Development and validation of a phase-field lattice Boltzmann method for non-Newtonian Herschel-Bulkley fluids in three dimensions
Abstract
The behaviour of non-Newtonian fluids, and their interaction with other fluid phases and components, is of interest in a diverse range of scientific and engineering problems. In the context of the lattice Boltzmann method (LBM), both non-Newtonian rheology and multiphase flows have received significant attention in the literature. This study builds on that work by presenting the development and validation of a phase-field LBM which combines these features in three-dimensional flows. Specifically, the model presented herein combines the simulation of Herschel-Bulkley fluids, which exhibit both a yield stress and power-law dependence on shear rate, interacting with a Newtonian fluid. The developed model is verified and validated using a diverse set of rheological properties and flow conditions, which in their totality represent an additional contribution of this work. Comparison with steady-state layered Poiseuille flow, where one fluid is Newtonian and the other is non-Newtonian, showed excellent correlation with the corresponding analytic solution. Validation against analytic solutions for the rise of a power-law fluid in a capillary tube also showed good correlation, but highlighted some sensitivity to initial conditions and high velocities occurring early in the simulation. A demonstration of the model in a microfluidic junction highlighted how non-Newtonian rheology can alter behaviour from cases where only Newtonian fluids are present. It also showed that significant changes in behaviour can occur when making small and smooth changes in non-Newtonian parameters. To summarise, this work broadens the range of physical phenomena that can be captured in computational analysis of complex fluid flows using the LBM.
Lattice Boltzmann simulation of transient blood flow in arterial geometries using a regularised, viscoplastic and shear-thinning fluid
Abstract
This paper presents a lattice Boltzmann framework for the transient simulation of blood flow using biologically inspired geometries and pressure boundary conditions. The Kuang-Luo rheological model is used to represent blood as a homogeneous continuum. This model includes the two primary non-Newtonian characteristics of blood, namely viscoplasticity and pseudoplasticity. This paper makes two contributions. First, the numerical challenges associated with zero strain rates and infinite viscosity, as a consequence of the yield stress in the Kuang-Luo model, were addressed by regularising the constitutive equation so that the viscosity tends towards a finite value at low strain rates. A two-relaxation-time operator, which exhibits improved performance over the single-relaxation-time operator and lower computational overhead than the multiple-relaxation-time operator, is employed in the collision process. The recursive relationship between the local strain rate and relaxation rate was addressed by use of an implicit solver for these two quantities. The implemented model was benchmarked against analytic solutions for Poiseuille flow between parallel plates in two dimensions and in a cylindrical tube in three dimensions. More importantly, the transient performance of the implemented model was demonstrated by matching the predicted start-up flow of the Poiseuille flow of a Bingham fluid with the corresponding analytical solution. Second, the numerical developments were applied in the simulation of transient blood flow in complex configurations. The development and implementation of physically inspired pressure profiles highlighted the shortcomings of using a sinusoidal pressure profile in the prediction of velocity and stress distributions. Finally, the simulation of blood flow in a section of a carotid artery indicated a number of flow characteristics that will be of interest to future investigations of clinical problems.
Lattice Boltzmann modelling of a regularised Kuang-Luo fluid in a carotid artery
Abstract
In this work, a novel lattice Boltzmann (LB) framework for the simulation of non-Newtonian fluids was applied to study the flow of blood in a carotid artery. For this, the Kuang-Luo (KL) rheological model was used to represent the blood as a homogeneous continuum. This captured the primary non-Newtonian characteristics of blood, namely visco- and pseudo-plasticity. The study makes two major contributions to the field. Firstly, it addresses the numerical complexities associated with the yield stress in the KL model through regularisation of the constitutive equation. Secondly, the developed model was applied to simulate transient blood flow in a carotid artery geometry. Two oscillatory pressure profiles are applied to examine the importance of inflow conditions on wall shear stress. The preliminary, high-fidelity analysis of this geometry provided insight into flow characteristics that will be of interest to future investigations of clinical problems.
Development and evaluation of multiphase closure models used in the simulation of unconventional wellbore dynamics
Abstract
A detailed understanding of wellbore flow is essential for production engineers in both the design of site equipment and optimisation of operation conditions. With the depletion of conventional resources, the need for unconventional extraction techniques to leverage untapped reserves has seen the generation of new downhole flow conditions. In particular, the extraction of natural gas from coal seams has led to scenarios where liquid removal from the reservoir can cause the development of a counter-current multiphase flow in the well annulus in pumped wells. In this work, high-fidelity computational fluid dynamics is used to capture the momentum interaction between gas and liquid phases in such a flow configuration, allowing for the evaluation and modification of closure relations used in upscaled models. The computational fluid dynamics model is based on a recently proposed formulation developed using phase-field theory in the lattice Boltzmann (LB) framework. It has been previously applied to the analysis of Taylor bubbles in tubular and annular pipes at a range of inclinations and flow directions. The robustness of the numerical formulation has been proven with a range of benchmark scenarios that extend upon previously reported results in the LB literature. Future investigations will look to apply the developed closure relations into the two-fluid model and compare with in-house experimental and mechanistic results. Using the multiphase lattice Boltzmann model, the drag force closure relations are investigated for bubbles covering a range of parameters. This assesses the accuracy of existing closures and provides confidence in the developed computational tool. Following on from this, the size of the liquid slug behind a Taylor bubble is analysed. Comparison of the results with pre-existing relations provides a means to modify current large-scale simulators to accurately capture the momentum exchange between gas and liquid phases in a wellbore. With the improved understanding of phase interactions developed in this study, upscaling work is to be conducted through the implementation of closure models within a two-fluid-type model, not unlike OLGA, as well as in a recent mechanistic model. The novelty of the high-fidelity computational model is in its ability to resolve high density ratio (liquid-gas) flows under complex, dynamic conditions within the lattice Boltzmann framework. Additionally, the development and validation of novel closure relations for mechanistic and two-fluid models improves the accuracy of predictions associated with wellbore operations, ultimately allowing for more optimised production.