Transmission Line Modeling of Inclined Compressible Fluid Flows

Compressible fluid flow modeling for inclined lines is a challenging phenomenon due to the nonlinearity of the governing equations and the spatial-temporal dependency of the fluid density. In this paper, the transmission line analytical model is applied to the determination of inclined compressible fluid flow's dynamics. To establish this model, an exact transcendent solution is developed by solving the Navier-Stokes equation in the Laplace domain. A transfer function approximation, allowing the fluid flow transients determination, is recovered from the exact solution using residual calculations. The error resulting from the polynomial fraction approximation of the transfer functions is circumvented through frequency response corrections for the approximation to meet the exact function steady-state behavior. The effect of gravity and fluid, compressibility on the fluid flow dynamics as well as the interplay between those two factors are illustrated through the pressure and flow rate's frequency and time responses.