On the critical-throat boundary condition in quasi-one-dimensional linearised-Euler equation models

Based on the assumption of locally quasi-steady behaviour, Duran & Moreau (2013 J. Fluid Mech. 723, 190–231), assumed that, at a critical nozzle throat, the fluctuations of the Mach number vanish for linear perturbations of a quasi-one-dimensional isentropic flow. This appears to be valid only in the quasi-steady-flow limit. Based on the analytical model of Marble & Candel (1977 J. Sound Vib. 55, 225–243) an alternative boundary condition is obtained, which is valid for nozzle geometries with a finite limit of the second spatial derivative of the cross-section on the subsonic side of the throat. When the nozzle geometry does not satisfy this condition, the application of a quasi-one-dimensional theory becomes questionable. The consequences of this for the quasi-one-dimensional modelling of the acoustic response of choked nozzles are discussed for three specific nozzle geometries. Surprisingly, the relative error in the inlet nozzle admittance and acoustic wave transmission coefficient remains below a per cent, when the quasi-steady boundary condition is used at the throat. However, the prediction of the acoustic fluctuations assuming a quasi-steady critical-throat behaviour is incorrect, because the predicted acoustic field is singular at the throat.