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Controlled impact of a disk on a water surface: cavity dynamics

Published online by Cambridge University Press:  25 August 2009

RAYMOND BERGMANN ,
DEVARAJ VAN DER MEER ,
STEPHAN GEKLE ,
ARJAN VAN DER BOS  and
DETLEF LOHSE
RAYMOND BERGMANN
Affiliation:
Department of Applied Physics and J. M. Burgers Centre for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
DEVARAJ VAN DER MEER*
Affiliation:
Department of Applied Physics and J. M. Burgers Centre for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
STEPHAN GEKLE
Affiliation:
Department of Applied Physics and J. M. Burgers Centre for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
ARJAN VAN DER BOS
Affiliation:
Department of Applied Physics and J. M. Burgers Centre for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
DETLEF LOHSE
Affiliation:
Department of Applied Physics and J. M. Burgers Centre for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
*
‡Email address for correspondence: [email protected]
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Abstract

In this paper we study the transient surface cavity which is created by the controlled impact of a disk of radius h0 on a water surface at Froude numbers below 200. The dynamics of the transient free surface is recorded by high-speed imaging and compared to boundary integral simulations giving excellent agreement. The flow surrounding the cavity is measured with high-speed particle image velocimetry and is found to also agree perfectly with the flow field obtained from the simulations.

We present a simple model for the radial dynamics of the cavity based on the collapse of an infinite cylinder. This model accounts for the observed asymmetry of the radial dynamics between the expansion and the contraction phases of the cavity. It reproduces the scaling of the closure depth and total depth of the cavity which are both found to scale roughly as ∝ Fr1/2 with a weakly Froude-number-dependent prefactor. In addition, the model accurately captures the dynamics of the minimal radius of the cavity and the scaling of the volume Vbubble of air entrained by the process, namely, Vbubble/h03∝(1 + 0.26Fr1/2)Fr1/2.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 633 , 25 August 2009 , pp. 381 - 409
Copyright
Copyright © Cambridge University Press 2009

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