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Through particle‐resolved direct numerical simulations of flow past arrays of ellipsoids, the hydrodynamic force on ellipsoids depends on the particle orientation, aspect ratio, particle Reynolds number, and solid volume fraction is revealed at moderate Reynolds numbers. The results show that the mean drag force on arrays of prolate/oblate ellipsoids decreases/increases as the Hermans orientation factor increases when flows are in the reference direction defined by the average symmetric axis of particles. The individual drag force on a prolate/oblate ellipsoid increases/decreases with the increase of incidence angle, and it is also affected by the orientation of surrounding particles. The individual lift force is also significant when the aspect ratio is away from unity at large particle Reynolds numbers. Based on simulation results, correlations for the hydrodynamic force on ellipsoids at arbitrary particle Reynolds numbers, solid volume fractions, Hermans orientation factors, incidence angles, and aspect ratios are formulated. [ABSTRACT FROM AUTHOR]

During the pyrolysis and gasification processes inside fluidized bed reactors, a single reactive particle is generally surrounded by multiple inert heat carrier particles. In this work, we focus on the simplest mixed particle pair (one reactive particle: P1, and one inert particle: P2) to investigate the joint effects of the Stefan Reynolds number (Resf), the particle Reynolds number (Re), separation distance normalized by particle diameter (L), and relative orientation (α) on the drag force exerting on each particle by particle-resolved direct numerical simulations. The results show that when particles are placed in a tandem arrangement, the blocking effect on P2 is weakened/strengthened with negative/positive Stefan flow since the effective diameter of P1 is smaller/larger than its real diameter. When L = 1.25, Re = 3, and particles are placed in tandem, the drag force of P1 decreases as Resf increases, but the reduction of the drag force decreases as Re increases. Under such conditions, the positive Stefan flow induces the repulsion between the two particles; thus, the drag force of P2 increases as Resf increases. When Resf = 3 and P2 is located downstream, the repulsive force felt by P1 can partially offset the drag force at L = 1.25, Re = 3. Moreover, the negative/positive Stefan flow enhances/weakens the drag force of P2 when it is located upstream. The Stefan flow has a negligible effect on the drag force of P2 when L = 3. [ABSTRACT FROM AUTHOR]

Resolving the sharp interface between the dilute and dense phases in gas–solid flows is a bottleneck in fine-grid simulations. This study addresses this issue through the theoretical analysis of an infinite gas–structure interface with arbitrary flow directions. The drag force at the interface is decomposed into three parts: the homogeneous drag forces of the dilute and dense regions and a stress divergence difference term. All the three parts are expressed as the functions of the solid volume fractions, particle Reynolds numbers, and stress divergences of the interface grid and its adjacent grids. The developed theoretical drag models at the interface are verified and improved based on particle-resolved direct numerical simulations (PR-DNSs) of flows past plug-like structures. The models are then tested against PR-DNSs of flows past bubble-containing, spherical, ellipsoidal structures. They yield significantly better performance than the traditional Beetstra et al.'s model [Beetstra et al., "Drag force of intermediate Reynolds number flow past mono‐ and bidisperse arrays of spheres," AIChE J. 53(2), 489–501 (2007)]. [ABSTRACT FROM AUTHOR]

Three-dimensional large eddy simulations are conducted to investigate the sinusoidal oscillating flow over the two tandem square cylinder at Reynolds number Re = 1000 and the spacing ratio L/D = 3.5 (L : center-to-center distance between the cylinders, D : cylinder width). The velocity U of sinusoidal oscillating flow is set as U = U 0 (1+ A R sin2π(f ∗ U 0 / D) t), where A R is the velocity amplitude ratio varied from 0.05 to 0.50, and f ∗ (= f u D / U 0) is the non-dimensional frequency ranged from 0.05 to 0.15 with f u being the sinusoidal frequency. The main attention is paid on effects of A R and f ∗ on the flow structure and aerodynamic forces. The results indicate that the flow structures around the cylinders are sensitive to A R and f ∗, and classified into three patterns: reattachment, bistable, and coshedding patterns. At lower value of f ∗ = 0.05, the three flow patterns occur at 0 ≤ A R ≤ 0.25, A R = 0.30 and 0.35 ≤ A R ≤ 0.5, respectively; however, at larger value of f ∗ = 0.10 and 0.15, the occurrence of reattachment pattern is absent and the A R that the bistable pattern appears is advanced to A R = 0.1 at f ∗ = 0.10 and even no occurrence of bistable pattern at f ∗ = 0.15. Correspondingly, the wake structures, Strouhal number and aerodynamic forces exhibit a strong correlation with the flow pattern, leading to a mutation at the transition of flow pattern. Both cylinders in the coshedding flow experience greater mean-drag and fluctuating lift compared to those in the reattachment flow. • Effects of sinusoidal oscillating flow on two tandem square cylinders are investigated by conducting the three-dimensional large eddy simulations. • The flow structures around the cylinders are sensitive to A R and f ∗, and classified into three patterns: reattachment, bistable, and coshedding patterns. • The flow structures, vortices shedding and fluid-dynamic forces vary according to changes in the flow pattern. [ABSTRACT FROM AUTHOR]

Through particle‐resolved direct numerical simulations of flows past random arrays of oblate ellipsoids at low Reynolds numbers, this work demonstrates how the drag force on oblate ellipsoids depends on the Hermans orientation factor S, the mean crosswise sphericity φ⊥, the aspect ratio AR, and the solid volume fraction c. Wide ranges of S, AR, and c are considered and they are in the intervals (−0.5, 1), (0.2, 0.8), and (0.1, 0.4), respectively. This study extends the work on prolate ellipsoids by Li et al (AIChE Journal, 2019, 65, e16621). Based on the simulation results, two models are respectively developed using S and φ⊥as the independent orientation factor. The model based on S could give accurate prediction of the drag force and the lateral force exerted on arrays of particles. The model based on φ⊥ is able to use one generalized drag correlation for both oblate and prolate ellipsoids. [ABSTRACT FROM AUTHOR]

Numerical study of forced convection heat transfer from arrays of prolate particles is performed using the second-order Immersed Boundary-Lattice Boltzmann Method (IB-LBM). Prolate particle is studied with aspect ratio of 2.5 with solid volume fraction variation from 0.1 to 0.3. For each solid volume fraction, arrays of prolate particles are generated and simulations have been performed to calculate Nusselt number for four different Hermans orientation factors and various Reynolds numbers. From the simulation results, it has been observed that, for any specific value of Hermans orientation factor, Nusselt number increases with the increase of the Reynolds number and solid volume fraction. More importantly, it is found that the effect of orientations on Nusselt number is significant. Nusselt number correlation is developed for ellipsoidal particles as function of Reynolds number, Prandtl number, solid volume fraction, and orientation factors. This correlation is valid for 0.1 ≤ c ≤ 0.3 and 0 < Re ≤ 100. [ABSTRACT FROM AUTHOR]

This study conducts three-dimensional large eddy simulations at a subcritical Reynolds number of 103 to investigate the effects of sinusoidal streamwise flow on the flow structure, Strouhal number, and aerodynamic forces of two tandem circular cylinders. The center-to-center spacing L between the two cylinders is fixed at 3.5 D , where D is the cylinder diameter. The velocity U of sinusoidal streamwise flow is set as U* = U / U 0 = 1 + A* sin(2π(f*U 0 /D) t), where A* denotes the velocity amplitude ratio, and f* ((f u D/U 0) /St 0) denotes the non-dimensional frequency of sinusoidal flow, with f u being the frequency of sinusoidal flow and St 0 being the Strouhal number of two tandem cylinders with L / D = 3.5 under the uniform approaching flow. The results show that the variations of f* (0–2.67) and A* (0–0.25) lead to the generation of not only the reattachment and coshedding flows independently but also their joint flow involving intermittent occurrences of the reattachment and coshedding flows. A map of the dependence of the flow structure on f* and A* is presented, marking the borders of various flow patterns in the f* − A* plane. Flow separation, Strouhal number, and aerodynamic forces on the two cylinders are found to be sensitive to f* and A* , exhibiting distinct variations following the flow structures. A time-frequency analysis of the bistable pattern is presented, identifying the two distinct vortex-shedding frequencies and confirming the time dependence and bi-stability of the bistable flow. • A map of the flow structure dependence on f* and A* is presented, marking borders of various flow patterns in f* - A* plane. • The bistable flow pattern around the two tandem cylinders, involving intermittent occurrences of the reattachment and coshedding flows, is observed. • The two distinct vortex-shedding frequencies is identified and the time dependence and bi-stability of the bistable flow is confirmed. [ABSTRACT FROM AUTHOR]

Three-dimensional large eddy simulations were carried out to investigate the flow over two tandem square cylinders for a fixed spacing ratio of L/D = 4 and a Reynolds number of 5.3 × 103, where L is the cylinder center-to-center distance between the cylinders and D is the cylinder width. The corners of each cylinder were chamfered with a ratio of ξ = B/D = 0%, 5%, 10%, and 15%, where B is the chamfered corner dimension. The focus is given on how ξ influences the flow structure, wake recirculation bubble, flow separation bubble, Strouhal number (St), aerodynamic force, and phase lag (ϕ) between vortex sheddings from the cylinders. With increasing ξ, the recirculation bubble length and minimum velocity in the wake of the upstream cylinder remain more or less constant and are close to those of a single cylinder, while the minimum velocity in the wake of the downstream cylinder dramatically drops between ξ = 0% and 5%. While the flow over the downstream remains attached on the side surfaces, that over the upstream cylinder forms primary and secondary side-surface bubbles on the side surface, and both shrink with increasing ξ. In addition, the leading chamfered corners are accompanied by corner bubbles that play an important role in the flow structure modification. Therefore, the time-mean drag and fluctuating lift of the upstream cylinder remarkably decrease for 0% ≤ ξ ≤ 5% and remain almost unchanged for 5% < ξ ≤ 15%, whereas those on the downstream cylinder diminish in the whole range of 0% ≤ ξ ≤ 15%. The Strouhal number (St) being identical for the two cylinders grows from 0.104 to 0.132 when ξ is increased from 0% to 15%. Overall, the influence of ξ on the wake structure and aerodynamics is remarkable for 0% ≤ ξ ≤ 5% because of the corner bubbles and is less for 5% < ξ ≤ 15%. [ABSTRACT FROM AUTHOR]

Three-dimensional large eddy simulations were carried out to investigate the flow around two tandem circular cylinders at a subcritical Reynolds number of Re = 103. The cylinder center-to-center spacing ratio L/D is varied from 1.25 to 6, where D is the cylinder diameter. In order to enhance the understanding of flow physics around two circular cylinders, particular attention is devoted to fluctuating forces, shear-layer reattachment, flow separation, wake recirculation, Strouhal number (St), and phase lag (ϕ) between the fluctuating lift of the two cylinders. The flow structure around the cylinders is highly sensitive to L/D. A change in L/D thus leads to overshoot flow (L/D ≤ 1.25), reattachment flow (1.5 ≤ L/D ≤ 3.5), and coshedding flow (L/D ≥ 4). The boundaries are characterized by drastic changes in the flow structure and a discontinuous drop/rise in St and forces. The St drops at the boundary between overshoot and reattachment flow regimes and jumps at the boundary between reattachment and coshedding flow regimes, while fluctuating forces and ϕ both jump at both boundaries. The flow separation on the downstream cylinder is much delayed (122°–128°) in the reattachment flow regime compared to that on the single cylinder (95°) or upstream cylinder (92°–95.5°). The fluctuating pressure on the entire surface of either cylinder is low for the overshoot flow because the two cylinders are enclosed by the upstream-cylinder-generated shear layers having the longest wake recirculation. The ϕ is almost zero in the overshoot flow. With increasing L/D, ϕ linearly increases in the reattachment and coshedding regimes with different gradients, larger in the latter regime than in the former, by nearly twice. [ABSTRACT FROM AUTHOR]

Three-dimensional large eddy simulations were carried out to investigate the flow around two tandem circular cylinders at a subcritical Reynolds number of Re = 103. The cylinder center-to-center spacing ratio L/D is varied from 1.25 to 6, where D is the cylinder diameter. In order to enhance the understanding of flow physics around two circular cylinders, particular attention is devoted to fluctuating forces, shear-layer reattachment, flow separation, wake recirculation, Strouhal number (St), and phase lag (ϕ) between the fluctuating lift of the two cylinders. The flow structure around the cylinders is highly sensitive to L/D. A change in L/D thus leads to overshoot flow (L/D ≤ 1.25), reattachment flow (1.5 ≤ L/D ≤ 3.5), and coshedding flow (L/D ≥ 4). The boundaries are characterized by drastic changes in the flow structure and a discontinuous drop/rise in St and forces. The St drops at the boundary between overshoot and reattachment flow regimes and jumps at the boundary between reattachment and coshedding flow regimes, while fluctuating forces and ϕ both jump at both boundaries. The flow separation on the downstream cylinder is much delayed (122°–128°) in the reattachment flow regime compared to that on the single cylinder (95°) or upstream cylinder (92°–95.5°). The fluctuating pressure on the entire surface of either cylinder is low for the overshoot flow because the two cylinders are enclosed by the upstream-cylinder-generated shear layers having the longest wake recirculation. The ϕ is almost zero in the overshoot flow. With increasing L/D, ϕ linearly increases in the reattachment and coshedding regimes with different gradients, larger in the latter regime than in the former, by nearly twice. [ABSTRACT FROM AUTHOR]

Three-dimensional large eddy simulations are carried out to investigate the effect of streamwise gust amplitude ratio A R on the flow structure around and dynamic forces on two tandem circular cylinders at a subcritical Reynolds number of Re = 1 × 103. The center-to-center space L between the two cylinders is fixed at 3.5 D , where D is the cylinder diameter. The velocity U of sinusoidal streamwise gust is set as U = U 0 (1+ A R sin2π f u t), where the velocity amplitude ratio A R is varied from 0 to 0.25, U 0 is the mean velocity, f u is the frequency of the sinusoidal streamwise gust, and t is the time. In order to enhance the understanding of the streamwise gust effect on the physical properties of the flow around the two tandem cylinders, the shear-layer reattachment, flow separation, wake recirculation, Strouhal number (St), unsteady forces, and phase lag (φ) between the fluctuating lift forces of the two cylinders are explicated. The results show that the flow structure around the cylinders is sensitive to A R. A change in A R thus leads to modification of reattaching flow (A R ≤ 0.15) to co-shedding flow (A R ≥ 0.20). The St , fluctuating forces and φ thus jumps at the boundary between the reattaching and co-shedding regimes. A stronger gust effect appears on the fluctuating drag of the upstream cylinder than that of the downstream cylinder. Besides the dominant component of the fluctuating lift induced by the vortex shedding, two other components are observed with the frequencies equaling to the superposition and subtraction of the gust and vortex-shedding frequencies, respectively. In addition, two more cases with L / D = 1.5 and 6.0 are conducted for deeper understanding of A R effects. • The effects of stream-wise gust on the flow structures and forces on the two tandem cylinders were studied. • A change in the velocity amplitude ratio A R of oncoming flow leads to modification of reattaching flow (A R ≤ 0.15) to co-shedding flow (A R ≥ 0.20) around the two cylinders. • Besides the dominant component of lift induced by vortex shedding, there are two other components with the superposition and subtraction frequencies of the gust and vortex-shedding, respectively. [ABSTRACT FROM AUTHOR]

Lattice Boltzmann simulations of flows past fixed monodisperse spheres are employed to obtain the drag force on spheres at low Reynolds numbers. The fixed spheres are comprised of center and surrounding parts. Spheres in the center part are distributed with structures, while those in the surrounding part are distributed in random homogeneous configurations. The results show that the solid volume fraction in the surrounding part (also referred to as "surrounding solid volume fraction") has a significant impact on the drag force of the center particles. This drag variation due to the change of surrounding solid volume fraction becomes even larger as the solid volume fraction or the inhomogeneities of the central particles increase. A new drag model considering the surrounding influence is proposed and it is very promising in resolving the gas-solid interactions in flows with complex structures such as riser flows. [Display omitted] • The influence of surrounding solid volume fraction (SSVF) on the drag is studied by PR-DNS. • The drag variations due to the change of SSVF for different particle con'urations are analyzed. • A microscopic drag correction model considering the impact of SSVF is proposed. • The drag correction model is applicable to the range of grid sizes 3 d p ~ 6 d p in CFD-DEM/TFM simulations. [ABSTRACT FROM AUTHOR]

The filtered interphase heat‐transfer coefficient for coarse‐grid simulations of gas–solid flows can be obtained via a correction (Q) to its microscopic counterpart. The numerical results show that a good linear correlation between Q and the subgrid drift temperature exists at various filtered solid volume fractions, filter sizes and Reynolds numbers, where the subgrid drift temperature is the correlation between the fluctuating temperature of the gas phase and the fluctuation of the gas volume fraction. Since Q can be determined solely by one subgrid quantity, closure for Q is directly pursued. It is found that Q correlates surprisingly well with the product of the filtered solid volume fraction and the filtered temperature difference between the two phases normalized by the filtered heat transfer at a larger scale than the considered coarse grid. A fitting correlation is formulated based on this observation, and its predictability is evaluated in an a priori test. [ABSTRACT FROM AUTHOR]

Direct numerical simulations are performed to study the effect of particle orientation on flows through fixed random arrays of prolate ellipsoids at low Reynolds numbers. The Hermans orientation factor and Beta distribution are introduced to quantify the mean orientation and orientation deviation of the particles. The simulation results show that the effect of particle orientation is profound especially when the solid volume fraction and the aspect ratio are large. With the increase of Hermans orientation factors, the drag force decreases when the flow follows a reference direction defined by the average direction of all particles' semi‐major axes, while increases when the flow is perpendicular to the reference direction. Comparisons show that the traditional drag force correlations for ellipsoidal particles significantly under‐predict the drag force. Based on current simulation results, new drag relations are proposed for prolate ellipsoidal particles at arbitrary aspect ratios, Hermans orientation factors and solid volume fractions. [ABSTRACT FROM AUTHOR]

Direct numerical simulations with a second-order immersed boundary-lattice Boltzmann method are used to investigate the effect of particle fluctuation on flows in fixed random arrays of spheres at low and moderate particle Reynolds numbers. Random velocities obeying the isotropic Maxwellian distribution are imposed to all particles in the computational domain to mimic the granular temperature due to particle collisions. The simulation results show that the effect of particle fluctuation on the drag force is significant especially when the solid volume fraction and the particle Reynolds number are small. The drag increment due to the particle fluctuation increases with the increase of the granular temperature-based Reynolds number, however, it decreases with the increase of the solid volume fraction and the particle Reynolds number. On the basis of the simulation results, a new drag force relation based on the stationary drag in random arrays of spheres for arbitrary solid volume fractions, granular temperature-based Reynolds numbers, and particle Reynolds numbers is formulated. The fluctuations of the drag force on individual particles with respect to the mean drag are also analyzed. It is found that the drag on individual particles can differ up to 40% from the mean at small granular temperature-based Reynolds numbers and the difference increases rapidly with the increase of the granular temperature-based Reynolds number, indicating the particle fluctuation can affect the individual drag force significantly. The present results also show the drag force on individual particles well follows Gaussian distribution. The mean relative deviation is found to increase with the increase of the granular temperature-based Reynolds number and the solid volume fraction but is not affected much by the particle Reynolds number. [ABSTRACT FROM AUTHOR]

Particle-resolved direct numerical simulations of flows past various fixed structures of spheres are performed to study the drag force at local Reynolds numbers up to 250. At the gas–solid interface, the drag force is found to be 5 % ∼ 800 % of that estimated by BVK law (Beetstra et al. AIChE Journal, 2007, 53(2):489-501) at different particle Reynolds numbers and solid volume fraction gradients. Thus a microscale drag model at the cluster interface is developed as a function of the particle Reynolds number and the solid concentrations of dense and dilute phases. Assessments of the proposed drag model are performed with direct numerical simulations of flows past plug-like, spherical, ellipsoidal clusters as well as bubble-containing structures. The results show that the new model well captures the drag variations at microscales of several sphere diameters and correlates well with the solid concentrations and velocities of dense and dilute phases. • Significant deviation from BVK law is found at structure interface at moderate Reynolds numbers. • A microscopic drag model considering the interface effect is established via PR-DNSs. • The new drag model is suitable for flow in arbitrary direction with Reynolds number less than 250. [ABSTRACT FROM AUTHOR]

An expression of the filtered Eulerian drag force is proposed based on the second order Taylor polynomial approximation of a microscopic drag coefficient. Theoretical computations of the expression at low particle Reynolds numbers show that four sub-grid quantities, the gas drift velocity, the solid drift velocity, the scalar variance of solid volume fraction and a third-order moment, are significant for an accurate estimation of the filtered drag force. Various drag models with different combinations of the four sub-grid quantities are proposed and their coefficients are optimized based on fine-grid two fluid model results. The gas drift velocity is demonstrated to be the most important marker in predicting the filtered drag force. The model with the solid drift velocity and the scalar variance of the solid volume fraction is found to be promising in computational fluid dynamic-discrete element model simulations due to the ready availability of the two sub-grid quantities. Unlabelled Image • Four sub-grid quantities are demonstrated to significantly affect filtered drag force. • Gas drift velocity is the most important marker in predicting filtered drag force. • Models with different combinations of the four sub-grid quantities are established. [ABSTRACT FROM AUTHOR]

• The variation of Nu caused by Stefan flow is more evident than drag coefficient. • The increase in Re and c can only partially offset the reduction of Nu. • Stefan flow induces the variation of Re and Nu along the streamwise direction. • A heat transfer correction factor is developed based on the simulation data. By using a particle-resolved direct numerical simulation, the impact of Stefan flow on interphase heat transfer in flow past static random particle arrays is investigated. The findings demonstrate that the temperature boundary layer of particles is thickened/thinned by the outward/inward Stefan flow and therefore hinders/improves the contact between main gas flow and particles. With the impact of positive Stefan Reynolds number (Re sf), the maximum percentage reduction of Nusselt number could be over 3 times of the maximum percentage reduction of drag coefficient at the same condition. The rise in particle Reynolds number (Re) or solid volume fraction (c) can partially offset the impact of Stefan flow. Finally, the simulation data are used to develop a correction factor for interphase heat transfer considering the impact of Stefan flow for −3 < Re sf < 6, 0 < Re < 100, and 0 < c < 0.5. Note that the scalar in current work is chosen to be the dimensionless temperature, but the results are general and applicable to any passive scalar. [ABSTRACT FROM AUTHOR]

• The reduction of drag force caused by Stefan flow decreases as Re increases. • The thickened boundary layer is suppressed by the surrounding inert particles. • The drag force reduction is non-negligible even at higher solid volume fraction. • A drag correlation is proposed based on the simulation results. Single reactive particle is generally surrounded by a sea of inert sand particles in thermo-chemical conversion process of solid fuels inside fluidized bed reactors. The drag force of the reactive particle under such special condition is affected by the combination of Stefan flow from the reactive particle, particle Reynolds number (Re), and solid holdup (c). This work quantifies this combinational effect via particle-resolved direct numerical simulations. It is found that the outward Stefan flow weakens the drag force, while the inward Stefan flow strengthens the drag force. The effect of Stefan flow becomes weak as c or Re increases. The variation of Re has negligible effect on the reduction of the drag force when c is relatively high. Finally, a drag correlation considering the joint influences of Stefan flow, Re and c is proposed based on the simulation data. [ABSTRACT FROM AUTHOR]

• Drag force on particles decreases as the Stefan Reynolds number increases. • The drag force reduction is weakened as the solid volume fraction increases. • Particle boundary layer is suppressed by Stefan flow from neighboring particles. • A novel drag correction coefficient is developed based on the simulation data. Stefan flow is a mass flow perpendicular to the particle surface induced by the reaction or component diffusion occurring inside particles. It significantly affects the interphase transfer process in gas–solid reacting flows. In this work, a second-order immersed boundary-lattice Boltzmann method (IB-LBM) is adopted for analyzing the influence of Stefan flow on the drag force in flows past fixed random arrays of spherical particles. The effect of Stefan flow is introduced by assigning specific fluid velocities at Lagrangian markers on the sphere surface. The simulation results show that the drag force exerting on particles decreases as the Stefan Reynolds number increases. The drag force reduction caused by Stefan flow is weakened as the solid volume fraction increases. This is because the thick boundary layer caused by Stefan flow on each particle is suppressed by Stefan flow from their neighboring particles. Based on the simulation results, a novel drag correction coefficient is developed, which considers the joint influence of the Stefan Reynolds number, particle Reynolds number and solid volume fraction. [ABSTRACT FROM AUTHOR]