Material flow in a silicon furnace

This project falls within the EPSRC Continuum mechanics research areas.
This project is undertaken with Industrial Partner Elkem.


Elkem is a major producer of silicon alloys. Silicon is produced in three-electrodes submerged arc furnaces through reactions between melted quartz, various carbon materials, silicon carbide and silicon monoxide gas at very high temperatures. Particles of carbon (approx. 1 cm diameter) and quartz (2-10 cm) are fed at the furnace top, where they form a granular furnace charge. As this charge flows down the particles are heated, and the quartz particles crack and disintegrate, as well as soften and melt. This melting, combined with gas condensation reactions, glues the charge together, creating a viscous "crust region" above a gas cavity. The properties of the quartz are crucial to the flow of the charge and the production of silicon, with furnace operation changing in response to a different quartz input. The flow is influenced by the thermally dependent viscosity of the quartz and the crust, as well as by discontinuous and unstable tapping of liquid silicon from the furnace base.

In this project we will build mathematical models to explore the downward flow of material in the furnace, considering the effects of heat transfer, disintegration, phase changes, softening and melting of quartz, and chemical reactions, as well as accounting for quartz properties, such as particle size, melting temperature, and density. We will consider how a single quartz particle undergoes heating, thermal stress, phase change, and then will use this understanding in a macroscale model of flow in the furnace. Of particular interest is the transition from granular flow in the upper charge to viscous flow in the crust. Our models will account for the strong coupling between i) the flow behaviour, ii) the thermal distribution, and iii) the cracking, heating, phase transition, softening and melting of quartz particles, and will be solved using analytical and numerical approaches.

This research project will be part of a larger project on "High Temperature Quartz", partially funded by the Norwegian Research Council. Relevant results from this will feed into our mathematical models.

Potential outcomes:
(i) Models describing the cracking, disintegration, heating, phase transition, softening, melting, and viscosity changes in quartz particles.
(ii) Models of the charge flow accounting for granular and viscous regimes, with coupled thermal and chemical effects.
(iii) Three dimensional numerical simulations of the flow patterns within a silicon furnace.

The CDT in Industrially Focused Mathematical Modelling has been designed by academics and industrialists to enable modern quantitative methods to be readily and efficiently applied to industrial problems, thereby creating rapid impact through competitive advantage. The training includes aspects that will allow students to appreciate the business context within which the application of their mathematical research sits and hence understand where such application might have greatest influence. The emphasis on team working and interaction with different disciplines will create an environment where the insight gained from the mathematical ideas can be fully exploited. The cohort-based training of the CDT is directly aimed at ensuring that the students have continual active interactions and discussions so that identifying opportunities for technology transfer between the many industrial projects that they engage in will be a natural activity. The impact will be realised both through direct exploitation of the mathematical ideas by our partner companies and through more general dissemination routes to a wider industry base, for example through our annual meeting and appropriate forms of publication. The mini-projects enable new partners to engage at a relatively easily level, where they can assess possible impact, before progressing through to the longer research project element.

Our industrial partners have given some indication of the level of impact that they expect from the interaction with the CDT. In particular several letters highlight the extensive track records they have in funding Oxford internships and DPhils associated with supervisors who will be in the CDT. Furthermore, our students will graduate with the skills needed to operate successfully in industry and, as several companies indicate in their letters of support, will be ideal employees.

We have specifically engaged two partners, the Smith Institute in the UK and Teknova in Norway who have a major role in facilitating mathematical interaction between industry and academia. We are therefore ideally placed to ensure that the widest possible set of companies are aware of the CDT and its benefits. These partners will also be in a position to identify where the outputs of the CDT might be exploited through technology transfer opportunities.

We will have annual events where the cohorts will present their ideas and where we draw in a larger industrial audience in order both to widen our connections and possible partners but also to disseminate the ideas into the industrial community where possible exploitation might be identified.