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