Effect of heat source on transient energy growth analysis of a thermoacoustic system

Transient growth of acoustical energy associated with mitigating thermoacoustic oscillations

“…To gain insight on the finite-time (transient) stability behaviors, transient growth analysis of acoustical energy in a thermoacoustic system receives more attention recently [16][17][18]. A choked thermoacoustic combustor is studied to gain insight on its nonnormality.…”

“…It is found that the maximum transient growth can be 10 3 times greater than the initial disturbances energy. Experimental measurement of the transient growth was conducted on a premixed gas turbine combustor [15] mean valuê approximation value [16][17][18]. However, most of thermoacoustics systems studied previously are open-ended one, of which pressure nodes are expected at both inlet and outlet [3].…”

“…Thus it is important to gain insight on the onset of thermoacoustic instability [12,13,2] and to develop mitigation/-control approaches. Over last few decades, thermoacoustic instability has been intensively studied [14][15][16][17][18][19][20]. Generally, linear modal analysis is conducted via calculating the eigenfrequencies of thermoacoustic systems [3].…”

Theoretical and experimental investigation of thermoacoustics transfer function

“…The previous studies [21][22][23][24] have shown that the flame response can be described by a linear transfer function for small-amplitude flow perturbations. However, when flow perturbations are large enough, the flame may respond nonlinearly to the perturbations.…”

“…By numerically integrating the classical flame front tracking equation, i.e. G-equation [24], the flame response was determined for both uniform and convective oscillations in the velocity field over a broad frequency range. Later they developed an explicit analytical model describing the flame response to small velocity perturbations by linearizing G(r,z,t) equation.…”