Discharge coefficient equation for critical-flow toroidal-throat venturi nozzles covering the boundary-layer transition regime

A single, simple correlating equation between the discharge coefficient of critical-flow Venturi nozzles (CFVNs) having an ISO 9300 toroidal throat and their Reynolds number is proposed in the Reynolds number range from 2.1×10⁴ to 3.2×10⁷. The equation covers the whole Reynolds number range from laminar to turbulent boundary-layer regimes and can thus be used instead of the two correlating equations defined in ISO 9300 : 2005. The deviation of the discharge coefficients of well-made CFVNs is expected to be less than ±0.2% throughout the Reynolds number range. Tolerances for the diffuser length, inlet curvature and inlet diameter are also proposed. It is shown that the widely-accepted theories that estimate the core flow distribution result in significant error when the inlet curvature is small and that removing the third term in Hall?s equation results in very good agreement with the experimental data regardless of the magnitude of the inlet curvature. The use of CFVNs with the inlet curvature of 1.0D is discussed in order to reduce the uncertainty owing to undefined boundary-layer transition Reynolds number. A possibility is shown that such a CFVN may not have an apparent boundary-layer transition in the investigated Reynolds number range from 1.5×10⁴ to 2.0×10⁶.