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Research Papers: Multiphase Flows

Creation and Maintenance of Cavities Under Horizontal Surfaces in Steady and Gust Flows

[+] Author and Article Information
R. E. A. Arndt, W. T. Hambleton, E. Kawakami

Saint Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN 55414

E. L. Amromin

 Mechmath LLC, Prior Lake, MN 55372-1283

J. Fluids Eng 131(11), 111301 (Oct 13, 2009) (10 pages) doi:10.1115/1.4000241 History: Received March 18, 2008; Revised September 02, 2009; Published October 13, 2009

An experimental study of air supply to bottom cavities stabilized within a recess under a horizontal surface has been carried out in a specially designed water tunnel. The air supply necessary for creating and maintaining an air cavity in steady and gust flows has been determined over a wide range of speed. Flux-free ventilated cavitation at low flow speeds has been observed. Stable multiwave cavity forms at subcritical values of Froude number were also observed. It was found that the cross-sectional area of the air supply ducting has a substantial effect on the air demand. Air supply scaling laws were deduced and verified with the experimental data obtained.

Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Normalized drag coefficient CD of the OK-2003 hydrofoil at 6-deg angle of attack with natural cavitation (NC) and ventilated cavitation (VC). CD0 is drag coefficient for cavitation-free conditions

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Figure 2

Buttocks with a bottom recess, computed cavities of length LC=0.55L and stern seals of computed shape at various Fr. All buttocks coincide upstream of the stern seals (x≈0.75). One can see that an increase in Fr leads to the increase in cavity tail thickness by dh. For ventilated cavitation, this increase in tail thickness will result in a drag penalty and an additional air demand.

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Figure 3

Normalized air supply versus flow speed for σ=0.05 and ambient pressure of 2 atms

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Figure 11

Comparison of cavity surfaces under the new model in steady flow of 1 m/s speed (at subcritical speed, in the top), 1.5 m/s (in the middle), and 2 m/s (in the bottom). Bubble density on the cavity sharply increases with the speed.

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Figure 12

Cavity shapes under the first model at an intermediate Fr=0.41. Flow is from left to right.

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Figure 13

Measured air flux/demand for creating and maintaining bottom cavities in steady flow together with its scaling dependencies deduced below

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Figure 14

(a) Normalized ratio of air initial velocity UA to the water velocity U and (b) effect of this velocity on air demand. Data O-C and O-M relate to the old model and coincide, with given in Fig. 1; data W-C and W-M describe cavity creation and maintenance for the old model with widened holes for air supply.

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Figure 15

Comparison of cavity shapes for the old model with initial (two upper photos) and widened ducting of the air supply (two lower photos) at U=1 m/s (first and third photos from the top) and U=4 m/s (second and fourth photos from the top)

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Figure 22

Wavelength effect on shape of ventilated cavities on the hydrofoil OK-2003 at the same cavitation number and wave amplitude. T is the wave period. The flow is from right to left.

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Figure 23

Air demand for creation (top) and maintenance (bottom) of the cavity under the old model for various ratios of wavelength to the body length

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Figure 24

Air demand for creation and maintenance of bottom cavities under wave impact for the new model versus speed at the different wavelengths. Data for cavity creation are marked by C, data for cavity maintenance are marked by M. Values of ratio of wavelength λ to the model length L are shown in the legend (M-0.25 means maintenance of cavity for wavelength λ=0.25L, etc.)

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Figure 25

Dimensionless ratio Q∗/max Q∗ versus flow speed for different wavelengths. Rhombuses corresponds to λ=0.5L, squares to 0.75L and triangles to L.

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Figure 26

Comparison of unsteady air flux with the total volume of cavity fragments moving through its tail and calculated with the use of video recording. Due to the large error in measuring the bubble volume flux, the excellent agreement shown can only be consider fortuitous until further study.

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Figure 16

View of the gust simulator installed in the tunnel (top) Flow is from left to right. A schematic of the setup is also shown (bottom).

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Figure 17

Computationally estimated effect of distance from the wall Y on gust magnitude (top; the heights of the water tunnel test section ≈0.2 m) and dependency of RPM on flow speed at fixed wavelength (bottom). The model bottom is at 0.025 m from the wall.

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Figure 18

Extrapolated dependency of the middle plane measured max{v}/U on flap frequency for a 6.35 cm distance from the wall (top) in comparison with measured v for U=4 m/s (bottom). This position relative to the model is 3.81 cm directly below the aft end of the bow where the cavity forms.

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Figure 19

Two opposite phases of cavity oscillation for Fr=2.3 and λ=0.5L under the old model

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Figure 20

Different phases of cavity oscillation under the new model for the wave of wavelength λ=0.75L at the flow speed 3 m/s (left) and at 6 m/s (right)

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Figure 21

Different phases of cavity oscillation under impact of the wave of wavelength λ=L (left) and λ=0.5L (right; this wavelength coincides with the cavity length) at the same flow speed 3 m/s.

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Figure 4

Experiment setup in SAFL water tunnel. The bottom of the ship is modeled with a variable bow B and stern D that replace the water tunnel ceiling. For steady flows, the flaps are immobile.

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Figure 5

Views of the model: dry (above) and wetted with a cavity in the water tunnel (bottom). The air supply is discharged at the backward step of where cavity detachment occurs

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Figure 6

Buttock comparison for the old (first) model (solid curve) and new (second) model (dashed curve). All coordinates are normalized by the body length L. The cutout length is 0.5L as shown. Note the expanded vertical scale.

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Figure 7

View of several cavities under the first model. These and the following photos of the air cavities have been obtained through the glass wall. Flow is from left to right. The top photo shows a steady cavity at U=1 m/s and Q=0 (no air supply for cavity maintenance is necessary in this case, though its generation required some initial air supply). The middle photo shows a steady cavity at U=6.5 m/s and Q=27.5 l/min. The bottom photos shows an expanding cavity at U=4 m/s and Q=40 LPM.

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Figure 8

Cavity creation under the first model at the water tunnel speed U=1.1 m/s. Air supply rate QC=0.5 l/min; dt is the cavity creation time, photos were made with the time step dt/5. Flow is from left to right.

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Figure 9

Cavity creation under the first model at the water tunnel speed U=7 m/s with the air supply rate QC=57.5 l/min; dt is the cavity creation time and t1 is considered as the moment of creation start. Flow is from left to right.

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Figure 10

Cavity steady shapes under the first model at low water tunnel speeds. Froude number is defined as Fr=U/(gL)1/2, where L is the model length. The top photo relates to Fr=0.504, the second to Fr=0.446, the third to Fr=0.29, and the fourth to Fr=0.2.

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