Acoustic and entropic transfer functions of a generalised subsonic nozzle

The knowledge of the acoustic and entropic transfer functions at the boundaries of combustors is crucial to understand the fate of flame-generated pressure perturbations and to predict and prevent the emergence of combustion instabilities. Traditional models often rely on the isentropic assumption for nozzle guide vanes. In real systems, however, pressure losses and local flow recirculations may occur, as evidenced by drops in the static pressure. In this work we relax the isentropic assumption and derive a parametric model to predict the acoustic and entropic transfer functions of generalised convergent-divergent nozzles with subsonic-to-sonic throat conditions in the low frequency domain. By tuning two parameters, this model can retrieve the impedance of three limit cases known from the literature: the isentropic nozzle, the orifice plate and the convergent nozzle duct termination. The generalised model also includes the conversion of entropy to sound through orifice plates and non-isentropic nozzles, yet to be considered in the literature. These analytical results are then compared with the experimental data acquired in the Cambridge Entropy Generator. The comparison highlights the need to correctly account for the losses in the system to properly explain the transfer functions of nozzles, as isentropic predictions differ substantially from the acquired experimental data