The effect of time-frequency discretization on the accuracy of the transmission line modelling of fluid transients

The operation of the transmission line models requires an input signal in the frequency domain describing the nature of the transient disturbance (for example, a valve closure) and an exact solution of the linearized mass and momentum equations for unsteady pipe flow. The use of the transmission line models does not require a strict adherence to a time-space discretization grid governed by the Courant condition, but it does require that the input signal be discretized in the frequency domain. This paper investigates the errors induced by the discretization of the input signal and provides guidelines for the appropriate selection of discretization size for the linear transmission line models. The accuracy of the model is quantified through comparison with a finely discretisated method of characteristics (MOC) model. The results show that the transmission line models are sensitive to the time-frequency discretization size and unlike the MOC, the appropriate size of the discretization changes depending on the transient event being modelled as well as the energy losses in the system.