A second-order multi-fluid model for evaporating sprays

Dufour, Guillaume; Villedieu, Philippe

doi:10.1051/m2an:2005041

Cited by 18 publications

(32 citation statements)

References 32 publications

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“…It can be seen as a generalization of the reconstruction used in [13] except that the considered moments were moments of order 0 and 3/2 instead of integer moments here. The coefficients ξ 0 , .…”

Section: Ndf Reconstruction Through the Maximum Entropy Formalismmentioning

confidence: 99%

“…It needs the calculation of abscissas and weights from moments. It can be noted that the computation of M(t) from M(0) does not need the separation between flux and transport and could be done, like in [27] or [13], using directly the following formula :…”

Section: Lemma 32 the Evolution Equation On The Moments Can Be Writmentioning

confidence: 99%

“…This function is then discretized using a "finite-volume" approach that yields conservation equations for mass, momentum (and eventually other properties such as temperature) of droplets in fixed size intervals called "sections" extending the original work of Tambour, Greenberg and collaborators [19,20] for evaporating sprays. Even though this approach has recently been extended to second order by Laurent [27] and Dufour [12,13] for evaporating sprays, the necessity to discretize the size phase space can be a stumbling block for applications implying a drift velocity in the size phase space such as evaporation since it introduces intrinsic numerical diffusion and then requires fine grids in size phase space. Moment methods such as DQMOM introduced by [32], on the other hand, do not encounter this limitation and have proved in [15] to perform quite well on a number of configurations.…”

mentioning

confidence: 99%

“…Solutions have already been proposed in order to define reasonable fluxes up to order two by taking moment vectors of dimension one [28,27] or two [13,27]. However, in the present paper we are not concerned with the perspective of numerical analysis which characterizes the behavior of a numerical scheme as the section width is approaching zero, but with the design of a new scheme for which the use of only up to 3 sections is enough for a very good accuracy and for which we can use some ingredients from QMOM or DQMOM.…”

mentioning

confidence: 99%

“…But the moment space of positive polynomial functions is only a sub-space of the moment space and a modified method is introduced in this article in the case of two moments, using a reconstruction with a bi-affine function instead of an affine one. An other extension were developed in [13] with the use of moments of order 0 and 3/2. It is then show that a function of the type exp(ax + b) can be used and a preservation of the moment space was also taken for.…”

mentioning

confidence: 99%

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A Robust Moment Method for Evaluation of the Disappearance Rate of Evaporating Sprays

Massot¹,

Laurent²,

Kah³

et al. 2010

SIAM J. Appl. Math.

131

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Abstract. In this paper we tackle a critical issue in the numerical modeling, by Eulerian moment methods, of polydisperse multiphase systems, constituted of dispersed particles or droplets, a general class of systems which include aerosols. Their modeling starts at a mesoscopic scale with an equation on the number density function NDF of particles/droplets which satisfies a population balance equation. (PBE, also called Williams equation in the spray community). In order to limit the computational cost, moment methods provide a system of conservation equation with an eventual closure problem which can be solved using quadrature methods in order to retrieve the unclosed terms from the considered set of moments. However, a drift velocity, that is, the rate of change due to continuous phenomena of the internal coordinate such as the size of the particles, has sometimes to be taken into account; it can be either positive like molecular growth, or negative such as for evaporation of droplets in aerosols or oxidation of soots. When negative, it leads to the disappearance of droplets/particles thus creating a negative flux at zero size. Its closure requires an evaluation of the reconstructed NDF at zero size from the knowledge of a given finite set of moments. The nature of this information, pointwise in internal coordinate, and its influence on moment dynamics results in a difficulty from both a modeling and a numerical point of view. We obtain in the present contribution a comprehensive solution to this important issue. Since we introduce some new tools in order to resolve the flux evaluation, we also introduce a new Eulerian type of description which will combine both the flexibility of Eulerian models for which the size phase space is discretized into "sections" (i.e. size intervals) and the efficiency of Direct Quadrature Method of Moments (DQMOM). It yields a precise and stable description of moment dynamics with a minimal number of variables which should lead to a low computational cost in multi-dimensional configurations.

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Section: Ndf Reconstruction Through the Maximum Entropy Formalismmentioning

confidence: 99%

Section: Lemma 32 the Evolution Equation On The Moments Can Be Writmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

A Robust Moment Method for Evaluation of the Disappearance Rate of Evaporating Sprays

Massot¹,

Laurent²,

Kah³

et al. 2010

SIAM J. Appl. Math.

131

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Modeling and Simulation of Evaporating Spray Flows with Coalescence in an Eulerian Framework

Gopireddy

Humza

Gutheil

2012

Chemie Ingenieur Technik

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The study concerns the modeling and simulation of gas-droplet and droplet-droplet interactions on spray dynamics and droplet size distribution in turbulent spray flows where the spray is described in an Eulerian framework. The primary focus is to develop a suitable mathematical model that can describe the underlying physics including the polydispersion of the spray, evaporation, drag, coalescence, and interaction with the convective gas flow. This is achieved by applying the direct quadrature method of moments, which is extended to account for evaporation, drag force and coalescence by implementing well-established standard models available in literature. The model is developed and formulated in three-dimensional physical space, whereas the computations are carried out in a one-dimensional geometric configuration since the reference experimental setup is only one-dimensional. A water spray carried by nitrogen was injected through a hollow cone nozzle into a cylindrical spray chamber. The results reveal that evaporation and coalescence have a significant effect on the droplet size distribution whereas the droplet velocity is influenced by drag force as anticipated. Computational and experimental results agree very well when coalescence is considered.

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Eulerian Multi-Fluid Models for Polydisperse Evaporating Sprays

Massot

Multiphase Reacting Flows: Modelling and Simulation

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A second-order multi-fluid model for evaporating sprays

Cited by 18 publications

References 32 publications

A Robust Moment Method for Evaluation of the Disappearance Rate of Evaporating Sprays

A Robust Moment Method for Evaluation of the Disappearance Rate of Evaporating Sprays

Modeling and Simulation of Evaporating Spray Flows with Coalescence in an Eulerian Framework

Eulerian Multi-Fluid Models for Polydisperse Evaporating Sprays

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