Semianalytical solution of unsteady quasi-one-dimensional cavitating nozzle flows

Delale C. F., Pasinlioğlu Ş., Baskaya Z., Schnerr G. H.

JOURNAL OF ENGINEERING MATHEMATICS, vol.86, pp.49-70, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 86
  • Publication Date: 2014
  • Doi Number: 10.1007/s10665-013-9645-6
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.49-70
  • Istanbul Technical University Affiliated: Yes


Unsteady quasi-one-dimensional bubbly cavitating nozzle flows are considered by employing a homogeneous bubbly liquid flow model, where the nonlinear dynamics of cavitating bubbles is described by a modified Rayleigh-Plesset equation. The model equations are uncoupled by scale separation leading to two evolution equations, one for the flow speed and the other for the bubble radius. The initial-boundary value problem of the evolution equations is then formulated and a semianalytical solution is constructed. The solution for the mixture pressure, the mixture density, and the void fraction are then explicitly related to the solution of the evolution equations. In particular, a relation independent of flow dimensionality is established between the mixture pressure, the void fraction, and the flow dilation for unsteady bubbly cavitating flows in the model considered. The steady-state compressible and incompressible limits of the solution are also discussed. The solution algorithm is first validated against the numerical solution of Preston et al. [Phys Fluids 14:300-311, 2002] for an essentially quasi-one-dimensional nozzle. Results obtained for a two-dimensional nozzle seem to be in good agreement with the mean pressure measurements at the nozzle wall for attached cavitation sheets despite the observed two-dimensional cavitation structures.