Front Tracking simulations on liquid-liquid systems; an - PowerPoint PPT Presentation

Front Tracking simulations on liquid-liquid systems; an investigation of the drag force on droplets Ivo Roghair, Wouter Dijkhuizen, Martin van Sint Annaland and Hans Kuipers Fundamentals of Chemical Reaction Engineering CFD2008-071 – June 12th, 2008 12/06/08 I. Roghair, CFD2008 1

Contents • Introduction • Objectives • Numerical simulations – Grid dependency study – Drag force study • Conclusions and outlook 12/06/08 I. Roghair, CFD2008 2

Introduction Multi-level modelling strategy for multiphase flow Large scale structures Multi-fluid continuum model Medium scale structures Discrete element model Closures for: - Drag , lift, virtual mass - Swarm effects - Mass transfer coefficients Direct numerical simulations 12/06/08 I. Roghair, CFD2008 3

Introduction Direct Numerical Simulations (DNS) • Fully resolved – Based only on fundamental equations for fluid flow • Navier-Stokes + continuity equation for incompressible flow – Can be used to derive closures for forces on • Bubbles • Droplets • Particles • Only valid when grid independence can be shown! 12/06/08 I. Roghair, CFD2008 4

Front tracking • Incompressible fluids • Fixed Eulerian grid • Interface consists of Lagrangian marker points that build up a triangular mesh – Points are moved with the interpolated fluid flow – Straightforward surface tension force calculation • Advantages – Calculation of surface tension force with sub-grid accuracy. – No numerical coalescence of dispersed phase elements 12/06/08 I. Roghair, CFD2008 5

Front tracking 12/06/08 I. Roghair, CFD2008 6

Drag force Forces acting on a F P Σ F droplet F L  dv b F VM = ∑  dt =  F G   F P   F D   F L   m b F Stationary force balance Droplet velocity in the rise direction 2   3 − 1  c − d  g  2 C D  c  2 = 0 u c , z  6 d eq 4 d eq u d , z −  F D F VM F G F D 4   c − d  g d eq C D = 3  c   u c , z  u d , z −  12/06/08 I. Roghair, CFD2008 7

Drag force • Determine drag force coefficient by different averaging procedures – Average rise velocity, then determine C D – Determine C D as a function of time, average this value → No difference 12/06/08 I. Roghair, CFD2008 8

Drag force Correlations from literature (bubbly flow) C D = 24  Rigid sphere: Re Re  0.5  C D = 16 2  Mei et al. (1994): 1  1  16 Re  3.315 Re  Tomiyama (1998): C D = max [ min [ Eo  4 ] Re ] , 8 16 0.687  , 48 Eo  1  0.15 Re – Pure Re 3 C D = max [ Eo  4 ] 0.687  , 8 24 Eo  1  0.15 Re – Contaminated Re 3   c − d  g d eq 2 Re = c  u d d eq Eo =   c 12/06/08 I. Roghair, CFD2008 9

Drag force • Experiments and simulations on drag force for bubbly flow From: Wouter Dijkhuizen, PhD thesis, University of Twente, 2008 12/06/08 I. Roghair, CFD2008 10

Objectives • Investigate the behavior of the Front Tracking model for liquid-liquid systems • Simulate droplets in an infinite quiescent liquid to derive drag force closures • Investigate the relation between gas- liquid and liquid-liquid drag force and their dependencies 12/06/08 I. Roghair, CFD2008 11

Grid dependency •Vary resolution in droplet, domain 5 times droplet size •Vary resolution in droplet, keep domain at 100 3 cells •Keep resolution in droplet at 20 cells, vary domain size Simulation parameters: ρ c = 1000 kg/m 3 , μ c = 10 -3 Pa·s ρ d = 800 kg/m 3 , μ d = 10 -1 Pa·s σ = 52.9 mN/m, d eq = 1 mm t end = 1 s dt = 10 -5 s 12/06/08 I. Roghair, CFD2008 12

Grid dependency • Vary resolution in droplet, domain 5 times droplet size •Vary resolution in droplet, keep domain at 100 3 cells •Keep resolution in droplet at 20 cells, vary domain size 6 30 20 100 12/06/08 I. Roghair, CFD2008 13

Grid dependency •Vary resolution in droplet, domain 5 times droplet size • Vary resolution in droplet, keep domain at 100 3 cells •Keep resolution in droplet at 20 cells, vary domain size 8 100 20 100 12/06/08 I. Roghair, CFD2008 14

Grid dependency •Vary resolution in droplet, domain 5 times droplet size •Vary resolution in droplet, keep domain at 100 3 cells • Keep resolution in droplet at 20 cells, vary domain size 20 50 20 100 12/06/08 I. Roghair, CFD2008 15

Drag force simulations • Used settings: – 20 grid cells in droplet diameter – 100 3 grid cells in domain • Variation of continuous phase viscosity between 0.001 - 0.2 Pa·s • Variation of equivalent droplet diameter between 0.2 – 5 mm • “Dodecane droplet in water” system: – ρ c = 1000 kg/m3; – ρ d = 746 kg/m3; μ d = 1.34·10 -3 Pa·s – σ = 0.0529 N/m; 12/06/08 I. Roghair, CFD2008 16

Drag force simulations • Variation of continuous phase viscosity 12/06/08 I. Roghair, CFD2008 17

Drag force simulations • Variation of dispersed phase viscosity between 10 -3 – 10 -1 Pa·s • Variation of equivalent droplet diameter between 0.2 – 7 mm • Physical properties – ρ c = 1000 kg/m 3 ; μ c = 10 -1 Pa·s – ρ d = 800 kg/m 3 ; – σ = 0.0529 N/m; 12/06/08 I. Roghair, CFD2008 18

Drag force simulations • Variation of dispersed phase viscosity 12/06/08 I. Roghair, CFD2008 19

Drag force simulations • Due to volume losses more detailed simulations: – Computational grid 150 3 cells – 30 cells within droplet diameter – Higher surface tension 12/06/08 I. Roghair, CFD2008 20

Drag force simulations Simulation parameters: ρ c = 1000 kg/m 3 ; μ c = 10 -3 Pa·s ρ d = 800 kg/m 3 ; μ d = 10 -1 Pa·s σ = 0.1 N/m; d eq = 0.5 - 7 mm 12/06/08 I. Roghair, CFD2008 21

Drag force simulations Simulation parameters: ρ c = 1000 kg/m 3 ; μ c = 10 -3 Pa·s ρ d = 800 kg/m 3 ; μ d = 10 -3 - 0.5 Pa·s σ = 0.1 N/m; d eq = 1 mm 12/06/08 I. Roghair, CFD2008 22

Conclusions and outlook • Front tracking model can simulate dispersed liquid phases but a high resolution is required • Volume loss strongly depending on droplet resolution • Correlations of Mei et al. and Tomiyama for bubbly flow are well predicted – Some overshoot due to wall effects • Transition of free-slip to no-slip condition as a function of μ d shown • Outlook: – Eo dependence of drag force coefficient – Droplet and bubble swarms 12/06/08 I. Roghair, CFD2008 23

Thank you Thank you for your attention 12/06/08 I. Roghair, CFD2008 24

Front tracking  Surface tension is mapped from the b interface mesh to the c Eulerian grid. n c n b t m,c F b F a =σ    n a  t m,a × F c m t m,b F b =σ    n b  t m,b × t m,a F a F c =σ    n c  t m,c × n a a 12/06/08 I. Roghair, CFD2008 25