### 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 language | English (US) |
---|---|

Pages (from-to) | 271-284 |

Number of pages | 14 |

Journal | Combustion Science and Technology |

Volume | 183 |

Issue number | 3 |

DOIs | |

State | Published - Mar 2011 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Combustion Science and Technology*, vol. 183, no. 3, pp. 271-284. https://doi.org/10.1080/00102202.2010.519362

}

TY - JOUR

T1 - Calculation of the drop size distribution and velocities from the integral form of the conservation equations

AU - Lee, Taewoo

AU - Robinson, Dan

PY - 2011/3

Y1 - 2011/3

N2 - 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.

AB - 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.

KW - Atomization

KW - Drop size distribution

KW - Integral method

UR - http://www.scopus.com/inward/record.url?scp=78650661846&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650661846&partnerID=8YFLogxK

U2 - 10.1080/00102202.2010.519362

DO - 10.1080/00102202.2010.519362

M3 - Article

AN - SCOPUS:78650661846

VL - 183

SP - 271

EP - 284

JO - Combustion Science and Technology

JF - Combustion Science and Technology

SN - 0010-2202

IS - 3

ER -