Extended Lee model for the turbine meter & calibrations with surrogate fluids

We developed a physical model termed the “extended Lee model” for calibrating turbine meters to account for (1) fluid drag on the rotor, (2) bearing static drag and (3) bearing viscous drag. We tested the extended Lee model using a dual rotor, 2.5 cm diameter turbine meter and accurate flow measurements spanning a 200:1 flow range (503500Re>3500, the model correlates the volumetric flow data within 0.2%. For Re<3500Re<3500, deviations from the model increase, reaching 3.6% at the lowest flows. The same data has a maximum deviation of 17% from the commonly used Strouhal versus Roshko (or ReRe) correlation. For all the mixtures tested, the static bearing friction dominates the rotor’s behavior when Re<1350Re<1350 and it results in corrections as large as 51% of the calibration factor. In a second set of experiments, we compared our calibration using Stoddard solvent (a kerosene-like hydrocarbon with ν≈1.2×10−6m2/s at 21 °C) with our calibrations using four different mixtures of propylene glycol and water (PG+W). Within the viscosity independent range of this turbine meter (Re>∼7700Re>∼7700), where the Strouhal versus Roshko correlation works well, the PG+W calibrations had an RMS deviation of 0.056% from the Stoddard solvent calibration; this is well within the long-term reproducibility of the meter. We confirmed this result in the viscosity independent range of a 1.25 cm diameter turbine meter using Stoddard solvent and a 1.2×10−6m2/sν PG+W mixture; these two calibrations agreed within 0.02%. Therefore, turbine meters can be calibrated with environmentally benign solutions of PG+W and used with more hazardous fluids without an increased uncertainty. The present results also show that using turbine meters at ReRe below the viscosity independent range of the calibration curve will lead to large errors, unless one accounts for the temperature dependent bearing drag. For example, if the 2.5 cm diameter meter modeled here is calibrated at Re=500Re=500 using Stoddard solvent at 20 °C and then used with Stoddard solvent at 30 °C, the decrease of the kinematic viscosity will introduce an error of −0.9%, unless the temperature dependence of the bearing drag is considered.

► We model the physics of turbine meter performance.
► We tested replacing hazardous liquids for meter calibrations.
► Our model explains the turbine meter calibration curve.
► Environment friendly mixtures can replace hazardous fuels in meter calibrations.