Reynolds Number Scaling of the Propulsive Performance of a Pitching Airfoil

Şentürk, Utku; Smits, Alexander J.

doi:10.2514/1.j058371

Cited by 47 publications

(75 citation statements)

References 7 publications

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“…In relation to the scaling of the average values, it is found that C T = 2St 2 ð Þ ! e a ð Þ for k !1, or large St, in qualitative agreement with the model by Senturk and Smits (2019), based on a previous scaling by Floryan et al (2017) for small St and fixed pitch axis location. It is found that C P 1 À a ð Þsina 0 = 2St 3 ð Þ !…”

Section: Discussionsupporting

confidence: 87%

“…It is interesting to note that the generation of turbulence strongly depends on the Strouhal number St, in spite of the fact that the Reynolds number based on the chord-length and the upstream velocity is the same in all the simulations. For this value Re = 16000 (and even for Re = 32000), Senturk and Smits (2019) claim that the boundary layer remains laminar, but it is clear in Figure 10 In the first case the turbulence intensity is very weak, being only appreciable far downstream in the wake. Consequently, it has no practical effect on the aerodynamic force and moment on the foil because only the vorticity field in, or close to, the boundary layer, together with the vorticity shed at the trailing edge in its close vicinity, affect the forces and moment on a flapping foil (Martín-Alc antara et al , 2015).…”

Section: Scaling Laws and Turbulence Effectsmentioning

confidence: 92%

“…This is the main aim of the present study, where such accurate numerical method is provided, and where the mean thrust and propulsive efficiency of pitching foils are characterized at very high reduced frequencies, much higher than in any previous published work to our knowledge, for a Reynolds number Re = 16000. We have selected this value because it is in the range of interest in bio-inspired propulsion (Wu, 2011), and because, according to the recent laminar flow numerical simulations by Senturk and Smits (2019), the average thrust and power are relatively insensitive to Reynolds numbers greater than about 16 000. In addition, these authors claim that the boundary layer on the pitching foil remains laminar for this, and even higher, Reynolds number.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerical study of the propulsive performance of two-dimensional pitching foils at very high frequencies: scaling laws and turbulence effects

Sanmiguel‐Rojas

Fernández‐Feria

2021

HFF

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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 = 8o, 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.

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Section: Discussionsupporting

confidence: 87%

Section: Scaling Laws and Turbulence Effectsmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical study of the propulsive performance of two-dimensional pitching foils at very high frequencies: scaling laws and turbulence effects

Sanmiguel‐Rojas

Fernández‐Feria

2021

HFF

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“…The chord-wise Reynolds number Re = ρU ∞ C / μ = 5300, where ρ , μ are the fluid density and viscosity, is kept fixed to isolate influence of the geometry and kinematics. This Reynolds number is representative for a wide range of biological and robotic applications as the thrust and power coefficients of flapping foils at the same Strouhal number and similar offset drag are insensitive to the variation of chordwise Reynolds number between Re ≈ 5000 and Re ≈ 500 000 [ 25 , 26 ]. A range of Reynolds numbers Re = 1600 –150 000 is tested for a pitch-heave case (tail-like motion), at , sweep angle 20° and 40° which shows only minor variation in propulsive coefficients of force and power (see electronic supplementary material).…”

Section: Introductionmentioning

confidence: 99%

Fin sweep angle does not determine flapping propulsive performance

Zurman-Nasution

Ganapathisubramani

Weymouth

2021

J. R. Soc. Interface.

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The importance of the leading-edge sweep angle of propulsive surfaces used by unsteady swimming and flying animals has been an issue of debate for many years, spurring studies in biology, engineering, and robotics with mixed conclusions. In this work, we provide results from three-dimensional simulations on single-planform finite foils undergoing tail-like (pitch-heave) and flipper-like (twist-roll) kinematics for a range of sweep angles covering a substantial portion of animals while carefully controlling all other parameters. Our primary finding is the negligible 0.043 maximum correlation between the sweep angle and the propulsive force and power for both tail-like and flipper-like motions. This indicates that fish tails and mammal flukes with similar range and size can have a large range of potential sweep angles without significant negative propulsive impact. Although there is a slight benefit to avoiding large sweep angles, this is easily compensated by adjusting the fin’s motion parameters such as flapping frequency, amplitude and maximum angle of attack to gain higher thrust and efficiency.

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“…Our scaling relations show a good collapse of the data for a wide range of Reynolds number from Re = 9000 and Re = 13 600 in the experiments, to Re = ∞ in the inviscid simulations. Here, it should be noted that the determined coefficients are different among the experimental and numerical data sets, which highlights that the coefficients likely vary with Re as observed by Senturk & Smits (2019). Although it is clear that the Reynolds number can alter the coefficients, no additional terms need to be introduced to account for data obtained at different Re.…”

Section: Resultsmentioning

confidence: 88%