Accurate analytical models for fractional pressure rise in constant volume combustion

Laminar burning velocities SL can be obtained from the pressure history in a constant volume combustion experiment. In the analysis of results, the relation between pressure and mass fraction burnt, x(p), is crucial. The linear x(p) relation by Lewis and Von Elbe is still widely used. Yet, from their original work a more accurate relation for x(p) can be derived, as is demonstrated in this paper (“extended LvE”). In this work we introduce a two zone model that can be treated analytically, resulting in an x(p)-relation identical to “extended LvE”. We then extend our analytical approach to a multi-zone model, which is used to benchmark several other analytical x(p) relations. Results of the two-zone model are very close to the multi-zone results. Reported deviations between SL from bomb data and from other methods may be attributed to the limited accuracy of the linear x(p) relation, as is illustrated for stoichiometric methane-air combustion. Notably, for small x our new relation gives a factor of γb/γu difference in SL as compared to the linear one, which has long been assumed to be correct for small x. Our new x(p) result also leads to a new expression for the explosion constant KG in the cubic root law.