Математическое моделирование распространения и тушения лесного пожара водой в трехъярусном лесном массиве

Liliya Yu. Kataeva; Timofey S. Kiselev

doi:10.25726/k1582-1947-4677-v

Authors

Liliya Yu. Kataeva https://orcid.org/0000-0001-9217-9324 Nizhny Novgorod Institute of Railway Transport – Branch of the Volga State University of Railway Transport; R.E. Alekseev Nizhny Novgorod State Technical University, 603011, Nizhny Novgorod, Komsomolskaya Square, 3
Timofey S. Kiselev R.E. Alekseev Nizhny Novgorod State Technical University, 603155, Nizhny Novgorod, Minina St., 24

DOI: 10.25726/k1582-1947-4677-v EDN: NMSRDI

How to cite

GOST Kataeva L. Y., Kiselev T. S. Mathematical modeling of wildfire spread and water suppression in a three-tier forest stand // STROITEL'NYE I DOROZHNYE MASHINY. 2026. Vol. 70. No. 9. P. 104-116. DOI: 10.25726/k1582-1947-4677-v

APA Kataeva, L. Y. & Kiselev, T. S. (2026). Mathematical modeling of wildfire spread and water suppression in a three-tier forest stand. STROITEL'NYE I DOROZHNYE MASHINY, 70(9), 104-116. https://doi.org/10.25726/k1582-1947-4677-v

Abstract

A physical-mathematical and analytical model is presented for the spread and water suppression of a forest fire in a three-tier forest stand. The model is based on the mechanics of reacting multiphase media, where the gas phase is described by the density ρ₅ and mass concentrations Cα, the condensed phase by the volume fractions φᵢ, and free water by φ₄, the source term f(x,z,t), and the boiling rate R₄. The considered vertical structure consists of a 4 m lower combustible tier, a 1 m non-combustible inter-tier gap, and a 5 m upper combustible tier. Integral height averaging of the two-dimensional model is performed for each tier, while retaining inter-tier heat fluxes. It is shown that the middle layer does not form an independent combustion wave, but acts as a thermal bridge between the lower and upper reaction zones. For the combustible tiers, an analytical travelling-wave solution is obtained, together with a suppression condition expressed through the critical boiling rate of water. It is proved that, when all three tiers have identical properties, the system degenerates into the known solution for a homogeneous combustion wave in a porous layer. Numerical fields without suppression give fire-front propagation velocities of 3.10 m/s for the continuous forest stand and 3.41 m/s for the three-tier stand. The 10% increase in the three-tier case is caused by wind-driven displacement of the upper high-temperature zone, bending of the front in the inter-tier gap, and enhanced heating of the upper tier. The analytical model shows that water supply to the lower tier suppresses the near-ground wave, but may fail to destroy thermal coupling with the upper tier; water supply to the inter-tier gap weakens the thermal bridge; water supply to the upper tier lowers the crown-zone temperature, but leaves the lower pyrolysis source active. The results justify the need to account for water-supply height and vertical forest structure when selecting a suppression strategy.

Keywords

wildfire three-tier forest reacting media mechanics free water combustion wave height averaging fuel-strata gap water suppression

Funding

The authors did not declare any external funding for this research.

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Mathematical modeling of wildfire spread and water suppression in a three-tier forest stand

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