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

Abstract

In 2016, PTB introduced a function for the representation of the discharge coefficient cD of critical flow venturi nozzles (CFVN) (versus the Reynolds number Re) which covers the operating range for both laminar and turbulent boundary layers. It contains the parameters a for the impact of the core flow, blam for the Re-dependency in case of laminar and bturb in case of turbulent boundary layers. These parameters are not independent from each other but have the fixed relation of bturb = 0.003654blam1.736.Furthermore, the parameter a and the parameter blam are both direct functions of the local curvature radius Rc,throat of the nozzle at the throat. These relationships to Rc,throat are described by theoretical models. Consequently, the overall dependency of the discharge coefficient cD on Reynolds number Re can be derived from only one parameter.The paper describes how these relationships 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 for 33 nozzles. Finally, aspects of preconditions for such extrapolation and uncertainties are discussed.