Error sources in compressible Venturi flow measurement under cryogenic supercritical helium conditions

Conventional differential pressure Venturi flow measurement in cryogenic supercritical helium shows a clear dependence of the discharge coefficient on thermodynamic conditions. This behavior becomes more pronounced as operating conditions deviate from calibration, particularly at high Reynolds numbers. In this study, cryogenic calibration experiments are combined with computational fluid dynamics simulations to investigate the origin of this dependence. The results show that the observed deviation does not arise from a single source. Instead, it reflects the combined effects of thermodynamic modeling assumptions, velocity non-uniformity, and static-pressure tapping errors. To examine the role of thermodynamic modeling, an enthalpy-based formulation is used as a diagnostic tool to assess the consistency of the conventional compressible flow model. The analysis indicates that the apparent dependence on thermodynamic conditions mainly originates from limitations in the expansibility factor and the isentropic approximation. In addition, velocity distribution effects introduce a kinetic energy bias, while static pressure tapping errors further affect the measured pressure difference, especially at the throat where near-wall shear is stronger. Overall, this study clarifies the physical origin of discharge coefficient variation in cryogenic Venturi flow measurement and provides a basis for improving measurement reliability under non-calibration conditions.