Linear Dynamic Modeling of Flowing Fluid Lines

Abstract

An “exact” classical solution is presented for the linearized frequency domain characterization of a barotropic fluid in a rigid circular tube. The axial velocity profile (and thus, the phase velocity, attenuation, and impedance) is represented by a confluent hypergeometric function with complex arguments. The confluent hypergeometric function has not been tabulated for general complex arguments, precluding numerical evaluation of the “exact” model. An approximate solution in terms of Bessel functions is derived, and numerically evaluated. The two-port asymmetric model for a uniform circular line with through-flow is derived and compared to known symmetric models (zero through flow). The significance of the linearized energy equation in the through-flowing case is discussed.