# Numerical Study of Multiple Bio-Inspired Torsionally Hinged Flaps for Passive Flow Control

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## Abstract

**:**

## 1. Introduction

## 2. Problem Setup

## 3. Numerical Methodology

## 4. Results

#### 4.1. Qualitative Flow Features

#### 4.2. Performance Maps and Connections to Flap Dynamics

#### 4.3. Flow Physics of the Airfoil–Flap System with Dynamics Dominated by Flap 4

#### 4.4. Flow Physics of the Airfoil–Flap System Dominated by Dynamics of Flaps 1 and 4

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Projection-Based Immersed Boundary (IB) Method for Strongly Coupled Fluid–Structure Interaction (FSI) Problems

## References

- Mueller, T.J.; Delaurier, J.D. Aerodynamics of Small Vehicles. Annu. Rev. Fluid Mech.
**2003**, 35, 89–111. [Google Scholar] [CrossRef] - Lissaman, P. Low-Reynolds-Number Airfoils. Annu. Rev. Fluid Mech.
**1983**, 15, 223–239. [Google Scholar] [CrossRef] - Carruthers, A.; Thomas, A.; Taylor, G. Automatic aeroelastic devices in the wings of a steppe eagle Aquila nipalensis. J. Exp. Biol.
**2007**, 210, 4136–4149. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Schluter, J.U. Lift enhancement at low Reynolds numbers using self-activated movable flaps. J. Aircr.
**2010**, 47, 348–351. [Google Scholar] [CrossRef] - Wang, L.; Alam, M.M.; Zhou, Y. Experimental study of a passive control of airfoil lift using bioinspired feather flap. Bioinspir. Biomim.
**2019**, 14, 066005. [Google Scholar] [CrossRef] [PubMed] - Johnston, J.; Gopalarathnam, A. Investigation of a bio-inspired lift-enhancing effector on a 2D airfoil. Bioinspir. Biomim.
**2012**, 7, 036003. [Google Scholar] [CrossRef] [PubMed] - Duan, C.; Wissa, A. Covert-inspired flaps for lift enhancement and stall mitigation. Bioinspir. Biomim.
**2021**, 16, 046020. [Google Scholar] [CrossRef] [PubMed] - Meyer, R.; Hage, W.; Bechert, D.W.; Schatz, M.; Knacke, T.; Thiele, F. Separation Control by Self-Activated Movable Flaps. AIAA J.
**2007**, 45, 191–199. [Google Scholar] [CrossRef] - Izquierdo, D.O.; Marques, F.D. Experimental analysis of passive bio-inspired covert feathers for stall and post-stall performance enhancement. Meccanica
**2021**, 56, 2671–2689. [Google Scholar] [CrossRef] - Kernstine, K.; Moore, C.; Cutler, A.; Mittal, R. Initial Characterization of Self-Activated Movable Flaps, “Pop-Up Feathers”. In Proceedings of the 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, 7–10 January 2008; p. 369. [Google Scholar]
- Bramesfeld, G.; Maughmer, M.D. Experimental investigation of self-actuating, upper-surface, high-lift-enhancing effectors. J. Aircr.
**2002**, 39, 120–124. [Google Scholar] [CrossRef] - Nair, N.J.; Goza, A. Effects of Torsional Stiffness and Inertia on a Passively Deployable Flap for Aerodynamic Lift Enhancement. In Proceedings of the AIAA SCITECH 2022 Forum, San Diego, CA, USA, 3–7 January 2022; p. 1968. [Google Scholar]
- Rosti, M.E.; Omidyeganeh, M.; Pinelli, A. Passive control of the flow around unsteady aerofoils using a self-activated deployable flap. J. Turbul.
**2018**, 19, 204–228. [Google Scholar] [CrossRef] [Green Version] - Brücker, C.; Weidner, C. Influence of self-adaptive hairy flaps on the stall delay of an airfoil in ramp-up motion. J. Fluids Struct.
**2014**, 47, 31–40. [Google Scholar] [CrossRef] [Green Version] - Selig, M. Low Reynolds number airfoil design lecture notes. In VKI Lecture Series, November; University of Illinois: Urbana, IL, USA, 2003; pp. 24–28. [Google Scholar]
- Fang, Z.; Gong, C.; Revell, A.; Chen, G.; Harwood, A.; O’Connor, J. Passive separation control of a NACA0012 airfoil via a flexible flap. Phys. Fluids
**2019**, 31, 101904. [Google Scholar] - Goza, A.; Colonius, T. A strongly-coupled immersed-boundary formulation for thin elastic structures. J. Comput. Phys.
**2017**, 336, 401–411. [Google Scholar] [CrossRef] [Green Version] - Nair, N.J.; Goza, A. A strongly coupled immersed boundary method for fluid-structure interaction that mimics the efficiency of stationary body methods. arXiv
**2021**, arXiv:2103.06415. [Google Scholar] - Colonius, T.; Taira, K. A fast immersed boundary method using a nullspace approach and multi-domain far-field boundary conditions. Comput. Methods Appl. Mech. Eng.
**2008**, 197, 2131–2146. [Google Scholar] [CrossRef] - Taira, K.; Colonius, T. The immersed boundary method: A projection approach. J. Comput. Phys.
**2007**, 225, 2118–2137. [Google Scholar] [CrossRef]

**Figure 1.**Plot of ${C}_{l}$ v/s $\alpha $ for $Re=1000$. Gray shaded region denotes the amplitude of fluctuations in ${C}_{l}$.

**Figure 2.**Schematic of the airfoil body with five torsional flaps fixed at $0.2c$, $0.35c$, $0.5c$, $0.65c$ and $0.8c$.

**Figure 3.**Plots of flap deflection, $\beta $, and lift coefficient, ${C}_{l}$, versus dimensionless (convective) time. The lift plots provide both the flap-less case and the case of five flaps located at $0.2c$, $0.35c$, $0.5c$, $0.65c$ and $0.8c$ from the leading edge, ${k}_{\beta}=0.001$ and ${i}_{\beta}=0.001$.

**Figure 4.**Vorticity contours at different time instants in one period of a lift cycle for the case of ${k}_{\beta}=0.001$ and ${i}_{\beta}=0.001$.

**Figure 5.**Vorticity contours at different time instants in one period of lift cycle for the flap-less airfoil case.

**Figure 6.**Performance plots showing percentage change in mean lift with respect to the baseline airfoil case for the various values of inertia (${i}_{\beta}$) and stiffness (${k}_{\beta})$.

**Figure 9.**Vorticity contours at different time instants in one period of lift cycle for the case of ${k}_{\beta}=0.005$ and ${i}_{\beta}={10}^{-5}$.

**Figure 11.**Vorticity contours at $t/T=0.45$ demonstrating the downward-moving flap 4 countering the TEV and its reverse flow.

**Figure 13.**Vorticity contours at different time instants in one period of lift cycle for the case of ${k}_{\beta}=0.00025$ and ${i}_{\beta}=0.001$.

**Figure 15.**Vorticity contours at $t/T=0.45$ demonstrating the upward-moving flap 4 facilitating the upstream propagation of TEV-induced reverse flow.

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**MDPI and ACS Style**

Nair, N.J.; Flynn, Z.; Goza, A.
Numerical Study of Multiple Bio-Inspired Torsionally Hinged Flaps for Passive Flow Control. *Fluids* **2022**, *7*, 44.
https://doi.org/10.3390/fluids7020044

**AMA Style**

Nair NJ, Flynn Z, Goza A.
Numerical Study of Multiple Bio-Inspired Torsionally Hinged Flaps for Passive Flow Control. *Fluids*. 2022; 7(2):44.
https://doi.org/10.3390/fluids7020044

**Chicago/Turabian Style**

Nair, Nirmal J., Zoey Flynn, and Andres Goza.
2022. "Numerical Study of Multiple Bio-Inspired Torsionally Hinged Flaps for Passive Flow Control" *Fluids* 7, no. 2: 44.
https://doi.org/10.3390/fluids7020044