Closed algebraic expressions for the adiabatic limit value of the explosion constant in closed volume combustion

An exact algebraic expression for the upper limit value of the explosion constant of gaseous fuels, Kmax, is derived by using a two-zone model for the adiabatic combustion in closed vessels. The expression is formulated in terms of the mean specific heat ratio of the unburned reactants γ¯u and introduces the concept of an apparent specific heat ratio of the burned products gb. Computational data are presented for a set of representative fuels and for a range of equivalence ratio's, initial pressures and initial temperatures. A comparison of these data with correlations from literature shows that one correlation in particular is in close agreement with the exact result. This one-parameter correlation is based upon the almost linear relationship between the fraction of burned mass and the pressure, a relationship which is taken from the original work of Lewis and von Elbe. Based upon this theoretical work, formulas are suggested that can be used to estimate the explosion constant of fuel/air mixtures with a minimum level of computational effort. In addition, because the derivation in this paper is fairly straightforward and because the resulting expression is rather simple, the analysis presented in this paper can be used in combustion courses as an exercise in thermodynamics and as an illustration of the concept of the flame speed.