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

Can F. Delale, Şenay Pasinlioğlu, Zafer Başkaya, Günter H. Schnerr

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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.

Original languageEnglish
Pages (from-to)49-70
Number of pages22
JournalJournal of Engineering Mathematics
Issue number1
StatePublished - Jun 2014


  • Evolution equations
  • Nonlinear bubble dynamics
  • Quasi-one-dimensional nozzle flows
  • Unsteady cavitating flows


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