Multiphysics algorithms for the simulation of geological materials under extreme conditions: the evolution and transport of ablated material

One of the biggest challenges to deep geothermal is the ability to drill sufficiently deep into very hot bedrock. The state of the art in conventional, mechanical drilling falls short at this task due to severe wearing effects. Millimetre wave (MMW) drilling is a non-contact technology that uses directed millimetre waves produced by a gyrotron to vaporise and ablate bedrock, creating a borehole cavity, with the vaporised material being removed by a purge gas. As an immature technology, it presents new challenges that are difficult to study experimentally due to the extreme conditions. This study is concerned with the design and implementation of a numerical model capable of simulating dust-laden flow resulting from MMW drilling, as a preliminary step to allow for a better understanding of the problem, that issues can be identified and future optimisations be made. Given that the quantity of particles can vary greatly depending on their size, with orders of magnitude upwards of 106 particles, it follows that a method which considers particles and fluid as interpenetrating continua is the natural choice. Unfortunately, there exist a large number of continuum gas-solid models in the literature, which do not necessarily agree with each other. To eliminate such ambiguity in this work, the multiphase gas-solid model is derived directly from the kinetic theory, cumulating in a fully compressible model valid for all dilute to dense regimes, addressing the kinetic to frictional transition and accounting for viscosity. The equations are discretised into a Cartesian grid, with each phase treated separately using a modified HLLC solver. In particular, the granular phase equations suffer from instability when the particle concentration is dense, stemming from the diverging internal stresses near the maximum packing limit. Several methods are introduced to increase the robustness of the system, by limiting the magnitude of frictional pressure and introducing a dissipative term in the numerical flux when the particle volume fraction is high. Unique to MMW drilling is the structure of the waveguide and launcher, which directs both the MMW beam itself and the purge gas with which to circulate the ablated material. The compressible interaction of a viscous, particle laden gas and complex geometry is fundamental to the flow in question, which is confined within the annular region. To allow for easy representation of arbitrary geometries, a diffuse-interface embedded boundary method has been implemented. This retains the Cartesian mesh, allowing for the developed numerical solvers to be used with minimal changes that are only applied in the vicinity of the boundaries. The model is then used to perform a preliminary study with conditions expected of the MMW drilling process, elucidating the nonlinear interactions between a hot particle cloud and the cool impinging jet. It was found that the MMW waveguide configurations significantly alter the flow of the purge gas, affecting its ability to cool and extrude the ablated material. Coupling between the gas flow and dust phase is greatly dependent on the particle size, and is hence correlated to the amount of dusty material recirculating at the base of the cavity. This emphasises the need to combine computational study with further experimentation, to obtain an accurate prediction of particle distribution, and to identify the effects dust particles have on the MMW radiation process.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2024

Author dc:creator

• Lim, Cassandra

Advisor dc:contributor.advisor

• Nikiforakis, Nikolaos

• Computational physics
• Deep geothermal
• Dusty gas
• Immersed boundary method
• Kinetic theory of granular flow
• Multiphase flow

Licence

• https://www.repository.cam.ac.uk/bitstreams/deee039e-42db-45e7-86e0-ac18e314b5b1/download
• http://purl.org/NET/rdflicense/allrightsreserved

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.119784

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/386660