Universal Scaling Laws for Propulsive Performance of Thrust Producing Foils Undergoing Continuous or Intermittent Pitching
High efficiency thrust generating foils are extensively being researched for potential use as thrusters in micro air vehicles and biomimetic autonomous underwater vehicles. Here, we propose a simple reduced order model for prediction of thrust generation attributes of foils that are pitched either c...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-04-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/7/4/142 |
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| author | Anil Das Ratnesh K. Shukla Raghuraman N. Govardhan |
| author_facet | Anil Das Ratnesh K. Shukla Raghuraman N. Govardhan |
| author_sort | Anil Das |
| collection | DOAJ |
| description | High efficiency thrust generating foils are extensively being researched for potential use as thrusters in micro air vehicles and biomimetic autonomous underwater vehicles. Here, we propose a simple reduced order model for prediction of thrust generation attributes of foils that are pitched either continuously or intermittently in a periodic and possibly asymmetric fashion. Our model accounts for the distinct thrust contributions from added mass, leading edge suction, quasi steady and wake terms, all deduced from a rigorous generalization of linearized potential theory to foils undergoing small amplitude multimodal flapping motion. Additionally, the model relies on Bone-Lighthill boundary layer thinning hypothesis to account for the pitching motion induced increase in the drag force exerted on the foil. We derive generic forms of the thrust coefficient for prescribed multimodal pitching motions and specifically in the limit of large reduced frequencies, demonstrate a convergence to rather simplified scaling laws that are functions of just the Reynolds number and Strouhal number based on root mean square of the foil’s trailing edge velocity. Comparisons with previously reported experimental and simulation-based investigations demonstrate that the scaling laws capture the influence of imposed pitch on thrust generation characteristics over a range of pitching waveforms ranging from sinusoidal to square or triangular-shaped waveforms and also waveforms corresponding to intermittent pitching. The generalized relations derived in our work and the asymptotic scaling laws deduced from them are applicable to a wide spectrum of self-propulsion enabling and thrust producing waveforms including the ones that can potentially be employed in burst and coast swimming. |
| first_indexed | 2024-03-09T10:36:02Z |
| format | Article |
| id | doaj.art-42f7250a52514280ae025e48293bf613 |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-03-09T10:36:02Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-42f7250a52514280ae025e48293bf6132023-12-01T20:53:19ZengMDPI AGFluids2311-55212022-04-017414210.3390/fluids7040142Universal Scaling Laws for Propulsive Performance of Thrust Producing Foils Undergoing Continuous or Intermittent PitchingAnil Das0Ratnesh K. Shukla1Raghuraman N. Govardhan2Department of Mechanical Engineering, Indian Institute of Science, Bengaluru 560012, IndiaDepartment of Mechanical Engineering, Indian Institute of Science, Bengaluru 560012, IndiaDepartment of Mechanical Engineering, Indian Institute of Science, Bengaluru 560012, IndiaHigh efficiency thrust generating foils are extensively being researched for potential use as thrusters in micro air vehicles and biomimetic autonomous underwater vehicles. Here, we propose a simple reduced order model for prediction of thrust generation attributes of foils that are pitched either continuously or intermittently in a periodic and possibly asymmetric fashion. Our model accounts for the distinct thrust contributions from added mass, leading edge suction, quasi steady and wake terms, all deduced from a rigorous generalization of linearized potential theory to foils undergoing small amplitude multimodal flapping motion. Additionally, the model relies on Bone-Lighthill boundary layer thinning hypothesis to account for the pitching motion induced increase in the drag force exerted on the foil. We derive generic forms of the thrust coefficient for prescribed multimodal pitching motions and specifically in the limit of large reduced frequencies, demonstrate a convergence to rather simplified scaling laws that are functions of just the Reynolds number and Strouhal number based on root mean square of the foil’s trailing edge velocity. Comparisons with previously reported experimental and simulation-based investigations demonstrate that the scaling laws capture the influence of imposed pitch on thrust generation characteristics over a range of pitching waveforms ranging from sinusoidal to square or triangular-shaped waveforms and also waveforms corresponding to intermittent pitching. The generalized relations derived in our work and the asymptotic scaling laws deduced from them are applicable to a wide spectrum of self-propulsion enabling and thrust producing waveforms including the ones that can potentially be employed in burst and coast swimming.https://www.mdpi.com/2311-5521/7/4/142biolocomotionflying and swimmingflapping foils |
| spellingShingle | Anil Das Ratnesh K. Shukla Raghuraman N. Govardhan Universal Scaling Laws for Propulsive Performance of Thrust Producing Foils Undergoing Continuous or Intermittent Pitching Fluids biolocomotion flying and swimming flapping foils |
| title | Universal Scaling Laws for Propulsive Performance of Thrust Producing Foils Undergoing Continuous or Intermittent Pitching |
| title_full | Universal Scaling Laws for Propulsive Performance of Thrust Producing Foils Undergoing Continuous or Intermittent Pitching |
| title_fullStr | Universal Scaling Laws for Propulsive Performance of Thrust Producing Foils Undergoing Continuous or Intermittent Pitching |
| title_full_unstemmed | Universal Scaling Laws for Propulsive Performance of Thrust Producing Foils Undergoing Continuous or Intermittent Pitching |
| title_short | Universal Scaling Laws for Propulsive Performance of Thrust Producing Foils Undergoing Continuous or Intermittent Pitching |
| title_sort | universal scaling laws for propulsive performance of thrust producing foils undergoing continuous or intermittent pitching |
| topic | biolocomotion flying and swimming flapping foils |
| url | https://www.mdpi.com/2311-5521/7/4/142 |
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