# Leading-Edge Roughness Affecting Diamond-Wing Aerodynamic Characteristics

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Wind Tunnel Facility

#### 2.2. Wind Tunnel Model

^{2}and the mean aerodynamic chord ${l}_{\mu}$ = 0.800 m. The maximum relative test section blockage of $4.8\%$ is reached at the highest angle of attack of $\alpha ={32}^{\circ}$. Figure 1a includes an upstream view of the test section with the mounted half wing model. The geometric characteristics of the wind tunnel model are shown in Figure 1b and summarized in Table 1.

#### 2.3. Measurement Techniques

#### 2.3.1. Flow Field Visualization

#### 2.3.2. Balance Measurements

#### 2.3.3. Surface Pressure Measurements

#### 2.4. Test Cases

## 3. Results and Discussion

#### 3.1. Flow Field Visualization

#### 3.2. Mean Pressure Coefficient Distribution

#### 3.3. Reynolds Number Effect

#### 3.4. Leading-Edge Roughness Effect

#### 3.5. Analysis of Transient Surface Pressure Coefficient

#### 3.6. Spectral Analysis

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Gursul, I. Unsteady aerodynamics of nonslender delta wings. Prog. Aerosp. Sci.
**2005**, 41, 515–557. [Google Scholar] [CrossRef] [Green Version] - Luckring, J.M.; Boelens, O.J.; Breitsamter, C.; Hövelmann, A.; Knoth, F.; Malloy, D.J.; Deck, S. Objectives, approach, and scope for the AVT-183 diamond-wing investigations. Aerosp. Sci. Technol.
**2016**, 57, 2–17. [Google Scholar] [CrossRef] - Gursul, I. Recent developments in delta wing aerodynamics. Aeronaut. J.
**2004**, 108, 437–452. [Google Scholar] [CrossRef] - Earnshaw, P.B.; Lawford, J.A. Low-Speed Wind-Tunnel Experiments on a Series of Sharp-Edged Delta Wings; Technical Report 3424, Aeronautical Research Council. Reports and Memoranda; Ministry of Aviation, Royal Aircraft Establishment: London, UK, 1964.
- Wentz, W.; Kohlmann, D. Vortex breakdown on slender sharp-edged wings. J. Aircr.
**1971**, 8, 156–161. [Google Scholar] [CrossRef] - Taylor, G.S.; Schnorbus, T.; Gursul, I. An investigation of vortex flows over low sweep delta wings. In Proceedings of the 33rd AIAA Fluid Dynamics Conference and Exhibit, Fluid Dynamics and Co-located Conferences (AIAA 2003-4021), Orlando, FL, USA, 23–26 June 2003. [Google Scholar] [CrossRef]
- Taylor, G.S.; Gursul, I. Buffeting flows over a low-sweep delta wing. AIAA J.
**2004**, 42, 1737–1745. [Google Scholar] [CrossRef] - Gordnier, R.E.; Visbal, M.R. Compact difference scheme applied to simulation of low-sweep delta wing flow. AIAA J.
**2005**, 43, 1744–1752. [Google Scholar] [CrossRef] - Yaniktepe, B.; Rockwell, D. Flow structure on a delta wing of low sweep angle. AIAA J.
**2004**, 42, 513–523. [Google Scholar] [CrossRef] - Luckring, J.M. Reynolds number and leading-edge bluntness effect on a 65
^{∘}delta wing. In Proceedings of the 40th AIAA Aerospace Sciences Meeting & Exhibit (AIAA-2002-0419), Reno, NV, USA, 4–17 January 2002. [Google Scholar] [CrossRef] - Kulfan, R.M. Wing airfoil shape effects on the development of leading edge vortices. In Proceedings of the 5th AIAA Atmospheric Flight Mechanics Conference on Future Space Systems, Boulder, CO, USA, 6–8 August 1979. [Google Scholar] [CrossRef]
- Verhaagen, N. Effects of leading-edge radius on aerodynamic characteristics of 50
^{∘}delta wings. In Proceedings of the 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Aerospace Sciences Meetings (AIAA 2010-323), Orlando, FL, USA, 4–7 January 2010. [Google Scholar] [CrossRef] - Schütte, A. Numerical investigations of vortical flow on swept wings with round leading edges. J. Aircr.
**2017**, 54, 572–601. [Google Scholar] [CrossRef] - Hövelmann, A.; Knoth, F.; Breitsamter, C. AVT-183 diamond wing flow field characteristics Part 1: Varying leading-edge roughness and the effects on flow separation onset. Aerosp. Sci. Technol.
**2016**, 57, 18–30. [Google Scholar] [CrossRef] - Hövelmann, A.; Grawunder, M.; Buzica, A.; Breitsamter, C. AVT-183 diamond wing flow field characteristics Part 2: Experimental analysis of leading-edge vortex formation and progression. Aerosp. Sci. Technol.
**2016**, 57, 31–42. [Google Scholar] [CrossRef] - Reasor, D.A., Jr.; Malloy, D.J.; Daniel, D.T. Applicability of hybrid RANS/LES models in predicting separation onset of the AVT-183 diamond wing. In Proceedings of the 53rd AIAA Aerospace Sciences Meeting, AIAA SciTech Forum (AIAA 2015-0287), Kissimmee, FL, USA, 5–9 January 2015. [Google Scholar] [CrossRef]
- Frink, N.T. Numerical analysis of incipient separation on 53
^{∘}swept diamond wing. In Proceedings of the 53rd AIAA Aerospace Sciences Meeting, AIAA SciTech Forum, (AIAA 2015-0288), Kissimmee, FL, USA, 5–9 January 2015. [Google Scholar] [CrossRef] - Edefur, H.; Tormalm, M.; Coppin, J.; Birch, T.; Nangia, R.K. Numerical study of blunt leading edge separation on a 53 degree swept diamond wing (STO AVT-183) using the Edge and Cobalt flow solvers. In Proceedings of the 53rd AIAA Aerospace Sciences Meeting, AIAA SciTech Forum, (AIAA 2015-0290), Kissimmee, FL, USA, 5–9 January 2015. [Google Scholar] [CrossRef]
- Hitzel, S.M.; Boelens, O.J.; Rooij, M.; Hövelmann, A. Vortex development on the AVT-183 diamond wing configuration—Numerical and experimental findings. Aerosp. Sci. Technol.
**2016**, 57, 90–102. [Google Scholar] [CrossRef] - Luckring, J.M.; Boelens, O.J. A reduced-complexity investigation of blunt leading-edge separation motivated by UCAV aerodynamics. In Proceedings of the 53rd AIAA Aerospace Sciences Meeting, AIAA SciTech Forum, (AIAA-2015-0061), Kissimmee, FL, USA, 5–9 January 2015. [Google Scholar] [CrossRef]
- Breitsamter, C. Strömungsphysik und Modellgesetze; Lect. Notes; Technical University of Munich: Munich, Germany, 2012. [Google Scholar]
- Luckring, J.M. A survey of factors affecting blunt leading-edge separation for swept and semi-slender wings. In Proceedings of the 28th AIAA Applied Aerodynamics Conference (AIAA 2010-4820), Chicago, IL, USA, 28 June–1 July 2010. [Google Scholar] [CrossRef]
- Schlichting, H.; Gersten, K. Boundary-Layer Theory, 9th ed.; Springer: Berlin/Heidelberg, Germany, 2017. [Google Scholar]
- Gursul, I. Unsteady flow phenomena over delta wings at high angle of attack. AIAA J.
**1994**, 32, 225–231. [Google Scholar] [CrossRef] - Breitsamter, C. Unsteady flow phenomena associated with leading-edge vortices. Prog. Aerosp. Sci.
**2008**, 44, 48–65. [Google Scholar] [CrossRef]

**Figure 2.**Geometric parameters of the applied trip strips. (

**a**) Trip dot type, overview; (

**b**) Trip dot type, leading-edge sectional view; (

**c**) Carborundum grit type, overview; (

**d**) Carborundum grit type, leading-edge sectional view.

**Figure 3.**Applied trip strips. (

**a**) Trip dots, ${h}_{d}/{l}_{\mu}=0.019\%$ (${h}_{d}$ = 0.15 mm); (

**b**) Carborundum grit, ${h}_{d}/{l}_{\mu}=0.025\%$ (${h}_{d}$ = 0.20 mm); (

**c**) Carborundum grit, ${h}_{d}/{l}_{\mu}=0.069\%$ (${h}_{d}$ = 0.55 mm).

**Figure 4.**Additional very rough carborundum grits. (

**a**) ${h}_{d}/{l}_{\mu}=0.125\%$ (${h}_{d}$ = 1 mm); (

**b**) ${h}_{d}/{l}_{\mu}=0.250\%$ (${h}_{d}$ = 2 mm).

**Figure 5.**Nondimensional vorticity distribution in chord sections $0.1\le x/{c}_{r}\le 0.6$ at $\alpha ={16}^{\circ}$ and $Re=2.7\times {10}^{6}$. (

**a**) Free Transition, $h/{l}_{\mu}=0.000\%$; (

**b**) Trip Dots, $h/{l}_{\mu}=0.019\%$; (

**c**) Trip Strip, $h/{l}_{\mu}=0.069\%$.

**Figure 6.**Spanwise distribution of the pressure coefficient as function of angle of attack $\alpha $, at $x/{c}_{r}=0.295$ and $Re=2.7\times {10}^{\circ}$, for free transition conditions; arrows towards increasing $\alpha $.

**Figure 7.**Lift coefficient as function of angle of attack and Reynolds number. (

**a**) Free Transition; (

**b**) Detail view at post-stall for different disturbance heights.

**Figure 8.**Reynolds number effect on the pitching-moment coefficient as function of angle of attack—case with trip dots ${h}_{d}/{l}_{\mu}=0.019\%$.

**Figure 9.**Aerodynamic coefficients of the longitudinal motion as function of angle of attack and roughness height.

**Figure 10.**Reynolds number effect on the spanwise mean pressure coefficient distribution at $\alpha ={15}^{\circ}$—case with trip dots ${h}_{d}/{l}_{\mu}=0.019\%$.

**Figure 11.**Leading-edge roughness effect on the spanwise mean surface pressure distribution, at $Re=2.7\times {10}^{6}$ and $\alpha ={15}^{\circ}$.

**Figure 12.**Leading-edge roughness effect on the spanwise mean surface pressure distribution in the apex region ($x/{c}_{r}=0.1$ and 0.2), at $Re=2.7\times {10}^{6}$ and $\alpha ={29}^{\circ}$.

**Figure 13.**Pressure coefficient time sequences for the free transition case measured at (

**a**) $x/{c}_{r}=0.3$, $y/s\left(x\right)=0.65$ with increasing angle of attack, $\alpha =[{15}^{\circ},{18}^{\circ},{21}^{\circ},{24}^{\circ},{27}^{\circ},{30}^{\circ}]$; and at (

**b**) four different chordwise locations, $x/{c}_{r}=[0.3,0.4,0.5,0.6]$, $y/s\left(x\right)=0.75$, at an incidence of $\alpha ={15}^{\circ}$; $Re=2.7\times {10}^{6}$.

**Figure 14.**Time averaged ${c}_{p,avg}$ and rms values ${c}_{p,rms}$ of the pressure coefficient (circles and full squares, respectively) measured at $0.75$ local span as function of angle of attack $\alpha $ and local chordwise position $x/{c}_{r}$. Leading-edge roughness heights: (

**a**) ${h}_{d}/{l}_{\mu}=0.000\%$; (

**b**) ${h}_{d}/{l}_{\mu}=0.019\%$; (

**c**) ${h}_{d}/{l}_{\mu}=0.069\%$; (

**d**) ${h}_{d}/{l}_{\mu}=0.250\%$.

**Figure 15.**Power spectral density ($PSD$) of the pressure fluctuations ${c}_{p}^{\prime}$ as function of reduced frequency k, at $Re=2.7\times {10}^{6}$. (

**a**) Angle of attack variation; (

**b**) Position variation at $\alpha ={15}^{\circ}$.

**Figure 16.**Dominant peaks (first peak with full symbols, second one with empty symbols) measured at six sensor locations as function of angle of attack for three cases: free transition case ${h}_{d}/{l}_{\mu}=0.000\%$ (red squares), case with trip dots ${h}_{d}/{l}_{\mu}=0.019\%$ (blue triangles) and overtripped case ${h}_{d}/{l}_{\mu}=0.250\%$ (orange diamonds). Dashed curves follow the maximum and minimum empirical helical mode frequency typical for slender delta wings [25].

$\mathsf{\Lambda}$ (-) | ${\mathit{\phi}}_{\mathit{LE}}{(}^{\circ})$ | ${\mathit{\phi}}_{\mathit{TE}}{(}^{\circ})$ | ${\mathit{c}}_{\mathit{r}}$ (m) | s (m) | ${\mathit{x}}_{\mathit{MRP}}$ (m) | ${\mathit{l}}_{\mathit{\mu}}$ (m) | ${\mathit{S}}_{\mathit{ref}}$ (m${}^{2}$) | ${\mathit{h}}_{\mathit{pen}}$ (m) |
---|---|---|---|---|---|---|---|---|

2.191 | 53.0 | −26.5 | 1.200 | 0.657 | 0.491 | 0.800 | 0.394 | 0.090 |

Section | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

$\mathit{x}/{\mathit{c}}_{\mathit{r}}$ (-) | 0.100 | 150 | 0.200 | 250 | 0.295 | 0.305 | 350 | 0.395 | 0.405 | 0.450 | 0.500 | 0.550 | 0.600 |

x (m) | 0.120 | 0.180 | 0.240 | 0.300 | 0.354 | 0.366 | 0.420 | 0.474 | 0.486 | 0.540 | 0.600 | 0.660 | 0.720 |

$s\left(x\right)$ (m) | 0.090 | 0.136 | 0.181 | 0.226 | 0.267 | 0.276 | 0.317 | 0.357 | 0.366 | 0.407 | 0.452 | 0.498 | 0.543 |

Section | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

$x/{c}_{r}$ (-) | 0.100 | 0.200 | 0.295 | 0.305 | 0.395 | 0.405 | 0.500 | 0.600 |

$\mathit{\alpha}{(}^{\circ})$ | $\mathit{Re}\left({\mathbf{10}}^{\mathbf{6}}\right)$ | ${\mathit{h}}_{\mathit{d}}/{\mathit{l}}_{\mathit{\mu}}(\%)$ |
---|---|---|

$[-2,...,32]$ | $[2.1,2.4,2.7]$ | $[0.000,0.019,0.025,0.069,0.125,0.250]$ |

Trip Strip | Height of Adhesive | Roughness Height | Total Disturbance Height | Relative Disturbance Height |
---|---|---|---|---|

${\mathit{h}}_{\mathit{ad}}$ (mm) | ${\mathit{k}}_{\mathit{s}}$ (mm) | ${\mathit{h}}_{\mathit{ad}}+{\mathit{k}}_{\mathit{s}}={\mathit{h}}_{\mathit{d}}$ (mm) | ${\mathit{h}}_{\mathit{d}}/{\mathit{l}}_{\mathit{\mu}}\mathbf{(}\mathbf{\%}\mathbf{)}$ | |

Trip dots | - | 0.15 | 0.15 | 0.019 |

Carborundum grit | 0.12 | 0.08 | 0.20 | 0.025 |

Carborundum grit | - | 0.55 | 0.55 | 0.069 |

Carborundum grit | 0.12 | 0.88 | 1.00 | 0.125 |

Carborundum grit | 0.12 | 1.88 | 2.00 | 0.250 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Buzica, A.; Debschütz, L.; Knoth, F.; Breitsamter, C.
Leading-Edge Roughness Affecting Diamond-Wing Aerodynamic Characteristics. *Aerospace* **2018**, *5*, 98.
https://doi.org/10.3390/aerospace5030098

**AMA Style**

Buzica A, Debschütz L, Knoth F, Breitsamter C.
Leading-Edge Roughness Affecting Diamond-Wing Aerodynamic Characteristics. *Aerospace*. 2018; 5(3):98.
https://doi.org/10.3390/aerospace5030098

**Chicago/Turabian Style**

Buzica, Andrei, Lisa Debschütz, Florian Knoth, and Christian Breitsamter.
2018. "Leading-Edge Roughness Affecting Diamond-Wing Aerodynamic Characteristics" *Aerospace* 5, no. 3: 98.
https://doi.org/10.3390/aerospace5030098