Electrogenerated bubbles induced convection in narrow vertical cells: PIV measurements and Euler–Lagrange CFD simulation

Highlights

• This paper deals with bubbles hydrodynamics in vertical plane electrode reactors.

• The electrogenerated bubbles mean velocity field is measured using PIV.

• The flow is simulated using the Euler–Lagrange CFD approach.

• Numerical results were in good agreement with experimental data.

• Emphasis is put on the limits on the experimental and numerical approaches.

Abstract

This paper addresses the two-phase flow hydrodynamics in Vertical Plane Electrode Reactors with Gas Electrogeneration, VPERGEs: (1) An experimental investigation of the hydrodynamics in a laboratory-scale VPERGE reactor – for three different current densities – was carried out. Flow visualisation with a high-speed camera, using the gas bubbles as tracers allowed particular flow features to be evidenced. Moreover, thanks to suitable pre- and post- processing tools, the gas velocity fields have been obtained using a PIV algorithm. Measurement errors related to the use of this technique are discussed. The calculated velocity fields provided an overall picture of the flow behaviour, and constitute a data base that can serve for the validation of future numerical results. (2) The two-phase flow was simulated using the two-way momentum coupling Euler–Lagrange CFD approach. Bubbles were considered to be injected slightly away from the electrodes, and not directly at the electrodes surfaces. The shift in the injection position was taken as the average radius of the bubbles. This slight offset of the bubble injection location allowed to obtain a numerical solution that is quasi-independent of the mesh size. CFD results were in good agreement with experimental data, and reproduced key flow features such as spreading of the bubble curtains and bubbles dispersion toward the centre of the reactor.

Introduction

In many electrochemical systems, gas is generated at a single or at both electrodes, either as the desired product or by an unwanted side reaction. In the case of vertical electrodes, gas is released into the electrolyte solution as dispersed small bubbles, whose behaviour and significance in the vicinity of the electrode depend on the current density.

The mechanism of bubbles electrogeneration is the following: the electroactive species (e.g. H⁺ or OH⁻) is transferred to the electrode and then converted into dissolved molecular species (e.g. H₂ or O₂) which is gaseous under the reactor׳s operating conditions. When its local concentration exceeds saturation, it forms bubbles by heterogeneous nucleation: pre-existing gas nuclei on the electrode surface grow into gas bubbles due to dissolved gas transfer from the surrounding supersaturated electrolyte. Once they reach a sufficient size, these bubbles depart from the solid surface, rise up due to buoyancy and form a two-phase layer in the vicinity of the electrode (Fig. 1) that is referred as bubbles׳ curtain. Generally, plane electrodes are oriented vertically so as to prevent bubbles accumulation. Such electrochemical cells will be referred here as Vertical Plane Electrode Reactors with Gas Electrogeneration, VPERGEs. According to their geometry and operating conditions, three main VPERGE reactors types can be distinguished (Hreiz et al., accepted for publication): (1) The forced convection configuration, in which the electrolyte is circulated in the electrode gap by the mean of an external pump. (2) The free convection induced circulation configuration, in which the rising bubbles induce a net electrolyte flow by gas lift effect. (3) The No Net Flow Configuration, NNFC, which is addressed in the current investigation. In this last arrangement, the free surface of the liquid prevents occurrence of an overall liquid flow in the cell: near the electrodes, the electrolyte is dragged upward by the gas bubbles and moves downward near in the central part of the cell, forming two recirculation loops (Fig. 1). Hence, contrary to configuration number 2, in NNFC cells, no net liquid flow occurs across the reactor. Thus, whereas the first two configurations may be regarded as continuous reactors, NNFC cells rather correspond to discontinuous reactors. Additional details about VPERGEs configurations are given in Hreiz et al. (accepted for publication).

The efficiency of electrochemical processes is closely linked to the hydrodynamic behaviour of the bubble curtain(s) (Mandin et al., 2009). First, bubbles accelerate the electrolyte flow near the electrode and enhance agitation; they have therefore a pronounced impact on the convective transport of electrochemically active species. Secondly, bubbles act as moving electrical insulators, thus affecting the current density distribution and increasing the Ohmic drop across the reactor. As reported in the literature review by Hreiz et al. (accepted for publication), several authors have conducted experimental investigations on the hydrodynamics in VPERGE reactors. However, owing to the small gap separating the electrodes, many key aspects of the multiphase flow field are inaccessible to experimental measurements. In this context, CFD reveals to be a prime and powerful low-cost tool for assisting engineers in designing VPERGEs.

As reported in Hreiz et al. (accepted for publication), most studies dealing with the CFD simulation of VPERGEs have adopted the Euler–Euler model, and only Mandin et al. (2005) have resorted to the Euler–Lagrange model. According to these studies (e.g. Ph et al., 2005, Caire et al., 2009, Abdelouahed et al., 2014b), if no bubbles dispersion/transverse migration term is incorporated in the model, CFD generally fails to reproduce the widening of the bubbles curtain along the vertical direction (Fig. 1), which is however a key feature of the flow. Since the mechanisms involved in the spreading of the bubble curtain are not yet fully understood (Hreiz et al., accepted for publication), different terms for bubble dispersion and lateral migration have been introduced: empirical terms expressing the pseudo-turbulence effects in the relative velocity equation (Dahlkild, 2001, Wedin and Dahlkild, 2001, Ipek et al., 2008), bubbles diffusion term in the continuity equations (Mat et al., 2004, Aldas et al., 2008), lift force term in the momentum balance equations (Abdelouahed et al., 2014b), constant volumetric horizontal force Mandin et al. (2005).

In this paper, the case of a NNFC type (Fig. 1) VPERGE reactor is investigated experimentally and numerically: the investigation is related to the development of a pilot cell for iron electrochemical production by Allanore et al. (2010) in which solid particles of iron (III) oxide suspended in a hot concentrated sodium hydroxide solution, are reduced at the cathode to metal iron, whereas oxygen is generated at the anode which consists of parallel blades oriented perpendicularly to the flat cathode. Previous investigations had been carried out in the thin channel between two neighbouring anode blades (Abdelouahed et al., 2014a, Abdelouahed et al., 2014b): for the case of water electrolysis in 0.5 M sodium hydroxide at ambient temperature, current density distributions and bubbles diameter had been determined. Bubble velocity in the vicinity of the anode surface had been estimated by treatment of images taken with a high speed camera. An Euler–Euler approach of the two-phase flow and using ANSYS Fluent^® software could predict gas bubble velocity (Abdelouahed et al., 2014b), but the dispersion of the gas in the channel bulk could be reproduced only upon the introduction of a negative lift force coefficient. This surprising coefficient value for small electrochemical bubbles probably covers in a black-box manner some complex hydrodynamic effects that could not be accounted for in the Euler–Euler approach.

The present work represents a significant progress from the previous studies: flow visualisation through magnification with a high-speed camera, using the gas bubbles as tracers, allowed particular flow features to be evidenced in the channel volume. Moreover, treatment of the images by a PIV algorithm yielded gas velocity fields. The flow is simulated then using the two-way coupling Euler–Lagrange approach available with ANSYS Fluent^® 14.5. Unlike the previous CFD studies on the topic, the spreading of the bubble curtain and bubbles dispersion toward the centre of the reactor could be reproduced without incorporating any ‘artificial’ bubbles lateral migration term in the model. Moreover, a solution that is quasi-independent of the mesh size could be obtained, which is a prime issue when simulating VPERGE reactors using the Euler–Lagrange approach (Mandin et al., 2005). Numerical results were in good agreement with experimental data, for the present case of moderate current density at the anode surface and void fractions usually far below 10%. The effect of simulation conditions e.g. injection of the electrogenerated gas, bubble dimensions and meshing of the volume has been thoroughly investigated and discussed. Finally, it should be noted that the modelling strategy adopted in this paper may be applied to other flow phenomena including heterogeneous nucleation, such as boiling which exhibits numerous common features with gas electrogeneration, in spite of the differences between the two phenomena (Vogt et al. 2004).