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On the scaling of air entrainment from a ventilated partial cavity

Published online by Cambridge University Press:  30 August 2013

Simo A. Mäkiharju ,
Brian R. Elbing ,
Andrew Wiggins ,
Sarah Schinasi ,
Jean-Marc Vanden-Broeck ,
Marc Perlin ,
David R. Dowling  and
Steven L. Ceccio
Simo A. Mäkiharju*
Affiliation:
Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
Brian R. Elbing
Affiliation:
Mechanical Engineering, Oklahoma State University, Stillwater, OK 74078, USA
Andrew Wiggins
Affiliation:
Naval Architecture and Marine Engineering, University of Michigan, Ann Arbor, MI 48109, USA
Sarah Schinasi
Affiliation:
Naval Architecture and Marine Engineering, University of Michigan, Ann Arbor, MI 48109, USA
Jean-Marc Vanden-Broeck
Affiliation:
Mathematics Department, University College London, London WC1E 6BT, UK
Marc Perlin
Affiliation:
Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA Naval Architecture and Marine Engineering, University of Michigan, Ann Arbor, MI 48109, USA
David R. Dowling
Affiliation:
Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA Naval Architecture and Marine Engineering, University of Michigan, Ann Arbor, MI 48109, USA
Steven L. Ceccio
Affiliation:
Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA Naval Architecture and Marine Engineering, University of Michigan, Ann Arbor, MI 48109, USA
*
†Email address for correspondence: [email protected]
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Abstract

The behaviour of a nominally two-dimensional ventilated partial cavity was examined over a wide range of size scales and flow speeds to determine the influence of Froude, Reynolds, and Weber number on the cavity shape, dynamics, and gas entrainment rate. Two geometrically similar experiments were conducted with a 14:1 length scale ratio. The results were compared to a two-dimensional semi-analytical model of the cavity flow, and Froude scaling was found to be sufficient to match basic cavity shapes. However, the air flux required to maintain a stable cavity did not scale with Froude number alone, as the dynamics of the cavity closure changed with increasing Reynolds number. The required air flux differed over one order of magnitude between the lowest and highest Reynolds number flows. But, for sufficiently high Reynolds numbers, the rate of scaled entrainment appeared to approach Reynolds number independence. Modest changes in surface tension of the small-scale experiment suggested that the Weber number was important only at the lowest speeds and smaller length scale. Otherwise, the Weber numbers of the flows were sufficiently high to make the effects of interfacial tension negligible. We also observed that modest unsteadiness in the inflow to the large-scale cavity led to a significant increase in the required air flux needed to maintain a stable cavity, with the required excess gas flux nominally proportional to the flow’s perturbation amplitude. Finally, discussion is provided on how these results relate to model testing of partial cavity drag reduction (PCDR) systems for surface ships.

JFM classification

Flow Control: Drag reduction Multiphase and Particle-laden Flows: Multiphase flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 732 , 10 October 2013 , pp. 47 - 76
Copyright
©2013 Cambridge University Press 

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