{"title":"Drag force on an accelerating flat plate at low Reynolds numbers","authors":"Wenjie Liu, Mao Sun","doi":"10.1063/5.0223050","DOIUrl":null,"url":null,"abstract":"The accelerating flat plate is a useful model for studying the drag-based flapping flight (where drag is used to provide the weight-supporting force or thrust). Previous studies have mainly focused on the high Reynolds number (Re) regime pertaining to the flight of relatively large insects and birds. In this study, we numerically investigate the unsteady drag and flows of a uniformly accelerating flat plate at low Re that is typical of miniature insect flight (Re = 10–40). The following is shown. Unlike high-Re cases where the acceleration effect on drag is insensitive to Re, at low Re, the effect exhibits a strong dependence on Re: As Re decreases below 100, the acceleration effect increases rapidly, becoming 33%–56% greater than that of high-Re cases in the Re range of 10–40, before gradually decreasing. A simple model that consists of the quasi-steady, added-mass, and history force terms is proposed for drag at low Re. The scalings of the quasi-steady and added-mass force terms are well known; we find that the history force term scales approximately with the square root of the acceleration and velocity. The above result that relatively large drag is produced by the accelerating wing at Re = 10–40 is especially interesting and might explain why miniature insects fly in this Re range.","PeriodicalId":20066,"journal":{"name":"Physics of Fluids","volume":null,"pages":null},"PeriodicalIF":4.1000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physics of Fluids","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1063/5.0223050","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
The accelerating flat plate is a useful model for studying the drag-based flapping flight (where drag is used to provide the weight-supporting force or thrust). Previous studies have mainly focused on the high Reynolds number (Re) regime pertaining to the flight of relatively large insects and birds. In this study, we numerically investigate the unsteady drag and flows of a uniformly accelerating flat plate at low Re that is typical of miniature insect flight (Re = 10–40). The following is shown. Unlike high-Re cases where the acceleration effect on drag is insensitive to Re, at low Re, the effect exhibits a strong dependence on Re: As Re decreases below 100, the acceleration effect increases rapidly, becoming 33%–56% greater than that of high-Re cases in the Re range of 10–40, before gradually decreasing. A simple model that consists of the quasi-steady, added-mass, and history force terms is proposed for drag at low Re. The scalings of the quasi-steady and added-mass force terms are well known; we find that the history force term scales approximately with the square root of the acceleration and velocity. The above result that relatively large drag is produced by the accelerating wing at Re = 10–40 is especially interesting and might explain why miniature insects fly in this Re range.
加速平板是研究基于阻力的拍击飞行(利用阻力提供重量支撑力或推力)的有用模型。以往的研究主要集中在与相对较大的昆虫和鸟类飞行有关的高雷诺数 (Re) 机制。在本研究中,我们用数值方法研究了在低雷诺数(Re = 10-40)条件下均匀加速平板的非稳定阻力和流动,这是微型昆虫飞行的典型特征。结果如下。与加速度对阻力的影响对 Re 值不敏感的高 Re 值情况不同,在低 Re 值情况下,加速度对阻力的影响对 Re 值有很强的依赖性:当 Re 值减小到 100 以下时,加速度效应迅速增加,在 Re 值为 10-40 的范围内,加速度效应比高 Re 值情况下的加速度效应大 33%-56%,然后逐渐减小。针对低 Re 条件下的阻力,提出了一个由准稳定力、附加质量和历史力项组成的简单模型。准稳力和附加质量力项的标度是众所周知的;我们发现历史力项的标度近似于加速度和速度的平方根。上述结果特别有趣,即在 Re = 10-40 时,加速翼产生的阻力相对较大,这或许可以解释为什么微型昆虫会在此 Re 范围内飞行。
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