Rational Polynomial Transfer Function Approximations for Fluid Transients in Lines

This paper introduces a simple approach utilizing MATLAB^® computational tools for generating rational polynomial transfer functions for fluid transients in both liquid and gas fluid transmission lines. These transfer functions are obtained by curve fitting in the frequency domain the exact solution to the distributed parameter laminar flow “Dissipative Model” for fluid transients that includes nonlinear frequency dependent viscous friction terms as well as heat transfer effects in gas lines. These transfer functions are formulated so they are applicable to arbitrary line terminations and so they can be inserted directly into SIMULINK^® models for time domain simulation and analysis of a total system of which the fluid lines are only internal components. The inputs to the algorithm are the internal radius and length of the line; the kinematic viscosity, density, Prandtl number, and speed of sound of the fluid; and the maximum frequency to which an accurate curve fit of the exact solution is desired. This maximum frequency normally is equal to or greater than the bandwidth of the other components in the total system to be analyzed or the maximum frequency associated with the input. The simplicity of use and accuracy in the results of the exact solution representations are demonstrated for examples of a blocked fluid line and of a line terminating into a tank. The computational algorithms are available for download from the Author’s web site. This is the first of two papers pertaining to transfer functions for fluid transients. The second paper pertains to formulating simulation diagrams for total systems containing fluid lines represented by rational polynomial transfer functions.