Performance evaluation of an implicitly-regularised model for viscoplastic particle suspensions

Abstract

Firstly, I would like to show my appreciation towards my supervisor, Dr. Christopher Leonardi, for all of the support and advice over the last six months. Your thorough feedback and constant interest in and dedication to the project drove me to produce the highest quality work I could. My development throughout the project has been immeasurable, with the work opening my eyes to a world of future career possibilities, and for those things I am grateful.To Wojciech Regulski in Poland, thank you for the many code implementations, constant assistance, and the opportunity to share in your work. This was as much your project as it was mine. Good luck with your current work and future studies.Finally, to my family, thank you for keeping me grounded and providing an unwavering source of support that I could depend upon. To my friends, thank you for the much needed laughter (even if it did verge on hysterical at times) and for providing numerous outlets for me to blow off some steam. This year has been the most challenging of my life so far, but also the most enjoyable.ii Abstract Due to their unique properties, dense viscoplastic fluid-particle suspensions have significant potential to be used in a number of industrial applications, from hydraulic fracturing to pipeline particulate transport. However, the rheological properties of these suspensions are currently poorly understood, with no comprehensive modelling strategies existing to predict their behaviour. Numerous numerical difficulties arise when attempting to model viscoplastic suspensions, a key cause of which is the presence of a fluid yield-stress. Currently, a number of explicit regularisation techniques are used to approximate the yieldstress, the inherent numerical inaccuracies of which are quite often given little attention.A coupled LBM-DEM numerical approach presents an excellent solution to modelling the bulk movement of particles within suspensions, and has been successfully applied to the modelling of dense Newtonian suspensions. Of key importance, however, the LBM allows for an implicit regularisation of the yield-stress, in which the constitutive Bingham fluid is solved without the need for the approximations of current explicit solvers. Hence, it was hypothesised that the implicitly-regularised (IR) model is superior for the modelling of viscoplastic fluids, a claim which, if true, would lead to the eventual direct numerical simulation of dense viscoplastic particle suspensions. Consequently, the aim of the investigation was to evaluate the performance of the IR LBM-DEM in viscoplastic fluid-particle coupling, compared to that of the explicit Papanastasiou-regularised (PR) two-relaxation-time (TRT) method.To achieve this, five numerical testing models were developed, based off existing numerical and experimental studies of simplified benchmark problems in the literature. These 2-D and 3-D simulations provided a basis for the validation of the IR model, as well as a means for performance comparisons between the IR and TRT models.In initial 2-D simula...