Estimation of Decay Coefficients for Unsteady Friction for Instantaneous, Acceleration-Based Models

Abstract

This paper presents equations developed by using genetic algorithms (GA) to estimate decay coefficients for instantaneous acceleration–based (IAB) unsteady friction models in order to predict energy dissipation following sudden valve closures in simple elastic pipe systems. The GA searched for the optimum combination of IAB coefficients to reproduce pressure history at the valve location using the normalized root mean-squared error (NRMSE) as the minimization criteria. The measured results comprise nine downstream and five upstream sudden-valve-closure experiments performed in five laboratories around the globe. Three IAB unsteady models are compared: a one-coefficient model, a two-coefficient model discretizing the unsteady friction term using finite-difference approximations, and a new two-coefficient model that includes the unsteady friction term in the method of characteristics. The two-coefficient models produced a better match with the experimental data than the one-coefficient models. A new equation for the estimation of the decay coefficient of one-equation models, as well as average values for the decay coefficients for the two-coefficient models, is presented.