LES model of large scale hydrogen-air planar detonations: Verification by the ZND theory

Mateusz Zbikowski, Dmitriy Makarov, Vladimir Molkov

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

The large eddy simulation (LES) model of hydrogen-air detonation at very large scales, which doesn't require Arrhenius chemistry, is presented. The progress variable equation is applied for the first time to simulate propagation of a reaction front following and coupled with a leading shock. The gradient method, based on a product of pre-shock mixture density and detonation velocity, is employed as a source term in the progress variable equation. Chemical kinetics enters the combustion model only through its influence on the detonation velocity and modelling of detailed chemistry is omitted. The LES model is verified against theoretical solution by the Zel'dovich-von Neumann-Doring (ZND) theory for a case of planar 29.05% hydrogen-air detonation in elongated 3 x 3 x 100 in calculation domain. Thermodynamically calculated values of the specific heats ratio for burned mixture gamma = 1.22 and the standard heat of combustion Delta H-c = 3.2 MJ/kg are applied without any adjustment often applied in other models. Numerical simulation reproduced theoretical values of von Neumann spike, Chapman-Jouguet pressure, Taylor wave and detonation propagation velocity. There are no adjustable parameters in the model. Practically no grid sensitivity for the planar detonation wave is demonstrated by the LES model. Detonation velocity and pressures are shown to be nearly independent of the computational cell size in a wide range of cell sizes 0.1-1.0 m. Impulse depends to some extent on a cell size. Three-dimensional version of the LES model is under development to simulate pressure effects and identify design solutions, including mitigating techniques, for hydrogen safety engineering. There is no intention to use this oriented on large scale applications engineering LES model to reproduce fine structure of the detonation wave. (c) 2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.
LanguageEnglish
Pages4884-4892
JournalInternational Journal of Hydrogen Energy
Volume33
Issue number18
DOIs
Publication statusPublished - Sep 2008

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large eddy simulation
detonation
air
hydrogen
detonation waves
cells
shock
engineering
chemistry
heat of combustion
propagation velocity
pressure effects
spikes
impulses
wave propagation
safety
reaction kinetics
adjusting
fine structure
grids

Cite this

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title = "LES model of large scale hydrogen-air planar detonations: Verification by the ZND theory",
abstract = "The large eddy simulation (LES) model of hydrogen-air detonation at very large scales, which doesn't require Arrhenius chemistry, is presented. The progress variable equation is applied for the first time to simulate propagation of a reaction front following and coupled with a leading shock. The gradient method, based on a product of pre-shock mixture density and detonation velocity, is employed as a source term in the progress variable equation. Chemical kinetics enters the combustion model only through its influence on the detonation velocity and modelling of detailed chemistry is omitted. The LES model is verified against theoretical solution by the Zel'dovich-von Neumann-Doring (ZND) theory for a case of planar 29.05{\%} hydrogen-air detonation in elongated 3 x 3 x 100 in calculation domain. Thermodynamically calculated values of the specific heats ratio for burned mixture gamma = 1.22 and the standard heat of combustion Delta H-c = 3.2 MJ/kg are applied without any adjustment often applied in other models. Numerical simulation reproduced theoretical values of von Neumann spike, Chapman-Jouguet pressure, Taylor wave and detonation propagation velocity. There are no adjustable parameters in the model. Practically no grid sensitivity for the planar detonation wave is demonstrated by the LES model. Detonation velocity and pressures are shown to be nearly independent of the computational cell size in a wide range of cell sizes 0.1-1.0 m. Impulse depends to some extent on a cell size. Three-dimensional version of the LES model is under development to simulate pressure effects and identify design solutions, including mitigating techniques, for hydrogen safety engineering. There is no intention to use this oriented on large scale applications engineering LES model to reproduce fine structure of the detonation wave. (c) 2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.",
author = "Mateusz Zbikowski and Dmitriy Makarov and Vladimir Molkov",
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doi = "10.1016/j.ijhydene.2008.05.071",
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LES model of large scale hydrogen-air planar detonations: Verification by the ZND theory. / Zbikowski, Mateusz; Makarov, Dmitriy; Molkov, Vladimir.

Vol. 33, No. 18, 09.2008, p. 4884-4892.

Research output: Contribution to journalArticle

TY - JOUR

T1 - LES model of large scale hydrogen-air planar detonations: Verification by the ZND theory

AU - Zbikowski, Mateusz

AU - Makarov, Dmitriy

AU - Molkov, Vladimir

PY - 2008/9

Y1 - 2008/9

N2 - The large eddy simulation (LES) model of hydrogen-air detonation at very large scales, which doesn't require Arrhenius chemistry, is presented. The progress variable equation is applied for the first time to simulate propagation of a reaction front following and coupled with a leading shock. The gradient method, based on a product of pre-shock mixture density and detonation velocity, is employed as a source term in the progress variable equation. Chemical kinetics enters the combustion model only through its influence on the detonation velocity and modelling of detailed chemistry is omitted. The LES model is verified against theoretical solution by the Zel'dovich-von Neumann-Doring (ZND) theory for a case of planar 29.05% hydrogen-air detonation in elongated 3 x 3 x 100 in calculation domain. Thermodynamically calculated values of the specific heats ratio for burned mixture gamma = 1.22 and the standard heat of combustion Delta H-c = 3.2 MJ/kg are applied without any adjustment often applied in other models. Numerical simulation reproduced theoretical values of von Neumann spike, Chapman-Jouguet pressure, Taylor wave and detonation propagation velocity. There are no adjustable parameters in the model. Practically no grid sensitivity for the planar detonation wave is demonstrated by the LES model. Detonation velocity and pressures are shown to be nearly independent of the computational cell size in a wide range of cell sizes 0.1-1.0 m. Impulse depends to some extent on a cell size. Three-dimensional version of the LES model is under development to simulate pressure effects and identify design solutions, including mitigating techniques, for hydrogen safety engineering. There is no intention to use this oriented on large scale applications engineering LES model to reproduce fine structure of the detonation wave. (c) 2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.

AB - The large eddy simulation (LES) model of hydrogen-air detonation at very large scales, which doesn't require Arrhenius chemistry, is presented. The progress variable equation is applied for the first time to simulate propagation of a reaction front following and coupled with a leading shock. The gradient method, based on a product of pre-shock mixture density and detonation velocity, is employed as a source term in the progress variable equation. Chemical kinetics enters the combustion model only through its influence on the detonation velocity and modelling of detailed chemistry is omitted. The LES model is verified against theoretical solution by the Zel'dovich-von Neumann-Doring (ZND) theory for a case of planar 29.05% hydrogen-air detonation in elongated 3 x 3 x 100 in calculation domain. Thermodynamically calculated values of the specific heats ratio for burned mixture gamma = 1.22 and the standard heat of combustion Delta H-c = 3.2 MJ/kg are applied without any adjustment often applied in other models. Numerical simulation reproduced theoretical values of von Neumann spike, Chapman-Jouguet pressure, Taylor wave and detonation propagation velocity. There are no adjustable parameters in the model. Practically no grid sensitivity for the planar detonation wave is demonstrated by the LES model. Detonation velocity and pressures are shown to be nearly independent of the computational cell size in a wide range of cell sizes 0.1-1.0 m. Impulse depends to some extent on a cell size. Three-dimensional version of the LES model is under development to simulate pressure effects and identify design solutions, including mitigating techniques, for hydrogen safety engineering. There is no intention to use this oriented on large scale applications engineering LES model to reproduce fine structure of the detonation wave. (c) 2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.

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DO - 10.1016/j.ijhydene.2008.05.071

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SP - 4884

EP - 4892

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ER -