The present paper analyses the settling behavior of multiple spherical particles in a power-law fluid. The results were numerically solved by the lattice Boltzmann method for the fluid mass and ...momentum equations and the immersed boundary method for the particle dynamics. The transient particle position and velocity data were obtained for a constant Archimedes number of 1000 and density ratio of 2.25. The objects of the investigation were the solid volume fraction, between 0.2% and 3.3%, and the power-law index, from 0.6 to 1.25. The particles repel each other and avoid collision due to increased fluid viscosity in their gaps for the shear-thickening fluid. On the other hand, for shear-thinning fluids, a wake of low viscosity is formed behind the particles, which leads to a high occurrence of particle collisions. However, as the solid volume fraction increases, these effects become less noticeable, mainly because the settling transitions from viscous to collision-dominated. In all cases analyzed, the average terminal velocity was below the terminal velocity of a free particle.
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•Fully-resolved simulations of multiple spheres settling in a power-law fluid are discussed.•The effects of the power-law index and solid volume fraction are investigated.•An IB-LBM solver was implemented in GPU, enabling short turnaround times.•Tthe power-law index can change the settling regime at fixed Archimedes numbers•The mean particle density and viscosity field explain the particle dynamics.
•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.
In this work, the natural convection of a viscoplastic fluid inside an enclosure filled with many obstacles is solved numerically. The enclosure is characterized by differentially heated vertical ...walls, while the obstacles are heat-conducting square blocks. Due to the nature of the viscoplastic material, it is seen that if the buoyancy force is not strong enough, the whole fluid can be unyielded, and the heat transfer takes place only by conduction. The Bingham constitutive equation is chosen to represent the yield-stress material. Steady-state velocity and temperature fields are obtained for a wide range of Rayleigh and Bingham numbers and several numbers of blocks. We show that increasing the yield-stress has a quantitative effect on reducing the fluid circulation, and consequently, the heat transfer rate. At a certain yield-stress level, the fluid motion is abruptly interrupted. The critical Bingham number for complete unyielding does not depend on the Rayleigh or Prandtl numbers. However, the obstacles' configuration has a significant effect on this transition. Flow vs. no-flow diagrams and average Nusselt number correlations are proposed as aid for thermal engineering of similar arrangements.
•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.
•Simulation of natural convection inside C-shaped cavity filled with solid obstacles.•Observation of channeling, interference and discontinuous fin-like diffusion.•Diffusion is more significant as ...the thermal conductivity of the blocks increases.
This study considers the thermo-hydraulic effects of discrete solid blocks on the natural convection inside a fluid filled, horizontally heated side-open cavity. The cavity, having adiabatic horizontal surfaces and an isothermal hot wall, is open to a vast reservoir filled with a quiescent fluid maintained at a temperature lower than the cavity wall temperature. A fixed amount of solid material is progressively distributed inside the cavity as disconnected and conductive square blocks of different numbers and sizes, forming a uniform square lattice. The ensuing natural convection process is modeled analytically considering the fluid and solid constituents inside the cavity separately, and simulated through a validated numerically approach following a parametric analysis done in terms of the Rayleigh number (105 ≤ Ra ≤ 108), the total number of blocks (9 ≤ N ≤ 144) and the solid-to-fluid thermal conductivity ratio (0.1 ≤ κ ≤ 100). The cavity aspect ratio and fluid Prandtl number are kept equal to unity, and the volume-fraction of the solid constituent is equal to 0.36. The present study evaluate the thermo-hydraulic effects of the blocks in the permanent convection process through streamlines, isotherms, hot wall Nusselt mean number and dimensionless mass flow through the fluid reservoir cavity. The blocks affect the convection process in three ways: via channeling, flow interference, and discontinuous fin-like diffusion. The most important effect is interference, which is shown to be analytically predictable. The fin-like effect is the most complex and modulates mostly by the magnitude of κ. Finally, analytical correlations are presented for averaged hot-wall Nusselt number and the nondimensional mass flow rate as useful practical tools in helping the design and analysis of similar configurations.
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.
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.
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.
