Discharge coefficients for compressible flow through small-diameter orifices and convergent nozzles

Abstract

This paper presents a study of the compressible-flow behavior of light gases through small orifices and convergent nozzles with diameters ranging from 0.9 to 1.9 mm. The subsonic and critical-flow regions for 16 orifice and nozzle flow elements with the following geometries have been tested experimentally: sharp or knife-edge orifices, straight-bore orifices, rounded-entry nozzles, and elliptical-entry nozzles. Air flow was primarily studied, but data for carbon dioxide, argon, helium, and two distinct argon-helium mixtures were also collected. In addition, the upstream temperature was varied from 295 to 700 K. The data have been reduced for correlation purposes to a discharge coefficient defined as the fraction of the isentropic, adiabatic mass flow rate attained by real fluids in an actual orifice or nozzle. An error analysis shows that the reported discharge coefficients are accurate to ± 1.2% for air flow and ± 1.6% for the other gases studied. The discharge coefficient for knife-edge orifices correlates very well with a dimensionless pressure drop for the entire range of diameters, gases, pressures and temperatures studied. The discharge coefficient does not correlate with the throat Reynolds number for compressible flow through knife-edge orifices. Moreover, an analogous behavior of the discharge coefficient for larger diameters than those tested is expected for knife-edge and thin-plate orifices. Straight-bore orifices, with length-to-diameter ratios close to or slightly greater than unity, yield discharge coefficients which are approximately independent of flow rate, upstream temperature, and gas properties. These discharge coefficients are, however, highly sensitive to the length-to-diameter ratio of the straight bore. Finally, the discharge coefficients for both rounded- and elliptical-entry nozzles correlate well with a throat Reynolds number. The correlation shows that as the Reynolds number is decreased the discharge coefficient drops precipitously for Re < 20,000. For Re > 20,000 the discharge coefficient increases slowly with increasing Reynolds number. This behavior is consistent with both previous data and fluid dynamics theory for rounded- and elliptical-entry nozzles.