Discharge coefficients of CFVN predicted for high Reynolds numbers based on Low-Re-calibration

摘要

In 2016, PTB introduced a function for the representation of the discharge coefficient c_D of critical flow venturi nozzles (CFVN) (versus the Reynolds number Re) what covers the operating range with laminar boundary layers and with turbulent boundary layers as well. It contains the parameters a for the impact of the core flow, b_(lam) for the Re-dependency in case of laminar and b_(turb) in case of turbulent boundary layers. These parameters are not independent to each other but have the fixed relation of b_(turb) = 0.003654b_(lam)~(1.736). Furthermore, the parameter a and the parameter b_(lam) are both direct functions of the local curvature radius R_(c,throat) of the nozzle at the throat. These relationships to R_(c,throat) are described by theoretical models. Consequently, the overall dependency of the discharge coefficient c_D on Reynolds number Re can be derived from only one parameter. The paper describes how the relationships mentioned above can be used to extrapolate the calibration values of a CFVN determined with atmospheric air to high pressure gas flow applications covering a Reynolds range of about 1:60. It is shown in detail by examples and the reliability is demonstrated by comparison data for low and high pressure of 33 nozzles. Finally, aspects of preconditions for such extrapolation and uncertainties will be discussed.