Dynamic and steady-state sedimentation of polydisperse suspension and prediction of outlets particle-size distribution

Zeidan, Asad; Rohani, Sohrab; Bassi, Amarjeet

doi:10.1016/j.ces.2004.01.064

Cited by 19 publications

(12 citation statements)

References 45 publications

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“…Rather, we highlight the relevance of our analysis by mentioning that recent works that employ either the MLB model or the BW, DG or HS model include [26,35,37,45,49,50] and [19,22,28], respectively.…”

Section: Related Workmentioning

confidence: 99%

Hyperbolicity Analysis of Polydisperse Sedimentation Models via a Secular Equation for the Flux Jacobian

Bürger¹,

Donat²,

Mulet³

et al. 2010

SIAM J. Appl. Math.

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Abstract. Polydisperse suspensions consist of small particles which are dispersed in a viscous fluid, and which belong to a finite number N of species that differ in size or density. Spatially one-dimensional kinematic models for the sedimentation of such mixtures are given by systems of N non-linear first-order conservation laws for the vector Φ of the N local solids volume fractions of each species. The problem of hyperbolicity of this system is considered here for the models due to Masliyah, Lockett and Bassoon, Batchelor and Wen and Höfler and Schwarzer. In each of these models, the flux vector depends only on a small number m < N of independent scalar functions of Φ, so its Jacobian is a rank-m perturbation of a diagonal matrix. This allows to identify its eigenvalues as the zeros of a particular rational function R(λ), which in turn is the determinant of a certain m × m matrix. The coefficients of R(λ) follow from a representation formula due to Anderson [Lin. Alg. Appl. 246:49-70, 1996]. It is demonstrated that the secular equation R(λ) = 0 can be employed to efficiently localize the eigenvalues of the flux Jacobian, and thereby to identify parameter regions of guaranteed hyperbolicity for each model. Moreover, it provides the characteristic information required by certain numerical schemes to solve the respective systems of conservation laws.

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Section: Related Workmentioning

confidence: 99%

Hyperbolicity Analysis of Polydisperse Sedimentation Models via a Secular Equation for the Flux Jacobian

Bürger¹,

Donat²,

Mulet³

et al. 2010

SIAM J. Appl. Math.

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“…While the solution strategy of the Riemann problem and the front tracking algorithm are presented for general N , for the numerical example, which is based on experimental data by Schneider et al [47], we choose N = 2. While substantial advances were made in recent years in the global hyperbolicity (type) analysis [5,11] and in the design of high-resolution finite volume schemes for the sedimentation model (and related multi-species kinematic models) [10,12,52], the present paper contributes to providing insight into the structure of exact solutions of the model and a building block for the hyperfast front tracking method [22].…”

Section: Scopementioning

confidence: 99%

On Riemann problems and front tracking for a model of sedimentation of polydisperse suspensions

Berres

Bürger²

2007

Z Angew Math Mech

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This paper analyses a continuum model of the sedimentation of polydisperse suspensions, where the volume concentrations of the solids species are the sought unknowns. This leads to systems of conservation laws which are non-genuinely nonlinear ("non-convex") in the sense that they are only piecewise genuinely nonlinear. The solution of a Riemann problem is represented as a concatenation of elementary waves, where the linear degeneracy requires using the Liu entropy condition. After a general description of the composition of elementary waves, an algorithm for the computational construction is given. The solution of the Riemann problem is then utilized as a problem-adapted building block of a front tracking method. For the model of bidisperse suspensions, Riemann problems are classified by the location of the left and right state in the phase space of unknown variables. The front tracking method is applied to solve the initial value problem of a first-order hyperbolic 2 × 2 system of conservation laws describing the settling of a bidisperse suspension. The solution obtained by front tracking is compared with results obtained by an experiment and a finite difference scheme.

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“…[9,10] Mathematically speaking, stability is equivalent to hyperbolicity of the model equations, which ensures that all solution information, in particular concentration discontinuities such as the suspension-sediment interface, propagates at finite speeds, see Berres et al, [11] Bü rger et al, [12] Biesheuvel et al [13] and Basson et al [14] for further explanations. The latter property allows to simulate sedimentation processes reliably by solving the governing equations numerically by finite volume methods; we refer to Xue and Sun, [15] Zeidan et al, [16] and the present authors' papers for examples of successful implementations. The works cited so far are all related to gravity settling of polydisperse suspensions, but most results carry over to the centrifugal setup cited herein; for instance, finite volume methods are equally suited for the simulation of centrifugal separation of polydisperse suspensions.…”

Section: Related Workmentioning

confidence: 95%

Centrifugal Settling of Polydisperse Suspensions with a Continuous Particle Size Distribution: A Generalized Kinetic Description

Bürger

García

2008

Drying Technology

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The settling of a polydisperse suspension with a continuous particle size distribution (PSD) can be modeled by an equation of the generalized kinetic theory, which represents the limit case of a system of conservation laws for a finite number of size classes. A previous model of gravity settling of such a mixture is extended to settling in a rotating tube or basket centrifuge. A numerical scheme to approximate solutions of the generalized kinetic equation is defined and simulations are presented, illustrating the formation of sediment and the effect of various centrifuge geometries. In particular, the model predicts the radial variation of the composition of the sediment forming at the outer wall.

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Dynamic and steady-state sedimentation of polydisperse suspension and prediction of outlets particle-size distribution

Cited by 19 publications

References 45 publications

Hyperbolicity Analysis of Polydisperse Sedimentation Models via a Secular Equation for the Flux Jacobian

Hyperbolicity Analysis of Polydisperse Sedimentation Models via a Secular Equation for the Flux Jacobian

On Riemann problems and front tracking for a model of sedimentation of polydisperse suspensions

Centrifugal Settling of Polydisperse Suspensions with a Continuous Particle Size Distribution: A Generalized Kinetic Description

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