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Effect of equivalence ratio fluctuations on planar detonation discontinuities

Published online by Cambridge University Press:  28 September 2020

Alberto Cuadra Open the ORCID record for Alberto Cuadra [Opens in a new window] ,
César Huete Open the ORCID record for César Huete [Opens in a new window]  and
Marcos Vera Open the ORCID record for Marcos Vera [Opens in a new window]
Alberto Cuadra
Affiliation:
Departamento de Ingeniería Térmica y de Fluidos, Universidad Carlos III de Madrid, 28911Leganés, Spain
César Huete*
Affiliation:
Departamento de Ingeniería Térmica y de Fluidos, Universidad Carlos III de Madrid, 28911Leganés, Spain
Marcos Vera
Affiliation:
Departamento de Ingeniería Térmica y de Fluidos, Universidad Carlos III de Madrid, 28911Leganés, Spain
*
†Email address for correspondence: [email protected]
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Abstract

We propose a linear asymptotic theory to describe the propagation of planar detonation fronts through heterogeneous mixtures of reactive gases consisting of random fluctuations in the fuel mass fraction. The analysis starts with the derivation of the transfer functions that relate the upstream fuel mass fraction inhomogeneities with the burnt-gas perturbations via normal mode analysis. These results are then used in a Fourier analysis of a detonation wave interacting with two- and three-dimensional isotropic heterogeneous fields. This yields integral formulae for the turbulent kinetic energy, sonic energy and averaged vorticity and entropy production rates. Second-order corrections for the turbulent Rankine–Hugoniot conditions are also obtained, along with analytical expressions for the deviation of the detonation velocity with respect to that of the equivalent homogeneous mixture. Upstream inhomogeneities are found to speed up the detonation front in the vast majority of scenarios studied, with a velocity amplification factor that depends on the properties of the fuel–air mixture, particularly on the variation of the density and the heat release with the fuel mass fraction.

JFM classification

Compressible Flows: Detonation waves Compressible Flows: Shock waves Mixing: Turbulent mixing
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 903 , 25 November 2020 , A30
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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