Experimental determination of bubble-flow interaction at gas evolving electrode

Transcription

1 Experimental determination of bubble-flow interaction at gas evolving electrode Flora Tomasoni 1, Jeroen van Beeck 1, Michel Riethmuller 1 1: EA department, von Karman Institute for Fluid Dynamic, 1640 St-Genesius-Rode, Belgium, tomasoni@vki.ac.be Abstract Electrochemically generated bubbles behaviour is analysed in the Parallel Flow Reactor (PFR), a quasi-2d horizontal rectangular channel. The reaction is performed by imposing a constant (negative) potential difference between the working and the reference electrode in a 0.1M Na2SO4 solution. In this condition, hydrogen evolution occurs at the cathode, while oxygen evolution takes place at the anode. Quantitative measurements of the potential, bubble size and flow velocity are provided in order to characterise the coupling existing between the liquid flow and the hydrogen bubbles. The characterisation of the micro-bubbles size and velocity is performed by means of backlighting and Laser Doppler Velocimetry. A discussion relative to the two-phase flow interaction is presented and the experimental results are finally compared to those predicted by a theoretical model, based on bubble Lagrangian tracking. The outcomes of the methodology developed, i.e. having potential and in situ bubble size and flow assessment simultaneously, are here presented. 1. Introduction Gas evolving electrodes are electrochemical systems where bubbles are produced by a heterogeneous reaction. Bubbles are often only a reaction side-effect: during metal deposition, for instance, the interaction among bubble evolution, bubble induced flow and material deposition quality is extremely complex. The interaction between bubble growth and detachment and dissolved gas flux results furthermore in an increase of the effective mass transfer coefficient of dissolved gas, leading important consequences on industrial production. The flow of each phase is governed by the continuity, momentum and energy equations. Three main approaches are used to describe the interaction between the two phases: Eulerian-Eulerian (Reeks, 1980), Eulerian-Lagrangian (Mazzitelli, 2003) and the statistic modelling based on the Probability Density Function (Pope, 1994). It is essential to recognise that the equations of the two phases are coupled. The coupling can take place through mass, momentum and energy transfer between phases and it is expressed by the discontinuity of those quantities across the moving interface between the phases. Several experimental works have been focusing on the modification induced by the bubbles in the area close to the wall in a turbulent channel flow, because of the important consequences on the friction and on the mass and heat transfer. A detailed description of the wall region in a bubbly boundary layer has been provided by Marie et al. (1997). Bubbles were injected uniformly into the liquid upstream the inlet of the test sections; Laser Doppler Velocimetry (LDV) was used to characterise the turbulent, single-phase boundary layer, while an optical probe and a high-speed video camera were employed to determine the granulometry of the bubbles. So et al. (2002) performed LDV measurements of millimetric bubbles injected into an upward flow in a rectangular channel. Bubble size was determined by using a high-speed camera and image processing. In order to simulate the effects of the nucleation of bubbles and their departure from the wall in boiling flows, Gabillet et al. (2002) studied experimentally the bubble injection in a turbulent boundary layer. The void fraction, bubble velocity and diameter were measured with a fibre optic probe and the liquid flow in the bubble layer was characterised with a hot film anemometer, so they could not analyse the flow in the inner layers. The aim of this work is to describe the two-phase flow interaction at the level of the viscous sublayer and logarithmic layer by means of non-intrusive and optical based measurement techniques

2 2. Experimental 2.1 Experimental setup The parallel flow reactor (PFR) is used as electrochemical cell. The reactor, designed and built at von Karman Institute, consists in a quasi-two dimensional channel (Table 1), 1 m long (L), 1 dm wide (W) and 1 cm high (2H), Plexiglas made and totally transparent. The PFR (Fig. 1) can be considered as a small industrial prototype, where turbulence plays an important role. The flow is circulating in a close loop forced by a pump (IWAKI, centrifugal pump, series MD). The aperture of two vanes allows the solution to enter in contact with a free surface, so that the produced bubbles can escape from the reactor. The cell is equipped with one cathode at the bottom wall, two anodes at the top wall and an Ag/AgCl reference electrode in the middle of the anodes (Fig. 2). The titaniumplatinized electrodes are 10 cm wide and 5 cm long, not aligned (shifted of 5 cm) and located 50 cm downstream the inlet, so that the flow is fully developed at the electrode section. The ph of the 0.1M Na2SO4 solution is adjusted to 2.5 by adding concentrated H2SO4. Fig. 1. Parallel Flow Reactor. Fig. 2. Parallel Flow Reactor side view: electrodes detail. Table 1. PFR geometry. Le [mm] We [mm] L [mm] W [mm] 2H [mm] The hydrogen bubble evolution occurring on the cathode is characterised by means of the backlighting technique: a diffuse light source is placed on the opposite side of the PFR and shadow images are recorded at 10 Hz with a PCO pixelfly camera (Fig. 3). The bubble-electrolyte mixture velocity is measured along the boundary layer via a two components LDV system (TSI, IFA 750). Polyamide particles (Vestosint X7182, D50 = 22 µm, ρ = gcm 3 ) are used as seeding, both in the single-phase and two-phase flow experiments. The particle relaxation time is τp 40 µs, which therefore allows following the flow fluctuations (Kolmogorov time scale τk 45 µs). Measurements are performed both immediately downstream and 30H downstream the cathode. In order to distinguish between seeding particles and bubbles signal, the trigger lever of the signal intensity was adjusted. However, no important difference could be observed between the bubble velocity profile (high threshold) and the mixture velocity profile (low threshold), since micrometric bubbles have a too small slip velocity

3 Fig. 3. PFR, PCO camera and zoom lens, LDV and laser: top view. 2.2 Bubble sizing A new backlighting software has been developed in order to overcome the typical backlighting defocus bias problem. The blurred model from Bongiovanni et al. (1997) and Gaskill (1978) is considered. The irradiance profile \ (ρ) of an out of focus bubble, whose shadow can be assimilated to that of an opaque disk, is reported in Fig. 4, where is the out of focus, while Rp and R are the pupil size and the disk size projected on the object plane, respectively. Fig. 4. Irradiance profile (Bongiovanni et al.) for a system where R = 0.4 mm, d1 = 0.28 mm, d2 = 0.83 mm and = 2.5 mm. The image formation model is implemented in the code Focused-Recognition-Overlapping- Globule, FROG (Tomasoni, 2010) by using MATLAB (The MathWorks). The software first converts the image to binary image, based on a threshold (half of the maximum image intensity), then it labels connected components in the binary images and finally it provides the geometrical information of the detected bubbles. The region characteristics are obtained by measuring the - 3 -

4 properties of the image regions (blob analysis). By using the bubble image model, the threedimensional bubble location is found. By limiting the value of the accepted, it is possible to control the thickness of the measurement volume. All bubbles can be then subordinates to a validation procedure, so that the strongly out-of-focus bubbles are rejected. A checking criterion based on bubble eccentricity is also imposed. As the number of bubbles in the image increases, the proposed sizing procedures starts in fact to fail: bubbles are touching and a single blob is automatically detected, introducing therefore a high error into the size distribution (bias to higher diameter value). Under the assumption of spherical bubbles (R<1 mm), it is nonetheless possible to erode the cluster-image, to reconstruct the border of this blob and to reconduct it at the superimposition of individual bubbles (Fig. 5). The criteria implemented guarantee that more than 300 touching bubbles can be sized, whereas it allows to size up to four overlapping bubbles, leading to an increase of the void fraction assessment of four times (Tomasoni) respect to a standard backlighting software. Fig. 5. FROG, bubbles sized: erosion activated. Dashed line: in-focus bubbles; continuous line: overlapping bubbles. 3. Theoretical 3.1 Bubble departure The diameter at which a bubble departs from the surface is called break-off diameter. The break-off diameter in stagnant flow can be obtained from the force balance in the vertical-direction, which represents a compensation between the detaching and attaching forces acting on the forming bubble (Ramakrishnan et al., 1969). The lifting forces are the buoyancy and the momentum flux, the restraining forces are the liquid inertia, the surface tension and the drag. In the expansion stage the base of the bubble remains stationary, while the centre moves with a velocity equal to the rate of change of the bubble radius. In this state, it is assumed that the bubble immediately detaches from the surface (no elongation stage), therefore the solution of the force balance, neglecting the electrostatic force contribution, leads to the bubble break-off diameter: FIL + FD + Fσ+FB+FI = 0. (1) By assuming a bubble growth controlled by mass diffusion, an equation for the time t is found (Tomasoni 2010), that can be solved numerically providing the break-off time and bubble radius. By doing so, it appears that as the contact angle increases, the break-off diameter strongly increases as depicted in Fig

5 Fig. 6. Break-off radius vs contact angle, for different crevice diameters. 3.2 Bubble-flow interaction Once that those bubbles depart from the electrode, they interact with the main flow (the continuous phase). To understand the development of the bubble layer and the main phenomena playing a role in bubble-flow interaction, we model the problem of bubbles generated at the electrode, located on the lower wall of a channel, and entrained by a turbulent flow (Fig. 7). Fig. 7. Bubble generation at the bottom wall of a 2D channel and bubbles trajectory angle α formed with respect to the horizontal direction. As in Gabillet et al. (2002), no mass transfer is supposed to occur at the bubble interface, the bubbles interaction and the history forces are neglected, and, in addition, the liquid flow is considered fully developed; however, in our approach both the liquid velocity and the bubble diameter distribution imposed are obtained from the experiments discussed in 4. Under the assumption of steady state, fully developed channel flow, neglecting the bubble inertia compared to the liquid inertia, keeping the added mass coefficient equal to its standard value of 0.5 and setting the drag coefficient to the Hadamard's value, the equation for the bubble motion simplifies to: dv b = 24 ν L dt r (v v ) 2g + 2c (v v 2 L b L L b ) ω, (2) b where b and L stand for bubble and liquid, respectively, rb is the bubble radius, cl = 0.5 is the lift coefficient and ω is the vorticity. Such a system is solved by using the ode23t Matlab solver, that solves initial value problems for - 5 -

6 ordinary differential equations, by applying a trapezoidal rule using a free interpolant. The initial conditions and settings are summarised in Table 2. Table 2. Bubbly flow: initial conditions and ode settings. y(0) [m] v xb (0) [m/s] v yb (0) [m/s] RelTol MaxStep -H + r b 0 0 1E-5 τ b /8 The bubbles are injected along a 5 mm line, situated at the right edge of the bottom electrode with a distribution following a power law of the type xinj (x xmin) 5. The bubbles diameter is lognormally distributed (Table 3) and it is randomly associated to the injection location. The development of the bubble layer and of the void fraction are analysed numerically at different location (Table 3) downstream the electrode (Fig. 7, A, B, C), for a Reynolds number of Re = 1000 and Table 3. PFR: bubble injection boundary conditions. D[µm] µ σ A B C The vertical distribution of the void fraction is shown in Fig. 8. Moving from the bottom wall toward the centre, it is possible to observe an increase of the void fraction, whose maximum value location get higher moving from point A to point C. The void fraction goes then to zero outside the bubble layer. From Fig. 9, it is possible to observe that the bubbles are entrained by the flow and that they follow in average the liquid while rising. Fig. 8. Vertical void fraction profile at location A, B and C. Liquid flow: Re = Fig. 9. Bubble longitudinal velocity at location A, B and C. Liquid flow: Re = Experimental results and discussion 4.1 Single-phase flow Laser Doppler Velocimetry measurements are performed in order to characterise the flow in the Parallel Flow Reactor. Velocity profiles are taken at the inlet, at the electrode (x/h = 100, H = 5mm) and 30H downstream the electrode itself. As it is possible to see from Fig. 10, at the channel inlet the profile is rather flat, while at the electrode it shows the typical internal flow shape. The profile taken downstream the electrode is identical to the electrode one: it is concluded therefore - 6 -

7 that the flow under investigation is fully developed, at least downstream the electrode area. Fig. 10. Single-phase velocity profile (Re = 11000), at the channel inlet (x/h = 0), at the electrode (x/h = 100) and 30 H downstream the electrode. Measurements are then taken at the electrode (x/h = 100) for a Reynolds number, Re= 2Hu MEAN /ν L, of 1000, 2000, 4000 and (Table 4). The flow is fully turbulent for Re>1800, although transitional effects are evident up to Re = In the latter condition, the results are presented in terms of wall units: u + = u, y + = y u τ, (3) u τ ν L where uτ = τw/ρl is the skin friction velocity and νl is the liquid kinematic viscosity. Fig. 11. Single-phase and two-phase flow velocity profile (Re = 11000), wall units (log-scale). In Fig. 11 (triangles), the single-phase results for Re = are presented. It is possible to identify, for y + < 5, the viscous sub-layer, a region where the velocity u + grows linearly with the wall distance y + ; this region extends till y 200 µm. For y/h < 30 and y + >30 the logarithmic law is - 7 -

8 observed, i.e. the velocity profile can be described by the following equation: u + = 1 κ log(y + ) + B, (4) where κ= 0.41 is the universal von Karman constant and B is a coefficient that depends on the wall roughness (B = 5.2 for a smooth surface). The flow behaviour is therefore in agreement with the one predicted for a fully developed turbulent channel flow Pope (2000). Table 4. LDV measurements. Re u MEAN [m/s] u MAX [m/s] The bubble layer development Bubbles are generated by imposing a constant potential difference between the working V WE and the reference electrode VREF, being the working electrode the titanium platinized cathode (bottom electrode, Ae= 0.05 dm 2 ), the counter electrode the top right anode (Ae = 0.05 dm 2 ) and the reference electrode the Ag/AgCl electrode (Fig. 2). For each Reynolds number, tests are run for a set of potential difference, VWE/REF, ranging from -0.4 to -1.3 V. Using FROG, quantitative results are extracted. In Fig. 13, typical bubble images are displayed for Reynolds 1000 (a) and 2000 (b), when a potential difference of VWE/REF = -0.8 V is imposed. The images are taken immediately downstream the working electrode, at a rate of 10 Hz. The corresponding bubble diameter distributions (collected over 1300 images) are reported in Fig. 12. In both cases the distribution follows a lognormal law, with a mean diameter of 145 µm and 105 µm, respectively. Fig. 12. Bubble layer evolution, V WE/REF = -800 mv, for Reynolds number: Re = 1000 (left) and Re = 2000 (right). From the images it is possible to infer that the bubbles are carried by the flow and rise because of buoyancy. The angle that the bubble trajectory is forming with respect to the horizontal direction (Fig. 7) decreases with the flow velocity: from α = 2.8 at Re = 1000, to α = 1.6 at Re = These results are in good agreement (Fig. 13, c and d, respectively) with those predicted in 3.2, where the bubbles trajectory was computed numerically and the experimental velocity profile and bubble diameter distribution were used as input for the solver: the trajectory angles in the numerical simulations are in fact α = 2.9 at Re = 1000 and α = 1.2 at Re =

9 Fig. 13. Bubble layer evolution, VWE/REF = -800 mv, for Reynolds number: Re = 1000 (a) and Re = 2000 (b). Numerical simulation with Reynolds number: Re = 1000 (c) and Re = 2000 (d). 4.3 Two-phase interaction In Fig. 14 the mean bubble diameter is reported as function of the applied potential difference, for different Reynolds numbers. At low Reynolds number, it is possible to see that, as the voltage increases, the diameter decreases. Recalling (Lippmann, 1875), it is clear now that an increase of the electrode potential, causing a decrease in the contact angle (among other effects), induces a reduction in the break-off diameter ( 3.1). Furthermore, the higher the amount of the evolved bubbles, the higher the bubble-induced flow, which causing a solution stirring, leads to a premature bubble departure. These are therefore two possible explanations of the present experimental observation. When the Reynolds number increases, on the other hand, the dependency on the electrode potential becomes weaker and weaker, till the moment in which, at Re = 4000, the diameter is constant with VWE/REF. As the Reynolds number increase furthermore, the diameter decreases. The superimposition of a faster flow causes in fact a premature bubble detachment (Tan et al. 2000), which explains the diameter reduction and the less important influence of the contact angle. Unfortunately an accurate sizing at higher Reynolds number is still not possible, since the bubble layer thickness at such a high flow velocity is too small and only few bubbles are distinctly measurable. Not only the bubbles are influenced by the flow, but also the flow behaviour itself is changing in the region closer to the wall, because of the bubbles. In Fig. 11 (circles), the bubble-electrolyte mixture velocity is reported. While the centre-line velocity is mainly unchanged with respect to the single-phase velocity, in the viscous sub-layer and logarithmic layer a difference is found. The velocity variation is in fact steeper, which corresponds therefore to an increase of the shear stress, in - 9 -

10 agreement with the results reported by Gabillet et al. (2002). From the momentum balance in the longitudinal direction, they concluded in fact that the wall shear stress at the lower wall has to be greater to compensate for the additional pressure difference, due to the bubble presence in the flow. The wall shear stress was modified according to: y y ( 1 ε)τ t t τ 0 = ρ L g εd y d y, (5) x δ δ where τ t is the total shear stress, τ t 0 is the total shear stress without bubbles, ε is the void fraction and δ is the bubble layer thickness. From eq. 5 it appears therefore that the modification of the shear stress is mainly due to buoyancy. Fig. 14. Bubble mean diameter vs. working electrode potential difference. 5. Conclusions Quantitative results of bubble and flow properties are obtained for a turbulent bubbly flow, revealing the existence of a back-coupling between bubble evolution and turbulent flow. Bubble size was measured by means of backlighting, with the use of a novel recognition algorithm developed by the authors (FROG) and it was found to follow a log-normal distribution. It was possible to emphasise the influence of the flow both on bubble trajectory angle, which decreases with the Reynolds number, and on the bubble departure diameter, that becomes smaller as the Reynolds number increases. On the other hand, the flow field itself experienced the bubble presence, particularly in the sub-layer region, where the velocity gradient resulted higher compared to the single-phase flow condition, because of buoyancy and of the pressure difference increase. References Bongiovanni, C.; Chevaillier, J. P. & Fabre, J. (1997), Sizing of bubbles by incoherent imaging: defocus bias, Experiments in Fluids 23(3), Gabillet, C.; Colin, C. & Fabre, J. (2002), Experimental study of bubble injection in a turbulent boundary layer, International Journal of Multiphase Flow 28(4), Lippmann, G. (1875), Relations entre les phenomenes electriques et capillaires, Ann. Chim. Phys.. Marie, J.; Moursali, E. & Tran-Cong, S. (1997), Similarity law and turbulence intensity profiles in a

11 bubbly boundary layer at low void fractions, International Journal of Multiphase Flow 23(2), Mazzitelli, I. M.; Lohse, D. & Toschi, F. (2003), The effect of microbubbles on developed turbulence, Physics of Fluids 15(1), L5--L8. Pope, S. B. (2000), Turbulent Flows, Cambridge University Press. Pope, S. B. (1994), Lagrangian pdf methods for turbulent flows, Annual Review of Fluid Mechanics 26, Ramakrishnan, S.; Kumar, R. & Kuloor, N. R. (1969), Studies in bubble formation-i bubble formation under constant flow conditions, Chemical Engineering Science 24(4), Reeks, M. W. (1980), Eulerian direct interaction applied to the statistical motion of particles in a turbulent fluid, Journal of Fluid Mechanics 97(03), So, S.; Morikita, H.; Takagi, S. & Matsumoto, Y. (2002), Laser Doppler velocimetry measurement of turbulent bubbly channel flow, Experiments in Fluids 33, Tan, R.; Chen, W. & Tan, K. (2000), A non-spherical model for bubble formation with liquid crossflow, Chemical Engineering Science 55(24), Tomasoni, F. (2010), Non-intrusive assessment of transport phenomena at gas-evolving electrodes, PhD thesis, Vrije Universiteit Brussel and von Karman Institute for Fluid Dynamics. Tomasoni, F. & van Beeck, J. (in preparation), Backlighting extension for void fraction measurement