Effect of Pressure on Burning Velocity

Abstract

Two recent communications in Nature^1,2 have discussed the effect of pressure upon burning velocity and have referred to the square root law of Tanford and Pease³ as leading "to the inverse fourth root law for the variation of velocity with pressure". This statement is not strictly true. The square root law, after a number of simplifying assumptions, predicts that the burning velocity should vary with pressure as the square root of Σ 'x_i/B_i', where x_i is the mol fraction of an active species at the equilibrium surface, and B_i is a factor previously defined⁴, which is comparatively invariant with pressure. Where hydrogen atoms carry most of the burden of energy transfer into unburnt gas, we should expect x_H to vary approximately as the inverse square root of the pressure, and, hence, roughly an inverse fourth root variation of burning velocity. For precise calculation, however, equilibrium computation of the x_i is required. One mixture for which such a calculation has been made is stoichiometric butadiene – air⁵. The calculated burning velocity ratio for one atmosphere as against half an atmosphere pressure was found to be 0.88, as compared to a fourth root value of 0.84. Thus, as Gaydon and Wolfhard⁶ point out, the burning velocity may decrease with pressure less sharply than a fourth-root relation would predict.