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Title: Arrhenius Rate: constant volume burn

Abstract

A constant volume burn occurs for an idealized initial state in which a large volume of reactants at rest is suddenly raised to a high temperature and begins to burn. Due to the uniform spatial state, there is no fluid motion and no heat conduction. This reduces the time evolu tion to an ODE for the reaction progress variable. With an Arrhenius reaction rate, two characteristics of thermal ignition are illustrated: induction time and thermal runaway. The Frank-Kamenetskii approximation then leads to a simple expression for the adiabatic induction time. For a first order reaction, the analytic solution is derived and used to illustrate the effect of varying the activation temperature; in particular, on the induction time. In general, the ODE can be solved numerically. This is used to illustrate the effect of varying the reaction order. We note that for a first order reaction, the time evolution of the reaction progress variable has an exponential tail. In contrast, for a reaction order less than one, the reaction completes in a nite time. The reaction order also affects the induction time.

Authors:
 [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1412842
Report Number(s):
LA-UR-17-31024
DOE Contract Number:  
AC52-06NA25396
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Arrhenius rate; thermal explosion; constant volume burn

Citation Formats

Menikoff, Ralph. Arrhenius Rate: constant volume burn. United States: N. p., 2017. Web. doi:10.2172/1412842.
Menikoff, Ralph. Arrhenius Rate: constant volume burn. United States. doi:10.2172/1412842.
Menikoff, Ralph. Wed . "Arrhenius Rate: constant volume burn". United States. doi:10.2172/1412842. https://www.osti.gov/servlets/purl/1412842.
@article{osti_1412842,
title = {Arrhenius Rate: constant volume burn},
author = {Menikoff, Ralph},
abstractNote = {A constant volume burn occurs for an idealized initial state in which a large volume of reactants at rest is suddenly raised to a high temperature and begins to burn. Due to the uniform spatial state, there is no fluid motion and no heat conduction. This reduces the time evolu tion to an ODE for the reaction progress variable. With an Arrhenius reaction rate, two characteristics of thermal ignition are illustrated: induction time and thermal runaway. The Frank-Kamenetskii approximation then leads to a simple expression for the adiabatic induction time. For a first order reaction, the analytic solution is derived and used to illustrate the effect of varying the activation temperature; in particular, on the induction time. In general, the ODE can be solved numerically. This is used to illustrate the effect of varying the reaction order. We note that for a first order reaction, the time evolution of the reaction progress variable has an exponential tail. In contrast, for a reaction order less than one, the reaction completes in a nite time. The reaction order also affects the induction time.},
doi = {10.2172/1412842},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Wed Dec 06 00:00:00 EST 2017},
month = {Wed Dec 06 00:00:00 EST 2017}
}

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