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A model for the constant-density boundary layer surrounding fire whirls

Published online by Cambridge University Press:  06 August 2020

A. D. Weiss Open the ORCID record for A. D. Weiss [Opens in a new window] ,
P. Rajamanickam ,
W. Coenen Open the ORCID record for W. Coenen [Opens in a new window] ,
A. L. Sánchez Open the ORCID record for A. L. Sánchez [Opens in a new window]  and
F. A. Williams
A. D. Weiss
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, USA
P. Rajamanickam
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, USA
W. Coenen*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, USA Grupo de Mecánica de Fluidos, Departamento de Ingeniería Térmica y de Fluidos, Universidad Carlos III de Madrid, Leganés (Madrid), Spain
A. L. Sánchez
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, USA
F. A. Williams
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, USA
*
†Email address for correspondence: wcoenen@ing.uc3m.es
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Abstract

This paper investigates the steady axisymmetric structure of the cold boundary-layer flow surrounding fire whirls developing over localized fuel sources lying on a horizontal surface. The inviscid swirling motion found outside the boundary layer, driven by the entrainment of the buoyant turbulent plume of hot combustion products that develops above the fire, is described by an irrotational solution, obtained by combining Taylor's self-similar solution for the motion in the axial plane with the azimuthal motion induced by a line vortex of circulation $2 {\rm \pi}\Gamma$. The development of the boundary layer from a prescribed radial location is determined by numerical integration for different swirl levels, measured by the value of the radial-to-azimuthal velocity ratio $\sigma$ at the initial radial location. As in the case $\sigma =0$, treated in the seminal boundary-layer analysis of Burggraf et al. (Phys. Fluids, vol. 14, 1971, pp. 1821–1833), the pressure gradient associated with the centripetal acceleration of the inviscid flow is seen to generate a pronounced radial inflow. Specific attention is given to the terminal shape of the boundary-layer velocity near the axis, which displays a three-layered structure that is described by matched asymptotic expansions. The resulting composite expansion, dependent on the level of ambient swirl through the parameter $\sigma$, is employed as boundary condition to describe the deflection of the boundary-layer flow near the axis to form a vertical swirl jet. Numerical solutions of the resulting non-slender collision region for different values of $\sigma$ are presented both for inviscid flow and for viscous flow with moderately large values of the controlling Reynolds number $\Gamma /\nu$. The velocity description provided is useful in mathematical formulations of localized fire-whirl flows, providing consistent boundary conditions accounting for the ambient swirl level.

JFM classification

Reacting Flows: Flames Boundary Layers: Boundary layer structure
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 900 , 10 October 2020 , A22
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Footnotes

‡

Present address: Department of Aerospace Engineering, Auburn University, Auburn, USA.

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