Local and integral energy-based evaluation for the unsteady friction relevance in transient pipe flows

Unsteady friction and its modeling have been widely studied in transient pipe flows for its influences and modification effect on pressure waves. Such a feature is of great importance particularly in pipe systems where the extreme pressure values are due to the overlapping of pressure waves generated in different sections. This paper investigates the relevance of unsteady friction term by considering different models available in the literature. In particular, attention is focused on the following two commonly used one-dimensional (1D) models: the weighting function-based (WFB) model and the instantaneous acceleration-based (IAB) model. The investigation is executed using laboratory experiments and field tests as well as 1D/2D numerical simulations in simple pipeline systems. Realistic ranges of both initial (pretransient) conditions and geometrical characteristics are considered. The data collected in experimental tests are first used to calibrate the unsteady friction models under investigation. The validated models are then applied to identify their respective domains of applicability and the limitations. The differences between models and data are measured using the local transient analysis (LTA) norm and the integral total energy (ITE) norm along the pipeline, and the reasons for such discrepancies are explored in the paper. The practical implications of the use and improvements of different unsteady friction models for transient pipe flow simulations are discussed in the paper.