Shapes and terminal velocity of a drop rising in stagnant liquids
In this project, the effects of the density ratio 𝜂?, the viscosity ratio 𝜆?, the inverse viscosity number 𝑁?𝑓?, and the Eötvös number Eo on the shapes and terminal velocities of a drop rising in stagnant liquids are studied numerically using a front tracking method. It is found that mild variation...
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| Format: | Final Year Project (FYP) |
| Language: | English |
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2012
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| Online Access: | http://hdl.handle.net/10356/49435 |
| _version_ | 1826129719769169920 |
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| author | Liu, Lili. |
| author2 | School of Mechanical and Aerospace Engineering |
| author_facet | School of Mechanical and Aerospace Engineering Liu, Lili. |
| author_sort | Liu, Lili. |
| collection | NTU |
| description | In this project, the effects of the density ratio 𝜂?, the viscosity ratio 𝜆?, the inverse viscosity number 𝑁?𝑓?, and the Eötvös number Eo on the shapes and terminal velocities of a drop rising in stagnant liquids are studied numerically using a front tracking method. It is found that mild variation of 𝜂? barely changes the drop shape or terminal velocity, whereas 𝜆?, 𝑁?𝑓? and Eo significantly affect the drop dynamics. With the increase of 𝜆?, 𝑁?𝑓?, or Eo, the drop becomes either more dimpled or more crescent. When the drop is dimpled or ellipsoidal-cap, there is no recirculation flow in its rear. The recirculation zone appears and becomes larger when 𝜆? decreases or Eo increases. From the simulation results, the relationships between Fr, the non-dimensional terminal velocity of the drop, and 𝜆?, 𝑁?𝑓? and Eo are determined. For the correlation between Fr and 𝜆?, it is found that Fr= 𝑘?(1+𝐶?1𝜆?)/(2+𝐶?2𝜆?) for 5<𝑁?𝑓?<38, where 𝐶?1 = 1.245±0.165, and 𝐶?2 = 3.43±0.35, whereas Fr is a constant around 0.602 for 50<𝑁?𝑓?<100. The correlation between Fr and 𝑁?𝑓? follows a logarithmic trend for 𝑁?𝑓?<50. And Fr is also found to decrease with the increase of Eo. |
| first_indexed | 2024-10-01T07:44:45Z |
| format | Final Year Project (FYP) |
| id | ntu-10356/49435 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:44:45Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | ntu-10356/494352023-03-04T19:27:17Z Shapes and terminal velocity of a drop rising in stagnant liquids Liu, Lili. School of Mechanical and Aerospace Engineering Tang Hui DRNTU::Engineering::Mechanical engineering::Fluid mechanics In this project, the effects of the density ratio 𝜂?, the viscosity ratio 𝜆?, the inverse viscosity number 𝑁?𝑓?, and the Eötvös number Eo on the shapes and terminal velocities of a drop rising in stagnant liquids are studied numerically using a front tracking method. It is found that mild variation of 𝜂? barely changes the drop shape or terminal velocity, whereas 𝜆?, 𝑁?𝑓? and Eo significantly affect the drop dynamics. With the increase of 𝜆?, 𝑁?𝑓?, or Eo, the drop becomes either more dimpled or more crescent. When the drop is dimpled or ellipsoidal-cap, there is no recirculation flow in its rear. The recirculation zone appears and becomes larger when 𝜆? decreases or Eo increases. From the simulation results, the relationships between Fr, the non-dimensional terminal velocity of the drop, and 𝜆?, 𝑁?𝑓? and Eo are determined. For the correlation between Fr and 𝜆?, it is found that Fr= 𝑘?(1+𝐶?1𝜆?)/(2+𝐶?2𝜆?) for 5<𝑁?𝑓?<38, where 𝐶?1 = 1.245±0.165, and 𝐶?2 = 3.43±0.35, whereas Fr is a constant around 0.602 for 50<𝑁?𝑓?<100. The correlation between Fr and 𝑁?𝑓? follows a logarithmic trend for 𝑁?𝑓?<50. And Fr is also found to decrease with the increase of Eo. Bachelor of Engineering (Mechanical Engineering) 2012-05-18T07:16:59Z 2012-05-18T07:16:59Z 2012 2012 Final Year Project (FYP) http://hdl.handle.net/10356/49435 en Nanyang Technological University 42 p. application/pdf |
| spellingShingle | DRNTU::Engineering::Mechanical engineering::Fluid mechanics Liu, Lili. Shapes and terminal velocity of a drop rising in stagnant liquids |
| title | Shapes and terminal velocity of a drop rising in stagnant liquids |
| title_full | Shapes and terminal velocity of a drop rising in stagnant liquids |
| title_fullStr | Shapes and terminal velocity of a drop rising in stagnant liquids |
| title_full_unstemmed | Shapes and terminal velocity of a drop rising in stagnant liquids |
| title_short | Shapes and terminal velocity of a drop rising in stagnant liquids |
| title_sort | shapes and terminal velocity of a drop rising in stagnant liquids |
| topic | DRNTU::Engineering::Mechanical engineering::Fluid mechanics |
| url | http://hdl.handle.net/10356/49435 |
| work_keys_str_mv | AT liulili shapesandterminalvelocityofadroprisinginstagnantliquids |