11Institute for Fluid Mechanics and Heat Transfer Conex mid-term meeting, Oct 28th 2004, Warsaw

Numerical simulation of the flow in an Numerical simulation of the flow in an experimental device for emulsificationexperimental device for emulsification

Mag. Renate Teppner

Ass.-Prof. Dr. Helfried Steiner

Univ.-Prof. Dr. Günter Brenn

Part of the CONEX project:Part of the CONEX project:

„„Emulsions with Nanoparticles for New Materials“Emulsions with Nanoparticles for New Materials“

Conex mid-term meeting, Oct. 28Conex mid-term meeting, Oct. 28thth to 30 to 30th th 2004, 2004, Warsaw

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Numerical simulation: flow configuration

Cross section A-A

Cylindrical-gap emulsifier

Z

Detail Z: Processing element

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Boundary conditions:

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Parameters for the numerical simulation:

•Volumetric flow rate: Q = 0.13 l/s

•Properties of the fluid (emulsion of water and soybean oil):

977.6 kg/m3 2.5 x 10-3 Pas

-> Reynolds number at circular inlet (diameter D = 0.013 m):

Re 5000

•CFD-Code: FLUENT 6.1.22

•Turbulence models: - standard k- - realizable k-

- RNGnear wall treatment using low Reynolds number model

•Grid: 780.000 cells, structured & unstructured subdomains

55Institute for Fluid Mechanics and Heat Transfer Conex mid-term meeting, Oct 28th 2004, Warsaw

Results of the numerical simulation

Contours of axial velocity component in [m/s] upstream from gap#1

gap #1

66Institute for Fluid Mechanics and Heat Transfer Conex mid-term meeting, Oct 28th 2004, Warsaw

Results of the numerical simulation

Velocity vector field near gap#1

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Results of the numerical simulation

Contours of turbulent kinetic energy k in [m2/s2]

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Results of the numerical simulation

Contours of axial velocity component in [m/s]Contours of dissipation rate in [m2/s3]

BB

C

D

Contours of turbulent dissipation rate in [m2/s3]

A

A,B,C,D

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Results of the numerical simulation

inside gap #1:

A

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Results of the numerical simulation

inside gap #1:

A

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gap

inside gaps: & CA after gaps: & DB

Turbulent kinetic energy k in [m2/s2]

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inside gaps: & CA

Turbulence intensity : %1003/2

gapu

kTu

gap => v-prof

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CA after gaps: & DB

Dissipation rate in [m2/s3]

gap

: maximum of condition inside 2nd gap relevant for final dropsize distribution C

inside gaps: &

1616Institute for Fluid Mechanics and Heat Transfer Conex mid-term meeting, Oct 28th 2004, Warsaw

Estimation of maximum drop size dmax based on numerical results

4/13

max

cd

Turbulent kinetic energy spectrum

Kolmogorov-Hinze (1955):

inertial forces surface tension forces

maximum drop size 5/25/3

5/35/3

max 2

c

critWed

1717Institute for Fluid Mechanics and Heat Transfer Conex mid-term meeting, Oct 28th 2004, Warsaw

Estimation of maximum drop size dmax based on numerical results

mhddD gapioh 395

(Karabelas, 1978)

with

Consideration of viscous forces in dispersed phase (Davis,1985):

5/25/3

5/3

max 749.0

c

d

5/33/1

max5/25/3max 4

2

dKd d

c

235.1critWe

)749.0( Kwith

dmax according to Kolmogorov-Hinze (1955):

6/1

9.5

c

chccrit

uDWe

1818Institute for Fluid Mechanics and Heat Transfer Conex mid-term meeting, Oct 28th 2004, Warsaw

Estimation of maximum drop size dmax based on numerical results

Dissipation rate : volumetric average of numerical solution over annular gap volume

gapVgap

dVV

1

gapV

32/28022: sm#1gap

%2.8Tu %4.12Tu

32 /69217: sm#2gap

1919Institute for Fluid Mechanics and Heat Transfer Conex mid-term meeting, Oct 28th 2004, Warsaw

Estimation of maximum drop size dmax based on numerical results

Comparison with experimental data

Exptl. dropsize data provided by Slavka Tcholakova at the LCPE, Sofia

from measurements with cylindrical emulsifyer

Case 1 Case 2 Case 3

surface tension N/m

10 x 10-3 7 x 10-3 3.8 x 10-3

,/10130395 33 sm .Vμm, h -gap

sPamkgsPamkg ddcc3333 1050,/992,10,/998

2020Institute for Fluid Mechanics and Heat Transfer Conex mid-term meeting, Oct 28th 2004, Warsaw

Estimation of maximum drop size dmax based on numerical results

Case 1: d95 = 9.05 m

Experimental drop size pdf d95

Case 1 :

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Estimation of maximum drop size dmax based on numerical results

Case 2: d95 = 6.33 m

Experimental dropsize pdf d95

Case 2 :

2222Institute for Fluid Mechanics and Heat Transfer Conex mid-term meeting, Oct 28th 2004, Warsaw

Estimation of maximum drop size dmax based on numerical results

Case 3: d95 = 5.17 m

Experimental dropsize pdf d95

Case 3 :

2323Institute for Fluid Mechanics and Heat Transfer Conex mid-term meeting, Oct 28th 2004, Warsaw

Estimation of maximum drop size dmax based on numerical results

Comparison with experimental data

Exptl. drop size data provided by Slavka Cholakova at LCPE Sofia

from measurements with cylindrical emulsifier

Case 1 Case 2 Case 3

Experiments

d95 m9.05 6.33 5.17

Kolmogorov -Hinze (1955)

dmax m

8.68 7.01 4.86

Davis (1985) dmax m

16.24 15.01 13.6

2424Institute for Fluid Mechanics and Heat Transfer Conex mid-term meeting, Oct 28th 2004, Warsaw

Conclusions & further work

• strong contraction of the flow in the first gap enforces homogeneity in the circumferential direction

flow around the processing element = axisymmetric (2D)

flow is insensitive to up-stream conditions

• strong enhancement of turbulent motion in the wake downstream from every gap

• gap-to-gap increase of the mean dissipation rate inside the gap

design criterion for the processing element

• strong spatial variation of the dissipation rate inside each gap

identification of the relevant input value into break-up models ?

how assess the predictive capability of the break-up models ?

Conclusions:

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Further work

Simulation of the flow in the plane emulsifier:

flowgap

obstacles

gap

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Further work

Simulation of the flow in the plane emulsifier:

Main issues:

• Two cylindrical obstacles upstream from the gap: is the gap flow still

practically homogeneous in spanwise direction?

• Variation of the geometry of the processing element: 1,2,3 gaps

effect on achievable turbulence intensity and dissipation rate?