A Simplified Method for Formulating the Simulation Diagram for Systems Containing Lines With Fluid Transients

The overall objective of this paper is to present a simplified approach to formulating a time domain simulation diagram for a dynamic system containing liquid or gas lines with significant fluid transients without having to use questionable simplifying assumptions for the fluid transients model. To achieve this objective, formulation of a two-port model for the fluid transients in a line that is compatible with any line termination conditions and represented by rational polynomial transfer functions is presented. This linear two-port model is first achieved by obtaining an input/output causality matrix for a line with linear flow resistances representing transition losses or flow restrictions at each end. The laminar flow “Dissipative Model” for fluid transients that accounts for nonlinear frequency dependent friction effects and thermal effects in gas lines is used in the formulation in order to achieve the most comprehensive model for axial flow in a constant diameter tube. The next step in achieving the overall objective is to obtain rational polynomial transfer function approximations for the three transfer functions in the reformulated “Dissipative Model”. These rational polynomial transfer function approximations are obtained from least-squares curve fits in the frequency domain of the exact transfer functions from the “Dissipative Model”. Then, two step-by-step procedures, using these transfer functions, for drawing a simulation diagram for a dynamic system containing fluid lines are presented.