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Influence of ventilation on the shape of slender axisymmetric cavities

CAV2012, August 14-16, 2012, Singapore. Influence of ventilation on the shape of slender axisymmetric cavities. Igor Nesteruk Institute of Hydromechanics National Academy of Sciences of Ukraine. inesteruk@yahoo.com. The steady flow pattern and the following assumptions are used:.

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Influence of ventilation on the shape of slender axisymmetric cavities

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  1. CAV2012, August 14-16, 2012, Singapore Influence of ventilationon the shape of slender axisymmetric cavities Igor Nesteruk Institute of Hydromechanics National Academy of Sciences of Ukraine inesteruk@yahoo.com

  2. The steady flow pattern and the following assumptions are used: • External water flow is axisymmetric potential, inviscid and incompressible • Internal gas flow is one dimensional, inviscid and incompressible • Gravity and capillarity forces are neglected • Cavitator, cavity and hull are slender

  3. The external water flow potential and Bernoulli equation (Cole, 1968) , ,

  4. Bernoulli and continuity equations for the internal gas flow

  5. Basic differential equation and initial conditions (Manova, Nesteruk&Shepetyuk 2011) At the cavity surface: (1) ; ; Initial conditions at : ;

  6. Cavities on cylindrical hulls Base ventilated cavity on a cylindrical hull

  7. Cavities on cylindrical hulls,(Manova, Nesteruk&Shepetyuk 2011) Semi-length and maximum radius of ventilated cavities at: = 0; 0.5; 0.8; 0.9; 0.99 (curves 1-5 respectively)

  8. Cavities on cylindrical hulls,Critical values of ventilation rate, corresponding to unlimited cavities = 0; 0.5; 0.8; 0.9 (curves 1-4)

  9. Base cavities on cylindrical hulls, Ventilation diminishes the length(Nesteruk&Shepetyuk 2011) Base cavity length at: = 0; 0.5; 0.8; 0.9(curv.1-4)

  10. Asymptotic solution at small values of the ventilation rate

  11. Cavities on conical-cylindrical hulls.Calculations at the fixed conical part length and different values of cylinder radius (Nesteruk&Shepetyuk 2012)

  12. CONCLUSIONS • Ventilated steady slender axysimmetric cavity is considered with the use of one-dimensional inviscid flow of the incompressible gas in the channel between the cavity surface and the body of revolution. The non-linear differential equation and its numerical and asymptotic solutions were obtained. • For the disc and cone cavitators the ventilation can sufficiently increase the cavity dimensions and its rate is limited by two critical values. Ventilation sufficiently decreases the base cavity length. • Examples of calculations for cylindrical and cone-cylindrical shapes of the body located in the cavity are presented. It was shown that the cavity shape depends sufficiently on the values of Ve and the cavitation number at the same fixed cross-section. • Presented theoretical results allow explaining the experimental facts of both a weak and hysteresis dependence of the cavity length on ventilation and its abrupt increase.

  13. Acknowledgment The author thanks Professor Kai Yan for very useful discussions and his presentation of the paper on CAV2012.

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