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Reconsideration on the role of the specific heat ratio in Arrhenius law applications

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Abstract

Arrhenius law implicates that only those molecules which possess the internal energy greater than the activation energy E a can react. However, the internal energy will not be proportional to the gas temperature if the specific heat ratio γ and the gas constant R vary during chemical reaction processes. The varying γ may affect significantly the chemical reaction rate calculated with the Arrhenius law under the constant γ assumption, which has been widely accepted in detonation and combustion simulations for many years. In this paper, the roles of variable γ and R in Arrhenius law applications are reconsidered, and their effects on the chemical reaction rate are demonstrated by simulating one-dimensional C-J and two-dimensional cellular detonations. A new overall one-step detonation model with variable γ and R is proposed to improve the Arrhenius law. Numerical experiments demonstrate that this improved Arrhenius law works well in predicting detonation phenomena with the numerical results being in good agreement with experimental data.

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Authors and Affiliations

  1. Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100080, China

    Yunfeng Liu & Zonglin Jiang

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  1. Yunfeng Liu
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  2. Zonglin Jiang
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Correspondence to Yunfeng Liu.

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Liu, Y., Jiang, Z. Reconsideration on the role of the specific heat ratio in Arrhenius law applications. Acta Mech Sin 24, 261–266 (2008). https://doi.org/10.1007/s10409-008-0137-2

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  • DOI: https://doi.org/10.1007/s10409-008-0137-2

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