Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-19T02:31:04.831Z Has data issue: false hasContentIssue false
  • English
  • Français

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: smakihar@umich.edu
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Amromin, E. & Minize, I. 2003 Partial cavitation as drag reduction technique and problem of active flow control. Mar. Engng 40 (3), 181–188.Google Scholar
Amromin, E., Karafiath, G. & Metcalf, B. 2011 Ship drag reduction by air bottom ventilated cavitation in calm water and in waves. J. Ship Res. 55 (3), 196–207.CrossRefGoogle Scholar
Arndt, R. E. A., Hambleton, W. T., Kawakami, E. & Amromin, E. L. 2009 Creation and maintenance of cavities under horizontal surfaces in steady and gust flows. J. Fluids Engng 131, 111301.CrossRefGoogle Scholar
Butuzov, A. A. 1967 Artificial cavitation flow behind a slender wedge on the lower surface of a horizontal wall. Fluid Dyn. 3, 56–58.Google Scholar
Callenaere, M., Franc, J.-P., Michel, J.-M. & Riondet, M. 2001 The cavitation instability induced by the development of a re-entrant jet. J. Fluid Mech. 444, 223–256.Google Scholar
Ceccio, S. L. 2010 Friction drag reduction of external flows with bubble and gas injection. Annu. Rev. Fluid Mech. 42, 183–203.CrossRefGoogle Scholar
Chanson, H. 1996 Air Entrainment in Free-surface Turbulent Shear Flows. Academic.Google Scholar
Choi, K.-S., Prasad, K. K. & Truong, T. V. (Eds) 1996 Emerging Techniques in Drag Reduction. Mechanical Engineering Publications Limited.Google Scholar
Elbing, B. R., Winkel, E. S., Lay, K. A., Ceccio, S. L., Dowling, D. R. & Perlin, M. 2008 Bubble-induced skin-friction drag reduction and the abrupt transition to air-layer drag reduction. J. Fluid Mech. 612, 201–236.CrossRefGoogle Scholar
Etter, R. J., Cutbirth, J. M., Ceccio, S. L., Dowling, D. R. & Perlin, M. 2005 High Reynolds number experimentation in the US Navy’s William B. Morgan large cavitation channel. Meas. Sci. Technol. 16, 1701–1709.Google Scholar
Foeth, E.-J. 2011 Projects prove that air cavities reduce ship resistance. Maritime Reporter and Marine News 12, 16.Google Scholar
Gokcay, S., Insel, M. & Odabasi, A. Y. 2004 Revisiting artificial air cavity concept for high speed craft. Ocean Engng 31, 253–267.Google Scholar
Gorbachev, Y. & Amromin, E. 2012 Ship Drag Reduction by Hull Ventilation From Laval to Near Future: Challenges and Successes. ATMA 2012.Google Scholar
Evangelista, J. (Ed.) 2011 Airship of the sea. Surveyor: A Quarterly Magazine from ABS 3, 10–15.Google Scholar
Kiger, K. T. & Duncan, J. H. 2012 Air-entrainment mechanisms in plunging jets and breaking waves. Annu. Rev. Fluid Mech. 44, 563–596.CrossRefGoogle Scholar
Kodama, Y., Kakugawa, A., Takahashi, T. & Kawashima, H. 2000 Experimental study on microbubbles and their applicability to ships for skin friction reduction. Intl J. Heat Fluid Flow 21, 582–588.CrossRefGoogle Scholar
Kopriva, J., Arndt, R. E. A. & Amromin, E. L. 2008 Improvement of hydrofoil performance by partial ventilated cavitation in steady flow and periodic gusts. J. Fluids Engng 130 (3), 031301.Google Scholar
Lapham, G. S., Dowling, D. R. & Schultz, W. W. 1999 In situ force-balance tensiometry. Exp. Fluids 27 (2), 157–166.Google Scholar
Lay, K. A., Yakushiji, R., Mäkiharju, S., Perlin, M. & Ceccio, S. L. 2010 Partial cavity drag reduction at high Reynolds numbers. J. Ship Res. 54 (2), 109–119.CrossRefGoogle Scholar
Le, Q., Franc, J. P. & Michel, J. M. 1993 Partial cavities: global behavior and mean pressure distribution. J. Fluids Engng 115 (2), 243–248.Google Scholar
Liu, X. & Duncan, J. H. 2006 An experimental study of surfactant effects on spilling breakers. J. Fluid Mech. 567, 433–455.CrossRefGoogle Scholar
Madavan, N. K., Deutsch, S. & Merkle, C. L. 1985 Measurements of local skin friction in a microbubble modified turbulent boundary layer. J. Fluid Mech. 156, 237–256.CrossRefGoogle Scholar
Maki, K. J., Troesch, A. W. & Beck, R. F. 2008 Experiments on two-dimensional transom stern flow. J. Ship Res. 52 (4), 291–300.Google Scholar
Mäkiharju, S. (2012) The dynamics of ventilated partial cavities over a wide range of Reynolds numbers and quantitative 2D X-ray densitometry for multiphase Flow. PhD Thesis, University of Michigan.Google Scholar
Mäkiharju, S., Elbing, B. R., Wiggins, A., Dowling, D. R., Perlin, M. & Ceccio, S. L. 2010 Perturbed partial cavity drag reduction at high Reynolds numbers. In Proc. 28th Symposium on Naval Hydrodynamics, Pasadena, CA.Google Scholar
Matveev, K. I. 2007 Three-dimensional wave patterns in long air cavities on a horizontal plane. Ocean Engng 34, 1882–1891.CrossRefGoogle Scholar
Matveev, K. I., Burnett, T. J. & Ockfen, A. E. 2009 Study of air ventilated cavity under model hull on water surface. Ocean Engng 36, 930–940.Google Scholar
Park, J. T., Cutbirth, J. M. & Brewer, W. H. 2003 Hydrodynamic performance of the large cavitation channel (LCC). In Proc. 4th ASME–JSME Joint Fluids Engineering Conference, Honolulu, HI.Google Scholar
Ohtsu, I., Yasuda, Y. & Gotoh, H. 2011 Hydraulic condition for undular-jump formations. J. Hydraul. Res. 39 (2), 203–209.Google Scholar
Sanders, W. C., Winkel, E. S., Dowling, D. R., Perlin, M. & Ceccio, S. L. 2006 Bubble friction drag reduction in a high-Reynolds-number flat-plate turbulent boundary layer. J. Fluid Mech. 552, 353–380.Google Scholar
Schlichting, H. 1979 Boundary-Layer Theory, 7th English edn. McGraw-Hill.Google Scholar
Vanden-Broeck, J.-M. 1980 Nonlinear stern waves. J. Fluid Mech. 96, 601–610.Google Scholar
Vanden-Broeck, J.-M. 1996 Numerical calculations of the free-surface flow under a sluice gate. J. Fluid Mech. 330, 339–347.Google Scholar
Vanden-Broeck, J-M. 2010 Gravity–Capillary Free-Surface Flows. Cambridge University Press.CrossRefGoogle Scholar
White, C. M. & Mungal, M. G. 2008 Mechanics and prediction of turbulent drag reduction with polymer additives. Annu. Rev. Fluid Mech. 40, 235–256.Google Scholar
White, F. M. 2001 Fluid Mechanics, 5th edn. McGraw-Hill.Google Scholar
White, C. M., Dubief, Y. & Klewicki, J. 2012 Re-examining the logarithmic dependence of the mean velocity distribution in polymer drag reduced wall-bounded flow. Phys. Fluids 24.Google Scholar
Winkel, E. S., Ceccio, S. L., Dowling, D. R. & Perlin, M. 2004 Bubble-size distributions produced by wall injection of air into flowing freshwater, saltwater and surfactant solutions. Exp. Fluids 37, 802–810.CrossRefGoogle Scholar
Winkel, E. S., Oweis, G. F., Vanapalli, S. A., Dowling, D. R., Perlin, M., Solomon, M. J. & Ceccio, S. L. 2009 High-Reynolds-number turbulent boundary layer friction drag reduction from wall-injected polymer solutions. J. Fluid Mech. 621, 259–288.Google Scholar