Numerical N i l investigation i ti ti off the th deformation d f ti and d break-up mechanisms of droplets in high-pressure high pressure emulsification orifices with a Coupled Volume-of-Fluid/Level-Set Method Kathrin Kissling, Steffen Schütz, Manfred Piesche

5th. OpenFOAM Workshop Gothenburg g June 21-24 2010 Institute of Mechanical Process Engineering IMVT University of Stuttgart, Germany

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I.

Motivation

II. State of the art

III. Numerical Approach I.

Direct numerical simulation of the high pressure homogenizer

II. Development of a Coupled Level‐Set /Volume‐of‐Fluid Method in OpenFOAM® III. Testcases

IV. Results V. Conclusion and future perspective

Institute of Mechanical Process Engineering IMVT University of Stuttgart, Germany

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I. Motivation – High pressure homogenizing systems Area of application:Grocery technology; Mayonnaise, Cremes, … Cosmetics and Pharmacy Polymertechnology

ƒFree jet in laminar‐turbulent transition regime ƒPressure Pressure drop at orifice: 10  orifice: 10 ‐ 1000 bar 1000 bar ƒDispersed droplets in continuous liquid phase ƒCavitation Institute of Mechanical Process Engineering IMVT University of Stuttgart, Germany

Kissling, Schütz, Piesche

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II. State of the Art ƒ

First numerical investigations by Kleinig/Middleberg [5]

ƒ

] k‐epsilon p model Stevenson und Chen [[9]:

ƒ

Floury [3]: investigations of high‐pressure emulsification orifices: RNG k‐epsilon model

A RANS –Models M d l 2d axisymmetric

9 Insight:  Pressure drop, energy dissipation mean velocity values,…  values Detailed eta ed investigations est gat o s of o the t e flow o and of the mechanisms of droplet deformation and break‐up not possible DNS coupled with a detailed evaluation of the flow field and consideration of the droplets Institute of Mechanical Process Engineering IMVT University of Stuttgart, Germany

Dimotakis und Lye [2]

Kissling, Schütz, Piesche

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III.I Direct numerical simulation of the free jet Governing equations

Continuity equation: Momentum balance:

∇U = 0

ρ

d (U) + ρU∇U = −∇p + µ∇2U + ρg dt

DNS to describe phenomena in the laminar‐turbulent transition regime 1/4

Kolmogorov microscale

Institute of Mechanical Process Engineering IMVT University of Stuttgart, Germany

lkol

⎛ µc 3 ⎞ = ⎜⎜ 3 ⎟⎟ ⎝ ρc ε ⎠

Kissling, Schütz, Piesche 5

III.II Interface Capturing Methods: Volume‐of‐Fluid and Level Set Volume of Fluid [7]  ƒ

ƒ

Volumetric phase fraction α : Phase 1:

α = 1

Phase 2: 

α = 0

interface:

0