Nonorthogonality analysis of a thermoacoustic system with a premixed V-shaped flame

Thermoacoustic instability occurs in many combustion systems, such as aero-engine afterburners, rocket motors, ramjets and gas turbines. It most often arises due to the coupling between unsteady heat release and acoustic waves. In this work, nonorthogonality analysis of a choked combustor with a gutter confined is conducted. Such configuration is used as a simplified model of the afterburner of an aero-engine. A thermoacoustic model is developed first to study the nonnormal interaction between acoustic disturbances and a premixed V-shaped flame anchored to the tip of the gutter. Eigenmode nonorthogonality analysis is then conducted. The thermoacoustic system is shown to be nonnormal and characterized by nonorthogonal eigenmodes. The nonorthogonality is identified to arise from both the complex boundary condition and the monopole-like flame. However, the contribution from the Robin-type boundary is approximately 1.5% of that from the flame. Thus the flame is identified to play a dominant role. One practical conclusions is that acoustic disturbances undergo transient growth in a combustion system with nonorthogonal eigenmodes. Such finite-time growth, which cannot be predicted by using classical linear theory might trigger high-amplitude self-sustained oscillations.