Modelling and analysis of paste flow in high performance Soderberg electrodes
<p>The Søderberg electrode is a continuously consumed electrode invented about 100 years ago by the company now known as Elkem ASA. It remains the most commonly used electrode system, which provides the energy necessary for the production of ferroalloys and calcium carbide. The electrode paste...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
2021
|
| Subjects: |
| _version_ | 1826307023050899456 |
|---|---|
| author | Kamilova, AA |
| author2 | Hewitt, IJ |
| author_facet | Hewitt, IJ Kamilova, AA |
| author_sort | Kamilova, AA |
| collection | OXFORD |
| description | <p>The Søderberg electrode is a continuously consumed electrode invented about 100 years ago by the company now known as Elkem ASA. It remains the most commonly used electrode system, which provides the energy necessary for the production of ferroalloys and calcium carbide. The electrode paste is the raw material that makes the electrodes: a mixture of pitch tar binder and calcined anthracite. It can be added in the form of solid cylinders at the inlet of the steel casing that encloses the electrode column. As the temperature increases inside the electrode column, the paste softens and spreads until it reaches the electrode casing, and then is baked as
the temperature reaches 450 ◦ C. In normal operation, hot paste from lower down the casing may be recirculated up to the top, forming a viscous pool of paste which in urn contributes to the softening of new incoming cylinders.</p>
<p>In this thesis we derive mathematical models focusing on the top part of the electrode where the paste softening process occurs. An incorrect softening profile of the paste may lead to a baked electrode with non-uniform material properties, leading to costly and dangerous breakages. For the models presented in this work, we have incorporated an exponential dependence of viscosity on temperature to account for how sensitive the paste is to temperature variations. Temperature variations result from the heating supplied by hot air outside the casing, as well as electrical induction effects caused by the proximity of the copper tubes that supply the electrical current to the casing.</p>
<p>In Chapter 2, we begin by formulating a two-dimensional flow and temperature model in steady state, which is then asymptotically reduced to a one-dimensional extensional flow model. We obtain numerical solutions to understand which physical effects control the position where the paste touches the casing for the first time, x = λ. In Chapter 3, we investigate this model further by looking at time dependent solutions. We use boundary layer theory and the theory of multiple scales to understand how the addition of cylinders affects the time evolution of λ(t). In Chapter 4, we construct and solve a finite element model to gain some intuition on the role of the recirculating paste near the top of the electrode, and we discuss how we can make some conclusions on cylinder addition from this model. In Chapter 5, we use the structure of the solutions found in Chapter 4 to motivate a hybrid extensional flow model with lubrication flow near the walls where the temperature is higher and the viscosity is lower. We find asymptotic solutions for both the flow profile and the temperature distribution in the various boundary layers found in the problem, which we then interpret in the context of the industrial problem. We conclude this thesis with a summary and a discussion in Chapter 6.</p> |
| first_indexed | 2024-03-07T06:56:47Z |
| format | Thesis |
| id | oxford-uuid:fe65fdfa-3765-4df0-a47b-47d499da0086 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:56:47Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | oxford-uuid:fe65fdfa-3765-4df0-a47b-47d499da00862022-03-27T13:36:10ZModelling and analysis of paste flow in high performance Soderberg electrodesThesishttp://purl.org/coar/resource_type/c_db06uuid:fe65fdfa-3765-4df0-a47b-47d499da0086MathematicsAsymptotic expansionsEnglishHyrax Deposit2021Kamilova, AAHewitt, IJHowell, PDPlease, CPHicks, PD<p>The Søderberg electrode is a continuously consumed electrode invented about 100 years ago by the company now known as Elkem ASA. It remains the most commonly used electrode system, which provides the energy necessary for the production of ferroalloys and calcium carbide. The electrode paste is the raw material that makes the electrodes: a mixture of pitch tar binder and calcined anthracite. It can be added in the form of solid cylinders at the inlet of the steel casing that encloses the electrode column. As the temperature increases inside the electrode column, the paste softens and spreads until it reaches the electrode casing, and then is baked as the temperature reaches 450 ◦ C. In normal operation, hot paste from lower down the casing may be recirculated up to the top, forming a viscous pool of paste which in urn contributes to the softening of new incoming cylinders.</p> <p>In this thesis we derive mathematical models focusing on the top part of the electrode where the paste softening process occurs. An incorrect softening profile of the paste may lead to a baked electrode with non-uniform material properties, leading to costly and dangerous breakages. For the models presented in this work, we have incorporated an exponential dependence of viscosity on temperature to account for how sensitive the paste is to temperature variations. Temperature variations result from the heating supplied by hot air outside the casing, as well as electrical induction effects caused by the proximity of the copper tubes that supply the electrical current to the casing.</p> <p>In Chapter 2, we begin by formulating a two-dimensional flow and temperature model in steady state, which is then asymptotically reduced to a one-dimensional extensional flow model. We obtain numerical solutions to understand which physical effects control the position where the paste touches the casing for the first time, x = λ. In Chapter 3, we investigate this model further by looking at time dependent solutions. We use boundary layer theory and the theory of multiple scales to understand how the addition of cylinders affects the time evolution of λ(t). In Chapter 4, we construct and solve a finite element model to gain some intuition on the role of the recirculating paste near the top of the electrode, and we discuss how we can make some conclusions on cylinder addition from this model. In Chapter 5, we use the structure of the solutions found in Chapter 4 to motivate a hybrid extensional flow model with lubrication flow near the walls where the temperature is higher and the viscosity is lower. We find asymptotic solutions for both the flow profile and the temperature distribution in the various boundary layers found in the problem, which we then interpret in the context of the industrial problem. We conclude this thesis with a summary and a discussion in Chapter 6.</p> |
| spellingShingle | Mathematics Asymptotic expansions Kamilova, AA Modelling and analysis of paste flow in high performance Soderberg electrodes |
| title | Modelling and analysis of paste flow in high performance Soderberg electrodes |
| title_full | Modelling and analysis of paste flow in high performance Soderberg electrodes |
| title_fullStr | Modelling and analysis of paste flow in high performance Soderberg electrodes |
| title_full_unstemmed | Modelling and analysis of paste flow in high performance Soderberg electrodes |
| title_short | Modelling and analysis of paste flow in high performance Soderberg electrodes |
| title_sort | modelling and analysis of paste flow in high performance soderberg electrodes |
| topic | Mathematics Asymptotic expansions |
| work_keys_str_mv | AT kamilovaaa modellingandanalysisofpasteflowinhighperformancesoderbergelectrodes |