A Numerical Study of Metachronal Propulsion at Low to Intermediate Reynolds Numbers
Inspired by the forward swimming of long-tailed crustaceans, we study an underwater propulsion mechanism for a swimming body with multiple rigid paddles attached underneath undergoing cycles of power and return strokes with a constant phase-difference between neighboring paddles, a phenomenon known...
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MDPI AG
2020-05-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/5/2/86 |
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| author | Shawtaroh Granzier-Nakajima Robert D. Guy Calvin Zhang-Molina |
| author_facet | Shawtaroh Granzier-Nakajima Robert D. Guy Calvin Zhang-Molina |
| author_sort | Shawtaroh Granzier-Nakajima |
| collection | DOAJ |
| description | Inspired by the forward swimming of long-tailed crustaceans, we study an underwater propulsion mechanism for a swimming body with multiple rigid paddles attached underneath undergoing cycles of power and return strokes with a constant phase-difference between neighboring paddles, a phenomenon known as metachronal propulsion. To study how inter-paddle phase-difference affects flux production, we develop a computational fluid dynamics model and a numerical algorithm based on the immersed boundary method, which allows us to simulate metachronal propulsion at Reynolds numbers (RE) ranging from close to 0 to about 100. Our main finding is that the highest average flux is generated when nearest-neighbor paddles maintain an approximate 20%–25% phase-difference with the more posterior paddle leading the cycle; this result is independent of stroke frequency across the full range of RE considered here. We also find that the optimal paddle spacing and the number of paddles depend on RE; we see a qualitative transition in the dynamics of flow generated by metachronal propulsion as RE rises above 80. Roughly speaking, in terms of average flux generation, a tight paddle spacing is preferred when RE is less than 10, but a wider spacing becomes clearly favored when RE is close to or above 100. In terms of efficiency of flux generation, at RE 0.1 the maximum efficiency occurs at two paddles, and the efficiency decreases as the number of paddles increases. At RE 100 the efficiency increases as the number of paddles increases, and it appears to saturate by eight paddles, whereas using four paddles is a good tradeoff for both low and intermediate RE. |
| first_indexed | 2024-03-10T19:27:40Z |
| format | Article |
| id | doaj.art-60466157c75a4bddab7d0d8dcb56c4cb |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-03-10T19:27:40Z |
| publishDate | 2020-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-60466157c75a4bddab7d0d8dcb56c4cb2023-11-20T02:23:40ZengMDPI AGFluids2311-55212020-05-01528610.3390/fluids5020086A Numerical Study of Metachronal Propulsion at Low to Intermediate Reynolds NumbersShawtaroh Granzier-Nakajima0Robert D. Guy1Calvin Zhang-Molina2Department of Mathematics, University of Arizona, Tucson, AZ 85721, USADepartment of Mathematics, University of California, Davis, CA 95616, USADepartment of Mathematics, University of Arizona, Tucson, AZ 85721, USAInspired by the forward swimming of long-tailed crustaceans, we study an underwater propulsion mechanism for a swimming body with multiple rigid paddles attached underneath undergoing cycles of power and return strokes with a constant phase-difference between neighboring paddles, a phenomenon known as metachronal propulsion. To study how inter-paddle phase-difference affects flux production, we develop a computational fluid dynamics model and a numerical algorithm based on the immersed boundary method, which allows us to simulate metachronal propulsion at Reynolds numbers (RE) ranging from close to 0 to about 100. Our main finding is that the highest average flux is generated when nearest-neighbor paddles maintain an approximate 20%–25% phase-difference with the more posterior paddle leading the cycle; this result is independent of stroke frequency across the full range of RE considered here. We also find that the optimal paddle spacing and the number of paddles depend on RE; we see a qualitative transition in the dynamics of flow generated by metachronal propulsion as RE rises above 80. Roughly speaking, in terms of average flux generation, a tight paddle spacing is preferred when RE is less than 10, but a wider spacing becomes clearly favored when RE is close to or above 100. In terms of efficiency of flux generation, at RE 0.1 the maximum efficiency occurs at two paddles, and the efficiency decreases as the number of paddles increases. At RE 100 the efficiency increases as the number of paddles increases, and it appears to saturate by eight paddles, whereas using four paddles is a good tradeoff for both low and intermediate RE.https://www.mdpi.com/2311-5521/5/2/86metachronal waveslocomotioncrustacean swimmingbio-inspired propulsion |
| spellingShingle | Shawtaroh Granzier-Nakajima Robert D. Guy Calvin Zhang-Molina A Numerical Study of Metachronal Propulsion at Low to Intermediate Reynolds Numbers Fluids metachronal waves locomotion crustacean swimming bio-inspired propulsion |
| title | A Numerical Study of Metachronal Propulsion at Low to Intermediate Reynolds Numbers |
| title_full | A Numerical Study of Metachronal Propulsion at Low to Intermediate Reynolds Numbers |
| title_fullStr | A Numerical Study of Metachronal Propulsion at Low to Intermediate Reynolds Numbers |
| title_full_unstemmed | A Numerical Study of Metachronal Propulsion at Low to Intermediate Reynolds Numbers |
| title_short | A Numerical Study of Metachronal Propulsion at Low to Intermediate Reynolds Numbers |
| title_sort | numerical study of metachronal propulsion at low to intermediate reynolds numbers |
| topic | metachronal waves locomotion crustacean swimming bio-inspired propulsion |
| url | https://www.mdpi.com/2311-5521/5/2/86 |
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