Chemical effects on sound propagation

Abstract

A theoretical study of coupling between chemical kinetics and sound propagation is presented. Examination of equations governing propagation of a travelling acoustic wave in a chemically reacting, stagnant, gaseous medium shows that chemical effects are, in general, of two kinds; viz., those due to changes in mean conditions resulting from chemical reaction and those due to fluctuations in reaction rate resulting from acoustic waves. These coupled effects are found to depend on activation energy, enthalpy of reaction, and ratio of chemical to acoustic time, and have, in particular, different qualitative features for exothermic and endothermic reactions. Several cases have been investigated. When chemical time is long as compared with acoustic time, the main effects are due to fluctuations in the reaction rate. If reaction rates increase with rising temperatures, the acoustic waves are amplified for exothermic reactions and attenuated for endothermic reactions. The sound propagation speed is only slightly reduced from its isentropic frozen value within the region of validity of this quasisteady analysis. When the reaction rate is constant, the chemical effects are due to changes in the mean conditions. Contrary to what is predicted for the quasisteady case, the acoustic waves are here attenuated for exothermic reactions and amplified for endothermic reactions. Furthermore, effects on propagation speeds become pronounced. When both kinds of chemical effects are considered, the results depend strongly on activation energy. For the case of small activation energy, where the reaction rate is weakly dependent on temperature, the qualitative effects are similar to those observed for constant reaction rate. For large activation energy, however, effects due to fluctuations in reaction rate become pronounced, leading to amplification for exothermic reactions and attenuation for endothermic reactions. In all cases, chemical effects become more significant at higher reaction rates.