Purpose

This paper aims to analyze the propulsive performance of small-amplitude pitching foils at very high frequencies with double objectives: to find out scaling laws for the time-averaged thrust and propulsive efficiency at very high frequencies; and to characterize the Strouhal number above which the effect of turbulence on the mean values cannot be neglected.

Design/methodology/approach

The thrust force and propulsive efficiency of a pitching NACA0012 foil at high reduced frequencies (k) and a Reynolds number Re = 16 000 are analyzed using accurate numerical simulations, both assuming laminar flow and using a transition turbulence model. The time-averaged results are validated with available experimental data for k up to about 12 (Strouhal number, St, up to 0.6). This study also compares the present numerical results with the predictions of theoretical models and existing numerical results. For a foil pitching about its quarter chord with amplitude α₀ = 8^o, the reduced frequency is varied here up to k = 30 (St up to 2), much higher than in any previous numerical or experimental work.

Findings

For this pitch amplitude, turbulence effects are found negligible for St ≲ 0.8, and affecting less than 10% to the time-averaged thrust coefficient CT¯ for larger St Linear potential theory fails for very large k, even for the small pitch amplitude considered, particularly for the power coefficient, and therefore for the propulsive efficiency. It is found that CT¯ ∼ St² for large St, in agreement with recent models, and the propulsive efficiency decays as 1/k, in disagreement with the linear potential theory.

Originality/value

Pitching foils are increasingly studied as efficient propellers and energy harvesting devices. Their performance at very high reduced frequencies has not been sufficiently analyzed before. The authors provide accurate numerical simulations to discern when turbulence is relevant for the computation of the time-averaged thrust and efficiency and how their scaling with the reduced frequency is affected in relation to the laminar-flow predictions. This is relevant because some small-amplitude theoretical models predict high propulsive efficiency of pitching foils at very high frequencies over certain ranges of the structural parameters, and only very accurate numerical simulations may decide on these predictions.

中文翻译：

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二维俯仰翼片在高频下推进性能的数值研究：比例定律和湍流效应

目的

本文旨在通过双重目标分析小幅度俯仰翼在甚高频下的推进性能：找出在甚高频下的时间平均推力和推进效率的比例规律；并描述 Strouhal 数，在该数之上，湍流对平均值的影响不容忽视。

设计/方法/方法

在假设层流和过渡湍流模型的情况下，使用精确的数值模拟分析了在高缩减频率 ( k ) 和雷诺数 Re = 16 000下俯仰 NACA0012 翼片的推力和推进效率。时间平均结果通过可用的实验数据进行验证，k高达约 12（斯特劳哈尔数，St，高达 0.6）。本研究还将目前的数值结果与理论模型的预测和现有的数值结果进行了比较。对于振幅 α ₀ = 8 ^o围绕其四分之一弦倾斜的箔片，降低的频率在这里变化到k = 30（St 高达 2），远高于以前的任何数值或实验工作。

发现

对于这个俯仰幅度，湍流效应在 St ≲ 0.8 时可以忽略不计，对时间平均推力系数的影响不到 10% C吨¯对于较大的 St 线性势理论对于非常大的k失败，即使对于所考虑的小俯仰幅度，特别是对于功率系数，因此对于推进效率也是如此。发现 C吨¯ ～ St ²表示大 St，与最近的模型一致，推进效率衰减为 1/k，与线性势理论不一致。

原创性/价值

俯仰箔越来越多地被研究为高效的螺旋桨和能量收集装置。以前还没有充分分析它们在非常高的降低频率下的性能。作者提供了准确的数值模拟，以辨别湍流何时与时间平均推力和效率的计算相关，以及它们随频率降低的比例如何影响层流预测。这是相关的，因为一些小幅度理论模型预测在结构参数的某些范围内非常高频率下俯仰翼的高推进效率，并且只有非常准确的数值模拟才能决定这些预测。