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Numerical simulation and analysis of condensation shocks in cavitating flow

Published online by Cambridge University Press:  22 January 2018

Bernd Budich Open the ORCID record for Bernd Budich [Opens in a new window] ,
S. J. Schmidt  and
N. A. Adams
Bernd Budich*
Affiliation:
Technical University of Munich, Department of Mechanical Engineering, Chair of Aerodynamics and Fluid Mechanics, Boltzmannstr. 15, D-85748 Garching bei München, Germany
S. J. Schmidt
Affiliation:
Technical University of Munich, Department of Mechanical Engineering, Chair of Aerodynamics and Fluid Mechanics, Boltzmannstr. 15, D-85748 Garching bei München, Germany
N. A. Adams
Affiliation:
Technical University of Munich, Department of Mechanical Engineering, Chair of Aerodynamics and Fluid Mechanics, Boltzmannstr. 15, D-85748 Garching bei München, Germany
*
†Email address for correspondence: bernd.budich@tum.de
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Abstract

We analyse unsteady cavity dynamics, cavitation patterns and instability mechanisms governing partial cavitation in the flow past a sharp convergent–divergent wedge. Reproducing a recent reference experiment by numerical simulation, the investigated flow regime is characterised by large-scale cloud cavitation. In agreement with the experiments, we find that cloud shedding is dominated by the periodic occurrence of condensation shocks, propagating through the two-phase medium. The physical model is based on the homogeneous mixture approach, the assumption of thermodynamic equilibrium, and a closed-form barotropic equation of state. Compressibility of water and water vapour is taken into account. We deliberately suppress effects of molecular viscosity, in order to demonstrate that inertial effects dominate the flow evolution. We qualify the flow predictions, and validate the numerical approach by comparison with experiments. In agreement with the experiments, the vapour volume fraction within the partial cavity reaches values ${>}80\,\%$ for its spanwise average. Very good agreement is further obtained for the shedding Strouhal number, the cavity growth and collapse velocities, and for typical coherent flow structures. In accordance with the experiments, the simulations reproduce a condensation shock forming at the trailing part of the partial cavity. It is demonstrated that it satisfies locally Rankine–Hugoniot jump relations. Estimation of the shock propagation Mach number shows that the flow is supersonic. With a magnitude of only a few kPa, the pressure rise across the shock is much lower than for typical cavity collapse events. It is thus far too weak to cause cavitation erosion directly. However, by affecting the dynamics of the cavity, the flow aggressiveness can be significantly altered. Our results indicate that, in addition to classically observed re-entrant jets, condensation shocks feed an intrinsic instability mechanism of partial cavitation.

JFM classification

Drops and Bubbles: Cavitation Multiphase and Particle-laden Flows: Multiphase flow Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 838 , 10 March 2018 , pp. 759 - 813
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Copyright
© 2018 Cambridge University Press 

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