Bivariate extensions of the Extended Quadrature Method of Moments (EQMOM) to describe coupled droplet evaporation and heat-up

Pollack, Martin; Salenbauch, S.; Marchisio, Daniele; Hasse, Christian

doi:10.1016/j.jaerosci.2015.10.008

Cited by 12 publications

(8 citation statements)

References 61 publications

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“…Furthermore, a combination with EQMoM is possible [139], which enables improved estimation of underlying multivariate NDF from the moments. In [140], different bivariate CQMoM extensions with the EQMoM and the SQMoM are discussed. Application of CQMoM to multivariate problems may yield a weak hyperbolic system of moment equations which require thorough mathematical treatment due to the possibility of shock formation [111,141,142].…”

Section: Conditional Quadrature Methods Of Moments (Cqmom)mentioning

confidence: 99%

Approximate Moment Methods for Population Balance Equations in Particulate and Bioengineering Processes

Dürr

Bück

2020

Processes

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Population balance modeling is an established framework to describe the dynamics of particle populations in disperse phase systems found in a broad field of industrial, civil, and medical applications. The resulting population balance equations account for the dynamics of the number density distribution functions and represent (systems of) partial differential equations which require sophisticated numerical solution techniques due to the general lack of analytical solutions. A specific class of solution algorithms, so-called moment methods, is based on the reduction of complex models to a set of ordinary differential equations characterizing dynamics of integral quantities of the number density distribution function. However, in general, a closed set of moment equations is not found and one has to rely on approximate closure methods. In this contribution, a concise overview of the most prominent approximate moment methods is given.

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Section: Conditional Quadrature Methods Of Moments (Cqmom)mentioning

confidence: 99%

Approximate Moment Methods for Population Balance Equations in Particulate and Bioengineering Processes

Dürr

Bück

2020

Processes

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“…, 2n − q , where 2n − q ≥ 2 is the number of additional moments of negative order used in this algorithm and chosen by the user. The other moments of positive order are computed using the disappearance flux: (39) m…”

Section: 4mentioning

confidence: 99%

“…It allows to limit the computational cost and the number of systems of partial differential equations to be solved. We will not consider in the present study quadrature methods such as QMOM or EQMOM [34,32,49,39] since they lead to either difficulties in evaluating the evaporating flux at zero size or can not reach the integrality of the moment space, but rather focus on Maximum Entropy (ME) reconstruction such as with Eulerian Multi Size Moment (EMSM) and Correlated Size Velocity Moment models in [24,33,47,19]. They cover the whole moment space and show a great capacity in modeling the polydispersion and evaporation with a minimal number of variables.…”

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confidence: 99%

High Order Moment Model for Polydisperse Evaporating Sprays towards Interfacial Geometry Description

Essadki¹,

Chaisemartin²,

Laurent³

et al. 2018

SIAM J. Appl. Math.

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In this paper we propose a new Eulerian model and related accurate and robust numerical methods, describing polydisperse evaporating sprays, based on high order moment methods in size. The main novelty of this model relies on the use of fractional droplet surface moments and their ability to predict some geometrical variables of the droplet-gas interface, by analogy with the liquid-gas interface in interfacial flows. Evaporation is evaluated by using a Maximum Entropy (ME) reconstruction. The use of fractional moments introduces some theoretical and numerical difficulties. First, relying on a study of the moment space, we extend the ME reconstruction to the case of fractional moments. Then, we propose a new high order and robust algorithm to solve the moment evolution due to evaporation, which preserves the structure of the moment space. It involves some negative order fractional moments for which a novel treatment is introduced. The present model and numerical schemes yield an accurate and stable evaluation of the moment dynamics with minimal number of variables, as well as computational cost, but also provides an additional capacity of coupling with diffuse interface model and transport equation of averaged geometrical interface variables, which are essential in order to describe atomization.

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“…its moments m k (t, x), are solved. Moment methods have been applied successfully to a wide range of problems, such as nano-particles and aerosols [8], sprays [9], and combustion-related problems such as soot formation [10,11].…”

Section: Introductionmentioning

confidence: 99%

Evaluation of Quadrature-based Moment Methods in turbulent premixed combustion

Pollack

Ferraro

Janicka

et al. 2021

Proceedings of the Combustion Institute

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Transported probability density function (PDF) methods are widely used to model turbulent flames characterized by strong turbulence-chemistry interactions. Numerical methods directly resolving the PDF are commonly used, such as the Lagrangian particle or the stochastic fields (SF) approach. However, especially for premixed combustion configurations, characterized by high reaction rates and thin reaction zones, a fine PDF resolution is required, both in physical and in composition space, leading to high numerical costs. An alternative approach to solve a PDF is the method of moments, which has shown to be numerically efficient in a wide range of applications. In this work, two Quadrature-based Moment closures are evaluated in the context of turbulent premixed combustion. The Quadrature-based Moment Methods (QMOM) and the recently developed Extended QMOM (EQMOM) are used in combination with a tabulated chemistry approach to approximate the composition PDF. Both closures are first applied to an established benchmark case for PDF methods, a plug-flow reactor with imperfect mixing, and compared to reference results obtained from Lagrangian particle and SF approaches. Second, a set of turbulent premixed methane-air flames are simulated, varying the Karlovitz number and the turbulent length scale. The turbulent flame speeds obtained are compared with SF reference solutions. Further, spatial resolution requirements for simulating these premixed flames using QMOM are investigated and compared with the requirements of SF. The results demonstrate that both QMOM and EQMOM approaches are well suited to reproduce the turbulent flame properties. Additionally, it is shown that moment methods require lower spatial resolution compared to SF method.

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Bivariate extensions of the Extended Quadrature Method of Moments (EQMOM) to describe coupled droplet evaporation and heat-up

Cited by 12 publications

References 61 publications

Approximate Moment Methods for Population Balance Equations in Particulate and Bioengineering Processes

Approximate Moment Methods for Population Balance Equations in Particulate and Bioengineering Processes

High Order Moment Model for Polydisperse Evaporating Sprays towards Interfacial Geometry Description

Evaluation of Quadrature-based Moment Methods in turbulent premixed combustion

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