A new correlation to determine the discharge coefficient of a critical Venturi nozzle with turbulent boundary layer

A toroidal Venturi nozzle, operating mainly at critical conditions and shaped according to the recommendation of the ISO Standard 9300, was selected for the present study. The focus of this paper is to provide a new theoretical and numerical correlation for the calculus of the discharge coefficient on turbulent boundary layer conditions for gases at Pr = 0.7. This study was performed to investigate the effects of the viscous stresses in the boundary layer, dimensionless wall temperature in the throat nozzle, and the flow field curvature at the nucleus of the nozzle on the discharge coefficient. The determination of this coefficient was based on the turbulent boundary layer theory and a numerical simulation for a two-dimensional flow. The numerical simulation of the flow was carried out by means of the commercial CFD code. The correlation obtained was validated by means of a direct comparison between the experimental correlations of the discharge coefficient of ISO-9300 and the correlations obtained by the Korea Research Institute of Standards and Science (KRISS) with turbulent boundary layer. This validation was performed for throat Reynolds numbers from 1.4 to 2.6×10⁶. The agreement of the theoretical and measured discharge coefficients by these correlations was better than 0.2%.