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Journal ArticleDOI

Nonlinear mechanics of fluidization of beds of spherical particles

01 Apr 1987-Journal of Fluid Mechanics (Cambridge University Press)-Vol. 177, Iss: -1, pp 467-483
TL;DR: In this article, the authors describe a local rearrangement mechanism in which one sphere is captured in the wake of the other, and two local mechanisms are involved: drafting and kissing and tumbling into stable cross stream arrays.
Abstract: Experiments on fluidization with water of spherical particles falling against gravity in columns of rectangular cross-section are described. All of them are dominated by inertial effects associated with wakes. Two local mechanisms are involved: drafting and kissing and tumbling into stable cross-stream arrays. Drafting, kissing and tumbling are rearrangement mechanisms in which one sphere is captured in the wake of the other. The kissing spheres are aligned with the stream. The streamwise alignment is massively unstable and the kissing spheres tumble into more stable cross-stream pairs of doublets which can aggregate into larger relatively stable horizontal arrays. Cross-stream arrays in beds of spheres constrained to move in two dimensions are remarkable. These arrays may even coalesce into aggregations of close-packed spheres separated by regions of clear water. A somewhat weaker form of cooperative motion of cross-stream arrays of rising spheres is found in beds of square cross-section where the spheres may move freely in three dimensions. Horizontal arrays rise where drafting spheres fall because of greater drag. Aggregation of spheres seems to be associated with relatively stable cooperative motions of horizontal arrays of spheres rising in their own wakes.
Citations
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Journal ArticleDOI
TL;DR: In this paper, a front-tracking method for multiphase flows is presented, which is based on writing one set of governing equations for the whole computational domain and treating the different phases as one fluid with variable material properties.

2,011 citations

Journal ArticleDOI
TL;DR: In this article, a new Lagrange-multiplier based fictitious-domain method is presented for the direct numerical simulation of viscous incompressible flow with suspended solid particles, which uses a finite-element discretization in space and an operator-splitting technique for discretisation in time.

1,072 citations


Cites methods from "Nonlinear mechanics of fluidization..."

  • ...Johnson and Tezduyar apply their method to the sedimentation of polydisperse spheres; their simulations reproduce the microstructural across-the-stream structures associated with drafting, kissing, and tumbling (Fortes et al., 1987; Joseph et al.; 1987, and Joseph, 1996)....

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Journal ArticleDOI
TL;DR: In this paper, the Lagrange-multiplier-based fictitious domain methods are combined with finite element approximations of the Navier-Stokes equations occurring in the global model to simulate incompressible viscous fluid flow past moving rigid bodies.

982 citations


Cites background from "Nonlinear mechanics of fluidization..."

  • ...In [49] many experimental results related to this type of “almost two-dimensional” beds are presented....

    [...]

Book
07 Oct 2011
TL;DR: In this paper, a review of the state-of-the-art numerical methods used for direct numerical simulations of multiphase flows, with a particular emphasis on methods that use the so-called "one-field" formulation of the governing equations, is presented.
Abstract: Direct numerical simulations of bubbly flows are reviewed and recent progress is discussed. Simulations, of homogeneous bubble distribution in fully periodic domains at relatively low Reynolds numbers have already yielded considerable insight into the dynamics of such flows. Many aspects of the evolution converge rapidly with the size of the systems and results for the rise velocity, the velocity fluctuations, as well as the average relative orientation of bubble pairs have been obtained. The challenge now is to examine bubbles at higher Reynolds numbers, bubbles in channels and confined geometry, and bubble interactions with turbulent flows. We briefly review numerical methods used for direct numerical simulations of multiphase flows, with a particular emphasis on methods that use the so-called "one-field" formulation of the governing equations, and then discuss studies of bubbles in periodic domains, along with recent work on wobbly bubbles, bubbles in laminar and turbulent channel flows, and bubble formation in boiling.

584 citations

Journal ArticleDOI
TL;DR: In this article, the initial value problem for the sedimentation of circular and elliptical particles in a vertical channel is solved for the Navier-Stokes equations for moderate Reynolds numbers in the hundreds.
Abstract: This paper reports the result of direct simulations of fluid–particle motions in two dimensions. We solve the initial value problem for the sedimentation of circular and elliptical particles in a vertical channel. The fluid motion is computed from the Navier–Stokes equations for moderate Reynolds numbers in the hundreds. The particles are moved according to the equations of motion of a rigid body under the action of gravity and hydrodynamic forces arising from the motion of the fluid. The solutions are as exact as our finite-element calculations will allow. As the Reynolds number is increased to 600, a circular particle can be said to experience five different regimes of motion: steady motion with and without overshoot and weak, strong and irregular oscillations. An elliptic particle always turn its long axis perpendicular to the fall, and drifts to the centreline of the channel during sedimentation. Steady drift, damped oscillation and periodic oscillation of the particle are observed for different ranges of the Reynolds number. For two particles which interact while settling, a steady staggered structure, a periodic wake-action regime and an active drafting–kissing–tumbling scenario are realized at increasing Reynolds numbers. The non-linear effects of particle–fluid, particle–wall and interparticle interactions are analysed, and the mechanisms controlling the simulated flows are shown to be lubrication, turning couples on long bodies, steady and unsteady wakes and wake interactions. The results are compared to experimental and theoretical results previously published.

533 citations

References
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Journal ArticleDOI
TL;DR: In this article, the authors examined the characteristic lengths of the oscillating wakes of bluff bodies and concluded that these are equivalent at high Reynolds number, leading to the conclusion that there are two simultaneous characteristic lengths; the scale of the formation region and the width to which the free shear layers diffuse.
Abstract: The characteristic lengths of the oscillating wakes of bluff bodies is discussed; in particular, those used in the universal non-dimensional frequencies proposed by Roshko (1954b) and Goldburg, Washburn & Florsheim (1965). It is concluded that these are equivalent at high Reynolds number. A closer examination leads to the conclusion that there are two simultaneous characteristic lengths; the scale of the formation region, and the width to which the free shear layers diffuse. Discussion of the mechanics of the formation region results in a physical basis for the determination of the frequency by these two characteristic lengths. The ideas developed are applied to the effects of splitter plates in the wake. The possibility of a high-Reynolds-number symmetrical formation region is suggested as an explanation of the very small lift values observed in the absence of free-stream disturbances.

921 citations

Journal ArticleDOI
TL;DR: In this paper, the Strouhal number as a function of Reynolds number measured by Moller (1938) has been confirmed using water flow and the lower critical Reynolds number, first reported by Cometta (1957), was found to be Re = 6 × 103.
Abstract: Vortex shedding from spheres has been studied in the Reynolds number range 400 < Re < 5 × 106. At low Reynolds numbers, i.e. up to Re = 3 × 103, the values of the Strouhal number as a function of Reynolds number measured by Moller (1938) have been confirmed using water flow. The lower critical Reynolds number, first reported by Cometta (1957), was found to be Re = 6 × 103. Here a discontinuity in the relationship between the Strouhal and Reynolds numbers is obvious. From Re = 6 × 103 to Re = 3 × 105 strong periodic fluctuations in the wake flow were observed. Beyond the upper critical Reynolds number (Re = 3.7 × 105) periodic vortex shedding could not be detected by the present measurement techniques.The hot-wire measurements indicate that the signals recorded simultaneously at different positions on the 75° circle (normal to the flow) show a phase shift. Thus it appears that the vortex separation point rotates around the sphere. An attempt is made to interpret this experimental evidence.

477 citations

Journal ArticleDOI
TL;DR: In this paper, a nonlinear extension of Brinkman's self-consistent theory for the flow of a viscous fluid through a swarm of spherical particles is presented. But it does not consider the effects of inertia.
Abstract: It is argued that the appropriate generalization of Darcy's law when inertia effects are included takes the form ∇p = −(μ/k) V − (ρc/k½)|V|V, div V = 0, where k is the permeability of the medium and the ‘form drag constant’ c is a coefficient which is independent of the pressure p, the seepage velocity V, and the density ρ and viscosity μ of the fluid but which is dependent on the geometry of the medium. We formulate a nonlinear extension of Brinkman's self-consistent theory for the flow of a viscous fluid through a swarm of spherical particles. We equate the drag per unit volume given by the right hand side of the first of the above equations to the total drag ND on the N particles contained within that unit volume, in an infinite region Ω, where D is the drag on a single particle placed in a velocity field v subject to ρ(v · ∇)v + grad p = μ∇2v−μ/k v − (cρ/k½)|v|v, div v = 0, v|∂Ω is a prescribed constant, where μ is the viscosity. Without solving these equations, we obtain an estimate for c from the known experimental drag law for a solid sphere placed in a uniform stream.

229 citations

Journal ArticleDOI
TL;DR: In this paper, the propagation properties of instability waves in a two-dimensional liquid fluidized bed are reported. But, although the waves experience an initially exponential growth in amplitude, the ultimate state of motion exhibited is that of the complicated formation and destruction of cylindrical bubble-like structures.

135 citations