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Research Papers: Multiphase Flows

# An Examination of Trapped Bubbles for Viscous Drag Reduction on Submerged Surfaces

[+] Author and Article Information
Kelly A. Stephani

Department of Aerospace Engineering and Engineering Mechanics, University of Texas at Austin, 1 University Station, C0600 Austin, TX 78712-0235kelly.stephani@mail.utexas.edu

David B. Goldstein

Department of Aerospace Engineering and Engineering Mechanics, University of Texas at Austin, 1 University Station, C0600 Austin, TX 78712-0235david@cfdlab.ae.utexas.edu

J. Fluids Eng 132(4), 041303 (Apr 20, 2010) (9 pages) doi:10.1115/1.4001273 History: Received June 27, 2008; Revised February 09, 2010; Published April 20, 2010; Online April 20, 2010

## Abstract

Viscous drag reduction on a submerged surface can be obtained both in the limit of an unbroken gas film coating the solid and in the nanobubble or perhaps microbubble coating regime when an air layer is created with superhydrophobic coatings. We examine an intermediate bubble size regime with a trapped-bubble array (TBA) formed in a tap water environment using electrolysis to grow and maintain bubbles in thousands of millimeter-sized holes on a solid surface. We show that even though surface tension is sufficient to stabilize bubbles in a TBA against hydrostatic and shear forces beneath a turbulent boundary layer, no drag reduction is obtained. Drag measurements were acquired over Reynolds numbers based on plate length ranging from $7.2×104 using either a force balance for plates mounted in a vertical orientation, or by performing a momentum integral balance using a wake survey for a flat plate mounted in either vertical or horizontal orientation. In that the drag forces were small, emphasis was placed on minimizing experimental uncertainty. For comparison, the flow over a flat plate covered on one side by a large uninterrupted gas film was examined and found to produce large drag reductions of up to 32%.

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## Figures

Figure 5

Proximity sensor setup used in force balance measurements

Figure 1

Schematic of flat acrylic test plate assembly in vertical orientation with dark gray bubble plate inserts and thin flexures: (a) detailed view of the elliptical leading edge and (b) detailed view of the tapered trailing edge

Figure 2

Acrylic plate with large trapped bubble mounted horizontally in the test section

Figure 3

Vertically mounted plate in the water tunnel test section. Test plate, cathodes, and anode are outlined for clarity.

Figure 4

Photograph of TBA during electrolysis (left). Schematic of the electrolysis process for trapped-bubble formation (right).

Figure 6

Sample velocity profiles acquired at upstream and downstream stations of a horizontally mounted plate

Figure 7

Sample velocity profiles acquired at upstream and downstream stations of a vertically mounted plate

Figure 8

Reynolds ridge formation on the surface of a large trapped bubble. Note that the Reynolds ridge is nearly straight and spans virtually the entire bubble width. View taken from an oblique angle below bubble (see schematic).

Figure 9

Streamwise mean (line with open symbols) and rms (filled symbols) velocity profiles acquired over a large trapped bubble at three streamwise locations from y/δ=0 (y=0 mm, on the surface) to y/δ=5(y=20 mm) with U∞=0.17 m/s, where δ is based on 0.95U∞. Measurements taken at x=0.127 m from the leading edge correspond to the solid flat plate surface, x=0.234 m corresponds to the clean portion of the trapped bubble, and x=0.323 m corresponds to the contaminated portion of the trapped bubble (approximately 3 cm downstream of the Reynolds ridge).

Figure 10

Streamwise mean (line with symbols) and rms (filled symbols) velocity profiles acquired over a solid flat plate surface at three streamwise locations from y/δ=0 (surface) to y/δ=3 with U∞=0.17 m/s, where δ is based on 0.95U∞. Measurements taken at x=0.127 m are identical to the data set presented in Fig. 9. Measurements at x=0.234 m correspond to the second measurement location in Fig. 9, x=0.640 m corresponds to the end of the trapped-bubble array.

Figure 11

Drag profiles obtained by the LDA wake survey over a range of Reynolds numbers based on plate length (1.1×105<ReL<3.1×105) for a horizontal flat plate and a horizontal plate with a large trapped bubble. The one-seventh power law solution accounts for laminar flow up to the boundary layer trips, drag due to the trips and turbulent flow downstream of trips.

Figure 12

Drag measurements obtained for a vertical flat plate (7.2×104<ReL<3.1×105) with and without trapped bubbles using LDA and proximity sensor measurement systems. The one-seventh power law solution accounts for laminar flow up to the boundary layer trips, drag due to the trips and turbulent flow downstream of trips, and drag contributions from flexures (for vertical plate case). Error bars (based on a 95% level of confidence) are included for the proximity sensor data but are very small.

Figure 13

Detailed plot of proximity sensor drag measurements (triangle symbols) corresponding to ReL=1.15×105 from Fig. 1. Error bars are based on a 95% level of confidence. Circle symbol shows 7.8% increase in drag due to an additional roughness element affixed to the plate in comparison to a calculated 9.8% drag increase seen with the open diamond symbol.

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