Uncertainty analysis for a virtual flow meter using an air-handling unit chilled water valve

A virtual water flow meter is developed that uses the chilled water control valve on an air-handling unit as a measurement device. The flow rate of water through the valve is calculated using the differential pressure (DP) across the valve and its associated coil, the valve command, and an empirically determined valve characteristic curve. Thus, the uncertainty in the measurements could be significantly greater than for conventional hardware flow meters. In this article, mathematical models are developed and used to conduct uncertainty analyses for the virtual flow meter, and the results from the virtual meter are compared to measurements made with an ultrasonic flow meter. Theoretical uncertainty analysis shows that the total uncertainty in flow rates from the virtual flow meter is 1.46% with 95% confidence; comparison of virtual flow meter results with measurements from an ultrasonic flow meter yielded an uncertainty of 1.46% with 99% confidence. The comparable results from the theoretical uncertainty analysis and empirical comparison with the ultrasonic flow meter corroborate each other and tend to validate the approach to computationally estimating uncertainty for virtual sensors introduced in this study. Furthermore, the results show that the total uncertainty in flow rates from this virtual flow meter is adequately low for use in place of common physical flow meters for monitoring thermal energy use in air handlers and detecting operational and equipment faults that affect energy consumption.