Euler-Euler Modeling of Mass-Transfer in Bubbly Flows Roland Rzehak Eckhard Krepper Text optional: Institutsname Prof. Dr. Hans Mustermann www.fzd.de Mitglied der Leibniz-Gemeinschaft
Overview Motivation and Goal Baseline Model for Fluid Dynamics Including Mass Transfer Summary and Outlook Page 2
Two different perspectives on multiphase flow Averaging eliminiates small scales thus lower resolution suffices but closure models required Interface Dynamics: at each position either gas or liquid Two Fluid Model: both gas and liquid everywhere with certain probability Page 3
Motivation & Goal Simulation on industrial scale is feasible with Two-Fluid-Model but needs development of closure relations. To predict phenomena for a certain range of conditions models must work without adjustments. Same closures should work for all systems with same physics at the bubble scale. Baseline model provides starting point further development expands range of applicability and accuracy. Page 4
Closure is a very complex problem bubble forces effective viscosity bubble distribution & velocity bubble size bubble distribution & velocity bubble-induced turbulence rates bubble coalescence & breakup bubble size Page 5 without claiming completeness
Bubble Forces drag [1979_Ishii] (shear) lift [2002_Tomiyama] wall (lift) [2002_Hosokawa] turbulent dispersion [2004_Burns] virtual mass C VM = 1/2 lift F u L F disp µ α eff L G towards lower u L higher u L largely based on experiments with single bubbles in laminar flows air bubbles in water Page 6
Turbulence liquid phase only shear-induced SST model like for single phase flow bubble-induced source terms for k and ε / ω Page 7 k-source: power transferred to liquid by drag k SL = F drag L ε-source: dimensional argument similar to single phase case k ε SL S L = CεB τ τ andc εb from trial and error τ u G u = db kl Cε B no extra contribution needed in effective viscosity µ turb = ρ k ω L =1.0 (transformed to ω) (% limiter)
Pipe flow [1998_Liu] stationary simulation of narrow pipe sector valid for axisymmetric flow assuming monodisperse bubble size distribution taken from measurements fully developed conditions at measurement level uniform gas profile at inlet air bubbles in water (P = 1bar) outlet measure t L = 3.43m inlet D = 57.2 mm x z y flow gravity Page 8
Results void fraction: good in center, wall peak too high liquid velocity: quantitative deviations small, but too steep near wall turbulent energy: too high in center, too low near wall exception: double peaked profile Page 9
Bubble Column [2012_Akbar] 3D transient simulation (URANS) with fixed polydispersity taken from measurements 1 or 2 MUSIG groups individual nozzles at inlet air bubbles in water (P = 1bar) level wo gas measure t 200 mm 500 mm inlet x z y 2R = 240 mm Page 10
Results void fraction: quantitative deviations small, but too peaked near wall liquid velocity: zero-crossing at different position, dip in center turbulent energy: too low on average, peak near wall missed modeled contribution dominant Page 11
Processes involved in reactive mass transfer micro-mixing reactand A mass transfer turbulent diffusion slow reaction fast reaction reactand B Page 12 gas boundary bulk liquid bubble layer with turbulent eddies
Mass Transfer Coefficient penetration / renewal model good for thin concentration boundary layer transient diffusion in plane geometry time-averaged mass transfer coefficient gas liquid c sat c bulk k ( τ ) 1/ 2 2 1 L D L c π big question: What is the contact time τ c? three answers: laminar model [1935_Higbie] τ 1 c u = d rel B τ large eddy model [1967_Fortescue] 1/ 3 1 ε L Λ 2 ε L c 2 / 3 kl k Λ L small eddy model [1970_Lamont] τ 1 c ε L ν L 1/ 2 Page 13
Mass Transfer Coefficient Re Re Re B 0.43 B 0.5 B 0 Which answer is correct? Page 14 qualitative evidence laminar model: numerous investigations on bubbles rising in quiescent flow eddy models: situations where u rel is 0 like in horizontal bubbly flow d B tends to like in open channel flow quantitative analysis of available data laminar model: still good for moderate trubulence eddy models: favor large over small eddy model combined model: tentatively add inverse contact times downward vertical flow d B 0.5 5 mm u rel 0.25 m/s Re H 2500 0.47...0.56 Re Re Re 0 Re 0.46 0.69 [1970_Lamont] pipe flow d B ~ 4.5 11 mm
Mass Transfer Coefficient needs for better understanding! laminar model: include effects of bubble shape, path, oscillation, wake turbulent models: consider spectrum of eddies needs good model for bubble induced turbulence unite both mechanisms Page 15
Euler-Euler Simulations with Mass Transfer P D = 150 mm literature: validation only by integral quantities, e.g. integral k L a-value total gas holdup needed: validation using local information, e.g. axial profiles of gas fraction and concentration [1978_Deckwer]: cocurrent absorption of CO2 from air bubbles into water in a bubble column d B, k L L = 4400 mm peculiar: mean bubble size does not change bypass modeling of bubble coalescence and breakup use constant k L obtained from the data J L, J G, Y G CO2, α G Page 16
Results Gas1.CO2.Molar Fraction [-] 1.0 0.8 0.5 0.3 J G = 0.0275 m/s J G = 0.0342 m/s J G = 0.0463 m/s k L = 0.21 mm/s k L = 0.176 mm/s k L = 0.165 mm/s 16 CFX 0.0 z/hz Gas1.CO2.Molar Fraction [-] 1.0 0.8 0.5 0.3 17 CFX 0.0 z/hz Gas1.CO2.Molar Fraction [-] 1.0 0.8 0.5 0.3 19 CFX 0.0 z/hz 0.20 0.20 0.20 Gas1.Volume Fraction [-] 0.15 0.10 0.05 16 CFX Gas1.Volume Fraction [-] 0.15 0.10 0.05 17 CFX Gas1.Volume Fraction [-] 0.15 0.10 0.05 19 CFX 0.00 z/hz [-] Page 17 0.00 z/hz [-] homogeneous distribution over inlet J L = 0.0472 m/s d B = 2.9 mm 0.00 z/hz [-]
Results Gas1.CO2.Molar Fraction [-] 1.0 0.8 0.6 0.4 J G = 0.0275 m/s J G = 0.0342 m/s J G = 0.0463 m/s k L = 0.21 mm/s k L = 0.176 mm/s k L = 0.165 mm/s 16 k L = 2.0e-4 m/s k L = 4.0e-4 m/s 0.2 z/hz Gas1.CO2.Molar Fraction [-] 1.0 0.8 0.5 0.3 17 CFX 0.0 z/hz Gas1.CO2.Molar Fraction [-] 1.0 0.8 0.5 0.3 19 CFX 0.0 z/hz 0.20 0.20 0.20 Gas1.Volume Fraction [-] 0.15 0.10 0.05 16 k L = 2.0e-4 m/s k L = 4.0e-4 m/s Gas1.Volume Fraction [-] 0.15 0.10 0.05 17 CFX Gas1.Volume Fraction [-] 0.15 0.10 0.05 19 CFX 0.00 z/hz [-] Page 18 0.00 z/hz [-] homogeneous distribution over inlet J L = 0.0472 m/s d B = 2.9 mm 0.00 z/hz [-]
Results 0.15m 0.14m gas inlet 86% of total area liquid inlet 14% of total area Gas1.Volume Fraction [-] 0.15 0.10 0.05 16 inlet 1 inlet 2 0.00 z/hz [-] Gas1.CO2.Molar Fraction [-] 1.0 0.8 0.6 0.4 16 inlet 1 inlet 2 0.2 z/hz z / hz ~ 0.1 Page 19
With Variable Bubble Size inspired by [1978_Deckwer] mass transfer coefficient due to Brauer fixed bubble size with d B = 3 mm and 2 mm variable bubble size by MUSIG model 5.0 5.0 5.0 5.0 4.0 3.0 4.0 3.0 d B = 3.0 mm4.0 d B = 2.0 mm MUSIG 3.0 d B = 3.0 mm d B = 2.0 mm MUSIG 4.0 3.0 d B = 3.0 mm d B = 2.0 mm MUSIG x [m] x [m] x [m] x [m] 2.0 2.0 2.0 2.0 1.0 1.0 1.0 1.0 0.0 0.0 2 2.2 2.4 2.6 2.8 3 d B [mm] 0 0.05 0.1 0.15 0.2 α G [-] 0.0 0.0 0 200 400 600 ifarea [m -1 ] awaiting data for validation from partners in SPP 1740 0 0.0005 0.001 0.0015 Y L [-] Page 20
Summary established baseline approach works for fluid dynamics with fixed polydispersity rough quantitative agreement in certain parameter range some open issues remain, e.g. suitable inlet modeling initial validation for extension to mass-transfer model development in progress ongoing and future work promising candidate for bubble coalescence and breakup include more complex physics: chemical reaction extend to more complex systems: add particles Page 21
Thank you for your Attention! Thanks to the DFG for funding the work within the Priority Programme 1740. Page 22