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Investigation of coupled air-water turbulent boundary layers using direct numerical simulations
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10.1063/1.3156013
/content/aip/journal/pof2/21/6/10.1063/1.3156013
http://aip.metastore.ingenta.com/content/aip/journal/pof2/21/6/10.1063/1.3156013

Figures

Image of FIG. 1.
FIG. 1.

Definition sketch of a coupled air-water turbulent Couette flow.

Image of FIG. 2.
FIG. 2.

Schematics of air and water coupling in the numerical scheme.

Image of FIG. 3.
FIG. 3.

Profiles of (a) mean velocity and (b) steamwise velocity fluctuation obtained from DNS with grid resolutions of (——) , (– – – –) , and (–⋅–⋅–) .

Image of FIG. 4.
FIG. 4.

Profiles of velocity fluctuations: (– – – –) , (–⋅–⋅–) , (–⋅⋅–⋅⋅–) , and (——) . (b) , (c) , and (d) with comparison at various boundaries: (——) waterside near the interface, (– – – –) waterside near the bottom wall, (– –) airside near the interface, and (– –) airside near the top wall. Note that in (a), the velocities in the air and water domains are different.

Image of FIG. 5.
FIG. 5.

Comparison of mean velocity profiles of air and water near various boundaries in local coordinates. (●) water near the bottom wall, (◼) air near the top wall, (○) water near the interface, (◻) air near the interface, (– – – –) , (–⋅–⋅–) , and (–⋅⋅–⋅⋅–) . Plotted are the differences between the mean velocity and the respective boundary speed.

Image of FIG. 6.
FIG. 6.

[(a) and (b)] Profiles of vorticity fluctuations normalized by the corresponding value in each domain: (– – – –) , (–⋅–⋅–) , (–⋅⋅–⋅⋅–) , and (——) . (c) , (d) , and (e) with comparison at various boundaries: (——) waterside near the interface, (– – – –) waterside near the bottom wall, (–⋅–⋅–) airside near the interface, and (–⋅⋅–⋅⋅–) airside near the top wall.

Image of FIG. 7.
FIG. 7.

Profiles of TKE budget terms: (——) production, (– – – –) turbulence transport, (–⋅–⋅–) viscous diffusion, and (— —) dissipation. All the terms are normalized by the value of in the corresponding air or water domain.

Image of FIG. 8.
FIG. 8.

Comparison of TKE budget terms near various boundaries: (a) production, (b) viscous diffusion, (c) turbulence transport, and (d) dissipation. (——) Waterside near the interface, (– – – –) waterside near the bottom wall, (– –) airside near the interface, and (– –) airside near the top wall. All of the terms are normalized by the value of in the corresponding air or water domain and are plotted in local coordinates.

Image of FIG. 9.
FIG. 9.

Contours of steamwise velocity fluctuations on horizontal planes with different distances from the interface.

Image of FIG. 10.
FIG. 10.

Profiles of Taylor scales in [(a) and (b)] air and [(c) and (d)] water near the interface. [(a) and (c)] (——) , (– – – –) , and (–⋅–⋅–) . [(b) and (d)] (——) , (– – – –) , and (–⋅–⋅–) .

Image of FIG. 11.
FIG. 11.

Coherent vortices in water and interface contours of . The vortex structures are represented by the isosurface of the second largest eigenvalue of the tensor . In (a), representative structures of hairpin, interface-attached, and quasistreamwise vortices are marked. From (a) to (d), evolution of the hairpin vortex is highlighted by the circle.

Image of FIG. 12.
FIG. 12.

Definition sketch of two-dimensional vortex inclination angles and . The angle is from the positive- axis to the vortex projected to the ( , ) plane , and is from the positive- axis to the vortex projected to the ( , ) plane .

Image of FIG. 13.
FIG. 13.

Histograms of two-dimensional vortex inclination angles, and , at representative distances from the interface.

Image of FIG. 14.
FIG. 14.

Hairpin vortex in water near the interface in the conditionally averaged field. The vortex structure is represented by the isosurface of the second largest eigenvalue of the tensor .

Image of FIG. 15.
FIG. 15.

Vectors of velocity fluctuations ( , ) and contours of surface divergence on a vertical cross section passing through the center of the splat in a conditionally averaged flow field. The airside and the waterside motions are not plotted with the same velocity scales.

Image of FIG. 16.
FIG. 16.

Vectors of velocity fluctuations ( , ) and contours of streamwise vorticity on a vertical cross section passing through the center of the waterside quasistreamwise vortex in a conditionally averaged flow field.

Image of FIG. 17.
FIG. 17.

Vectors of velocity fluctuations ( , ) and contours of transverse vorticity on a vertical cross section passing through the center of the waterside hairpin vortex in a conditionally averaged flow field.

Image of FIG. 18.
FIG. 18.

Contours of scalar concentration fluctuations (top figure) and scalar concentration (bottom figure) on a vertical cross section passing through the center of the waterside hairpin vortex in a conditionally averaged flow field. and .

Image of FIG. 19.
FIG. 19.

Contours of scalar concentration fluctuations (top figure) and scalar concentration (bottom figure) on a vertical cross section passing through the center of the waterside streamwise vortex in a conditionally averaged field. and .

Image of FIG. 20.
FIG. 20.

Profiles of scalar [(a) and (b)] mean concentrations and [(c) and (d)] concentration fluctuations: (– – – –) , , and ; (–⋅–⋅–) , , and ; (–⋅⋅–⋅⋅–) , , and ; (——) , , and . The concentration scales are different between the air and water domains.

Image of FIG. 21.
FIG. 21.

Comparison of scalar concentration variance budget terms near various boundaries: (i) waterside near the bottom wall, (ii) waterside near the interface, and (iii) airside near the interface. (a) Production, (b) viscous diffusion, (c) turbulence transport, and (d) dissipation. (– – – –) , , and ; (–⋅–⋅–) , , and ; (–⋅⋅–⋅⋅–) , , and ; (——) , , and . All terms are normalized by the corresponding values of for different cases in each air or water domain.

Tables

Generic image for table
Table I.

Fluid properties of air and water at and 1 atm.

Generic image for table
Table II.

Schmidt numbers of scalars in air and water, Ostwald’s solubilities, DNS values of airside and waterside transfer velocities (normalized by the top plate velocity ), and relative resistance in air and water.

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/content/aip/journal/pof2/21/6/10.1063/1.3156013
2009-06-26
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Investigation of coupled air-water turbulent boundary layers using direct numerical simulations
http://aip.metastore.ingenta.com/content/aip/journal/pof2/21/6/10.1063/1.3156013
10.1063/1.3156013
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