Calculation of the drop size distribution and velocities from the integral form of the conservation equations

Taewoo Lee, Dan Robinson

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

A new formulation based on integral form of the conservation equations is developed for analyzing spray droplet and velocity statistics. Both averaged or distributions of the droplet size and velocities can be calculated using this approach, although in this work the authors focus on the droplet size statistics and only compute the averaged droplet velocities. The formulation is based on the conservation equations, and intrinsically involves few assumptions and required inputs. The key is to use the integral form so that the input and output variables are related without having to resolve the complex details of the atomization process. This new approach naturally leads to predictions of SMDs, as well as the drop size distributions and phase velocities, with SMD and drop size distributions achieving good agreement with experimental data if a liquid-phase viscous dissipation term is included. The latter point suggests that the effect of liquid-phase viscosity seems quite important, as the present method overpredicts the effect of injection pressure unless some form of the viscous dissipation is included in the energy balance equation. The use of momentgenerating function for the log-normal distribution within the present formulation permits an efficient algorithm that reproduces the experimentally observed droplet size distributions. Further work remains to ascertain some aspects of the present solution approach, in particular the exact form of the viscous dissipation on the spray energy balance. The present integral formulation and the solution approach provide a fundamentally sound basis for analyzing droplet size and velocity statistics with several key parameters that may be adapted for different injector geometries, such as swirl and air-blast sprays, and injection conditions.

Original languageEnglish (US)
Pages (from-to)271-284
Number of pages14
JournalCombustion Science and Technology
Volume183
Issue number3
DOIs
StatePublished - Mar 2011

Fingerprint

drop size
conservation equations
Conservation
sprayers
formulations
dissipation
statistics
liquid phases
aerial explosions
Surface mount technology
injection
Statistics
Energy balance
atomizing
injectors
phase velocity
normal density functions
Phase velocity
viscosity
Liquids

Keywords

  • Atomization
  • Drop size distribution
  • Integral method

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Chemical Engineering(all)
  • Energy Engineering and Power Technology
  • Fuel Technology
  • Chemistry(all)

Cite this

Calculation of the drop size distribution and velocities from the integral form of the conservation equations. / Lee, Taewoo; Robinson, Dan.

In: Combustion Science and Technology, Vol. 183, No. 3, 03.2011, p. 271-284.

Research output: Contribution to journalArticle

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