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

Abstract (Summary)

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.
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Bibliographical Information:

Advisor:

School:Pennsylvania State University

School Location:USA - Pennsylvania

Source Type:Master's Thesis

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