•Fully-resolved simulations of an ellipsoidal particle settling in Bingham fluid.•Critical yield number calculated for spheroids of many aspect ratios.•For inertial Bingham flow, the ellipsoid ...rotates and reaches a stable orientation.•A plastic belt surrounds the particle and constrains its rotation.•Terminal Reynolds number and drift angle tabulated for many aspect ratios.
Despite many particle shapes and motion patterns that can be present in viscoplastic settling, the scientific studies are mostly limited to spherical particles and cases in which the solid body motion is purely vertical or rotational. Here we tackle the problem of an ellipsoidal particle settling in Bingham fluid through fully-resolved simulations. Oblate and prolate spheroids of varied aspect ratios and initial orientations are analyzed. We use the Lattice Boltzmann Method (LBM), in which the Bingham constitutive equation is solved exactly. We employ the Immersed Boundary Method (IBM) to delineate the particle boundaries and enforce the no-slip condition over them. For the case of creeping flow around a settling ellipsoid, we benchmark results of the critical yield number for oblate and prolate spheroids against augmented Lagrangian method (ALM) data and provide values for different aspect ratios and initial orientations. Then, we analyze the dynamics of prolate and oblate spheroids settling in Bingham fluid at an inertial flow. We present the evolution of trajectory, orientation, angular momentum, Reynolds number, and drift angle for various aspect ratios and initial orientations.
•Fully-resolved simulations of a sphere settling in a thixo-viscoplastic fluid.•The fluid has dynamic and static yield stresses, and it is initially unstructured.•An IB-LBM solver is set up to the ...task, implemented in GPU.•Thixotropy strongly influences the mechanism of particle imprisonment.•Flow regime map and correlation predict particle retainment or terminal velocity.
This paper investigates the settling of a single spherical particle immersed in an initially unstructured thixo-viscoplastic fluid. The phenomenon was numerically solved using the lattice Boltzmann method (LBM) for the mass and momentum transport equations, the immersed boundary method (IBM) for the particle dynamics, and the advection-diffusion LBM for the structural parameter transport equation. We utilized a simplified version of the Houska model to represent the rheological behavior of an inelastic thixo-viscoplastic material. The model evaluates the yield stress effects, which change based on a structural parameter, in the particle settling of an aging fluid. We fixed the particle properties (diameter, density) and varied the fluid rheological properties, such as the static and dynamic Bingham numbers and the build-up and breakdown numbers. Detailed fields of velocity, rate-of-strain, and structural parameters are presented to enrich the flow interpretation. The numerical results reveal that, for a thixotropic fluid, the classical viscoplastic critical yield number criterion does not correctly predict the condition for which the particle will become stationary. Although a higher dynamic yield stress will help the particle's stoppage, the microstructural breakdown has a powerful effect in facilitating its settling.
•Implementation of LBM framework with domain transferring is disclosed.•It allows for particle settling simulations in virtually unbounded domain.•Memory demand may be reduced by an order of ...magnitude for IBM simulations.•With IBM, a detailed meshing procedure is described for ellipsoidal particles.•Very good agreement was found against experimental and independent CFD results.
Particle settling at moderate to high Reynolds number takes a considerable distance to reach a periodical or statistically steady regime. Hence, hardware memory limitations in fully resolved simulations constrain the maximum domain size for this flow class. Due to the locality in most of its algorithms, the Lattice Boltzmann Method (LBM) is increasingly popular for CFD studies. In the present paper, a domain transferring scheme is implemented in LBM, enabling simulations of particle motion in a virtually infinite domain, and it is combined with a high-quality Lagrangian mesh algorithm to be solved with the Immersed Boundary Method (IBM). A thorough mesh generation procedure for ellipsoidal particles is disclosed, as well as an extension of the internal mass compensation strategy of Suzuki and Inamuro (2011). Comparison with analytical results shows that the numerical model appropriately describes the particle rotation and can predict a terminal velocity close to Stokes solution. The numerical results of a buoyant sphere moving diagonally presented remarkable concordance with experimental data. Also, an excellent agreement with a numerical study of oblate spheroids settling in a vast domain was found. The domain transferring scheme reduced the memory demand in one order of magnitude.
We implement the moment representation of the lattice Boltzmann method in a graphic processing unit (GPU) environment to study the computational performance of three‐dimensional fluid flows. The ...moment representation of the lattice Boltzmann method (MRLBM) uses up to second‐order moments of the particle distribution function to regularize and reconstruct it. By adopting this method, there is a reduction in memory usage and global memory transfer and, therefore, increased performance. The results show an increase of up to 40% in speed compared to population schemes. The validation results show there was no loss of accuracy when using single precision for turbulent flows. The adoption of single‐precision also enables higher processing speed for GPUs with low double‐precision capability and reduces the memory footprint, which can further increase performance. The implementation here presented provides a fast and straightforward environment for fluid simulation by combining single‐precision and the MRLBM.
The moment representation of the lattice Boltzmann method can be used to reduce the memory footprint, which for our graphic processing unit (GPU) implementation in three‐dimensional domains, it was about a 7% reduction in memory usage. Because of the reduction in memory transfer, a performance uplift between 25% and 40% for GPU was achieved.
•A viscoplastic fluid flow solver is developed with lattice Boltzmann method (LBM).•“Infinite viscosity” is computed by setting the relaxation frequency to zero.•Regularization of ghost moments keeps ...the simulations numerically stable.•The numerical scheme is second-order accurate and good yield surfaces are obtained.•With GPU computation typical execution time for 3D simulations is 90 min.
In the Lattice Boltzmann Method (LBM) the viscosity is inversely proportional to the relaxation frequency. Hence, it should be possible to represent the singularity of some viscoplastic models by setting the relaxation frequency to zero. In the present paper we take full advantage of the LBM capabilities to propose an efficient and stable numerical scheme for viscoplastic fluid flow simulations invoking the exact Bingham constitutive equation. This scheme is expected to suit the need for more accurate viscoplastic simulations because it does compute the “infinite viscosity”, therefore dismissing the need for any viscosity regularization. Although allowing for a wide range of relaxation frequencies varying in space and time, we demonstrate that the present implementation does not degrade the standard LBM's error order. Numerical stability was promoted by of regularization of ghost moments for the lattice Boltzmann equation with force term. Since the locality of the LBM is preserved, so is the scheme's ability to be highly scalable in large computer clusters. We outline the method and the theory behind it through a detailed Chapman–Enskog expansion. Three laminar test cases are analyzed: parallel channel Poiseuille flow, square duct Poiseuille flow and lid-driven cavity flow. We show conformity with the standard LBM's error order for different wall boundary conditions and yield stress levels. Comparisons are made with other numerical studies employing augmented Lagrangian and viscosity regularization methods.
The bentonite-free water-based drilling fluid aids in reducing formation damage in offshore operations in ultra-deep wells. In this scenario, the material experiences high-pressure and ...high-temperature conditions. The material’s rheological behavior may be affected not only by the temperature but also by the pressure. Knowing the influence of these variables on the drilling fluid’s rheological characteristics is essential for successfully planning and executing the drilling process. This paper investigates the effect of pressure, temperature, and thermal aging in the liquid-like and solid-like regimes of a bentonite-free water-based drilling fluid. The main viscosifier in the fluid is xanthan gum. The experiments were carried out in a pressure cell coupled to a rotational rheometer. The results show a more relevant impact of temperature than pressure on the rheological behavior of the drilling fluid. The experiments also exhibit a critical aging temperature that induces irreversible fluid degradation. Lastly, these findings bring relevant information over an efficient range of bentonite-free water-based drilling fluids employed in the offshore drilling process.
Graphical abstract
The current experimental study investigates the rheological characterization of Carbopol gel solutions into a pipe flow using in situ visualization. The shear rate and shear stress profiles for ...different pressure-driven values are presented and correlated to obtain new steady-state flow curves compared with rheometrical data performed with cross-hatched parallel plate (CHPP) and smooth concentric cylindrical (SCC) geometries at a rotational rheometer. The rheological behavior for the test performed by the in situ visualization was well fitted by the generalized Herschel-Bulkley model, and different values for the coefficient of consistency (
K
), flow behavior index (
n
), and yield stress (
τ
0
) were fitted for the three gel solutions due to the presence of wall slip behavior. The discrepancies between the values of the rheological parameters suggest that conventional rheometrical measurements, which avoid the slippage of the fluid, lead to an overestimation of these parameters, and as a consequence, these discrepancies are extended to the dimensionless numbers calculated for the hydrodynamic flow description. Also, the experimental plug core velocity was compared with the analytical value obtained by the rotational rheometer tests to calculate an equivalent slip velocity, and such velocity depicts a quasi-linear trend with the wall shear stress. This is supported by the apparent viscosity profiles along the pipe diameter, suggesting that the slippage is an inherent characteristic of polymer gel solutions, and it is disseminated by the presence of layers near the pipe wall where the Newtonian like-behavior is presented. Finally, applying in situ visualization technique assures a better rheological characterization and accurate description of the flow conditions for fluids with complex behavior.
A comb-like network has a single manifold duct, which ramifies to several branches, all subject to a pressure reservoir. Applications for such networks include vascular systems such as microchannel ...heatsinks, in which a working fluid needs to be fed to a great number of small volume elements. A configuration with constant branches of diameter and spacing produces a non-uniform flow distribution: the first branch receives a large fraction of the inlet mass flow rate and the subsequent branches receive smaller and smaller fractions. To overcome this problem, two alternative configurations are proposed: variable diameters and variable spacings along the branches. The construction rules providing flow uniformity for both configurations are analytically determined by the method of constructal design and further validated numerically. It is shown that, when the system performance is evaluated at the most critical element, instead of the traditional global fluid flow resistance, the new configurations perform significantly better than the one with constant diameter and spacing. The importance of these results is elucidated under the view of constructal theory.
This study investigates the natural convection process within open cavities filled with viscoplastic fluid following the Bingham model with solid square conductive blocks uniformly distributed ...throughout the cavity. The problem is modeled as a two-dimensional laminar in a steady state with the heated surface parallel to the cavity opening and the other adiabatic surfaces. Three geometries are analyzed: the downward-facing cavity, side-facing cavity, and upward-facing cavity. Parametric analysis is performed in terms of Rayleigh number and Bingham number. The solid-fluid thermal conductivity ratio, the number of blocks, the Prandtl number, and the solid volume fraction within the cavity are fixed, with values of 10, 16, 500, and 0.36, respectively. The results are presented in streamlines, isotherms, unyielded regions, dimensionless velocity, dimensionless temperature, and Nusselt number on the heated surface. A comparison with the closed square cavity is performed, and it is noted that the natural convection has a greater magnitude in the open cavity. Rayleigh and Bingham's numbers have opposite effects on heat transfer. Effects of block interference and channeling of flow within the cavity are observed. For a given value of the Bingham number, there is an abrupt transition from the advective to conductive regime inside the cavity and a critical Bingham number (Bnmax) in which unyielded regions fill the entire geometry, i.e., without flow. Finally, average Nusselt number correlations for each geometry and flow, and no-flow diagrams are presented.
•Simulation of natural convection in open cavities with solid obstacles.•Observation of channeling and interference effects within the cavity.•Natural convection is more significant in a side-facing cavity.•There is a critical Bingham number (Bnmax) above which the fluid does not yield.
Following a series of discrepancies in the literature regarding the effects of nanoparticle concentration on the heat transfer rate, this paper proposes a simple homogeneous modeling for natural ...convection of nanofluids. The proposed modeling allows a custom choice of correlations for the nanofluid’s thermophysical properties, which proved to be very convenient in validations carried out for the case of natural convection inside a clear enclosure. The general heat transfer decreasing behavior for high concentrations of nanoparticles, previously observed in experimental and two-phase numerical works, was successfully represented. A very interesting and pioneer case study of laminar natural convection of nanofluids in a laterally heated enclosure with conductive solid blocks uniformly distributed within the enclosure was numerically investigated with the proposed modeling. To compute the nanofluids characteristics, Corcione’s correlations for thermal conductivity and dynamic viscosity for effective properties and generic correlations for density, specific heat and thermal expansion coefficient were employed. Therefore, it was possible to isolate the nanoparticle’s influence on the heat transfer rate, evaluated by the average Nusselt number. By isolating the nanoparticle’s parameters, the effects of diameter and material have been interpreted from the homogeneous solution. A parametric investigation was conducted by varying the number of blocks inside the enclosure and the effective Rayleigh number. A numerical correlation for the average Nusselt number was derived for a wide range of effective Rayleigh number and number of blocks. The model developed herein is suitable to other applications in which the total heat transfer rate needs to be computed.
