A generalized 2-D hyperbolic solver with application to orifice metering

by 1979- Leon, Daniel Eduardo

Hyperbolic systems of PDEs arise in many practical problems. This study presents the description, validation and application of a generalized 2-D solver. The Essentially Non- Oscillatory (ENO) Scheme is used to solve the homogeneous PDEs, while the forcing functions are solved using the Fifth Order Runge-Kutta Method. Prior to the deployment of the numerical methods for actual application, their performance was assessed by solving many benchmark problems with exact or reliable numerical solutions, which have the essential features of the actual PDEs that we desire to solve. After benchmarking, the solver is applied to a single pipeline to obtain a solution for the sudden valve closure problem and a comparison between the 1-D and 2-D models is conducted. Additionally, 2-D flow through a horizontal pipeline was simulated until a fully developed turbulent flow was achieved. More than 80% of gas metering is still performed by orifice meters and considering the actual price of natural gas, a small error of 1% can amount to a loss of millions of dollars per year. Measurements of flow rate are obtained using a semi-empirical equation recommended by the AGA which is known to generate an error of up to 3%. An improved model based on the fundamental conservation laws is presented for flow of natural gas through an orifice meter. The solution of the Navier-Stokes equations considers the viscous effects of the flow and the turbulent effects are accounted by using the Large-Eddy-Simulation (LES) approach. A final validation was achieved by matching experimental data of the mean velocity vector field for air. The maximum error in the axial velocity upstream the orifice-plate between the experimental data and the numerical results is within 3.5%. Moreover, a cross plot for the comparison downstream the plate shows a very good match between the measured data and the numerical predictions. Given the successful validation process, numerical predictions were made for the case of natural gas and a parametric study was conducted varying the Reynolds number, the specific gravity of the fluid and the Beta ratio. Among the most important accomplishments is the successful capturing of the recirculation phenomenon that takes place downstream of the plate. Additionally, the model predicts the flow rate by numerical integration of the axial velocity at a location where a fully developed flow exists. The error between the predicted flow rate and the specified value at the inlet is less than 1%. Moreover, the predictions obtained using the AGA-3 equation produced errors above 4% for most of the cases, with a maximum of 6.41% for the case of specific gravity equal to 0.77. iv