### Abstract

The models of heat and mass transfer and phase transition for "water droplet - flame" system have been developed using non-stationary nonlinear partial differential equations. The system of differential equations was solved by the finite-difference method. The locally one-dimensional method was used to solve the difference analogous of differential equations. One-dimensional differential equations were solved using an implicit four-point difference scheme. Nonlinear equations were solved by the iteration method. The evaporation rates of water droplets (with sizes from 0.05 mm to 5 mm) in the flame zone (at the temperatures from 500 K to 1200 K) were determined. Theoretical analysis established essentially nonlinear (close to exponential) form of dependence of the water droplet evaporation rate on the temperature of the external gas area and the temperature of a droplet surface. In particular, the water droplet evaporation rate varies from 0.25 to 0.29 kg/(m2s), when the temperature of external gas area is about 1100 K. On the other hand, the water droplet evaporation rate does not exceed 0.01 kg/(m2s) when the temperature of external gas area is about 350 K. Besides, it has been found out that droplets warm up at different rates depending on their initial temperature and velocity. As a result, the integral characteristics of droplet evaporation can increase substantially, when droplets move through the external gas area at the same temperature. We performed a similar investigation or droplet streams with 3 3 droplet concentration 0.001-0.005 m in 1 m of gas area (typical parameters for modern spray extinguishing systems).

Original language | English |
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Title of host publication | Proceedings of the 4th International Conference on Particle-Based Methods - Fundamentals and Applications, PARTICLES 2015 |

Publisher | International Center for Numerical Methods in Engineering |

Pages | 991-997 |

Number of pages | 7 |

ISBN (Electronic) | 9788494424472 |

Publication status | Published - 1 Jan 2015 |

Event | 4th International Conference on Particle-Based Methods, PARTICLES 2015 - Barcelona, Spain Duration: 28 Sep 2015 → 30 Sep 2015 |

### Other

Other | 4th International Conference on Particle-Based Methods, PARTICLES 2015 |
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Country | Spain |

City | Barcelona |

Period | 28.9.15 → 30.9.15 |

### Fingerprint

### Keywords

- Evaporation
- High-temperature gas environment
- Water droplet

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Proceedings of the 4th International Conference on Particle-Based Methods - Fundamentals and Applications, PARTICLES 2015*(pp. 991-997). International Center for Numerical Methods in Engineering.

**Numerical simulation of water and water emulsion droplets evaporation in flames with different temperatures.** / Strizhak, Pavel A.; Volkov, Roman S.; Zhdanova, Alena Olegovna.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 4th International Conference on Particle-Based Methods - Fundamentals and Applications, PARTICLES 2015.*International Center for Numerical Methods in Engineering, pp. 991-997, 4th International Conference on Particle-Based Methods, PARTICLES 2015, Barcelona, Spain, 28.9.15.

}

TY - GEN

T1 - Numerical simulation of water and water emulsion droplets evaporation in flames with different temperatures

AU - Strizhak, Pavel A.

AU - Volkov, Roman S.

AU - Zhdanova, Alena Olegovna

PY - 2015/1/1

Y1 - 2015/1/1

N2 - The models of heat and mass transfer and phase transition for "water droplet - flame" system have been developed using non-stationary nonlinear partial differential equations. The system of differential equations was solved by the finite-difference method. The locally one-dimensional method was used to solve the difference analogous of differential equations. One-dimensional differential equations were solved using an implicit four-point difference scheme. Nonlinear equations were solved by the iteration method. The evaporation rates of water droplets (with sizes from 0.05 mm to 5 mm) in the flame zone (at the temperatures from 500 K to 1200 K) were determined. Theoretical analysis established essentially nonlinear (close to exponential) form of dependence of the water droplet evaporation rate on the temperature of the external gas area and the temperature of a droplet surface. In particular, the water droplet evaporation rate varies from 0.25 to 0.29 kg/(m2s), when the temperature of external gas area is about 1100 K. On the other hand, the water droplet evaporation rate does not exceed 0.01 kg/(m2s) when the temperature of external gas area is about 350 K. Besides, it has been found out that droplets warm up at different rates depending on their initial temperature and velocity. As a result, the integral characteristics of droplet evaporation can increase substantially, when droplets move through the external gas area at the same temperature. We performed a similar investigation or droplet streams with 3 3 droplet concentration 0.001-0.005 m in 1 m of gas area (typical parameters for modern spray extinguishing systems).

AB - The models of heat and mass transfer and phase transition for "water droplet - flame" system have been developed using non-stationary nonlinear partial differential equations. The system of differential equations was solved by the finite-difference method. The locally one-dimensional method was used to solve the difference analogous of differential equations. One-dimensional differential equations were solved using an implicit four-point difference scheme. Nonlinear equations were solved by the iteration method. The evaporation rates of water droplets (with sizes from 0.05 mm to 5 mm) in the flame zone (at the temperatures from 500 K to 1200 K) were determined. Theoretical analysis established essentially nonlinear (close to exponential) form of dependence of the water droplet evaporation rate on the temperature of the external gas area and the temperature of a droplet surface. In particular, the water droplet evaporation rate varies from 0.25 to 0.29 kg/(m2s), when the temperature of external gas area is about 1100 K. On the other hand, the water droplet evaporation rate does not exceed 0.01 kg/(m2s) when the temperature of external gas area is about 350 K. Besides, it has been found out that droplets warm up at different rates depending on their initial temperature and velocity. As a result, the integral characteristics of droplet evaporation can increase substantially, when droplets move through the external gas area at the same temperature. We performed a similar investigation or droplet streams with 3 3 droplet concentration 0.001-0.005 m in 1 m of gas area (typical parameters for modern spray extinguishing systems).

KW - Evaporation

KW - High-temperature gas environment

KW - Water droplet

UR - http://www.scopus.com/inward/record.url?scp=84960395802&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84960395802&partnerID=8YFLogxK

M3 - Conference contribution

SP - 991

EP - 997

BT - Proceedings of the 4th International Conference on Particle-Based Methods - Fundamentals and Applications, PARTICLES 2015

PB - International Center for Numerical Methods in Engineering

ER -