Droplet breakup in turbulence - Lorentz Center - LBM.pdf · Conclusions • Droplet breakup in...
Transcript of Droplet breakup in turbulence - Lorentz Center - LBM.pdf · Conclusions • Droplet breakup in...
Droplet breakup in turbulence Prasad Perlekar Prof. F. Toschi, Prof. L. Biferale, Dr. M. Sbragaglia
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
Gopalan and Katz. Turbulent Shearing of Crude Oil Mixed with Dispersants Generates Long Microthreads and Microdroplets. PRL, 104, 054501 (2010)
Some recent work-Experiments
Qian et al., Simulation of bubble breakup dynamics in homogeneous turbulence. Chem. Engg. Commun. 193, 1038 (2006)
Some recent work- Simulations 1/2
Some recent work- Simulations 2/2
J.J. Dersksen and H.E.A. Van Den Akker, Chem. Engg. Res. (2006)
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
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)
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
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
LBM: Energy and enstrophy
N = 128
Rλ ≈ 18.8
E =1
2
ρu2
Ω =
ω2
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
• JUGENE (FZJ-JSC IBM Blue Gene/P)
• 23.5RM (about 15Mhours)
• 32-64 kprocs
• I/O HDF5
• Fully parallel code
Simulations
Droplet breakup in turbulence
0 2 4 6 8
5
10
15
t/ eddy
No.
of d
rops
Towards a stationary state!
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
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%
Droplet radius and volume distribution
N = 128, Reλ ≈ 18.8
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
Droplet PDF: Re dependence
d32 (LBM) 18.8 14.5 3.5e-8 29.1 24 2.85e-9
Reλ ε
Droplet trajectory
Although trajectory is smooth the acceleration is very noisy
Filetering
Filter the trajectory in frequency space Kc : Filtering frequency
PDF of acceleration
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
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
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