Alternative Approach for Modeling Transients in Smooth Pipe With Low Turbulent Flow

Abstract

A new simplified approach for modeling and simulating pressure transients resulting from the rapid acceleration or deceleration of turbulent flow in smooth-walled fluid lines is introduced. In contrast to previous approaches for modeling turbulence by modifying the head loss terms in the momentum partial differential equation, this approach is achieved by coupling the frequency domain analytical solution to the laminar flow version of the partial differential equations in series with a lumped resistance that has been sized so that the steady flow resistance for the line is equivalent to an empirical turbulent steady flow resistance. The model provides normalized pressure and flow transients that have good agreement with experimental data and with method-of-characteristics (MOC) solutions associated with previously validated turbulence models. The motivation for this research is based on the need for a practical means to simulate the effects of fluid transients in lines that are internal components within a total engineering system without the need to understand the different unsteady turbulence one- and two-dimensional (1D/2D) friction models and also be proficient with the complexities of nonlinear interaction of friction and interpolation errors encountered using MOC. This modeling approach utilizes a preprogramed inverse frequency algorithm, commonly used for system identification, which generates “equivalent” high-order normalized linear ordinary differential equations that can be coupled with models for other fluid power components and easily solved in the time domain using preprogramed numerical algorithms for ordinary differential equations.