Parametric study of the discharge coefficient on critical sonic nozzles ISO-9300 with turbulent boundary layer

A parametric study on determining discharge coefficient in ISO 9300 [1] toroidal sonic nozzles have been developed. The focus of this paper is to obtain the an analytical model for the calculus of this discharge coefficient on turbulent boundary layer conditions for gases at Pr=0.7. The problem is divided in two sections: one in which the viscous stresses are taking in to account to boundary layer zone, based on turbulent boundary layer theory and taking as starting point the work carried out by Stratford [2]. Then, curvature of flow field is studied at the nucleus of the nozzle, obtaining discharge coefficient values using numerical simulation for a two-dimensional flow. The results have a good agreement with correlations of ISO-9300 [1], experimental and numerical data of Wu-Yan [3] and the analytical model from Stratford [2].