We investigate the average drag, lift, and torque on static assemblies of capsule-like particles of aspect ratio 4. The performed simulations are from Stokes flow to high Reynolds numbers (0.1 ≤ Re ≤ 1,000) at different solids volume fraction (0.1 ≤ ɛ_s ≤ 0.5). Individual particle forces as a function of the incident angle ϕ with respect to the average flow are scattered. However, the average particle force as a function of ϕ is found to be independent of mutual particle orientations for all but the highest volume fractions. On average, a sine-squared scaling of drag and sine-cosine scaling of lift holds for static multiparticle systems of elongated particles. For a packed bed, our findings can be utilized to compute the pressure drop with knowledge of the particle-orientation distribution, and the average particle drag at ϕ = 0° and 90°. We propose closures for average forces to be used in Euler–Lagrange simulations of particles of aspect ratio 4.

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This work focuses on creating a recipe for parametrizing flow around assemblies of non-spherical particles. A multi-relaxation time lattice Boltzmann method (MRT-LBM) is used to simulate the flow. The research focuses on 3 different developments. First, different boundary conditions available in the literature for LBM are tested to identify the best for the flow problem. The second part of the thesis focuses on developing more widely applicable scaling laws for drag and lift of various isolated non-spherical particles. In the third part, a recipe to describe hydrodynamic forces on assemblies of axisymmetric, non-spherical particles is proposed. With the described parameters, drag, lift and torque correlations are proposed accordingly. This research is funded by the European Research Council under its consolidator grant scheme, contract no. 615096 (NonSphereFlow).@en

Fractures of particle assemblies happen frequently in dense gas-solid systems leading to a notable heterogeneity in the particle configuration, especially in case of cohesive powders and non-spherical particle interlocking. In this work, we investigate the influence of such heterogeneities on the hydrodynamic drag by studying the idealized case of a random arrangement of spheres with a channel-like void region. More specifically, we introduce this heterogeneity to a homogeneous particle arrangement by shifting apart two bulk regions, such that a void channel divides particle bulk. Single-relaxation-time lattice Boltzmann simulations were performed to resolve fluid flow through such arrested particle configurations and calculate the corresponding gas-particle momentum exchange and pressure drop. The calculated drag forces acting on the solids for random sphere arrangement are in good agreement with previously reported results of Hill et al. (2001b), Tenneti et al. (2011), and Tang et al. (2015). However, the overall momentum exchange obtained for configurations containing a heterogeneity is significantly lower. Obviously, the channel allows for a by-passing of a considerable amount of the flow leading to a reduced overall pressure drop and thereby underestimating the minimum fluidization velocity in a fluidized bed. Based on these direct numerical simulations, we examine the overall pressure drop dependence on the characteristic length scale (i.e. width) of the channel-like heterogeneity L c , the superficial Reynolds number (30 ⩽ Re ⩽ 300), and the solid volume fraction in the dense (i.e. bulk) region (0.4 ⩽ϕ p ⩽ 0.55). The width of the channel is varied within the order of magnitude of particle diameter D p (1 ⩽L c /D p ⩽4.36), decreasing an overall solid volume fraction (0.25 ⩽ϕ⩽ 0.55). In addition to the numerical simulations, we derive (semi)-analytic correlations for the dense bulk region as well as for the channel. As the simulations range from laminar to transitional flow, providing a single pressure drop correlation is very challenging. Therefore, we estimate the channel pressure drop with the appropriate correlations selected according to calculated superficial Reynolds number. For laminar flow, we achieved a good agreement between a combined (i.e. bulk and channel) analytical prediction of overall pressure drop and our resolved numerical simulation. In the transitional regime, the pressure drop values are more difficult to predict, with the better agreement as we approach the turbulent regime. We believe that this work can act as a basis for the development of future drag laws accounting for channel-like sub-grid heterogeneities. @en

In this paper, we present a number of key numerical methods that can be used to study elongated particles in fluid flows, with a specific emphasis on fluidised beds. Fluidised beds are frequently used for the production of biofuels, bioenergy, and other products from biomass particles, which often have an approximate elongated shape. This raises numerous issues in a numerical approach such as particle-particle contact detection and the accurate description of the various hydrodynamic forces, such as drag, lift, and torque, that elongated particles experience when moving in a fluid flow. The modelling is further complicated by a separation of length scales where industrial flow structures that can extend for many metres evolve subject to solid-solid and solid-fluid interactions at the millimetre scale. As a result, it is impossible to simulate both length scales using the same numerical approach, and a multiscale approach is necessary. First, we outline the direct numerical simulation (DNS) approach that may be employed to estimate hydrodynamic force closures for elongated particles in a fluid flow. We then describe the key aspects of a CFD-DEM approach, which can be used to simulate laboratory scale fluidisation processes, that must be addressed to study elongated particles. Finally, we briefly consider how current industrial-scale models, which concretely assume particle sphericity, could be adapted for the simulation of large collections of elongated particles subject to fluidisation.

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Various curved no-slip boundary conditions available in literature improve the accuracy of lattice Boltzmann simulations compared to the traditional staircase approximation of curved geometries. Usually, the required unknown distribution functions emerging from the solid nodes are computed based on the known distribution functions using interpolation or extrapolation schemes. On using such curved boundary schemes, there will be mass loss or gain at each time step during the simulations, especially apparent at high Reynolds numbers, which is called mass leakage. Such an issue becomes severe in periodic flows, where the mass leakage accumulation would affect the computed flow fields over time. In this paper, we examine mass leakage of the most well-known curved boundary treatments for high-Reynolds-number flows. Apart from the existing schemes, we also test different forced mass conservation schemes and a constant density scheme. The capability of each scheme is investigated and, finally, recommendations for choosing a proper boundary condition scheme are given for stable and accurate simulations.

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Accurate direct numerical simulations are performed to determine the drag, lift and torque coefficients of non-spherical particles. The numerical simulations are performed using the lattice Boltzmann method with multi-relaxation time. The motivation for this work is the need for accurate drag, lift and torque correlations for high Re regimes, which are encountered in Euler-Lagrangian simulations of fluidization and pneumatic conveying of larger non-spherical particles. The simulations are performed in the Reynolds number range 0.1 ≤ Re ≤ 2000 for different incident angles ϕ. Different tests are performed to analyse the influence of grid resolution and confinement effects for different Re. The measured drag, lift and torque coefficients are utilized to derive accurate correlations for specific non-spherical particle shapes, which can be used in unresolved simulations. The functional forms for the correlations are chosen to agree with the expected physics at Stokes flow as well as the observed leveling off of the drag coefficient at high Re flows. Therefore the fits can be extended to regimes outside the Re regimes simulated. We observe sine-squared scaling of the drag coefficient for the particles tested even at Re=2000 with C_D,ϕ=C_D,ϕ=0^∘ +(C_D,ϕ=90^∘ −C_D,ϕ=0^∘ )sin²ϕ. Furthermore, we also observe that the lift coefficient approximately scales as C_L,ϕ=(C_D,ϕ=90^∘ −C_D,ϕ=0^∘ )sinϕcosϕ for the elongated particles. The current work would greatly improve the accuracy of Euler-Lagrangian simulations of larger non-spherical particles considering the existing literature is mainly limited to steady flow regimes and lower Re.

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The flow around different prolate (needle-like) and oblate (disc-like) spheroids is studied using a multi-relaxation-time lattice Boltzmann method. We compute the mean drag coefficient CD,ϕ at different incident angles ϕ for a wide range of Reynolds numbers ( Re ). We show that the sine-squared drag law CD,ϕ=CD,ϕ=0∘+(CD,ϕ=90∘−CD,ϕ=0∘)sin2ϕ holds up to large Reynolds numbers, Re=2000 . Further, we explore the physical origin behind the sine-squared law, and reveal that, surprisingly, this does not occur due to linearity of flow fields. Instead, it occurs due to an interesting pattern of pressure distribution contributing to the drag at higher Re for different incident angles. The present results demonstrate that it is possible to perform just two simulations at ϕ=0∘ and ϕ=90∘ for a given Re and obtain particle-shape-specific CD at arbitrary incident angles. However, the model has limited applicability to flatter oblate spheroids, which do not exhibit the sine-squared interpolation, even for Re=100 , due to stronger wake-induced drag. Regarding lift coefficients, we find that the equivalent theoretical equation can provide a reasonable approximation, even at high Re , for prolate spheroids.@en