Unitary Framework for Hydraulic Mathematical Models of Transient Cavitation in Pipes: Numerical Analysis of 1D and 2D Flow

Abstract

This paper deals with two-phase flow models of transient cavitating pipe flow, showing how bubble-flow models and shallow-water models can be considered in a unitary framework by only changing the geometry of the cross section. A bubble-flow cavitation model and a shallow-water cavitation model are proposed, taking into account the convective terms. Computational results are compared with those of two previous simpler bubble-flow models and with experimental measurements reported in the literature. Both quasi-steady one-dimensional (1D) and quasi-two-dimensional (2D) forms of all models are considered. For the examined cases, numerical analysis shows that 1D models converge for similar grid resolution; 2D models reach convergence with coarser longitudinal grids than, or at most with same grids as, 1D models. Comparison with measurements reveals that in order to properly investigate the capabilities of models, the computation must proceed way in time. Indeed, the first cavitation event (or, in some cases, the first few cavitation events) is very well reproduced with all models, both 1D and 2D, but over time remarkable differences in numerical results can be observed. The 1D models overestimate head values, generally do not reproduce well the shape of the function, and are delayed in time with respect to measurements, whereas 2D models reproduce very well the peaks and shapes of the head as function of time, but their results are anticipated in time with respect to measurements, suggesting that energy dissipation is overestimated. The comparison of results of the different 2D models shows, for the examined cases, very small differences, justifying the adoption of simpler models.