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

Delale, Can F.; Pasinlioglu, Senay; Baskaya, Zafer; Schnerr, Guenter H.


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        "affiliation": "Isik Univ, Dept Mech Engn, TR-34980 Istanbul, Turkey", 
        "name": "Delale, Can F."
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      {
        "affiliation": "Istanbul Tech Univ, Dept Math, TR-34465 Istanbul, Turkey", 
        "name": "Pasinlioglu, Senay"
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      {
        "affiliation": "Istanbul Tech Univ, Fac Aeronaut & Astronaut, TR-34465 Istanbul, Turkey", 
        "name": "Baskaya, Zafer"
      }, 
      {
        "affiliation": "Tech Univ Munich, D-85748 Garching, Germany", 
        "name": "Schnerr, Guenter H."
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    "description": "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.", 
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