Developments and Limits of Discrete Vapor Cavity Models of Transient Cavitating Pipe Flow: 1D and 2D Flow Numerical Analysis

Abstract

The paper deals with discrete vapor cavity models (DVCM) to reproduce transient cavitating pipe flows. Since features and limits of the classic DVCM are well known from literature, some developments are here considered and analyzed: the continuity equation for the cavity is written in terms of mass balance instead of volume balance, allowing calculations with appropriate computational fine grids; a lower threshold is introduced for pressure, in order to prevent it from dropping below vapor pressure; prediction-correction steps are introduced in the numerical solution procedure; and the two-dimensional (2D) description of the flow field is considered assuming axial-symmetric flow, in order to evaluate unsteady friction without the need of parameters calibration. Computational results, which are sensitive also to a weighting parameter used in the numerical process, are compared with each other, with results of a bubble flow model, and with experimental measurements reported in the literature. In order for such comparisons to be meaningful, the numerical simulation must not be limited to the first few cavitation events but must be extended in time. All one-dimensional (1D) models are weakly sensitive to grid size, except for one case with severe cavitation, whereas 2D model results are practically grid-independent. The comparison of numerical and experimental results shows that the effects of the physically based corrections (mass balance and lower threshold for pressure) are generally small but not negligible and consist of a slight increase of dissipations. In general, 2D models improve the performance of DVCMs; in particular, their results better reproduce the shape of the head function and reduce numerical spikes, but also provide an excess of energy dissipation which causes numerical results to be anticipated with respect to experimental traces. The comparison of results of DVCMs and a bubble flow model, in their 1D and 2D forms, with experiments shows that the latter performs better. As a result of the present study, all DVCMs should therefore be used with care and be limited either to cases of weak cavitation or to the first phases of the phenomenon.