Lumped Parameter Modeling Of Fluid Line Dynamics With Turbulent Flow Conditions

Abstract

A procedure for obtaining rational polynomial transfer functions representing ordinary differential equations for time domain transient response simulations of systems with fluid transmission lines with incompressible turbulent flow is formulated and presented. The method is based on the use of an inverse frequency least squares algorithm applied to the distributed parameter model for laminar flow with added lumped resistance to match the additional resistance associated with turbulence. Guidelines for using the algorithm are included with focus on the use of weighting parameters, the number of resonant modes to be included, and the bandwidth of the pressure/flow pulsation dynamics in the line. Frequency and time domain comparisons are presented demonstrating the accuracy of the transfer function formulations.For special cases where the use of a lumped parameter model is preferred or is necessary for modeling and simulating the fluid pulsations in a line, guidelines for tapering the capacitance and inertance lump sizes for laminar and turbulent flow are presented. The improvement in matching the true mode frequencies and the improvement in the accuracy of transient responses achieved by tapering the size of the lumps as compared to using equal size lumps is demonstrated for a variety of boundary conditions associated with different causalities.The ability to obtain accurate rational polynomial transfer functions for pressure/flow pulsations in lines for both laminar and turbulent flow conditions, using either the inverse frequency algorithm or a tapered lumped model, makes it possible to include the line as a component in the model for a total dynamic system represented by ordinary differential equations for purposes of time domain simulations and the use of linear system analysis and control algorithms on the total system.