Experimental Study on Flow Structure Characteristics of Gap Flow Boundary Layer Based on PIV
The boundary layer is the main source of frictional resistance in gap flow, and the study of the flow structure characteristics of the gap flow boundary layer is of great significance for the study of gap flow theory. In this study, the PIV technique was utilized to experimentally investigate the ga...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-11-01
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| Series: | Water |
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| Online Access: | https://www.mdpi.com/2073-4441/15/22/3989 |
| _version_ | 1797457443636117504 |
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| author | Lei Sun Xihuan Sun Yongye Li Cheng Wang |
| author_facet | Lei Sun Xihuan Sun Yongye Li Cheng Wang |
| author_sort | Lei Sun |
| collection | DOAJ |
| description | The boundary layer is the main source of frictional resistance in gap flow, and the study of the flow structure characteristics of the gap flow boundary layer is of great significance for the study of gap flow theory. In this study, the PIV technique was utilized to experimentally investigate the gap flow boundary layers with Reynolds numbers of 16,587–56,870 and gap ratios of 0.6–0.8. The characteristics of the wall friction velocity, the boundary layer thickness, and the wall function of the gap flow boundary layer were analyzed, and the influences of the mean velocity of the gap flow and the gap ratio on the flow structure characteristics of the boundary layer were explored. The results show that using PIV to measure the velocity profile in the viscous sub-layer to solve for the wall friction velocity had good precision. The boundary layer thickness was inversely proportional to the mean velocity of the gap flow and the gap ratio. The wall functions of the boundary layer were as follows: in the viscous sub-layer (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi>y</mi></mrow><mrow><mo>+</mo></mrow></msup><mo><</mo></mrow></semantics></math></inline-formula> 5.5), <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi>u</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>=</mo><msup><mrow><mi>y</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></semantics></math></inline-formula>; in the transition layer (5.5 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo><</mo><msup><mrow><mi>y</mi></mrow><mrow><mo>+</mo></mrow></msup><mo><</mo></mrow></semantics></math></inline-formula> 26), <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi>u</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>0.071</mn></mrow></mfrac><mi>t</mi><mi>a</mi><mi>n</mi><mi>h</mi><mfenced separators="|"><mrow><mn>0.071</mn><msup><mrow><mi>y</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></mfenced></mrow></semantics></math></inline-formula>; and in the logarithmic layer (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi>y</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>></mo></mrow></semantics></math></inline-formula> 26), <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi>u</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>=</mo><mn>2.78</mn><mi>l</mi><mi>n</mi><mfenced separators="|"><mrow><msup><mrow><mi>y</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></mfenced><mo>+</mo><mn>3.8</mn></mrow></semantics></math></inline-formula>. The thickness of the logarithmic layer was proportional to the mean velocity of the gap flow and inversely proportional to the gap ratio. The inner region of the boundary layer extended to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>y</mi><mo><</mo></mrow></semantics></math></inline-formula> 0.18<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>δ</mi></mrow></semantics></math></inline-formula> or <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>y</mi><mo><</mo></mrow></semantics></math></inline-formula> 0.13(<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>h</mi></mrow></semantics></math></inline-formula>/2). |
| first_indexed | 2024-03-09T16:22:15Z |
| format | Article |
| id | doaj.art-000ecca8cd0244be8a38cf8017c166e6 |
| institution | Directory Open Access Journal |
| issn | 2073-4441 |
| language | English |
| last_indexed | 2024-03-09T16:22:15Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Water |
| spelling | doaj.art-000ecca8cd0244be8a38cf8017c166e62023-11-24T15:11:32ZengMDPI AGWater2073-44412023-11-011522398910.3390/w15223989Experimental Study on Flow Structure Characteristics of Gap Flow Boundary Layer Based on PIVLei Sun0Xihuan Sun1Yongye Li2Cheng Wang3College of Water Resources Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, ChinaCollege of Water Resources Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, ChinaCollege of Water Resources Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, ChinaCollege of Water Resources Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, ChinaThe boundary layer is the main source of frictional resistance in gap flow, and the study of the flow structure characteristics of the gap flow boundary layer is of great significance for the study of gap flow theory. In this study, the PIV technique was utilized to experimentally investigate the gap flow boundary layers with Reynolds numbers of 16,587–56,870 and gap ratios of 0.6–0.8. The characteristics of the wall friction velocity, the boundary layer thickness, and the wall function of the gap flow boundary layer were analyzed, and the influences of the mean velocity of the gap flow and the gap ratio on the flow structure characteristics of the boundary layer were explored. The results show that using PIV to measure the velocity profile in the viscous sub-layer to solve for the wall friction velocity had good precision. The boundary layer thickness was inversely proportional to the mean velocity of the gap flow and the gap ratio. The wall functions of the boundary layer were as follows: in the viscous sub-layer (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi>y</mi></mrow><mrow><mo>+</mo></mrow></msup><mo><</mo></mrow></semantics></math></inline-formula> 5.5), <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi>u</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>=</mo><msup><mrow><mi>y</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></semantics></math></inline-formula>; in the transition layer (5.5 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo><</mo><msup><mrow><mi>y</mi></mrow><mrow><mo>+</mo></mrow></msup><mo><</mo></mrow></semantics></math></inline-formula> 26), <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi>u</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>0.071</mn></mrow></mfrac><mi>t</mi><mi>a</mi><mi>n</mi><mi>h</mi><mfenced separators="|"><mrow><mn>0.071</mn><msup><mrow><mi>y</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></mfenced></mrow></semantics></math></inline-formula>; and in the logarithmic layer (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi>y</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>></mo></mrow></semantics></math></inline-formula> 26), <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi>u</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>=</mo><mn>2.78</mn><mi>l</mi><mi>n</mi><mfenced separators="|"><mrow><msup><mrow><mi>y</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></mfenced><mo>+</mo><mn>3.8</mn></mrow></semantics></math></inline-formula>. The thickness of the logarithmic layer was proportional to the mean velocity of the gap flow and inversely proportional to the gap ratio. The inner region of the boundary layer extended to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>y</mi><mo><</mo></mrow></semantics></math></inline-formula> 0.18<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>δ</mi></mrow></semantics></math></inline-formula> or <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>y</mi><mo><</mo></mrow></semantics></math></inline-formula> 0.13(<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>h</mi></mrow></semantics></math></inline-formula>/2).https://www.mdpi.com/2073-4441/15/22/3989gap flowboundary layergap ratiowall functionwall friction velocity |
| spellingShingle | Lei Sun Xihuan Sun Yongye Li Cheng Wang Experimental Study on Flow Structure Characteristics of Gap Flow Boundary Layer Based on PIV Water gap flow boundary layer gap ratio wall function wall friction velocity |
| title | Experimental Study on Flow Structure Characteristics of Gap Flow Boundary Layer Based on PIV |
| title_full | Experimental Study on Flow Structure Characteristics of Gap Flow Boundary Layer Based on PIV |
| title_fullStr | Experimental Study on Flow Structure Characteristics of Gap Flow Boundary Layer Based on PIV |
| title_full_unstemmed | Experimental Study on Flow Structure Characteristics of Gap Flow Boundary Layer Based on PIV |
| title_short | Experimental Study on Flow Structure Characteristics of Gap Flow Boundary Layer Based on PIV |
| title_sort | experimental study on flow structure characteristics of gap flow boundary layer based on piv |
| topic | gap flow boundary layer gap ratio wall function wall friction velocity |
| url | https://www.mdpi.com/2073-4441/15/22/3989 |
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