On the Development of Spray Submodels Based on Droplet Size Moments

Beck, J. C.; Watkins, A. P.

doi:10.1006/jcph.2002.7186

Cited by 41 publications

(76 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In other fields of application (sprays or particle-laden flows), moment methods have been introduced only recently [25] and were first used with a Rosin-Rammler distribution [loc. cit.]…”

Section: Choices For the Distribution Functionmentioning

confidence: 43%

A Comparative Study of B-, Γ- and Log-Normal Distributions in a Three-Moment Parameterization for Drop Sedimentation

Ziemer

Wacker

2014

Atmosphere

View full text Add to dashboard Cite

This paper examines different distribution functions used in a three-moment parameterization scheme with regard to their influence on the implementation and the results of the parameterization scheme. In parameterizations with moment methods, the prognostic variables are interpreted as statistical moments of a drop size distribution, for which a functional form has to be assumed. In cloud microphysics, parameterizations are frequently based on gamma-and log-normal distributions, while for particle-laden flows in engineering, the beta-distribution is sometimes used. In this study, the three-moment schemes with beta-, gamma-and log-normal distributions are tested in a 1D framework for drop sedimentation, and their results are compared with those of a spectral reference model. The gamma-distribution performs best. The results of the parameterization with the beta-and the log-normal distribution have less similarity to the reference solution, particularly with regard to number density and rain rate. Theoretical considerations reveal that (depending on the type of the distribution function) only selected combinations of moments can be predicted together. Among these is the important combination of "number density, liquid water content, radar reflectivity" for all three distributions. Advection or source/sink terms can only be calculated under certain conditions on the moment values (positivity of the Hankel-Hadamard determinant). These are derived from mathematical theory ("moment problem") and are more restrictive for three-moment than for two-moment schemes.Atmosphere 2014, 5 485

show abstract

“…In other fields of application (sprays or particle-laden flows), moment methods have been introduced only recently [25] and were first used with a Rosin-Rammler distribution [loc. cit.]…”

Section: Choices For the Distribution Functionmentioning

confidence: 43%

A Comparative Study of B-, Γ- and Log-Normal Distributions in a Three-Moment Parameterization for Drop Sedimentation

Ziemer

Wacker

2014

Atmosphere

View full text Add to dashboard Cite

show abstract

“…The second moments model is the four-moments model of Yue & Watkins (2004). In this spray model the four moments of the droplet size distribution used in the Beck & Watkins (2002) model and their respective moment-averaged velocities are calculated from transport equations. Three areas in the spray model still require a distribution; the inlet conditions, the droplet drag model, and the droplet breakup and collision models.…”

Section: Droplet Size Distribution Functions Used In the Moments Spramentioning

confidence: 43%

“…The volume distribution produced by this approximation is compared with the Rosin-Rammler distribution in Figure 4. This distribution provided an adequate representation of the spray droplet size distribution in the two-moments spray model (Beck & Watkins, 2002, 2003a, 2003b). The second moments model is the four-moments model of Yue & Watkins (2004).…”

Section: Droplet Size Distribution Functions Used In the Moments Spramentioning

confidence: 47%

Using the General Gamma Distribution to Represent the Droplet Size Distribution in a Spray Model

Emekwuru¹

2012

Hydrodynamics - Theory and Model

View full text Add to dashboard Cite

“…Using only one moment in size gives a simplified model which yields low computational cost but is not able to take into account the evaporation phenomenon since it provides no information on the mean size of the droplets. Therefore, some methods using several moments in size have been developed, allowing a more accurate description of the spray's physical behaviour (see for example [1][2][3][4]32,41]). The multi-fluid approach is based on a different point of view, which consists in first discretizing the size space before performing any average in size.…”

Section: Remark 12mentioning

confidence: 45%

“…In particular, breakup and coalescence cannot be taken into account in the standard two-fluid approach where only two moments in size of the distribution function are resolved (droplet number and droplet mass density). Some other Moment Methods have been developed (see for example [1,2,32,41]) and recently, Beck and Watkins proposed a real improvement on this kind of method, based on conservation equations for several droplet size moments allowing the development of spray submodels and the possibility to take into account some complex phenomena such as heat transfer, breakup and collision [3,4]. However, such a method still needs to presuppose a global shape for the whole size distribution of the spray, introducing some limitations.…”

Section: Introductionmentioning

confidence: 44%

A second-order multi-fluid model for evaporating sprays

Dufour¹,

Villedieu²

2005

ESAIM: M2AN

View full text Add to dashboard Cite

Abstract. The aim of this paper is to present a method using both the ideas of sectional approach and moment methods in order to accurately simulate evaporation phenomena in gas-droplets flows. we propose an extension of this approach based on a more accurate representation of the droplet size number density in each section ensuring the exact conservation of two moments (as opposed to only one moment used in the classical approach). A corresponding second-order numerical scheme, with respect to space and droplet size variables, is also introduced and can be proved to be positive and to satisfy a maximum principle on the velocity and the mean droplet mass under a suitable CFL-like condition. Numerical simulations have been performed and the results confirm the accuracy of this new method even when a very coarse mesh for the droplet size variable (i.e.: a low number of sections) is used.Mathematics Subject Classification. 35Q35, 65Z05, 76T10.

show abstract

On the Development of Spray Submodels Based on Droplet Size Moments

Cited by 41 publications

References 29 publications

A Comparative Study of B-, Γ- and Log-Normal Distributions in a Three-Moment Parameterization for Drop Sedimentation

A Comparative Study of B-, Γ- and Log-Normal Distributions in a Three-Moment Parameterization for Drop Sedimentation

Using the General Gamma Distribution to Represent the Droplet Size Distribution in a Spray Model

A second-order multi-fluid model for evaporating sprays

Contact Info

Product

Resources

About