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Aerodynamic Analysis of a Box Winglet: Viscous and Compressible Flow Predictions

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Abstract

The aerodynamic performance of a wing mounting a simple unconventional box winglet are analyzed in detail by CFD simulations. The decomposition of the computed drag in its irreversible (viscous) and reversible (lift-induced) components by a far field drag breakdown method allows for the determination of the span efficiency, not a trivial task in the case of viscous flow. The aerodynamic performance are compared with the ones obtained in case of a simple standard winglet and without any tip appendices.

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Abbreviations

:

Wing aspect ratio

b :

Wingspan

\(b_w\) :

Winglet wingspan

c :

Chord

\(C_D\) :

Drag coefficient

\(C_{D_i}\) :

Lift-induced drag coefficient

\(C_{D_i}^{\mathrm {ref}}\) :

Minimum lift-induced drag coefficient

\(C_{D_i}^{\mathrm {WS}}\) :

Lift-induced drag coefficient for a generic wing system

\(C_{D_{\mathrm {far}}}\) :

Far field drag coefficient

\(C_{D_{\mathrm {irr}}}\) :

Irreversible drag coefficient

\(C_{D_{\mathrm {near}}}\) :

Near field drag coefficient

\(C_{D_{\mathrm {rev}}}\) :

Reversible drag coefficient

\(C_f\) :

Skin friction coefficient

\(C_L\) :

Lift coefficient

\(C_{L_{\mathrm {near}}}\) :

Near field lift coefficient

\(C_p\) :

Pressure coefficient

\(D_i\) :

Lift-induced drag

\(D_i^{\mathrm {ref}}\) :

Minimum lift-induced drag

\(D_{\mathrm {far}}\) :

Far field drag

\(D_{\Delta s}\) :

Entropy drag

\(D_{v}\) :

Viscous drag

\(D_{w}\) :

Wave drag

\(D_{sp}\) :

Spurious drag

\(\Delta s\) :

Entropy variation

E :

Aerodynamic efficiency

\(h_w\) :

Winglet height

M :

Mach number

\(\mathbf {n}\) :

Unit normal vector

p :

Pressure

R :

Gas constant

Re :

Reynolds number

S :

Reference wing surface

\(\mathbf {V}\) :

Local velocity vector

\(\mathbb {V}\) :

Vertical aspect ratio

\(\alpha \) :

Angle of attack

\(\varepsilon \) :

Optimal aerodynamic efficiency ratio

\(\Phi \) :

Flow potential

\(\gamma \) :

Ratio of specific heats

\(\psi \) :

Stream function

\(\rho \) :

Density

\(\sigma \) :

Source strength

\(\zeta _x\) :

Vorticity component in free-stream direction

\(\infty \) subscript:

Free-stream conditions

BLI:

Boundary layer ingestion

BW:

Box winglet

BWD:

Best winglet design

CFD:

Computational fluid-dynamics

DEP:

Distributed electric propulsion

NW:

No winglet

SW:

Standard winglet

WBW:

Wing + box winglet

WFR:

Winglet fundamental rectangle

WPP:

Winglet primary properties

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Acknowledgements

An earlier version of this work was presented at the AIAA Aviation 2021 Forum, paper AIAA 2021-2544 (“Best Winglet of Minimum Induced Drag: Viscous and Compressible Flow Predictions”).

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Authors and Affiliations

  1. Department of Industrial Engineering, University of Naples Federico II, 80125, Naples, Italy

    Lorenzo Russo, Ettore Saetta & Renato Tognaccini

  2. Department of Aerospace Engineering, San Diego State University, San Diego, CA, 92182, USA

    Giulio Dacome & Luciano Demasi

Authors
  1. Lorenzo Russo
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  2. Ettore Saetta
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  3. Renato Tognaccini
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  4. Giulio Dacome
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  5. Luciano Demasi
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Correspondence to Luciano Demasi.

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Appendix A

Appendix A

In the following pages the results of the grid convergence analyses performed for the configurations analyzed are collected.

The number of cells of the fine grid level (LVL1), whose results were described in the previous sections was divided 2 and 4 times to obtain a medium (LVL2) and a coarse (LVL4) grid level. The near-field lift and drag coefficients against the grid levels are plotted in Fig. 13 for the BW configuration, Fig. 14 for the NW configuration and Fig. 15 for the SW configuration. Figure 14 clearly shows that the results for the simplest NW geometry are already converged at LVL2. On the contrary, this result is not clear for the more complex geometries. Therefore, in the case of BW configuration, an additional superfine grid level (LVL0.5) has been built-up doubling the number of cells of LVL1; the results of LVL0.5 show that a satisfactory convergence was indeed obtained by LVL1.

Fig. 13
figure 13

Grid convergence analysis for the Box Winglet (BW) configuration (\(Re_\infty =10^7, M_\infty =0.3\))

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Fig. 14
figure 14

Grid convergence analysis for the No Winglet (NW) configuration (\(Re_\infty =10^7, M_\infty =0.3\))

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Fig. 15
figure 15

Grid convergence analysis for the Standard Winglet (SW) configuration (\(Re_\infty =10^7, M_\infty =0.3\))

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Russo, L., Saetta, E., Tognaccini, R. et al. Aerodynamic Analysis of a Box Winglet: Viscous and Compressible Flow Predictions. Aerotec. Missili Spaz. 101, 321–334 (2022). https://doi.org/10.1007/s42496-022-00125-6

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