Multi-fluid modelling of laminar polydisperse spray flames: origin, assumptions and comparison of sectional and sampling methods

Laurent, Frédérique; Massot, Marc

doi:10.1088/1364-7830/5/4/303

Cited by 127 publications

(229 citation statements)

References 26 publications

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“…Multiphase flows with sprays governed by Boltzmann type equations [32], or derived multifluid sectional models for droplets [88], may also be investigated mathematically. …”

Section: Discussionmentioning

confidence: 99%

“…We notably address the mathematical structure of the transport linear systems and fast accurate evaluation of the transport coefficients [65,66,67,68,69,70,71]. We also present a typical numerical simulation of a complex chemistry Bunsen laminar flames [5,72,73,74] and discuss the impact of multicomponent transport [75,76,77,78,79,80] as well as possible extensions [81,82,83,84,85,86,87,88].…”

Section: Introductionmentioning

confidence: 99%

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Multicomponent flow modeling

Giovangigli

2011

Sci. China Math.

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We first present multicomponent flow models derived from the kinetic theory of gases. We then investigate the symmetric hyperbolic-parabolic structure of the resulting system of partial differential equations and discuss the Cauchy problem for smooth solutions. We also address the existence of deflagration waves also termed anchored waves. We further indicate related models which have a similar hyperbolic-parabolic structure, notably the Saint-Venant system with a temperature equation as well as the equations governing chemical equilibrium flows. We next investigate multicomponent ionized and magnetized flow models with anisotropic transport fluxes which have a different mathematical structure. We finally discuss numerical algorithms specifically devoted to complex chemistry flows, in particular the evaluation of multicomponent transport properties, as well as the impact of multicomponent transport.

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“…Multiphase flows with sprays governed by Boltzmann type equations [32], or derived multifluid sectional models for droplets [88], may also be investigated mathematically. …”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multicomponent flow modeling

Giovangigli

2011

Sci. China Math.

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“…A hypothesis on the velocity distribution has to be made in order to obtain a closed equation on the total number density conditioned on size, n(t, x, S). Following the example of what is done in the multi-fluid model [25,32,8], we suppose that there is no dispersion around the mean velocity. In other terms, we "project" f on a distribution with a single velocity conditioned on size:…”

Section: Spraymentioning

confidence: 99%

“…The closure of the velocity moments conditioned on size is classical and conducted through a usual hydrodynamic limit leading to an equilibrium velocity distribution, i.e. Maxwell-Boltzmann distribution up to zero temperature in the framework of direct numerical simulation [32,8,27]. Once a closure has been chosen in terms of velocity moments conditioned on droplet size, there are two options available for capturing the dynamics in the size phase space.…”

Section: Introductionmentioning

confidence: 99%

“…Once a closure has been chosen in terms of velocity moments conditioned on droplet size, there are two options available for capturing the dynamics in the size phase space. One can either rely on size phase space discretization, with low order size moments in each section, as done in the multi-fluid approach developed in [10,8,32] from [25]. The multi-fluid model considers only one size moment which accounts for the liquid mass density on small intervals of the size phase space called sections.…”

Section: Introductionmentioning

confidence: 99%

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A high order moment method simulating evaporation and advection of a polydisperse liquid spray

Kah

Laurent

Massot

et al. 2012

Journal of Computational Physics

109

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In this paper, we tackle the modeling and numerical simulation of sprays and aerosols, that is dilute gasdroplet flows for which polydispersity description is of paramount importance. Starting from a kinetic description for point particles experiencing transport either at the carrier phase velocity for aerosols or at their own velocity for sprays as well as evaporation, we focus on an Eulerian high order moment method in size and consider a system of partial differential equations (PDEs) on a vector of successive integer size moments of order 0 to N , N > 2, over a compact size interval. There exists a stumbling block for the usual approaches using high order moment methods resolved with high order finite volume methods: the transport algorithm does not preserve the moment space. Indeed, reconstruction of moments by polynomials inside computational cells coupled to the evolution algorithm can create N -dimensional vectors which fail to be moment vectors: it is impossible to find a size distribution for which there are the moments. We thus propose a new approach as well as an algorithm which is second order in space and time with very limited numerical diffusion and allows to accurately describe the advection process and naturally preserves the moment space. The algorithm also leads to a natural coupling with a recently designed algorithm for evaporation which also preserves the moment space; thus polydispersity is accounted for in the evaporation and advection process, very accurately and at a very reasonable computational cost. These modeling and algorithmic tools are referred to as the EMSM (Eulerian Multi Size Moment) model. We show that such an approach is very competitive compared to multi-fluid approaches, where the size phase space is discretized into several sections and low order moment methods are used in each section, as well as with other existing high order moment methods. An accuracy study assesses the order of the method as well as the low level of numerical diffusion on structured meshes. Whereas the extension to unstructured meshes is provided, we focus in this paper on cartesian meshes and two 2D test-cases are presented: Taylor-Green vortices and turbulent free jets, where the accuracy and efficiency of the approach are assessed.

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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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Multi-fluid modelling of laminar polydisperse spray flames: origin, assumptions and comparison of sectional and sampling methods

Cited by 127 publications

References 26 publications

Multicomponent flow modeling

Multicomponent flow modeling

A high order moment method simulating evaporation and advection of a polydisperse liquid spray

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

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