Helmholtz resonators (HRs) are commonly used to damp thermoacous-
tic oscillations in aero-engine and gas turbine combustors. In practice the
HR is often maintained at a cooler temperature than the combustor, but
this tends to be neglected when modelling. In this work, we derive an
analytical model for both the acoustic damping and the effect on the com-
bustor thermoacoustics of HRs whose volume is at a different temperature
to the combustor. The energy conservation equation based on stagnation
enthalpy, together with the mass and momentum conservation equations, is
incorporated into a linear HR sound absorption model. These are coupled
with linear wave-based models for the plane acoustic waves in the system
to which the HR is attached – here a combustor. The temperature differ-
ence is found to generate an entropy wave which advects downstream of the
resonator (and may generate further acoustic waves if accelerated), and to
change the acoustic damping near the resonant frequency. This model for
the HR acoustics is then incorporated into a low-order network model for
combustor thermoacoustics. The importance of capturing the effect of the
HR temperature difference on the overall thermoacoustic modes is clearly
demonstrated.