The dynamic behaviour of check valves in pipeline systems
A semi-empirical method is developed to describe the dynamic behaviour of check valves in pipeline systems. The method is based on parameterized valve models and dimensionless valve characteristics, which may be obtained from experiments. The check valve is considered as a black box with certain input and output characteristics. The check valve closure and associated pressure surges are the dominant phenomena. Undamped check valves may be considered as a special case of damped check valves. Much attention is paid to the description of the hydrodynamic (fluid) forces on the internal, moving valve elements. These elements may be considered as translating or rotating bodies with (at least) one plane of symmetry. The equations of motion for the constrained, unsteady motion of such a body in an unconfined, unsteady fluid flow are based on the dynamical theory of Kirchhoff, extended to an unsteady fluid flow. The equivalent equations for a body in a confined fluid are based on Lagrange's method of generalized coordinates. A general (dimensionless) valve equation of motion is developed, which is valid for most of the existing check valve types. Basic differential equations are derived for the transient flow in a pipe with constant initial flow deceleration. The equations are applied to describe the check valve closure under reflection free and reflecting boundary conditions in the form of dimensionless, analytical equations. The theory is based on conventional waterhammer theory. The pipe and valve equations are coupled via the integral form of the momentum equation. The uncoupled and coupled, (dimensionless) pipe and valve equations show formally which (dimensionless) variables and valve, system and fluid parameters are relevant to the dynamic behaviour of check valves in pipeline systems. In that sense they are used in a dimensional analysis to develop (dimensionless) valve characteristics and dynamic scale laws. Based on the dimensionless valve characteristics, models for undamped and damped check valves are developed and implemented in the waterhammer computer code CVWP (Check Valve Waterhammer Program). Experiments are performed in the test facility at Delft Hydraulics to measure several valve characteristics of weakly and strongly damped check valves. The dynamic scale laws are validated by means of numerical simulations. The valve models are validated against experimental data. The study has been performed within the Check Valve Research Project (CVRP).