Abstract

This study investigates the application of wetting boundary conditions for modelling flows in complex curved geometries, such as rough fractures. It implements and analyses two common variants of the wetting boundary condition within the three-dimensional (3D) phase field lattice Boltzmann method. It provides a straightforward and novel extension of the geometrical approach to curved three-dimensional surfaces. It additionally implements surface-energy approach. A novel interpolation-based mitigation of the staircase approximation for curved boundaries is then developed and consistently applied to both wetting boundary conditions. The objectives of simplicity and parallel compute efficiency in implementation are emphasised. Through detailed validation on a series of 3D benchmark cases involving curved surfaces, such as droplet spread on a sphere, capillary intrusion, and droplet impact on a sphere, the behaviour of the wetting boundary conditions are validated and the differences between methods are highlighted. To demonstrate the applicability of the proposed approach in complex geometries with varying surface curvatures, two-phase flow through a synthetic rough fracture is presented. The suitability of the methods for complex simulations is also verified by comparing the computational performance between all investigated methods using this fracture flow test case. The present work thus contributes to the field of multiphase flow modelling with the lattice Boltzmann method in realistic applications where addressing the impact of complex geometries is essential.

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.

Abstract

This study analyses an approach to consistently recover the second-order convergence of the lattice Boltzmann method (LBM), which is frequently degraded by an improper discretisation of the required source terms. The current work focuses on advection-diffusion models, in which the source terms are dependent on the intensity of transported fields. Such terms can be observed in reaction-type equations used in heat and mass transfer problems or multiphase flows. The investigated scheme is applicable to a wide range of formulations within the LBM framework. All considered source terms are interpreted as contributions to the zeroth-moment of the distribution function. These account for sources in a scalar field, such as density, concentration, temperature or a phase field. Further application of this work can be found in the method of manufactured solutions or in the immersed boundary method. This paper is dedicated to three aspects regarding proper inclusion of the source term in LBM schemes. Firstly, it identifies the differences observed between the ways in which source terms are included in the LBM schemes present in the literature. The algebraic manipulations are explicitly presented in this paper to clarify the observed differences, and to identify their origin. Secondly, it analyses in full detail, the implicit relation between the value of the transported macroscopic field, and the sum of the LBM densities. This relation is valid for any source term discretization scheme. It is a crucial ingredient for preserving the second-order convergence in the case of complex source terms. Moreover, three equivalent forms of the second-order accurate collision operator are presented. Finally, closed form solutions of this implicit relation are shown for a variety of common models, including general linear and second order terms; population growth models, such as the Logistic or Gompertz model and the Allen-Cahn equation. The second-order convergence of the proposed LBM schemes is verified on both linear and non-linear source terms. The pitfalls of the commonly used acoustic and diffusive scalings are identified and discussed. Furthermore, for a simplified case, the competing errors are shown visually with isolines of error in the space of spatial and temporal resolutions.

Particle clogging can occur in any scenario where a flow path or constriction is small relative to the size of objects trying to pass through it - think of flow through silos, blood flows through needles, and even the evacuation of crowds through barrieres. It originates from the formation of a single arch, behind which an entire flow path can become blocked. This work is the first time hydrodynamic clogging has been thoroughly investigated in planar channels. We also studied the effects of electrostatic forces, which become significant for micro-particles.

Abstract

The permeability of rocks is important in a range of geoscientific applications, including CO 2 sequestration, geothermal energy extraction, and in situ mineral recovery. This work presents an investigation of the change in permeability in porphyry rock samples due to blast-induced fracturing. Two samples were analysed before and after exposure to stress waves induced by the detonation of an explosive charge. Micro-computed tomography was used to image the interior of the samples at a pixel resolution of 10.3μm. The images were segmented into void, matrix, and grain to help quantify the differences in the rock samples. Following this, they were binarised as void or solid and the cumulant lattice Boltzmann method (LBM) was applied to simulate the flow of fluid through the connected void space. A correction required with the use of inlet and outlet reservoirs in computational permeability assessment was also proposed. Interrogation of the steady-state flow field allowed the pre- and post-loading permeability to be extracted. Conclusions were then drawn as to the effectiveness of blasting for enhancing fluid accessibility via the generation of microfractures in the rock matrix within the vicinity of a detonated charge. This paper makes contributions in three fundamental areas relating to the numerical assessment of permeability and the enhancement of fluid accessibility in low-porosity rocks. Firstly, a correction factor was proposed to account for the reservoirs commonly imposed on digitised rock samples when investigating sample permeability through numerical methods. Secondly, it validates the benefits of the LBM in handling complex geometries that would be intractable with conventional computational fluid dynamics methods that require body-fitted meshing. This is done with a novel implementation of the cumulant LBM in the open-source TCLB code. Finally, the improvement in fluid accessibility in low-permeability rock samples was shown through the assessment of multiple regions within two blasted samples. It was found that the blast-induced loading can generate extended microfractures that results in multiple orders of magnitude of permeability enhancement if the target rock possesses existing weaknesses and/or mineralisation.

Abstract

Thermal flows characterized by high Prandtl number are numerically challenging as the transfer of momentum and heat occurs at different time scales. To account for very low thermal conductivity and obey the Courant-Friedrichs-Lewy condition, the numerical diffusion of the scheme has to be reduced. As a consequence, the numerical artefacts are dominated by the dispersion errors commonly known as wiggles. In this study, we explore possible remedies for these issues in the framework of lattice Boltzmann method by means of applying novel collision kernels, lattices with large number of discrete velocities, namely D3Q27, and a second-order boundary conditions. For the first time, the cumulant-based collision operator is utilised to simulate both the hydrodynamic and the thermal field. Alternatively, the advected field is computed using the central moments’ collision operator. Different relaxation strategies have been examined to account for additional degrees of freedom introduced by a higher order lattice. To validate the proposed kernels for a pure advection-diffusion problem, the numerical simulations are compared against analytical solution of a Gaussian hill. The structure of the numerical dispersion is shown by simulating advection and diffusion of a square indicator function. Next, the influence of the interpolated boundary conditions on the quality of the results is measured in the case of the heat conduction between two concentric cylinders. Finally, a study of steady forced heat convection from a confined cylinder is performed and compared against a Finite Element Method solution. It is known from the literature, that the higher order moments contribute to the solution of the macroscopic advection-diffusion equation. Numerical results confirm that to profit from lattice with a larger number of discrete velocities, like D3Q27, it is not sufficient to relax only the first-order central moments/cumulants of the advected field. In all of the performed benchmarks, the kernel based on the two relaxation time approach has been shown to be superior or at least as good as counter-candidating kernels.

In this work we investigated the phenomenon of shear-induced migration for polydisperse suspensions for the first time. Shear-induced migration is basically the diffusion of particles in the direction of decreasing shear rate, caused by the accumlation of random particle collisions in sheared flows. In channels, it results in the accumulation of particles at the channel centre and a flattening of the velocity profile. These concepts have long been established and investigated for monodisperse suspensions (all particles of the same size), and some works have even investigated bidisperse suspensions (particles of two different sizes), demonstrating that the larger particles preferentially migrate towards the channel centre.

Abstract

The Lattice Boltzmann Method algorithm is simplified by assuming constant numerical viscosity (the relaxation time is fixed at τ=1). This leads to the removal of the distribution function from the computer memory. To test the solver the Poiseuille and Driven Cavity flows are simulated and analyzed. The error of the solution decreases with the grid size L as L−2. Compared to the standard algorithm, the presented formulation is simpler and shorter in implementation. It is less error-prone and needs significantly less working memory in low Reynolds number flows. Our tests showed that the algorithm is less efficient in multiphase flows. To overcome this problem, further extension and the moments-only formulation was derived, inspired by the Multi-Relaxation Time (MRT) approach for single component multiphase flows.

Abstract

Particle suspensions form a fundamental yet complex component of many scientific and engineering endeavours. This paper proposes a numerical coupling between the lattice Boltzmann and discrete element methods that resolves particle suspensions exposed to thermal influences due to temperature-dependent fluid viscosity and conjugate heat transfer between components. Validation of the model was performed via the study of the relative viscosity of suspensions. This numerically corroborated the proposed temperature-dependence of the relative viscosity of suspensions. The model was finally used to interrogate the macroscopic behaviour of sheared suspensions at a range of solid volume fractions. This demonstrated changes in suspension flow behaviour due to temperature related effects. Future work based on these results would examine how particle properties could be modified to exacerbate and control temperature-based phenomena potentially leading to improvements in domains such as industrial material processing and manufacture.

Abstract

This paper introduces the development of a new predictive model in support of proppant injection in naturally fractured coal seam gas (CSG) reservoirs. In the proposed model, the finite element method (FEM) is used for the prediction of proppant embedment and elastoplastic deformation of the coal. The lattice Boltzmann method (LBM) is applied to the modelling of fluid flow through propped fractures, in which the modified partially saturated method (MPSM) is implemented to characterise the fluid–solid interactions. Permeability diagrams of the fractures are then generated as functions of particle packing ratio and effective stress. Finally, these results are incorporated into a radial Darcy flow analytical solution to predict the productivity index of the CSG wells under various proppant injection pressures and cleat compressibilities. The developed model is applied to selected coal samples from the Bowen and Surat Basins in Queensland, Australia. Modelling results indicate that proppant injection leads to increased fracture permeabilities and enhanced well productivity indexes. The elastoplastic deformation results in smaller permeability increase and less production enhancement when compared to the traditional linear elastic models. Although focused on Australian coals, the developed workflow can be broadly applicable to the assessment of potential stimulation efficacy in other unconventional reservoirs. In addition, a better understanding and implementation of the proppant injection scheme can effectively improve the post-fracturing performance, particularly in low-permeability coal intervals, which benefits the CSG industry.

Abstract

A three-dimensional phase-field lattice Boltzmann method has been applied to investigate the rise of Taylor bubbles within annular pipes. The approach couples the conservative phase-field model with a velocity-based lattice Boltzmann scheme. The implementation uses 27 discrete velocities to resolve both the interfacial dynamics and the hydrodynamics. To assist numerical stability for the high-density ratio, two-phase flows a weighted multiple-relaxation-time collision operator is employed. This paper makes contributions in three areas. First, the model is employed to capture the behaviour of Taylor bubbles in five combinations of vertical annular pipes, with results compared to experimental findings from the literature for air-water flows. From this, shortcomings were identified in the ability of existing correlations to accurately predict rise velocities for bubbles in various liquids. Second, the effect of pipe inclination on the rise behaviour of the bubbles was investigated. From the findings, a preliminary correlation describing the rise velocity was proposed. The first two components of the study were conducted with the Taylor bubble rising in stagnant fluid. The final component of this study imposed liquid flow in a concentric annular pipe to determine the impact of this on the bubble’s dynamics. The liquid velocity was defined through a Reynolds number based on the average inlet velocity up to an absolute value of 10. The viscosity was varied to examine Morton numbers from 2.56e-3 to 6.55e-5. To this end both co- and counter-current flow was analysed and a distribution parameter proposed to capture the liquid-gas interaction. To extend this work, future investigations will look to extend the parameter range assessed to ensure the universality of the correlations identified.

Abstract

We present the usage of an adjoint Lattice Boltzmann Method (LBM) for open-loop control of two-dimensional flapping wing motion. Movement of the wing is parametrised with periodic B-Splines, while the wing interacts with the surrounding flow via an Immersed Boundary (IB) method. Multi-objective optimisation is performed using a gradient optimisation algorithm, for which sensitivities are calculated with an adjoint method. The objectives selected were the mean lift force and mechanical power. To achieve performance suitable for optimisation, we also present an efficient GPU implementation of the LBM and adjoint LBM. The Immersed Boundary approach employed for the LBM is verified against results from the literature, while for the flapping case it is compared with two different Finite Volume Method (FVM) approaches. The obtained Pareto front of optimal designs shows a clear discrepancy between the power consumption and the mean lift force. A significant improvement of the basic wing design is demonstrated, and highlights the applicability of adjoint LBM simulations in complex open-loop control problems.

Abstract

Particle suspensions are present in a wide variety of practical settings. Modelling these numerically is a challenging task that often requires the combination of multiple methodologies. This paper examines particle transport within a temperature-dependent viscosity fluid utilising a coupled approach of the lattice Boltzmann method and the discrete element method. This technique takes advantage of the locality of the lattice Boltzmann method to allow both the individual particle behaviour to be fully resolved and to permit fine-scale variation of fluid viscosity throughout the tested domains. It is firstly shown that a total energy conserving form of the lattice Boltzmann method is needed to accurately reconstruct the non-linear temperature profiles observed on Couette flows of fluids with changing viscosity. This model is then coupled to the discrete element method to demonstrate the quantitative and qualitative changes to particle motion that arise in channel-based geometries in the presence of a temperature-dependent viscosity fluid exposed to a constant temperature gradient. In particular, it is demonstrated that the particles settled faster in such and appear less likely to deviate into side channels in the presence of such fluids. These results demonstrate that temperature-dependent viscosity requires special consideration to be simulated correctly and does have quantitative impact on particle transport. This impact should be considered in models of fluids of changing temperature.

Abstract

In this work, a conservative phase-field model for the simulation of immiscible multiphase flows is developed using an incompressible, velocity-based, cascaded lattice Boltzmann method (CLBM). Extensions are made to the lattice Boltzmann (LB) equations for interface tracking and incompressible hydrodynamics, proposed by Fakhari et al. [1], by performing relaxation operations in central moment space. This was motivated by the work of Fei et al. [2,3], where promising results from such a transformation were observed. The relaxation of central moments is defined in a reference frame moving with the fluid, while the existing multiple-relaxation time [4,5] scheme performs collision in a fixed frame of reference. Moreover, the derivations make use of continuous, Maxwellian distribution functions. As a result, the CLBM enhances the Galilean invariance and stability of the method when high lattice Mach numbers are evident. The cascaded scheme has been previously used in the literature to simulate multiphase flows based on the pseudo-potential model, where it allowed for high density and viscosity contrasts to be captured [6,7]. Here, the CLBM is implemented within the phase-field framework and is verified through the analysis of a layered Poiseuille flow. The performance of the CLBM is then investigated in terms of spurious currents, Galilean invariance and computational efficiency. Finally, the work of Fakhari et al. [1] is extended by validating the model’s ability to capture the relation between surface tension and the rise velocity of a planar Taylor bubble, in both stagnant and flowing fluids. New counter-current results indicate that the rise velocity model of Ha-Ngoc and Fabre [8] also applies in this regime.

Abstract

Modelling the thermodynamic and hydrodynamic interactions of suspended particles is a significant and ongoing numerical challenge. Addressing this is necessary in order to be able to fully model numerous industrial and scientific processes of practical interest. This paper describes extensions to a local and a non-local technique for the calculation of transient conjugate heat transfer within a lattice Boltzmann framework. The interface transition between phases in both methods has been incorporated via a partially saturated boundary condition that weights material properties and allows straight and curved boundaries to be captured. Transient and steady-state performance of the two methods has been compared using a number of static and dynamic problems to evaluate their suitability for modelling particle suspensions. In a number of the static tests the non-local method produced better results however for the dynamic cases the local method demonstrated more accurate behaviour.

Abstract

Based on the recent work by Fakhari et al. (2017b), a three-dimensional phase-field lattice Boltzmann method was developed to investigate the rise of a Taylor bubble in a duct. The proposed approach couples the conservative phase-field equation with a velocity-based lattice Boltzmann scheme equipped with a weighted multiple-relaxation-time collision operator to enhance numerical stability. This makes the model ideal for numerical simulation of immiscible fluids at high density ratios and relatively high Reynolds numbers. Several benchmark problems, including the deformation of a droplet in a shear flow, the Rayleigh–Taylor instability, and the rise of a Taylor bubble through a quiescent fluid, were considered to asses the accuracy of the proposed solver. The Rayleigh–Taylor instability simulations were conducted for a configuration mimicking an air-water system, which has received little attention in the literature. After detailed verification and validation, the presented formulation was applied to study the flow field surrounding a Taylor bubble, for which numerical results were compared with the experimental work of Bugg and Saad (2002). The findings highlighted that the experimental bubble rise velocity, instantaneous flow field, and interface profile can be accurately captured by the presented model. In particular, the rise velocity of the present model indicated an improvement in accuracy when compared to the reference numerical solutions. The agreement between various numerical schemes, in some instances, indicated potential experimental difficulties in measuring the local flow field. Future application of the present model will facilitate detailed investigation of the pressure and flow profile surrounding Taylor bubbles evolving in co-current and counter-current flows.

Abstract

We use Lattice Boltzmann Method (LBM) MRT and Cumulant schemes to study the performance and accuracy of single-phase flow modeling for propped fractures. The simulations are run using both the two- and three-dimensional Stokes equations, and a 2.5D Stokes–Brinkman approximate model. The LBM results are validated against Finite Element Method (FEM) simulations and an analytical solution to the Stokes–Brinkman flow around an isolated circular obstacle. Both LBM and FEM 2.5D Stokes–Brinkman models are able to reproduce the analytical solution for an isolated circular obstacle. In the case of 2D Stokes and 2.5D Stokes–Brinkman models, the differences between the extrapolated fracture permeabilities obtained with LBM and FEM simulations for fractures with multiple obstacles are below 1%. The differences between the fracture permeabilities computed using 3D Stokes LBM and FEM simulations are below 8%. The differences between the 3D Stokes and 2.5 Stokes–Brinkman results are less than 7% for FEM study, and 8% for the LBM case. The velocity perturbations that are introduced around the obstacles are not fully captured by the parabolic velocity profile inherent to the 2.5D Stokes–Brinkman model.

Abstract

In this paper we present a topology optimization technique applicable to a broad range of flow design problems. We propose also a discrete adjoint formulation effective for a wide class of Lattice Boltzmann Methods (LBM). This adjoint formulation is used to calculate sensitivity of the LBM solution to several type of parameters, both global and local. The numerical scheme for solving the adjoint problem has many properties of the original system, including locality and explicit time-stepping. Thus it is possible to integrate it with the standard LBM solver, allowing for straightforward and efficient parallelization (overcoming limitations typical for the discrete adjoint solvers). This approach is successfully used for the channel flow to design a free-topology mixer and a heat exchanger. Both resulting geometries being very complex maximize their objective functions, while keeping viscous losses at acceptable level.

Abstract

The unique properties of ceramic foams make them well suited to a range of applications in science and engineering such as heat transfer, reaction catalysis, flow stabilization, and filtration. Consequently, a detailed understanding of the transport properties (i.e. permeability, pressure drop) of these foams is essential. This paper presents the results of both numerical and experimental investigations of the morphology and pressure drop in 10. ppi (pores per inch), 20. ppi and 30. ppi ceramic foam specimens with porosity in the range of 75-79%. The numerical simulations were carried out using a GPU implementation of the three-dimensional, multiple-relaxation-time lattice Boltzmann method (MRT-LBM) on geometries of up to 360 million nodes in size. The experiments were undertaken using a water channel. Foam morphology (porosity and specific surface area) was studied on post-processed, computed tomography (CT) images, and the sensitivity of these results to CT image thresholding was also investigated. Comparison of the numerical and experimental data for pressure drop exhibited very good agreement. Additionally, the results of this study were verified against other researchers[U+05F3] data and correlations, with varying outcomes.