Flowrate Determination for Arbitrary Multipath Arrangement Based on Generalized Inverse of Matrix

As a widely used method in flow measurement, Gaussian quadrature is traditionally applied to determine the flowrate with multiple acoustic paths. However, it is only available to parallel path arrangement and the path position cannot be customized by users because of the nature of numerical integration principle. Accuracy of flowrate determination is greatly restricted meanwhile. In this paper, a new method based on generalized inverse of matrix (GIM) is proposed to work out the flowrate in arbitrary multipath arrangement. With an integrable model of flow distribution established, the GIM method will find the optimal weights and achieve highly accurate flowrate. Three perfect profile assumptions, including Jacobi, optimal weighted integration for circular sections, and typical power-law profile, are, respectively, adopted in this paper to explore the performance of GIM. Its effects are at first experimentally validated in parallel path arrangement of Gauss-Jacobi on a commercially available ultrasonic flowmeter. Then, four representative types that Gaussian quadrature is not feasible to are studied via numerical simulation, including a parallel and three crossed path arrangements. Performance of the proposed GIM method is verified under straight pipe, single bend, and double bend with an expander as well as on eight installation angles. Results reveal that GIM is applicable to accurate flowrate determination for arbitrary multipath arrangement and crossed paths could provide high determination accuracy and good robustness even under complicated flow field.