A generalised model for acoustic and entropic transfer function of nozzles with losses

Abstract

We investigate the low frequency transfer functions for acoustic and entropic perturbations through nozzles and nozzle guide vanes. Previous theories rely on the isentropic assumption; in real systems, however, pressure losses associated with local friction and flow recirculation may occur, as evidenced by a drop in static pressure. In this work we relax the isentropic assumption and derive a parametric model to predict the acoustic and entropic transfer functions of a generic nozzle with subsonic-to-sonic throat conditions in the low frequency domain. For a given geometry and operating conditions, the model can retrieve the acoustic impedance of three limit cases known from the literature, as a function of a pressure loss parameter: the isentropic nozzle, the orifice plate and the converging nozzle terminating a duct. The generalised model is also able to predict the conversion of entropy to sound through orifice plates and non-isentropic nozzles given a measured or estimated static pressure loss parameter. The analytical predictions compare favourably with experimental measurements acquired in the Cambridge Entropy Generator for circular orifices and nozzles with subsonic-to-sonic throat conditions. The results highlight the need to correctly account for pressure losses in the system in order to properly capture the transfer functions of nozzles, as isentropic predictions differ substantially from the acquired experimental data.