Interface resolved simulations of continuum scale electrochemical hydrogen evolution

An important aspect of improving the efficiency of water electrolysis is to remove the electrochemically generated hydrogen and oxygen bubbles. The evolution of these gases, which are associated with increased electrical resistance, are driven by electrochemical reactions causing supersaturation of the electrolyte which leads to bubble nucleation, growth, and eventual detachment from the electrode. Due to the different physics as well as the length and time scales associated with the process, referred to as the multiscale and multiphysics nature, predicting the bubble evolution using analytical models is challenging. As numerical modelling approaches, like Computational Fluid Dynamics (CFD), predicts the fluid flow based on the underlying governing equations, it can be used to study electrochemical bubble evolution. The work undertaken during the PhD is primarily to develop and verify a multiphysics CFD framework based on the Volume of Fluid (VOF) method available in OpenFOAM® for continuum scale hydrogen bubbles. In the context of this work, continuum scale bubbles refers to bubble diameters which are larger than a few hundred micrometers. The VOF method is customized by adding the physics and numerical techniques relevant to treating electrochemical reactions, dissolved gas transport, charge transport, interfacial mass transfer and associated bubble growth (from a pre-existing submillimeter bubble). The proposed framework is developed incrementally, with each step corresponding to implementation and verification of a multiphysics module, eventually culminating in the fully coupled multiphysics framework. This modularized approach allows for verification of the implemented functionality with existing theoretical models and/or computational benchmarks. The thesis, in essence, provides context to the undertaken research, review of the various modelling techniques used to treat the multiphysics nature of electrochemical hydrogen evolution and details of developed framework. In addition, the thesis also summarizes knowledge gained during the PhD about the solution procedure used in OpenFOAM® and the VOF method to enable knowledge dissemination for further research

Numerical simulation of continuum scale electrochemical hydrogen bubble evolution

One of the important aspects in improving the efficiency of electrochemical processes, such as water electrolysis, is the efficient removal of bubbles which evolve from the electrodes. Numerical modelling based on Computational Fluid Dynamics (CFD) can describe the process, provide insights into its complexity, elucidate the underlying mechanisms of how bubbles evolve and their effect as well as aid in developing strategies to reduce the impact of the bubble. In this paper, a Volume of Fluid (VOF) based simulation framework to study the evolution of hydrogen bubbles in the order of few hundred micrometers, refered to as continuum scale bubbles, is proposed. The framework accounts for the multiphase nature of the process, electrochemical reactions, dissolved gas transport, charge transport, interfacial mass transfer and associated bubble growth. The proposed solver is verified, for two-dimensional cases, by comparison to analytical solution of bubble growth in supersaturated solutions, stationary bubble, rising bubbles and qualitative analysis based on experimental observations of the variations in current based on static simulations. The proposed solver is used to simulate the evolution of a single bubble under various wetting conditions of the electrode as well as the coalescence driven evolution of two bubbles. The results show that as the bubbles detach, its surface oscillates and the shape of the rising bubble is determined by the balance between drag force and surface tension. These surface oscillations, which causes the bubble to get flattened and elongated, results in temporal variation of the electrical current. The reduction of current due to bubble growth is visible only when these surface oscillations have reduced. The simulations also show the current as a function of the position of the bubble in the interelectrode gap. The framework also predicts the increase in current as a result of bubbles leaving the surface which is larger when the process is coalescence driven. The simulations indicate that bubble coalescence is the underlying mechanism for continuum scale bubble detachment

ON MODELLING ELECTROCHEMICAL GAS EVOLUTION USING THE VOLUME OF FLUID METHOD

In this work we describe the various building block relevant in simulating electrochemical gas evolution using Volume of Fluid (VOF) method. These building blocks are implemented in the VOF solver available in OpenFOAM® and its predictions are compared to the theoretical models reported in literature. The fully coupled solver to model electrochemical gas evolution is used to model the case of a bubble evolving on a vertical electrode under constant potential condition to showcase its ability.publishedVersio

On sharp surface force model: effect of sharpening coefficient

Amongst the multitude of approaches available in literature to reduce spurious velocities in Volume of Fluid approach, the Sharp Surface Force (SSF) model is increasingly being used due to its relative ease to implement. The SSF approach relies on a user-defined parameter, the sharpening coefficient, which determines the extent of the smeared nature of interface used to determine the surface tension force. In this paper, we use the SSF model implemented in OpenFOAM® to investigate the effect of this sharpening coefficient on spurious velocities and accuracy of dynamic, i.e., capillary rise, and static bubble simulations. Results show that increasing the sharpening coefficient generally reduces the spurious velocities in both static and dynamic cases. Although static millimeter sized bubbles were simulated with the whole range of sharpening coefficients, sub-millimeter sized bubbles show nonphysical behavior for values larger than 0.3. The accuracy of the capillary rise simulations has been observed to change non-linearly with the sharpening coefficient. This work illustrates the importance of using an optimized value of the sharpening coefficient with respect to spurious velocities and accuracy of the simulation

Numerical simulation of bubble growth in a supersaturated solution

In this paper, a Volume of Fluid (VOF) based approach to simulate the growth of a pre-existing bubble in a supersaturated solution is developed and implemented in OpenFOAMⓇ. The model incorporates the Compressive Continuous Species Transfer approach to describe the transport of dissolved gas and surface tension is treated using the Sharp Surface Force method. The driving force for bubble growth is defined using Fick’s 1st law and a Sherwood number based correlation. The source terms for the governing equations are implemented by extending the work by Hardt and Wondra, J. Comp. Phys. 227 (2008) 5871–5895. The predictions of the proposed solver is compared against theoretical models for bubble growth in supersaturated solutions. The effect of spurious currents, which are generated while modelling surface tension, on bubble growth is also investigated. The proposed approach is used to model the growth of a rising bubble in the supersaturated solution

Comparison of Surface Tension Models for the Volume of Fluid Method

With the increasing use of Computational Fluid Dynamics to investigate multiphase flow scenarios, modelling surface tension effects has been a topic of active research. A well known associated problem is the generation of spurious velocities (or currents), arising due to inaccuracies in calculations of the surface tension force. These spurious currents cause nonphysical flows which can adversely affect the predictive capability of these simulations. In this paper, we implement the Continuum Surface Force (CSF), Smoothed CSF and Sharp Surface Force (SSF) models in OpenFOAM. The models were validated for various multiphase flow scenarios for Capillary numbers of 10 −3 –10. All the surface tension models provide reasonable agreement with benchmarking data for rising bubble simulations. Both CSF and SSF models successfully predicted the capillary rise between two parallel plates, but Smoothed CSF could not provide reliable results. The evolution of spurious current were studied for millimetre-sized stationary bubbles. The results shows that SSF and CSF models generate the least and most spurious currents, respectively. We also show that maximum time step, mesh resolution and the under-relaxation factor used in the simulations affect the magnitude of spurious currents

ON MODELLING ELECTROCHEMICAL GAS EVOLUTION USING THE VOLUME OF FLUID METHOD

In this work we describe the various building block relevant in simulating electrochemical gas evolution using Volume of Fluid (VOF) method. These building blocks are implemented in the VOF solver available in OpenFOAM® and its predictions are compared to the theoretical models reported in literature. The fully coupled solver to model electrochemical gas evolution is used to model the case of a bubble evolving on a vertical electrode under constant potential condition to showcase its ability

ON MODELLING ELECTROCHEMICAL GAS EVOLUTION USING THE VOLUME OF FLUID METHOD

In this work we describe the various building block relevant in simulating electrochemical gas evolution using Volume of Fluid (VOF) method. These building blocks are implemented in the VOF solver available in OpenFOAM® and its predictions are compared to the theoretical models reported in literature. The fully coupled solver to model electrochemical gas evolution is used to model the case of a bubble evolving on a vertical electrode under constant potential condition to showcase its ability.publishedVersio

On modelling electrochemical gas evolution using the volume of fluid method

In this work we describe the various building block relevant in simulating electrochemical gas evolution using Volume of Fluid (VOF) method. These building blocks are implemented in the VOF solver available in OpenFOAM® and its predictions are compared to the theoretical models reported in literature. The fully coupled solver to model electrochemical gas evolution is used to model the case of a bubble evolving on a vertical electrode under constant potential condition to showcase its ability

Comparison of Surface Tension Models for the Volume of Fluid Method

With the increasing use of Computational Fluid Dynamics to investigate multiphase flow scenarios, modelling surface tension effects has been a topic of active research. A well known associated problem is the generation of spurious velocities (or currents), arising due to inaccuracies in calculations of the surface tension force. These spurious currents cause nonphysical flows which can adversely affect the predictive capability of these simulations. In this paper, we implement the Continuum Surface Force (CSF), Smoothed CSF and Sharp Surface Force (SSF) models in OpenFOAM. The models were validated for various multiphase flow scenarios for Capillary numbers of 10 − 3 –10. All the surface tension models provide reasonable agreement with benchmarking data for rising bubble simulations. Both CSF and SSF models successfully predicted the capillary rise between two parallel plates, but Smoothed CSF could not provide reliable results. The evolution of spurious current were studied for millimetre-sized stationary bubbles. The results shows that SSF and CSF models generate the least and most spurious currents, respectively. We also show that maximum time step, mesh resolution and the under-relaxation factor used in the simulations affect the magnitude of spurious currents