Interpolation schemes for valve closure modelling

Abstract

In transient flow condition the pressure variation will depend, among other factors, on the valve closure law, whose insertion into the water hammer’s software code is an impractical task since there are so many closing laws as valve types, forcing to modify the program whenever a specific valve has to be considered. It is more practical to calculate the valve closure (τ) at a certain time intervals and to transfer this information to the software’s data entry file. As the adopted temporal discretization for the valve closure’s law will not necessarily coincide with the simulation time step (Δt), the τ calculation at each Δt must be done by interpolation of two or more points belonging to the valve closure curve. The results will depend mainly of the valve type, the interpolation scheme used, and the interpolation order (IO) applied. In this article different interpolation methods are applied on two curve types: the first of linear type, characterized by having straight segments with abrupt slope changes; the second with softer forms. The results are compared with the exact solution. It is concluded that Newton-Gregory is the best interpolation method because it generates a lower computational cost and negligible interpolation errors regardless of the valve closure curve’s shape.