The Emptying of a Perforated Bottle: Influence of Perforation Size on Emptying Time and the Physical Nature of the Process
An inverted bottle empties in a time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mrow><mi>e</mi><mo>,</mo><mn>0</mn></mrow></ms...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-08-01
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| Series: | Fluids |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2311-5521/8/8/225 |
| _version_ | 1797584802936782848 |
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| author | Callen Schwefler Peyton Nienaber Hans C. Mayer |
| author_facet | Callen Schwefler Peyton Nienaber Hans C. Mayer |
| author_sort | Callen Schwefler |
| collection | DOAJ |
| description | An inverted bottle empties in a time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mrow><mi>e</mi><mo>,</mo><mn>0</mn></mrow></msub></semantics></math></inline-formula> through a process called “glugging”, whereby gas and liquid compete at the neck (of diameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>D</mi><mi>N</mi></msub></semantics></math></inline-formula>). In contrast, an open-top container empties in a much shorter time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mi>e</mi></msub></semantics></math></inline-formula> through “jetting” due to the lack of gas–liquid competition. Experiments and theory demonstrate that, by introducing a perforation (diameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>d</mi><mi>p</mi></msub></semantics></math></inline-formula>), a bottle empties through glugging, jetting, or a combination of the two. For a certain range of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>d</mi><mi>p</mi></msub><mo>/</mo><msub><mi>D</mi><mi>N</mi></msub></mrow></semantics></math></inline-formula>, the perforation increases the emptying time, and a particular value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>d</mi><mi>p</mi></msub><mo>/</mo><msub><mi>D</mi><mi>N</mi></msub></mrow></semantics></math></inline-formula> is associated with a maximum emptying time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mrow><mi>e</mi><mo>,</mo><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></semantics></math></inline-formula>. We show that the transition from jetting to glugging is initiated by the jet velocity reaching a low threshold, thereby allowing a slug of air entry into the neck that stops jetting and starts the glugging. Once initiated, the glugging proceeds as though there is no perforation. Experimental results covered a range of Eötvös numbers from <i>Eo</i>∼ 20–200 (equivalent to a range of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>D</mi><mi>N</mi></msub><mo>/</mo><msub><mi>L</mi><mi>c</mi></msub><mo>∼</mo></mrow></semantics></math></inline-formula> 4–15, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mi>c</mi></msub></semantics></math></inline-formula> is the capillary length). The phenomenon of bottle emptying with a perforation adds to the body of bottle literature, which has already considered the influence of shape, inclination, liquid properties, etc. |
| first_indexed | 2024-03-10T23:57:52Z |
| format | Article |
| id | doaj.art-fcdf7c0d911548ce9ca1e9ff8d1d0636 |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-03-10T23:57:52Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-fcdf7c0d911548ce9ca1e9ff8d1d06362023-11-19T01:04:40ZengMDPI AGFluids2311-55212023-08-018822510.3390/fluids8080225The Emptying of a Perforated Bottle: Influence of Perforation Size on Emptying Time and the Physical Nature of the ProcessCallen Schwefler0Peyton Nienaber1Hans C. Mayer2Department of Mechanical Engineering, California Polytechnic State University, San Luis Obispo, CA 93407, USADepartment of Mechanical Engineering, California Polytechnic State University, San Luis Obispo, CA 93407, USADepartment of Mechanical Engineering, California Polytechnic State University, San Luis Obispo, CA 93407, USAAn inverted bottle empties in a time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mrow><mi>e</mi><mo>,</mo><mn>0</mn></mrow></msub></semantics></math></inline-formula> through a process called “glugging”, whereby gas and liquid compete at the neck (of diameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>D</mi><mi>N</mi></msub></semantics></math></inline-formula>). In contrast, an open-top container empties in a much shorter time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mi>e</mi></msub></semantics></math></inline-formula> through “jetting” due to the lack of gas–liquid competition. Experiments and theory demonstrate that, by introducing a perforation (diameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>d</mi><mi>p</mi></msub></semantics></math></inline-formula>), a bottle empties through glugging, jetting, or a combination of the two. For a certain range of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>d</mi><mi>p</mi></msub><mo>/</mo><msub><mi>D</mi><mi>N</mi></msub></mrow></semantics></math></inline-formula>, the perforation increases the emptying time, and a particular value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>d</mi><mi>p</mi></msub><mo>/</mo><msub><mi>D</mi><mi>N</mi></msub></mrow></semantics></math></inline-formula> is associated with a maximum emptying time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mrow><mi>e</mi><mo>,</mo><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></semantics></math></inline-formula>. We show that the transition from jetting to glugging is initiated by the jet velocity reaching a low threshold, thereby allowing a slug of air entry into the neck that stops jetting and starts the glugging. Once initiated, the glugging proceeds as though there is no perforation. Experimental results covered a range of Eötvös numbers from <i>Eo</i>∼ 20–200 (equivalent to a range of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>D</mi><mi>N</mi></msub><mo>/</mo><msub><mi>L</mi><mi>c</mi></msub><mo>∼</mo></mrow></semantics></math></inline-formula> 4–15, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mi>c</mi></msub></semantics></math></inline-formula> is the capillary length). The phenomenon of bottle emptying with a perforation adds to the body of bottle literature, which has already considered the influence of shape, inclination, liquid properties, etc.https://www.mdpi.com/2311-5521/8/8/225gluggingjettingair–water flowtwo-phase flowbubble risebottle |
| spellingShingle | Callen Schwefler Peyton Nienaber Hans C. Mayer The Emptying of a Perforated Bottle: Influence of Perforation Size on Emptying Time and the Physical Nature of the Process Fluids glugging jetting air–water flow two-phase flow bubble rise bottle |
| title | The Emptying of a Perforated Bottle: Influence of Perforation Size on Emptying Time and the Physical Nature of the Process |
| title_full | The Emptying of a Perforated Bottle: Influence of Perforation Size on Emptying Time and the Physical Nature of the Process |
| title_fullStr | The Emptying of a Perforated Bottle: Influence of Perforation Size on Emptying Time and the Physical Nature of the Process |
| title_full_unstemmed | The Emptying of a Perforated Bottle: Influence of Perforation Size on Emptying Time and the Physical Nature of the Process |
| title_short | The Emptying of a Perforated Bottle: Influence of Perforation Size on Emptying Time and the Physical Nature of the Process |
| title_sort | emptying of a perforated bottle influence of perforation size on emptying time and the physical nature of the process |
| topic | glugging jetting air–water flow two-phase flow bubble rise bottle |
| url | https://www.mdpi.com/2311-5521/8/8/225 |
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