molecular simulation of fluid dynamics on the nanoscalehorsch/pdt/slides/2010_ICCFD2.pdf · PROF.DR.-ING.HABIL. JADRAN VRABEC THERMODYNAMIK UND ENERGIETECHNIK INSTITUT FÜR VERFAHRENSTECHNIK

PROF. DR.-ING. HABIL. JADRAN VRABECTHERMODYNAMIK UND ENERGIETECHNIK

INSTITUT FÜRVERFAHRENSTECHNIK

ThEt

Properties of nanoscopic Poiseuille flow

Page 12: Molecular simulation of fluid dynamics on the nanoscalehorsch/pdt/slides/2010_ICCFD2.pdf · PROF.DR.-ING.HABIL. JADRAN VRABEC THERMODYNAMIK UND ENERGIETECHNIK INSTITUT FÜR VERFAHRENSTECHNIK

PROF. DR.-ING. HABIL. JADRAN VRABECTHERMODYNAMIK UND ENERGIETECHNIK

INSTITUT FÜRVERFAHRENSTECHNIK

ThEt

Grand canonical MD simulation

Grand canonical molecular dynamics (GCMD) :

• Specification of μ, V, and T

• Test insertions and deletions of single particles

in alternation with canonical MD steps:

Application: Chemical potential gradient induced Poiseuille flow

maxμ minμ

T

UμP insΔ

ins exp,1max

T

UμP delΔ

del exp,1max

Page 13: Molecular simulation of fluid dynamics on the nanoscalehorsch/pdt/slides/2010_ICCFD2.pdf · PROF.DR.-ING.HABIL. JADRAN VRABEC THERMODYNAMIK UND ENERGIETECHNIK INSTITUT FÜR VERFAHRENSTECHNIK

PROF. DR.-ING. HABIL. JADRAN VRABECTHERMODYNAMIK UND ENERGIETECHNIK

INSTITUT FÜRVERFAHRENSTECHNIK

ThEt

Fluid flow induced by a chemical potential gradient

Page 14: Molecular simulation of fluid dynamics on the nanoscalehorsch/pdt/slides/2010_ICCFD2.pdf · PROF.DR.-ING.HABIL. JADRAN VRABEC THERMODYNAMIK UND ENERGIETECHNIK INSTITUT FÜR VERFAHRENSTECHNIK

PROF. DR.-ING. HABIL. JADRAN VRABECTHERMODYNAMIK UND ENERGIETECHNIK

INSTITUT FÜRVERFAHRENSTECHNIK

ThEt

y coordinate in units of

-15 -10 -5 0 5 10 15

fluid

density in u

nits o

f -3

0

1

2

3

h = 24

h = 72

saturated bulk liquid

heterogeneous system:

GCMD simulation of adsorption

Graphite + argon (LJTS), T = 0.85 ε/k, μ = μs(T)

min

')(y

ρyρdyΓ

Page 15: Molecular simulation of fluid dynamics on the nanoscalehorsch/pdt/slides/2010_ICCFD2.pdf · PROF.DR.-ING.HABIL. JADRAN VRABEC THERMODYNAMIK UND ENERGIETECHNIK INSTITUT FÜR VERFAHRENSTECHNIK

PROF. DR.-ING. HABIL. JADRAN VRABECTHERMODYNAMIK UND ENERGIETECHNIK

INSTITUT FÜRVERFAHRENSTECHNIK

ThEt

Scenario: Slit pore with a cylindrical cavity

612

fw 4)(rσ

rσ Cεru

Page 16: Molecular simulation of fluid dynamics on the nanoscalehorsch/pdt/slides/2010_ICCFD2.pdf · PROF.DR.-ING.HABIL. JADRAN VRABEC THERMODYNAMIK UND ENERGIETECHNIK INSTITUT FÜR VERFAHRENSTECHNIK

PROF. DR.-ING. HABIL. JADRAN VRABECTHERMODYNAMIK UND ENERGIETECHNIK

INSTITUT FÜRVERFAHRENSTECHNIK

ThEt

Rotation inside the cavity

2D

v = 0.8

C = 0.5

Oliver et al. (2006)

3D

v = 0.82

C = 0.5

(present)

… induced by stationary Poiseuille flow:

i

i

i prN

J 1

Page 17: Molecular simulation of fluid dynamics on the nanoscalehorsch/pdt/slides/2010_ICCFD2.pdf · PROF.DR.-ING.HABIL. JADRAN VRABEC THERMODYNAMIK UND ENERGIETECHNIK INSTITUT FÜR VERFAHRENSTECHNIK

PROF. DR.-ING. HABIL. JADRAN VRABECTHERMODYNAMIK UND ENERGIETECHNIK

INSTITUT FÜRVERFAHRENSTECHNIK

ThEt

Massively parallel MD simulation

Spatial domain decomposition:

processors calculate interactions within spatially defined subdomains

Linked cell communication:

each subdomain exchanges information with its 26 neighbours

Halo bins:

contain relevant molecules from

adjoining subdomains

excellent scalability of the MD software

Concurrency in space but NOT in time!

Page 18: Molecular simulation of fluid dynamics on the nanoscalehorsch/pdt/slides/2010_ICCFD2.pdf · PROF.DR.-ING.HABIL. JADRAN VRABEC THERMODYNAMIK UND ENERGIETECHNIK INSTITUT FÜR VERFAHRENSTECHNIK

PROF. DR.-ING. HABIL. JADRAN VRABECTHERMODYNAMIK UND ENERGIETECHNIK

INSTITUT FÜRVERFAHRENSTECHNIK

ThEt

processes50 100 150

speedup

25

50

75

100

number of processes8 32 128 512 2048

co

mp

utin

g tim

e in

units o

f s

1

10

100

simulation loopinput/output

2 000, 4 000, 8 000, and 16 000 particles per process

HLRS nehalem cluster Baku/Laki

uniform subdomains

static load balancing

methane + graphite

Scaling of the ls1 mardyn program

homogeneous truncated-shifted LJ system

Page 19: Molecular simulation of fluid dynamics on the nanoscalehorsch/pdt/slides/2010_ICCFD2.pdf · PROF.DR.-ING.HABIL. JADRAN VRABEC THERMODYNAMIK UND ENERGIETECHNIK INSTITUT FÜR VERFAHRENSTECHNIK

PROF. DR.-ING. HABIL. JADRAN VRABECTHERMODYNAMIK UND ENERGIETECHNIK

INSTITUT FÜRVERFAHRENSTECHNIK

ThEt

Communication and load balance

OpenMPI, gcc-4.1.2, HLRS nehalem cluster Baku/Laki.

Page 20: Molecular simulation of fluid dynamics on the nanoscalehorsch/pdt/slides/2010_ICCFD2.pdf · PROF.DR.-ING.HABIL. JADRAN VRABEC THERMODYNAMIK UND ENERGIETECHNIK INSTITUT FÜR VERFAHRENSTECHNIK

PROF. DR.-ING. HABIL. JADRAN VRABECTHERMODYNAMIK UND ENERGIETECHNIK

INSTITUT FÜRVERFAHRENSTECHNIK

ThEt

Innovative HPC-Methoden und Einsatz für

hochskalierbare Molekulare Simulation (IMEMO)

Associated enterprises:

Participants:

2008 – 2011

Page 21: Molecular simulation of fluid dynamics on the nanoscalehorsch/pdt/slides/2010_ICCFD2.pdf · PROF.DR.-ING.HABIL. JADRAN VRABEC THERMODYNAMIK UND ENERGIETECHNIK INSTITUT FÜR VERFAHRENSTECHNIK

PROF. DR.-ING. HABIL. JADRAN VRABECTHERMODYNAMIK UND ENERGIETECHNIK

INSTITUT FÜRVERFAHRENSTECHNIK

ThEt

Conclusion

• Based on a uniform additional force, Couette and Poiseuille flow can be

simulated for real fluids in nanoscopic channels.

• The velocity profile remains approximately linear (Couette) or parabolic

(Poiseuille) and Darcy’s law holds down to the molecular length scale.

However, boundary slip cannot be neglected for diameters below 100 nm.

• By grand canonical MD simulation, adsorbed layers and the behaviour of

the confined fluid can be investigated as if they were in equilibrium with a

specified state of the bulk fluid.

• The present approach is viable for more elaborate geometries as well.

• High performance computing permits MD simulation of systems with

characteristic volumes up to (100 nm)3 or interfaces up to 1 μm2.