droplet breakup in turbulence - lorentz center - lbm.pdf · conclusions • droplet breakup in...
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Droplet breakup in turbulence Prasad Perlekar Prof. F. Toschi, Prof. L. Biferale, Dr. M. Sbragaglia
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Applications: Industry • Two phase flow chemical reactors, gas-liquid separators, liquid atomization,
spray systems, aeration process etc.
Science Droplet dispersion occur in many physical phenomena
Physics of elasticity Energy transfer from fluid to elastic modes
Motivation
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Gopalan and Katz. Turbulent Shearing of Crude Oil Mixed with Dispersants Generates Long Microthreads and Microdroplets. PRL, 104, 054501 (2010)
Some recent work-Experiments
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Qian et al., Simulation of bubble breakup dynamics in homogeneous turbulence. Chem. Engg. Commun. 193, 1038 (2006)
Some recent work- Simulations 1/2
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Some recent work- Simulations 2/2
J.J. Dersksen and H.E.A. Van Den Akker, Chem. Engg. Res. (2006)
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J.O. Hinze, A.I.Ch.E, (1955)
Phenomenology (Hinze)
Maximum droplet diameter that does not undergo breakup Inertial force Surface tension force Weber number:
R
ud
We =ρu2
dR
σ
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d > dmax: Droplet breaks; d < dmax: Droplet does not break
We =ρu2
dR
σ
K41 : u2 ∼ d2/32/3
dmax = 0.75 ρ
σ
−3/5−2/5
Phenomenology (Hinze)
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Boltzmann equation
D3Q19 model
f ≡ f(x, v, t)
∂tf + (v ·∇)f = Ω− (F ·∇)f
fα(x+ eα, t+ 1) = fα(x, t)−fα(x, t)− f (eq)
α (x, t)
τ
Lattice Boltzmann method (LBM)
D3Q19 model:
Multicomponent using Shan-Chen force
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LBM: Turbulence
• Forcing: Large scale forcing in first two Fourier modes
fx =
k≤√2
f0[sin(kyy + φ2k) + sin(kzz + φ3
k)]
fy =
k≤√2
f0[sin(kxx+ φ1k) + sin(kzz + φ3
k)]
fz =
k≤√2
f0[sin(kxx+ φ1k) + sin(kyy + φ2
k)]
φik Random phases generated from Uhlenbeck-Ornstein process
N = 5123
ν = 5× 10−3
λ ≈ 13.89lu
η ≈ 6lu
σ ≈ 0.028
Reλ ≈ 29.13
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LBM: Energy and enstrophy
N = 128
Rλ ≈ 18.8
E =1
2
ρu2
Ω =
ω2
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LBM: Energy and acceleration
Acceleration of a fluid parcel N = 128
Reλ ≈ 18.8a =
Du
Dt; a ≈ −∇p ≈ −c2s∇ρ
SC: acceleration for single component flow
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• JUGENE (FZJ-JSC IBM Blue Gene/P)
• 23.5RM (about 15Mhours)
• 32-64 kprocs
• I/O HDF5
• Fully parallel code
Simulations
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Droplet breakup in turbulence
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0 2 4 6 8
5
10
15
t/ eddy
No.
of d
rops
Towards a stationary state!
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G (LU)
D (Hinze)
D (LBE)
We
RUN0 29.1 512 0.5/0.5 0.005 N/A 6 - - -
RUN1 29.1 512 2.038/0.362
0.005 0.03 6 24.2 24+/-1 0.075 0.3%
RUN2 29.1 512 1.757/0.088
0.005 0.08 6 39.5 36+/-1 0.033 0.3%
Simulations 5123
ρh/ρlReλ N ν η φ
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Simulations 1283
G (LU)
D (Hinze)
D (LBE)
We
RUN0 18.8 128 0.5/0.5 0.005 N/A 3 - - -
RUN1-4 18.8 128 2.038/0.362
0.005 0.03 3 8.65 11,13,15,18
0.12 0.07,0.5,5,10%
Increasing vol. fraction
ρh/ρlReλ N ν η φ
φ = 0.07% φ = 0.5% φ = 5% φ = 10%
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Droplet radius and volume distribution
N = 128, Reλ ≈ 18.8
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Sauter diameter
d32 =
dmax
dmind3p(d)
dmax
dmind2p(d)
Sauter dimension: Estimate to characterize the droplet diameter
Expt : 1.6− 2.2
Expt.: Pacek et al. Chem. Engg. Res. (1998)
N = 128, Reλ ≈ 18.8
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Droplet PDF: Re dependence
d32 (LBM) 18.8 14.5 3.5e-8 29.1 24 2.85e-9
Reλ ε
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Droplet trajectory
Although trajectory is smooth the acceleration is very noisy
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Filetering
Filter the trajectory in frequency space Kc : Filtering frequency
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PDF of acceleration
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Presence of droplets leads to a modification of the energy transfer.
Energy spectrum
sc
mc
sd
mc-sc
N=512, Re=29.1 sc: Single component mc: Multicomponent sd: Static droplet
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Energy spectrum: volume fraction
5% vol. fraction
Single component
Diff.
Larger volume fraction => More surface => larger modification of the energy spectrum
N=128, Re=18.8
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Conclusions
• Droplet breakup in turbulence using LBM can be used to study stationary droplet dispersion in turbulence.
• Dependence of PDF of droplet dispersion on the volume fraction and Reynolds number dispersion studied.
• Energy spectrum shows that the droplet deformations lead to transfer of energy between different modes.
• More statistics needed for acceleration studies