Air-Water Bubbly Flow by Multiple Vents on a Hydrofoil in a Steady Free-Stream
Flow features, due to air injection through multiple vents on the surface of a hydrofoil inclined at an angle with respect to the free-stream in a cavitation tunnel, are presented here. The hydrofoil, with a chord length, <i>c</i>, is oriented at the angle of inclination, <inline-form...
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| Autores principales: | , , , , , |
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| Formato: | article |
| Lenguaje: | EN |
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MDPI AG
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/8a780d68cced445cbace27a90aaef97f |
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| Sumario: | Flow features, due to air injection through multiple vents on the surface of a hydrofoil inclined at an angle with respect to the free-stream in a cavitation tunnel, are presented here. The hydrofoil, with a chord length, <i>c</i>, is oriented at the angle of inclination, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> = 3.5°. The Froude number, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>n</mi></mrow></semantics></math></inline-formula>, based on the free-stream velocity, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>V</mi><mo>∞</mo></msub></semantics></math></inline-formula>, and air injection vent diameter, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>d</mi><mi>h</mi></msub></semantics></math></inline-formula>, is 30.30, 50.51 and 70.71. Air is injected through multiple vents on the hydrofoil at the non-dimensional air injection coefficient, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>C</mi><mi>q</mi></msub><mo>∼</mo><mn>16</mn><mo>−</mo><mn>8917</mn></mrow></semantics></math></inline-formula>. The air bubble packing per unit area is quantified using spatial density, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>S</mi><mi>D</mi></msub></semantics></math></inline-formula>, at various combinations of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>n</mi><mo>,</mo><msub><mi>C</mi><mi>q</mi></msub></mrow></semantics></math></inline-formula> based on a high-speed video from the side view. The time-averaged spatial density, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo><</mo><msub><mi>S</mi><mi>D</mi></msub><mo>></mo></mrow></semantics></math></inline-formula>, is observed to increase in a logarithmic manner with an increase in the air injection rate, <i>Q</i>, at various Froude numbers. There is an increase in the mean spatial density of the bubbles with the increase in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>C</mi><mi>q</mi></msub></semantics></math></inline-formula> at all <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>n</mi></mrow></semantics></math></inline-formula>. A power–law relation is shown to exist between the time-averaged spatial density, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo><</mo><msub><mi>S</mi><mi>D</mi></msub><mo>></mo></mrow></semantics></math></inline-formula>, and the non-dimensional flow variables, Reynolds number, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>R</mi><mi>e</mi></mrow><mrow><mi>a</mi><mi>i</mi><mi>r</mi></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>n</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>C</mi><mi>q</mi></msub></semantics></math></inline-formula> based on a regression analysis. By tracking individual finite volume bubbles flowing with the free-stream, the bubble dimensions in pixels are quantified using quantities such as the deformation rate, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula>, and standardization, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ϵ</mi><mi>S</mi></msub></semantics></math></inline-formula>, from the side-view videos. It is observed that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ϵ</mi><mi>S</mi></msub></semantics></math></inline-formula> change with time, even as they become advected with the free-stream. Through high-speed imaging from the top view, we characterize the bubbly flow features’ time-averaged thickness, <i>t</i>, at various combinations of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>n</mi><mo>,</mo><msub><mi>C</mi><mi>q</mi></msub></mrow></semantics></math></inline-formula> at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> = 3.5°. We obtain a power-law relation between the non-dimensional time-averaged jet thickness, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>t</mi><mo>/</mo><mi>c</mi></mrow></semantics></math></inline-formula>, and the non-dimensional flow parameters such as, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>R</mi><mi>e</mi></mrow><mrow><mi>a</mi><mi>i</mi><mi>r</mi></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>n</mi><mo>,</mo><msub><mi>C</mi><mi>q</mi></msub></mrow></semantics></math></inline-formula> and the non-dimensional streamwise distance, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>x</mi><mo>/</mo><msub><mi>x</mi><mrow><mi>r</mi><mi>e</mi><mi>f</mi></mrow></msub></mrow></semantics></math></inline-formula>, based on a regression analysis, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>x</mi><mrow><mi>r</mi><mi>e</mi><mi>f</mi></mrow></msub></semantics></math></inline-formula> is a reference distance. The results are relevant to engineering applications where the air–water bubbly flow in a free-stream is important. |
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