Highly parallelisable simulations of time-dependent viscoplastic fluid flow simulations with structured adaptive mesh refinement

We present the extension of an efficient and highly parallelisable framework for incompressible fluid flow simulations to viscoplastic fluids. The system is governed by incompressible conservation of mass, the Cauchy momentum equation and a generalised Newtonian constitutive law. In order to simulate a wide range of viscoplastic fluids, we employ the Herschel-Bulkley model for yield-stress fluids with nonlinear stress-strain dependency above the yield limit. We utilise Papanastasiou regularisation in our algorithm to deal with the singularity in apparent viscosity. The resulting system of partial differential equations is solved using the IAMR code (Incompressible Adaptive Mesh Refinement), which uses second-order Godunov methodology for the advective terms and semi-implicit diffusion in the context of an approximate projection method to solve on adaptively refined meshes. By augmenting the IAMR code with the ability to simulate regularised Herschel-Bulkley fluids, we obtain efficient numerical software for time-dependent viscoplastic flow in three dimensions, which can be used to investigate systems not considered previously due to computational expense. We validate results from simulations using this new capability against previously published data for Bingham plastics and power-law fluids in the two-dimensional lid-driven cavity. In doing so, we expand the range of Bingham and Reynolds numbers which have been considered in the benchmark tests. Moreover, extensions to time-dependent flow of Herschel-Bulkley fluids and three spatial dimensions offer new insights into the flow of viscoplastic fluids in this test case, and we provide missing benchmark results for these extensions.Funding and technical support from BP through the BP International Centre for Advanced Materials (BP-ICAM) which made this research possible

Thermal Simulation of Millimetre Wave Ablation of Geological Materials

This work is concerned with the numerical simulation of ablation of geological materials using a millimetre wave source. To this end, a new mathematical model is developed for a thermal approach to the problem, allowing for large scale simulations, whilst being able to include the strong temperature dependence of material parameters to ensure accurate modelling of power input into the rock. The model presented is implemented within an adaptive meshing framework, such that resolution can be placed where needed, for example at the borehole wall, to further improve the computational efficiency of large scale simulations. This approach allows for both the heating of the rock, and the removal of evaporated material, allowing rate of penetration and the shape of the resulting borehole to be quantified. The model is validated against experimental results, which indicates that the approach can accurately predict temperatures, and temperature gradients within the rock. The validated model is then exercised to obtain initial results demonstrating its capabilities for simulating the millimetre wave drilling process. The effects of the conditions at the surface of the rock are investigated, highlighting the importance of understanding the physical processes which occur between the wave guide and the rock. Additionally, the absorptivity of the rock, and the impact this has on the evaporation behaviour is considered. Simulations are carried out both for isotropic rock, and also for a multi-strata configuration. It is found that strata between similar rock types, such as granite and basalt, absorptive properties pose little problem for uniform drilling. However, larger variations in material parameters are shown to have strong implications on the evaporation behaviour of the wellbore, and hence the resulting structure.Comment: 13 Pages, 12 figure

A multi-physics method for fracture and fragmentation at high strain-rates

This work outlines a diffuse interface method for the study of fracture and fragmentation in ductile metals at high strain-rates in Eulerian finite volume simulations. The work is based on an existing diffuse interface method capable of simulating a broad range of different multi-physics applications, including multi-material interaction, damage and void opening. The work at hand extends this method with a technique to model realistic material inhomogeneities, and examines the performance of the method on a selection of challenging problems. Material inhomogeneities are included by evolving a scalar field that perturbs a material's plastic yield stress. This perturbation results in non-uniform fragments with a measurable statistical distribution, allowing for underlying defects in a material to be modelled. As the underlying numerical scheme is three dimensional, parallelisable and multi-physics-capable, the scheme can be tested on a range of strenuous problems. These problems especially include a three-dimensional explosively driven fracture study, with an explicitly resolved condensed phase explosive. The new scheme compares well with both experiment and previous numerical studies

Propagation of gaseous detonation waves in a spatially inhomogeneous reactive medium

Detonation propagation in a compressible medium wherein the energy release has been made spatially inhomogeneous is examined via numerical simulation. The inhomogeneity is introduced via step functions in the reaction progress variable, with the local value of energy release correspondingly increased so as to maintain the same average energy density in the medium, and thus a constant Chapman Jouguet (CJ) detonation velocity. A one-step Arrhenius rate governs the rate of energy release in the reactive zones. The resulting dynamics of a detonation propagating in such systems with one-dimensional layers and two-dimensional squares are simulated using a Godunov-type finite-volume scheme. The resulting wave dynamics are analyzed by computing the average wave velocity and one-dimensional averaged wave structure. In the case of sufficiently inhomogeneous media wherein the spacing between reactive zones is greater than the inherent reaction zone length, average wave speeds significantly greater than the corresponding CJ speed of the homogenized medium are obtained. If the shock transit time between reactive zones is less than the reaction time scale, then the classical CJ detonation velocity is recovered. The spatio-temporal averaged structure of the waves in these systems is analyzed via a Favre averaging technique, with terms associated with the thermal and mechanical fluctuations being explicitly computed. The analysis of the averaged wave structure identifies the super-CJ detonations as weak detonations owing to the existence of mechanical non-equilibrium at the effective sonic point embedded within the wave structure. The correspondence of the super-CJ behavior identified in this study with real detonation phenomena that may be observed in experiments is discussed