60055 - Isentropic Formulation of the Linearized Euler Equations for Perfectly Premixed Combustion Systems 

The linearized Euler equations (LEE) provide an accurate –yet computationally efficient– description of propagation and damping of acoustic waves in geometrically complex, non-uniform reactive mean flows like those found in gas turbine combustion chambers. However, direct application of the LEE to perfectly premixed combustors generates unphysical entropy waves as the LEE's solution inherently contains coupled acoustic, vortical and entropy modes. In the present work, the LEE are decomposed into isentropic and non-isentropic parts ultimately obtaining a simplified set of isentropic LEE, in which only acoustic and vortical modes propagate. In the isentropic LEE, only continuity and momentum equations are required to be solved. The energy equation is replaced by the isentropic relation between acoustic pressure and density. From the decomposition, the unsteady heat release term, which acts as a source in the energy equation, naturally arises as a source in the continuity equation. This way, the thermoacoustic coupling is still preserved in the isentropic formulation. The derived isentropic set of equations is tested with a one-dimensional benchmark configuration consisting of a mean flow temperature jump, non-uniform mean flow velocity and unsteady heat release sources. Solutions of the non-isentropic and isentropic set of LEE are compared and the avoidance of entropy waves proved. Finally, the isentropic LEE are used for reproducing the frequency of the self-excited first transversal mode of a lab-scale swirl-stabilized premixed combustor. This shows the capability of isentropic LEE to correctly predict acoustic propagation at high frequencies in industrial-sized applications