CFD Modelling of Turbulent Mass Transfer in a Mixing Channel

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1 CFD Modelling of Turbulent Mass Transfer in a Mixing Channel Lene K. Hjertager Osenbroch, Bjørn H. Hjertager and Tron Solberg Aalborg University Esbjerg Esbjerg, Denmark Homepage: hugin.aue.auc.dk Prepared for Computational Fluid Dynamics in Chemical Reaction Engineering IV June 19-24, 2005, Il Ciocco Hotel and Conference Center Barga, Italy

2 Overview Objectives Flow Configuration PIV/PLIF Experiment Governing Equations Turbulence and Micromixing Models Numerical Results Conclusions

3 Objectives Objectives of current project PIV/PLIF measurements of mass transfer and chemical reactions in turbulent liquid flows pure mixing/mass transfer acid-base chemical reaction (Poster presentation) CFD modelling of mass transfer and chemical reactions (Poster presentation) in turbulent liquid flows

4 Flow Configuration Confined wake flow Channel dimensions Mixing channel Length 640 mm Cross-section 60 mm x 60 mm Feed channel Length mm y,v D=60 mm d=20 mm x, U Cross-section 20 mm x 60 mm Flow conditions 330 mm Fluid : Water Feed channel A : V A,b /V B,b = 1, 0.5, 0.25 Feed channel B : Re B = ρ V B,b D h,b /µ = 5100 V A,b C A,b V B,b C B,b

5 PIV/PLIF System y/d=22.94 Position 3 Rhodamine 6G + 5µm polyamid particles y/d=19.59 y/d=5.94 Nd:YAG Laser z y x Mirror Mirror 570 nm filter 532 nm filter PIV camera PLIF camera D=60 mm d=20 mm V A,b C A,b V B,b C B,b y/d=2.94 y/d=2.59 y/d= Position 2 Position 1

6 C = 1 PIV/PLIF Measurements (1) Instantanous velocity and concentration C = 0 y x 20 mm

7 PIV/PLIF Measurements (2) Pure mixing experiment Concentration of species A High concentration (C=1) red Low concentration (C=0) blue Instantaneous images at three different heights C = 1 C = 0 Note heterogeneous structures Averages produced using 200 images

8 C = 1 C = 0

9 C = 1 C = 0 1:1 0.5:1 0.25:1

10 PIV/PLIF Measurements (3) Mean concentrations 1:1 0.25:1 0.5:1

11 PIV/PLIF Measurements (4) RMS concentrations 1:1 0.25:1 0.5:1

12 Conservation Equations Mass Momentum U x j j = 0 ( ) p τ ij U U i j 2 ρ U j Ui = + ; τ ij = ( µ + µ T) + δij ρk xj xj xj xj xi 3 Mixture fraction φ = C CA, b ( ) φ µ µ T ρu φ = Γ ; Γ = + x x x Sc Sc j φ φ j j j φ T

13 Turbulence and mixing models Turbulence Models Standard k-ε model RNG k-ε model Chen-Kim k-ε model Micromixing model Multi-peak presumed PDF model (Fox 1998)

14 Multi-Peak PDF Model (1) Presumed PDF ( ;, ) = (, ) (, ) n= 1 Transport equation for probability p n t N p n ( n ) fφ ψ x t p x t δ ψ φ x t x ( ) ( ) n ρ p + ρ U p = Γ G ( p) Transport equation for probability-weighted concentration s n x p x n j n T + j j j n t x x s x ( ) ( ) n ρ s + ρ U s = Γ + M ( p s) n j n T, n j j j Conservation relations Np Np Np p = 1; G = 0; M = 0 n n n n= 1 n= 1 n= 1

15 Multi-Peak PDF Model (2) Local concentration in environment/peak n Mean concentration φ φ = Variance of concentration fluctuations n N p s p n n = p φ = N p s n n n n= 1 n= 1 N p φ = p φ φ 2 2 n n n= 1 2

16 Multi-Peak PDF Model (3) Five environement/peak micromixing model Inlet stream 1: Inlet stream 2: φ 1 = 1 φ 2 < 1 1> φ3 > 0 φ 4 > 0 φ 5 = 0 p = 1 p = 1 1 Typical modelling of G n and M n for environment/peak 3 G = r + r 2 r; M = r φ + r φ 2r φ Probability fluxes rn = γ p n 1 1 k Rate of micromixingγ = ; τm ; Cφ 1.0 τ = C ε = m φ 5

17 Mean Axial Velocity (V) 1:1 0.5:1 0.25:1

18 Mean Transverse Velocity (U) 1:1 0.5:1 0.25:1

19 Turbulence Velocities 1:1 0.5:1 0.25:1

20 Mean Concentration Turbulence models; 1:1 case Turbulent Schmidt number; 1:1 case

21 Mean Concentration 1:1 0.5:1 0.25:1

22 Concentration Fluctuations 1:1 0.5:1 0.25:1

23 Five-peak presumed PDF model 1:1 Probability Density Functions

24 Five-peak presumed PDF model 0.5:1 Probability Density Functions

25 Five-peak presumed PDF model 0.25:1 Probability Density Functions

26 Overall mixing characteristics Coefficient of variation => Measure of macromixing CoV N i= 1 2 ( C ) i C = N 1 A area C A A Decay function => Measure of micromixing d = crms C A A

27 Coefficient of variation (CoV) and decay function (d) 1:1 0.5:1 0.25:1

28 Concluding remarks (1) The different k-ε turbulence models do not manage to capture the correct recovery from wake to channel flow, especially for the 1:1 case The defects in the flow modelling also transfers to the mixing predictions A reduction of the turbulent Schmidt number (0.15 for 1:1 case and for the other) is needed to achieve good predictions of both mean and rms concentrations The five-peak presumed PDF model predicts the streamwise decay of micromixing reasonably correct

29 Concluding remarks (2) The concentration PDF s are reasonably predicted by the five-peak presumed PDF model The overall mixing characteristics (CoV and decay function) are reasonably predicted A LES turbulence model is probably required to improve the flow modeling Solution of the multi-peak PDF method should use the direct quadratic method of moment (DQMOM) technique

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