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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)
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
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
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)
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
PROF. DR.-ING. HABIL. JADRAN VRABECTHERMODYNAMIK UND ENERGIETECHNIK
INSTITUT FÜRVERFAHRENSTECHNIK
ThEt
Poiseuille flow of methane in a graphite channel
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
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
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
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)
PROF. DR.-ING. HABIL. JADRAN VRABECTHERMODYNAMIK UND ENERGIETECHNIK
INSTITUT FÜRVERFAHRENSTECHNIK
ThEt
Properties of nanoscopic Poiseuille flow
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
PROF. DR.-ING. HABIL. JADRAN VRABECTHERMODYNAMIK UND ENERGIETECHNIK
INSTITUT FÜRVERFAHRENSTECHNIK
ThEt
Fluid flow induced by a chemical potential gradient
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
PROF. DR.-ING. HABIL. JADRAN VRABECTHERMODYNAMIK UND ENERGIETECHNIK
INSTITUT FÜRVERFAHRENSTECHNIK
ThEt
Scenario: Slit pore with a cylindrical cavity
612
fw 4)(rσ
rσ Cεru
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
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!
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
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.
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
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.