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Wake behind a three-dimensional dry transom stern. Part 1. Flow structure and large-scale air entrainment

Published online by Cambridge University Press:  26 July 2019

Kelli Hendrickson Open the ORCID record for Kelli Hendrickson [Opens in a new window] ,
Gabriel D. Weymouth Open the ORCID record for Gabriel D. Weymouth [Opens in a new window] ,
Xiangming Yu  and
Dick K.-P. Yue Open the ORCID record for Dick K.-P. Yue [Opens in a new window]
Kelli Hendrickson*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Gabriel D. Weymouth
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Xiangming Yu
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Dick K.-P. Yue
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: khendrk@mit.edu
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Abstract

We present high-resolution implicit large eddy simulation (iLES) of the turbulent air-entraining flow in the wake of three-dimensional rectangular dry transom sterns with varying speeds and half-beam-to-draft ratios $B/D$. We employ two-phase (air/water), time-dependent simulations utilizing conservative volume-of-fluid (cVOF) and boundary data immersion (BDIM) methods to obtain the flow structure and large-scale air entrainment in the wake. We confirm that the convergent-corner-wave region that forms immediately aft of the stern wake is ballistic, thus predictable only by the speed and (rectangular) geometry of the ship. We show that the flow structure in the air–water mixed region contains a shear layer with a streamwise jet and secondary vortex structures due to the presence of the quasi-steady, three-dimensional breaking waves. We apply a Lagrangian cavity identification technique to quantify the air entrainment in the wake and show that the strongest entrainment is where wave breaking occurs. We identify an inverse dependence of the maximum average void fraction and total volume entrained with $B/D$. We determine that the average surface entrainment rate initially peaks at a location that scales with draft Froude number and that the normalized average air cavity density spectrum has a consistent value providing there is active air entrainment. A small parametric study of the rectangular geometry and stern speed establishes and confirms the scaling of the interface characteristics with draft Froude number and geometry. In Part 2 (Hendrikson & Yue, J. Fluid Mech., vol. 875, 2019, pp. 884–913) we examine the incompressible highly variable density turbulence characteristics and turbulence closure modelling.

JFM classification

Wakes/Jets: Wakes Waves/Free-surface Flows: Wave breaking Multiphase and Particle-laden Flows: Multiphase flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 875 , 25 September 2019 , pp. 854 - 883
Copyright
© 2019 Cambridge University Press 

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Footnotes

‡

Present address: Southampton Marine and Maritime Institute, University of Southampton, SO16 7QF, UK.

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Hendrickson Supplementary Movie 1

Instantaneous isosurface of volume fraction f=0.5 for B/D=1, Fr=2.53 within the interrogation domain. Flow is from left to right (+x). Viewed from above.

Download Hendrickson Supplementary Movie 1(Video)
Video 10.4 MB

Hendrickson Supplementary Movie 2

Instantaneous isosurface of volume fraction f=0.5 for B/D=1, Fr=2.53 within the interrogation domain. Flow is from left to right (+x). Viewed from side.

Download Hendrickson Supplementary Movie 2(Video)
Video 8.3 MB

Hendrickson Supplementary Movie 3

Instantaneous isosurface of volume fraction f=0.5 for B/D=1.25, Fr=2.53 within the interrogation domain. Flow is from left to right (+x). Viewed from above.

Download Hendrickson Supplementary Movie 3(Video)
Video 11.3 MB

Hendrickson Supplementary Movie 4

Instantaneous isosurface of volume fraction f=0.5 for B/D=1.25, Fr=2.53 within the interrogation domain. Flow is from left to right (+x). Viewed from side.

Download Hendrickson Supplementary Movie 4(Video)
Video 8.8 MB

Hendrickson Supplementary Movie 5

Instantaneous isosurface of volume fraction f=0.5 for B/D=1.77, Fr=2.53 within the interrogation domain. Flow is from left to right (+x). Viewed from above.

Download Hendrickson Supplementary Movie 5(Video)
Video 10 MB

Hendrickson Supplementary Movie 6

Instantaneous isosurface of volume fraction f=0.5 for B/D=1.77, Fr=2.53 within the interrogation domain. Flow is from left to right (+x). Viewed from side.

Download Hendrickson Supplementary Movie 6(Video)
Video 9.1 MB