Development of a Numerically Inexpensive 3D CFD Model of Slag Reduction in a Submerged Arc Furnace for Phosphorus Recovery from Sewage Sludge

Phosphorus is an essential resource for numerous industrial applications. However, its uneven global distribution makes Europe heavily dependent on imports. Recovering phosphorus from waste streams is therefore crucial for improving resource security. The FlashPhos project addresses this challenge by developing a process to recover phosphorus from sewage sludge, in which phosphorus-rich slag is produced in a flash reactor and subsequently reduced in a Submerged Arc Furnace (SAF). In this process, approximately 250 kg/h of sewage sludge is converted into slag, which is further processed in the SAF to recover about 8 kg/h of white phosphorus. This work focuses on the development of a computational model of the SAF, with particular emphasis on slag behaviour. Due to the extreme operating conditions, which severely limit experimental access, a numerically efficient three-dimensional CFD model was developed to investigate the internal flow of the three-phase, AC-powered SAF. The model accounts for multiphase interactions, dynamic bubble generation and energy sinks associated with the reduction reaction, and Joule heating. A temperature control loop adjusts electrode currents to reach and maintain a prescribed target temperature. To further reduce computational cost, a novel simulation approach is introduced, achieving a reduction in simulation time of up to 300%. This approach replaces the solution of the electric potential equation with time-averaged Joule-heating values obtained from a preceding simulation. The system requires transient simulation and reaches a pseudo-steady state after approximately 337 s. The results demonstrate effective slag mixing, with gas bubbles significantly enhancing flow velocities compared to natural convection alone, leading to maximum slag velocities of 0.9–1.0 m/s. The temperature field is largely uniform and closely matches the target temperature within ±2 K, indicating efficient mixing and control. A parameter study reveals a strong sensitivity of the flow behaviour to the slag viscosity, while electrode spacing shows no clear influence. Overall, the model provides a robust basis for further development and future coupling with the gas phase.