Discrete vapour cavity model with improved timing of opening and collapse of cavities

Transient vaporous cavitation occurs in hydraulic piping systems when the liquid pressure falls to the vapour pressure. Cavitation may occur as a localized vapour cavity (large void fraction) or as distributed vaporous cavitation (small void fraction). The discrete vapour cavity model (DVCM) with steady pipe flow friction term is widely used in standard water hammer software packages. The DVCM may generate unrealistic pressure pulses (spikes) due to the collapse of multi-cavities, but the model gives reasonably accurate results when the number of reaches is restricted. Recent studies of the DVCM have suggested that an advanced treatment of the growth and collapse of cavities would improve the model and the present paper explores this suggestion in detail. The exact timing of column separation events cannot be achieved in numerical schemes. Time adjustments for cavity opening and collapse are implemented into the DVCM and their influence on pressure spikes and the time of cavity existence is investigated. A single diamond method of characteristics grid is used to avoid grid-separation errors. The paper presents a number of experimental results and corresponding numerical simulations of transient vaporous cavitation events generated by a downstream fast valve closure. The experimental apparatus is comprised of a 37.2 m long constant-sloping pipe of 22.1 mm internal diameter connecting two pressurized tanks. It has been found that proper timing of cavity opening and collapse has an influence on the numerical results. The simulation results show that adjustment of the timing of the cavity collapse has a greater influence on pressure pulses than the time adjustment for cavity opening. Results without time adjustments for cavity opening and collapse are presented as a baseline solution.