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Shocks in Quasi-One-Dimensional Bubbly Cavitating Nozzle Flows

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Bubble Dynamics and Shock Waves

Part of the book series: Shock Wave Science and Technology Reference Library ((SHOCKWAVES,volume 8))

Abstract

Stationary and propagating shock waves in bubbly cavitating flows through quasi-one-dimensional converging-diverging nozzles 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 semi-analytical 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. The steady-state compressible limit of the solution with stationary shocks is obtained and the stability of such shocks are examined. Finally, results obtained using the semi-analytical constructed algorithm for propagating shock waves in bubbly cavitating flows through converging-diverging nozzles, which agree with those of previous numerical investigations, are presented.

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Işık University, 34980, Şile, Istanbul, Turkey

    Can F. Delale

  2. Emeritus Professor, Technische Universität München, D-85748, Garching, Germany

    Günter H. Schnerr

  3. Department of Mathematics, Istanbul Technical University, 34469, Maslak, Istanbul, Turkey

    Şenay Pasinlioğlu

Authors
  1. Can F. Delale
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  2. Günter H. Schnerr
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  3. Şenay Pasinlioğlu
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Corresponding author

Correspondence to Can F. Delale .

Editor information

Editors and Affiliations

  1. , Department of Mechanical Engineering, Isik University, Mesrutiyet Koyu, Universite Sokak 2, Sile, 34980, Turkey

    Can F. Delale

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Delale, C.F., Schnerr, G.H., Pasinlioğlu, Ş. (2013). Shocks in Quasi-One-Dimensional Bubbly Cavitating Nozzle Flows. In: Delale, C. (eds) Bubble Dynamics and Shock Waves. Shock Wave Science and Technology Reference Library, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34297-4_7

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