The acoustic wave propagation equation in a turbulent combusting flow

Sound generation by turbulent flames originates from the fluctuating heat release in the flame. The description of this fluctuating heat release and its effect on acoustics in turbulent flames is complicated due to the interaction of chemical reactions with turbulence, mixing and pressure fluctuations. In a turbulent flame the instantaneous density, velocity, pressure, temperature and species concentrations are determined by the transport equations for mass, momentum, enthalpy and species and by the equation of state. In this paper an equation is formulated that describes the propagation of acoustic pressure
fluctuations, and that determines the source terms. Subsequently events are ordered on basis of their typical time scale. That way source terms can be evaluated for the situation where the combustion is described with the use of time averaged chemical reaction progress variables and a mixture fraction variable. Subsequently the consequences of Reynolds and Favre averaging
on these source terms and conservation of acoustical variables in a domain with turbulent flow are discussed. The use of the reaction progress variables, as a basis for acoustic propagation prediction, in a Reynolds averaged Navier-Stokes flow calculation, is demonstrated on a premixed turbulent natural gas flame with finite combustion kinetics.