Thermal boundary layers in critical flow venturis

Abstract

We improve the usefulness of small (diameter < 10 mm) critical flow venturis (CFVs) as transfer standards for gas flow by measuring and explaining how their discharge coefficients depend on the temperature T of their environment. At Reynolds numbers Re < 2.5 × 105 (e.g., a 2 mm diameter throat; inlet air at 1 MPa), CFVs exhibit sensitivity to the environmental temperature of approximately 0.02 % K−1 due to biased measurements of the stagnation temperature T0 (temperature “sampling” error) and from ignoring the low-density, annular, thermal boundary layer generated by heat transfer from the CFV's body to the gas flowing through the CFV. To reduce temperature sampling errors, we used a non-metallic approach pipe and a temperature sensor with a low stem-conduction error. To correct for thermal boundary layer effects on the flow, we used Geropp's functional form: CT=1+KTRe−1/2ΔT/T0 where ΔT is the difference between the CFV's inner wall temperature and the stagnation temperature. For CFVs made of stainless steel and copper with diameters of d = 0.56 mm, 1.1 mm, and 3.2 mm we measured KT ≈ −7 while theoretical predictions of KT by Geropp and Ding et al. are −1.7 and −3.845 respectively. Introducing the correction for room temperature changes (CT) measured in this work, reduces the room temperature sensitivity of the flow measured with the 0.56 mm diameter CFVs from 0.02 % K−1 to less than 0.003 % K−1. Smaller, but significant, improvements are achieved with larger CFVs.