STUDY OF ELECTROCHEMICALLY GENERATED TWO-PHASE FLOWS Jonathan SCHILLINGS, J. DESEURE, O. DOCHE 1 LEPMI / SIMAP (CNRS/Grenoble INP/Université Joseph Fourier/Université de Savoie) PHELMA Campus 1130, rue de la Piscine - BP 75 F-38402 - St-Martin d'hères Cedex
1 - CONTEXT 2
1.1 CONTEXT : GAS GENERATION DURING ELECTROCHEMICAL PROCESSES Gas bubbles are frequently generated in electrochemical processes As principal product (e.g. in electrolysis) High gas recuperation rate must be reached As a by-product (e.g. in electrodeposition) Negative impact on the principal reaction should be avoided Bubbles behavior in electrolyte strongly affects process performances 3
1.1 CONTEXT : GAS GENERATION DURING ELECTROCHEMICAL PROCESSES S eff < S geom Natural convection Mixing Bubble-induced Natural convection Mixing Surface coverage Mass transfer limitation Bulk conductivity drop Current limitation i σ eff < σ liq Risk of plume mixing Decreased yield Energy production (H 2 + O 2 ) 4 Gas bubbles Gas-evolving electrode Electrolyte
1.2 - PHYSICAL INSIGHT TO ENHANCE CELL'S DESIGN generates Electrochemistry Bubbles (dispersed phase) momentum transfer modify charge transfer Electrolyte (continuous phase) ion transport Strong coupling between physical phenomena Difficulty to control the process Numerous parameters for empirical analysis Necessity of a realistic model 5
2 MODEL DESCRIPTION, RESULTS AND DISCUSSION 6
2.1 - MIXTURE MODEL [1] CFD equations : Laminar, Newtonian fluid, ρ D ρ C, void fraction α U = 0 U D = 0 (Mixture volume conservation) (Dispersed phase volume conservation) ρ C 1 α q q = P + ρ C gαz + μ α q + q T [ 2 μ(α) q] 3 (Momentum conservation) Closure model for relative flux : small rigid spheres approximation U R = U D αu = U Stokes + U Hdiff + U Sdiff + U Smig + U Saff [2] y 0, 6α 2 Terminal Shear-induced 6. Shear-induced Hydrodynamic 46 rrising 2 b γ diffusion bubble migration, self-diffusion velocity, in a of τ relative uniformly a bubble to sheared plume rising e due motion in plume 6π to a non-uniform ν x a τ shear concentrated plume Lift force (Saffman force) of γ U= v a x, β α = 1 S = 2 r 2 b gρ C rotating bubble in a sheared, f α 9 μ 3 α2 : τ = μ v hindering function 1 + 0. 5e 8.8α plume x U U Hdiff Stokes Smig Saff αf(α)u U 2 Sdiff = r 2 bb γ S βf U α S S sgn e α D α y γ x [1] M. Ishii, T. Hibiki, Thermo-Fluid Dynamics of Two-Phase Flow, Springer, New York, NY, 2011. [2] R. Wedin, A.A. Dahlkild, Ind. Eng. Chem. Res. 40 (2001) 5228 5233 7
2.1 - MIXTURE MODEL : ASSUMPTIONS Electrokinetics not computed Uniform current approximation Small influence on two-phase flow results C ~ 0 due to strong mixing Heat generation neglected Thermal-induced convection << bubble-induced convection 8
v (m/s) v (m/s) v (m/s) 2.2 - MODEL VALIDATION : SIMULATING EXPERIMENTAL RESULTS 0.12 Velocities measured by Byrne & Boissonneau compared to numerical results (Position 3) Water alkaline electrolysis, bubble-induced convection 0.08 0.04 0 0.12 0.08 0.04 0 0.12 0.08 (Position 2) (Position 1) Experimental 2000 A/m² Numerical 2000 A/m² Experimental 1000 A/m² Numerical 1000 A/m² Experimental 500 A/m² Numerical 500 A/m² [3] P. Boissonneau, P. Byrne, J. Appl. Electrochem. 30 (2000) 767 775 0.04 0 0 0.5 1 1.5 2 2.5 3 x (mm) 9
2.2 - MODEL VALIDATION : SIMULATING EXPERIMENTAL RESULTS Water alkaline electrolysis, bubble-induced convection Void fraction evolution and streamlines (2000 A/m²) 10 [3] P. Boissonneau, P. Byrne, J. Appl. Electrochem. 30 (2000) 767 775
2.3 CREATING NEW MODEL : THE THERMAL ANALOGY [4] Bubble plume ~ thermal boundary layer Buoyancy forces and void fraction concentrated in the vicinity of electrodes δ α Dispersed phase conservation ~ convectionconduction equation α U x + U α x y = y x K α ~ au S K α α x Pr α = ν K α L Boundary layer thickness scale analysis Rayleigh-like number Rα e,f = νu ge 5 a 6 gl δ α e ~Rα e,f 1/4 2e 11 [4] Schillings et al., Int. J. Heat Mass Transfer 85 (2015) 292 299
2.3 - PR α >> 1 Relative plume thickness vs. Rayleigh-like number (log-scale) At high currents Strong shear U Sdiff,x U Hdiff,x K α ~ r 2 b γ δ α ~ r b e e 2 L Important result : δ α e ~ r b 6 gl νu g e 5 0,25 12
δ α /e 2.3 - PR α << 1 : LIMITING CASE Relative plume thickness vs. current density 1 0.96 0.92 0.88 0.84 0.8 0 500 1000 1500 2000 2500 3000 3500 4000 i av (A/m²) U Saff 13
2.4 - SENSIBILITY TO FORCED CONVECTION Plume development in a Poiseuille flow : δ α e ~ L e 1 3 1/3 1/3 Prα Re DH Relative plume thickness vs. Reynolds-Prandtl (log scale) Forced convection decreases δ α 14
3 RECENT WORKS & PROSPECTS Experiments High speed camera recorder Flow caracterization (bubbleinduced & forced convection) Electrochemical Impedance Spectroscopy DNS Implementation of Lagrangian tracking Two-way coupling between the dispersed and continuous phase Simulation of collisions between bubbles 15
ANY QUESTION? Jonathan SCHILLINGS, J. DESEURE, O. DOCHE 16 LEPMI / SIMAP (CNRS/Grenoble INP/Université Joseph Fourier/Université de Savoie) PHELMA Campus 1130, rue de la Piscine - BP 75 F-38402 - St-Martin d'hères Cedex