On the Hierarchy of Models for Pipe Transients: From Quasi-Two-Dimensional Water Hammer Models to Full Three-Dimensional Computational Fluid Dynamics Models

Abstract

A hierarchy of models exists in the literature for the simulation of pipe transients. One-dimensional (1D) water hammer models provide a cost-effective tool for the analysis of such transients. Traditional 1D models implement a quasi-steady approximation of the frictional term, which results in poor modeling of the attenuation of the transient. To improve the modeling of the attenuation phenomenon, alternative unsteady friction models were developed for the 1D water hammer formulation. Moreover, quasi-two-dimensional (quasi-2D) water hammer models were introduced, which allow the computation of the unsteady velocity profile and hence provide improved modeling of the attenuation phenomenon. Recently, interest has developed in the use of computational fluid dynamics (CFD) models based on the Navier–Stokes equations in the simulation of fluid transients. Both axisymmetric and full three-dimensional (3D) CFD models are used in this regard. The aim of the current paper is to carry out a comparative study between the performance of quasi-2D water hammer models, axisymmetric CFD models, and full 3D CFD models. Numerical computations using the three models are performed for both laminar and turbulent flow cases. Present results show that the quasi-2D water hammer model and the axisymmetric CFD model provide near identical results in terms of computing the magnitude, phase, and attenuation of the transient. Reported results also demonstrate the computational efficiency of the quasi-2D model, which provides results that agree reasonably well with the full 3D CFD model results while using a grid density, which is an order of magnitude lower than the grid requirements for the full 3D CFD model.