A variational method is used to derive numerical models for transient flow simulation in fluid transmission lines. These are generalizations of models derived using the more traditional modal method. Three different transient compressible laminar pipe flow models are considered (inviscous, one-dimensional linear viscous, and two-dimensional dissipative viscous flow), and a model for transient turbulent pipe flow is given. The (model) equations in the laminar case are given in the form of a set of constant coefficient ordinary differential equations, and for the turbulent case (model) in the form of a set of nonlinear ordinary differential equations. Explicit equations are given for various end conditions. Attenuation factors, similar to the window functions used in spectral analysis, are used to attenuate Gibbs phenomenon oscillations. [S0022-0434(00)03201-9]
Fluid Transmission Line Modeling Using a Variational Method
Contributed by the Dynamic Systems and Control Division for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the Dynamic Systems and Control Division November 4, 1998. Associate Technical Editor: R. Chandran.
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Ma¨kinen, J., Piche´, R., and Ellman, A. (November 4, 1998). "Fluid Transmission Line Modeling Using a Variational Method ." ASME. J. Dyn. Sys., Meas., Control. March 2000; 122(1): 153–162. https://doi.org/10.1115/1.482449
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