# Effect of the Extended Rigid Flapping Trailing Edge Fringe on an S833 Airfoil

^{*}

## Abstract

**:**

_{e}) and flapping frequencies (f

_{e}) of the fringe are the key parameters that dominate the impact on the airfoil and the flow field, given that the oscillation angular amplitude is fixed at 5°. The simulation results demonstrated that the airfoil with an extended fringe of 10% of the chord at a flapping frequency of f

_{e}= 110 Hz showed a substantial effect on the pressure distribution on the airfoil and the flow characteristics downstream of the airfoil. An irregular vortex street was predicted downstream, thus causing attenuations of the vorticities, and shorter streamwise gaps between each pair of vortices. The extended flapping fringe at a lower frequency than the natural shedding vortex frequency can effectively break the large vortex structure up into smaller scales, thus leading to an accelerated attenuation of vorticities in the wake.

## 1. Introduction

_{e}) at four different flapping frequencies (f

_{e}) are evaluated thoroughly. The analysis focuses on the flapping-induced changes on the Q-criterion and velocity distributions within the flow field, and the aerodynamic pressure distributions over the airfoil.

## 2. Materials and Methods

#### 2.1. Computational Model

^{3}and 1.84 × 10

^{−5}Pa s, respectively, to match the air property at room temperature. This boundary condition corresponds to a Reynolds number (Re) of 40,000, which is the same as the Re number evaluated in the experiment. This Re number falls within the range of the Re number of owls’ flight. The outlet boundary condition is defined as zero static pressure, and surfaces on the airfoil, as well as the top and bottom walls, are defined as non-slip wall conditions. The airfoil’s angle of attack is set at 9 degrees, which is also consistent with the experimental study [24]. The fringe length (L

_{e}) ranges from 8% to 12% of the chord, with a step increment of 2%. The flapping frequency (f

_{e}) ranges from 80 Hz to 170 Hz, with a step increment of 30 Hz. The initial f

_{e}is determined as the shedding vortex frequency (f) of the baseline bare airfoil model, which is 140 Hz, obtained via the power spectral density analysis of the velocity in the downstream wake [25]. The dynamic motion of the trailing edge fringe can be expressed as θ = Asin(2πft), where A is the amplitude flapping angle (A = 5°). The connection point of the flapping motion is fixed at the tip of the trailing edge.

#### 2.2. CFD Simulations

^{−5}s. The mean computational time for each simulation case was about 23 h.

## 3. Results and Discussion

#### 3.1. Effect of the Flapping Motion on the Q-Criterion and Velocity Distributions

_{e}are presented in Figure 3, Figure 4 and Figure 5. The large-scale vortices initiated over the upper surface of the airfoil were broken up into smaller scale vortices compared to the shed vortices of the bare airfoil model. The flapping motion at the flapping frequency of 80 Hz creates an irregular pattern of vortices compared to the cases with higher frequencies (110–170 Hz), as shown in Figure 3. The time-averaged Q-criterion distributions demonstrate an accelerated decay of vortices by the extended fringe with a low flapping frequency (80 Hz), resulting from the unstructured small-scale vortices being shed irregularly. This observation might be induced by the velocity “offset effect” between induced vortices and the shed vortices from upstream. With the increased flapping frequency, the vortices decayed slowly. This might be attributed to the fact that the contribution from the flapping fringe to the overall swirling strength becomes more dominant with the increased flapping frequency.

_{e}= 110, 140, or 170 Hz shows evenly shed vortices, as shown in Figure 4. The increased flapping frequency seems to shorten the gap between each pair of vortices, which is directly correlated to the flapping frequency of the fringe. From the comparison of the four flapping frequencies, it is suggested that when the flapping frequency f

_{e}is 60 Hz (40%) lower than f (natural vortex shedding frequency of the bare airfoil model, 140 Hz), the regular vortex shedding is interfered with, and results in an irregular vortex distribution with non-uniform scales and shorter gaps between each pair. As can be observed, the flapping trailing edge fringe with f

_{e}= 80 and 100 Hz alters the coherent structure of the large-scale vortices in the wake, and at the same time, reduces the vorticity in the flow field (Figure 4).

_{e}= 80 Hz, f

_{e}= 110 Hz, f

_{e}= 140 Hz, and f

_{e}= 170 Hz, respectively. Overall, higher flapping frequencies tend to generate a lower time-averaged pressure coefficient over the upper surface, which would result in an increase in the lift coefficient.

_{e}(<140 Hz) can break the large-scale vortex into small-scale vortices at the trailing edge, and, subsequently, alter the coherent structure of the vortex shedding. The irregularly shed vortices and the increased gap between each pair of vortices for cases with a lower f

_{e}accelerated the vortex decay compared to those with a higher f

_{e}. As the flapping frequency goes up to 170 Hz, the shedding frequency of the vortex is dominated by the flapping motion, which results in a regulated pattern of the shedding vortices. The time-averaged Q-criterion distributions show that the resultant time-averaged vortex strength has been elevated by the flapping fringe. It is indicated that the extended flapping fringe did not always facilitate the reduction of vorticity; conversely, it could promote the vortex domination in the wake, its interaction with the blunt trailing edge, and, possibly, the consequent noise emission from the trailing edge of the airfoil.

#### 3.2. Effect of the Extended Flapping Fringe on the Lift and Drag Coefficients

_{e}= 12%C and f

_{e}= 170 Hz generated the minimum drag coefficient, i.e., 22.5% lower than the baseline, and the maximum lift coefficient, i.e., 63.2% higher than the baseline, as can be observed in Figure 15. However, this combination would not alleviate the swirling strength of vortices shedding in the wake. For this case, the flapping fringe serves more like a propeller tail, such as the tail of a fish, and thus, reduces the drag, and improves the lift. The drag coefficients of the models with f

_{e}= 80 Hz are slightly lower than that of the baseline model, whereas the lift coefficients are elevated dramatically. An f

_{e}= 140 Hz, which is the natural shedding frequency for the bare airfoil, did not generate drastically different results. The difference in the lift and drag generation due to the fringe length is the minimum for this case.

_{e}should be determined according to the nature shedding frequency, f, of the bare airfoil model. The structure of the shedding vortices or their strength would be either maintained or elevated by the vibration of the fringe at a higher f

_{e}(>f). A higher flapping frequency (f

_{e}) tends to serve as a booster, rather than a disturber, to increase the local velocity at the trailing edge, resulting in the elevation of the swirling strength, and a shrinking of the dimension of vortices. However, most importantly, a lower f

_{e}was able to destruct the shedding vortices’ coherent structure due to the disruption of the fringe on the original shedding pattern from the bare airfoil. Consequently, the swirling strength of vortices became weak, and the irregular distribution made it easy to dissipate.

#### 3.3. Limitation of the Current Study

## 4. Conclusions

_{e}= 0.01 m (10% of the airfoil chord) at a flapping frequency of f

_{e}= 110 Hz outperforms other cases, and shows an overall substantially better aerodynamic performance of the airfoil, as well as more favorable vortex characteristics downstream of the airfoil. In spite of the limitations of the study, we can observe the aerodynamic benefits of using an extended flapping fringe at the trailing edge. The pressure alteration around the airfoil would potentially reduce the noise generation for wind turbines especially, which will be studied in our future work as well.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Zhao, M.; Cao, H.; Zhang, M.; Liao, C.; Zhou, T. Optimal design of aeroacoustic airfoils with owl-inspired trailing edge serrations. Bioinspir. Biomim.
**2021**, 16, 056004. [Google Scholar] [CrossRef] [PubMed] - Oerlemans, S.; Fisher, M.; Maeder, T.; Kögler, K. Reduction of wind turbine noise using optimized airfoils and trailing-edge serrations. AIAA J.
**2009**, 47, 1470–1481. [Google Scholar] [CrossRef] - Li, D.; Liu, X.; Hu, F.; Wang, L. Effect of trailing-edge serrations on noise reduction in a coupled bionic aerofoil inspired by barn owls. Bioinspir. Biomim.
**2019**, 15, 16009. [Google Scholar] [CrossRef] [PubMed] - Talboys, E.; Geyer, T.F.; Prüfer, F.; Brücker, C. A parametric study of the effect of self-oscillating trailing-edge flaplets on aerofoil self-noise. Appl. Acoust.
**2021**, 177, 107907. [Google Scholar] [CrossRef] - Geissler, W.; van der Wall, B.G. Dynamic stall control on flapping wing airfoils. Aerosp. Sci. Technol.
**2017**, 62, 1–10. [Google Scholar] [CrossRef] - Xinyu, L.; Bifeng, S.; Wenqing, Y.; Wenping, S. Aerodynamic performance of owl-like airfoil undergoing bio-inspired flapping kinematics. Chin. J. Aeronaut.
**2021**, 34, 239–252. [Google Scholar] - Moreau, D.J.; Doolan, C.J. Noise-reduction mechanism of a flat-plate serrated trailing edge. AIAA J.
**2013**, 51, 2513–2522. [Google Scholar] [CrossRef] [Green Version] - Winzen, A.; Klaas, M.; Schröder, W. PIV measurements comparing natural and model owl wings. In Proceedings of the 17th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 7–10 July 2014. [Google Scholar]
- Winzen, A.; Klän, S.; Klaas, M.; Schröder, W. Flow field analysis and contour detection of a natural owl wing using PIV measurements. In Nature-Inspired Fluid Mechanics; Springer: Berlin/Heidelberg, Germany, 2012; pp. 119–134. [Google Scholar]
- Lilley, G. A study of the silent flight of the owl. In Proceedings of the 4th AIAA/CEAS Aeroacoustics Conference, Toulouse, France, 2–4 June 1998; p. 2340. [Google Scholar]
- Sarradj, E.; Fritzsche, C.; Geyer, T. Silent owl flight: Bird flyover noise measurements. AIAA J.
**2011**, 49, 769–779. [Google Scholar] [CrossRef] - Kerho, M.; Hutcherson, S.; Blackwelder, R.F.; Liebeck, R.H. Vortex generators used to control laminar separation bubbles. J. Aircr.
**1993**, 30, 315–319. [Google Scholar] [CrossRef] - Klan, S.; Bachmann, T.; Klaas, M.; Wagner, H.; Schröder, W. Experimental analysis of the flow field over a novel owl based airfoil. In Animal Locomotion; Springer: Berlin/Heidelberg, Germany, 2010; pp. 413–427. [Google Scholar]
- Miao, J.M.; Ho, M.H. Effect of flexure on aerodynamic propulsive efficiency of flapping flexible airfoil. J. Fluids Struct.
**2006**, 22, 401–419. [Google Scholar] [CrossRef] - Shan, H.; Jiang, L.; Liu, C.; Love, M.; Maines, B. Numerical study of passive and active flow separation control over a NACA0012 airfoil. Comput. Fluids
**2008**, 37, 975–992. [Google Scholar] [CrossRef] - Veldhuis, L.L.M.; Jansen, D.P.; El Haddar, J.; Correale, G. Novel Passive and Active Flow Control for High Lift. In Proceedings of the 28th International Congress Aeronautucal Science, Brisbane, Australia, 23–28 September 2012. [Google Scholar]
- Finez, A.; Jacob, M.; Jondeau, E.; Roger, M. Broadband noise reduction with trailing edge brushes. In Proceedings of the 16th AIAA/CEAS Aeroacoustics Conference, Stockholm, Sweden, 7–9 June 2010; p. 3980. [Google Scholar]
- Herr, M.; Dobrzynski, W. Experimental Investigations in Low-Noise Trailing Edge Design. AIAA J.
**2005**, 43, 1167–1175. [Google Scholar] [CrossRef] - Das, C. An Experimental Investigation of Flow-Induced Noise Mechanism of a Flexible Flat-Plate Trailing-Edge. 2015. Available online: https://www.semanticscholar.org/paper/AN-EXPERIMENTAL-INVESTIGATION-OF-FLOW-INDUCED-NOISE-Das-Mimani/6b0724fa4ad87b65336240d253d30b5a3b1c4176#citing-papers (accessed on 10 October 2021).
- Schlanderer, S.C.; Sandberg, R.D. DNS of a compliant trailing-edge flow. In Proceedings of the 19th AIAA/CEAS Aeroacoustics Conference, Berlin, Germany, 27–29 May 2013; p. 2013. [Google Scholar]
- Kamps, L.; Brücker, C.; Geyer, T.F.; Sarradj, E. Airfoil self noise reduction at low Reynolds numbers using a passive flexible trailing edge. In Proceedings of the 23rd AIAA/CEAS Aeroacoustics Conference, Denver, CO, USA, 5–9 June 2017; p. 3496. [Google Scholar]
- Talboys, E.; Geyer, T.F.; Brücker, C. An aeroacoustic investigation into the effect of self-oscillating trailing edge flaplets. J. Fluids Struct.
**2019**, 91, 102598. [Google Scholar] [CrossRef] [Green Version] - Murayama, Y.; Nakata, T.; Liu, H. Flexible flaps inspired by avian feathers can enhance aerodynamic robustness in low Reynolds number airfoils. Front. Bioeng. Biotechnol.
**2021**, 9, 374. [Google Scholar] [CrossRef] [PubMed] - Yang, Z.; He, Z.; Chen, F. Study on the Vortex Wake of an Airfoil Equipped with Flexible Trailing Edge Fringe. In Proceedings of the 53rd AIAA Aerospace Sciences Meeting, Kissimmee, FL, USA, 5–9 January 2015; p. 1707. [Google Scholar] [CrossRef] [Green Version]
- Yu, H.; Yang, Z. A numerical simulation on the airfoil s833 equipped with flapping trailing edge fringes. J. Appl. Fluid Mech.
**2020**, 13, 571–582. [Google Scholar] [CrossRef] - Somers, D.M. S833, S834, and S835 Airfoils: November 2001–November 2002; National Renewable Energy Lab. (NREL): Golden, CO, USA, 2005. [Google Scholar]
- Walters, D.K.; Leylek, J.H. A new model for boundary layer transition using a single-point RANS approach. J. Turbomach.
**2004**, 126, 193–202. [Google Scholar] [CrossRef] - Walters, D.K.; Cokljat, D. A three-equation eddy-viscosity model for Reynolds-averaged Navier–Stokes simulations of transitional flow. J. Fluids Eng.
**2008**, 130, 121401. [Google Scholar] [CrossRef]

**Figure 1.**The 2-dimensional computational domain and boundary conditions for the CFD simulation. C: chord length of the airfoil; u: velocity in the x-direction; v: velocity in the y-direction; ρ: density of the fluid; μ: viscosity of the fluid; P: pressure; θ: dynamic motion of the trailing edge fringe; A: amplitude of the flapping angle and set at 5 degrees; f: frequency of the flapping motion.

**Figure 2.**The simulated instantaneous (time = 1 s) and time-averaged Q-criterion and velocity distributions with streamline of the bare airfoil model.

**Figure 3.**Q-criterion distributions around the airfoil model with the fringe length of 8% chord at different flapping frequencies. Left column: instantaneous Q-criterion distributions at the fringe tip moved to the top; Middle column: instantaneous Q-criterion distributions at the fringe tip moved to the bottom; Right column: time-averaged Q-criterion distribution.

**Figure 4.**Instantaneous Q-criterion distributions in the wake of the airfoil model with the fringe length of 8% chord at different flapping frequencies at t = 1.5 s.

**Figure 5.**The velocity distribution around the airfoil model with the fringe length of 8% chord at different flapping frequencies.

**Left column**: instantaneous velocity distributions when the fringe tip moved to the top;

**Middle column**: instantaneous Q-criterion distributions when the fringe tip moved to the bottom;

**Right column**: time-averaged Q-criterion distribution.

**Figure 6.**Pressure coefficient distribution over the airfoil model with the fringe length of 8% chord at four flapping frequencies.

**Figure 7.**Q-criterion distributions around the airfoil model with the fringe length of 10% chord at different flapping frequencies.

**Figure 8.**Instantaneous Q-criterion distributions in the wake of the airfoil model with the fringe length of 10% chord at different flapping frequencies at t = 1.5 s.

**Figure 9.**The velocity distribution around the airfoil model with the fringe length of 10% chord at different flapping frequencies.

**Figure 10.**Pressure coefficient distribution over the airfoil model with the fringe length of 10% chord at different flapping frequencies.

**Figure 11.**Q-criterion distributions around the airfoil model with the fringe length of 12% chord at different flapping frequencies.

**Figure 12.**Instantaneous Q-criterion distributions in the wake of the airfoil model with the fringe length of 12% chord at different flapping frequencies at t = 1.5 s.

**Figure 13.**The velocity distribution around the airfoil model with the fringe length of 12% chord at different flapping frequencies.

**Figure 14.**Pressure coefficient distribution over the airfoil model with the fringe length of 12% chord at different flapping frequencies.

**Figure 15.**Time-averaged force coefficients for airfoil models with different fringe lengths at different flapping frequencies: (

**a**) Drag coefficient; (

**b**) Lift Coefficient.

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**MDPI and ACS Style**

Yu, H.; Yang, Z.
Effect of the Extended Rigid Flapping Trailing Edge Fringe on an S833 Airfoil. *Appl. Sci.* **2022**, *12*, 444.
https://doi.org/10.3390/app12010444

**AMA Style**

Yu H, Yang Z.
Effect of the Extended Rigid Flapping Trailing Edge Fringe on an S833 Airfoil. *Applied Sciences*. 2022; 12(1):444.
https://doi.org/10.3390/app12010444

**Chicago/Turabian Style**

Yu, Hongtao, and Zifeng Yang.
2022. "Effect of the Extended Rigid Flapping Trailing Edge Fringe on an S833 Airfoil" *Applied Sciences* 12, no. 1: 444.
https://doi.org/10.3390/app12010444