Optimization of an algorithm for the measurement of unsteady flow-rates in high-pressure pipelines and application of a newly designed flowmeter to volumetric pump analysis

An innovative, efficient, and robust algorithm is presented for the evaluation of the instantaneous flow-rate in high-pressure liquid flow pipelines. This algorithm is based on the pressure time histories measured at two locations. A simple ordinary differential equation has been derived from the mass and momentum conservation laws and has been solved analytically. This equation allows the flow-rate time fluctuations to be evaluated accurately around their mean value, without any need for initial datum on the liquid flow velocity. A measuring device has been designed and realized to evaluate the flow-rate. The proposed flowmeter layout consists of a piece of pipeline endowed with two piezoresistive pressure sensors equipped with miniaturized thermocouples, the pressure sensor conditioners and a central processing unit (CPU), in which the algorithm for the evaluation of the flow-rate has been implemented. A more sophisticated version of the flowmeter algorithm, which includes unsteady friction in the flow-rate evaluation, has also been developed. Different algorithm versions have been assessed and successfully validated through a comparison with numerical flow-rate data predicted using a reliable onedimensional model of a common rail (CR) fuel injection system. The prototypal flowmeter has been installed at the delivery section of a CR volumetric pump in order to investigate the flow-rate ripple. The flowmeter traces have been compared with the predictions of a previously developed theoretical model for the pump delivered instantaneous flow-rate, in order to further assess the reliability of both the model and the flowmeter as well as to have a better understanding of the cause and effect relationships between the flow-rate time history and the dynamic working of the pump. The effects that the actuation of the fuel metering valve (FMV), which is placed at the CR pump inlet, has on the instantaneous delivered flow-rate have also been analyzed.