Acoustic perturbation equation for combustion generated sound using method of multiple scales

The method of multiple scales (MMS) is used to derive the perturbation equations corresponding to different length scales and time scales. The multiple length scales and time scales are a consequence of low Mach number combustion. A solution expansion is constructed with acoustic perturbation variables as corrections to the hydrodynamic variables. We have obtained a set of equations governing the hydrodynamics, and a set of equations governing the acoustic perturbations. The perturbation equations are obtained for two time scales and two length scales. The set of perturbation equations with the sources from combustion suits well for computing sound generated by combustion.