Research Papers: Multiphase Flows

Microbubble Drag Reduction Downstream of Ventilated Partial Cavity

[+] Author and Article Information
Eduard Amromin

 Mechmath LLC, Prior Lake, MN 55372-1283

J. Fluids Eng 132(5), 051302 (May 13, 2010) (5 pages) doi:10.1115/1.4001489 History: Received March 31, 2009; Revised March 19, 2010; Published May 13, 2010; Online May 13, 2010

The effect of air flux from ventilated partial cavities on drag of bodies was studied. An integral equation method for estimation of air bubble effects on drag was employed and validated with earlier known experimental data for flat plates and bodies. The qualitative difference in the effects of flow speed and air supply rate on drag of flat plates and bodies was numerically confirmed and explained as a combined effect of the boundary layer density decrease and the increase in its displacement thickness. The numerical analysis shows reduction in the total drag of ventilated bodies with increasing air flux rate up to an optimum, but the drag rise for greater rates. A synergy of friction reduction under attached ventilated cavity and microbubble drag reduction downstream of it was shown.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

Comparison of computed (lines) and measured (symbols, after Ref. 11) effects of air volumetric ratio at the slot β0 on the drag ratio Cf/Cf0 for two measurement points and two speeds. The upper plot presents computations without air diffusion account in Eq. 2. The lower plot presents computation with air diffusion described by the law dβ/dx=−0.0025β/δ tuned to the experimental data (11). The first numbers in the legend indicate the distance from the plate leading edge to the point (in m). The second numbers indicate flow speed (in m/s). Letter T means theory (our computation) and E means experimental data.

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Figure 2

Comparison of computed and measured (after Ref. 11) distributions of the drag ratio Cf/Cf0 along the flat plate. The first numbers in the legend indicate the flow speed (in m/s). The second numbers indicate the value of β0. Letter T means theory (our computation) and E means experimental data.

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Figure 3

Effect of air supply on the ratio of drag coefficients for plates with air ejections on their different sides and for an axisymmetric body with air ejections (after Ref. 9; the abscissa axis is graduated by a parameter Q proportional to β0, but with an undetermined factor)

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Figure 4

Dependency of drag rate on the air flux Q for the ventilated hydrofoil OK-2003 (3)

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Figure 5

Buttock of a ship hull with cavities in a recess/niche (the dotted curve shows the cavity surface for Fr=0.54, and the solid curve shows the cavity surface for Fr=0.48). Flow goes from the left, and z is the vertical coordinate; z=0 corresponds to the free surface.

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Figure 6

Comparison of friction coefficient and pressure coefficients along the buttock shown in Fig. 5 at Fr=0.54 (solid line) and Fr=0.48 (dashed line) for β0=0.2

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Figure 7

Ratio of drag coefficient versus air concentration for the buttock shown in Fig. 5. The index M at the curves relates to the buttock of the 5.5 m length, and the index FS relates to 50 m length.

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Figure 8

Distributions of thickness displacement along the part of the buttock shown in Fig. 4 and in the wake near the stern at Fr=0.48 and different values of β0 (shown at the curves)



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