The Integral Momentum Balance Applied to Metering Orifices to Obtain the Pressure Drop and the Flow Rate With High Accuracy

Abstract

Abstract The established method of calculating the pressure loss and the flow rate of flows through metering orifices requires empirical correction coefficients. In this paper, a completely momentum-based approach is presented to predict the flow rate and the pressure loss. It is shown that the proposed approach is as precise as the established method but without any empirical coefficient. The required physical coefficients solely base on physics. They pinpoint the sources of the inaccuracy that effects the employment of an empirical correction coefficient to correct the established method—and confirm the empirical correction coefficient on a physical foundation. Ultimately, the physical coefficients evade the effort to experimentally calibrate the theory with the experiments. The integral momentum balance is applied to a control volume comprising the orifice reaching up to the respective pressure metering cross section. Depending on the location of the control volume's open boundaries, the pressure loss or the flow rate can be obtained. To substitute the integral with averaged expressions, the introduced physical coefficients are deduced directly from numerical simulations and parametrized by simple analytical fit functions to complete the momentum-based approach. The numerical model and the proposed approach are both verified by the comparison with the results obtained by the standard ISO 5167:2003. The agreement with the classical calculation method as per ISO 5167:2003 is very high and within the specified limits, which shows that no empirical coefficient is necessary for high-accuracy flow metering using the momentum balance.