# Wake-Model Effects on Induced Drag Prediction of Staggered Boxwings

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## Abstract

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## 1. Introduction

#### 1.1. Problem Definition

#### 1.2. Contribution of Present Work

## 2. Relevant Theory

## 3. Computational Models

#### 3.1. Test Cases

#### 3.2. Higher-Order Potential-Flow Model

#### 3.3. Euler-Flow Model

## 4. Results and Discussion

#### 4.1. Spanwise Load Distribution

#### 4.2. Computed Span Efficiency Factor

#### 4.3. Wake Traces on Partition Surface

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

b | Wing span |

${C}_{n}=\frac{2\xb7\Gamma (\eta ,\zeta )}{c}$ | Sectional normal force coefficient |

${C}_{n,\phantom{\rule{4.pt}{0ex}}opt}=\frac{2\xb7{\Gamma}_{opt}(\eta ,\zeta )}{c}$ | Optimum sectional normal force coefficient |

c | Chord length |

${c}_{ref}=\frac{{S}_{1,2}}{b}$ | Reference chord length |

${d}_{TE}$ | Longitudinal trailing edge separation |

${D}_{i}$ | Induced drag |

$e=\frac{{D}_{i,\mathrm{ref}}}{{D}_{i}}=\frac{{\left(L/{q}_{\infty}\right)}^{2}}{\pi \xb7{b}^{2}\xb7\left({D}_{i}/{q}_{\infty}\right)}$ | Span efficiency factor |

$(h/b)$ | Height-to-span ratio |

L | Lift |

${l}_{1\to 2}=\frac{{d}_{TE}}{{c}_{ref}}$ | Stagger factor |

${q}_{\infty}=\frac{{\rho}_{\infty}}{2}\xb7{V}_{\infty}$ | Freestream stagnation pressure |

${V}_{\infty}$ | Freestream velocity |

x, y, z | Cartesian coordinates |

$\alpha $ | Freestream angle of attack |

$\Gamma $ | Circulation |

$\eta =\frac{y}{b}$ | Non-dimensional wing span |

${\Lambda}_{1,2}=\frac{{b}_{1,2}^{2}}{{S}_{1,2}}$ | Single wing aspect ratio |

${\rho}_{\infty}$ | Freestream air density |

$\zeta =\frac{z}{h}$ | Non-dimensional height |

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**Figure 2.**Schematic illustration of the flowfield, transverse plane (TP) and the correction volume ${\Omega}_{wake}$ enclosing the wake region to compute the spurious entropy drag contribution.

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**MDPI and ACS Style**

Schirra, J.; Bissonnette, W.; Bramesfeld, G. Wake-Model Effects on Induced Drag Prediction of Staggered Boxwings. *Aerospace* **2018**, *5*, 14.
https://doi.org/10.3390/aerospace5010014

**AMA Style**

Schirra J, Bissonnette W, Bramesfeld G. Wake-Model Effects on Induced Drag Prediction of Staggered Boxwings. *Aerospace*. 2018; 5(1):14.
https://doi.org/10.3390/aerospace5010014

**Chicago/Turabian Style**

Schirra, Julian, William Bissonnette, and Götz Bramesfeld. 2018. "Wake-Model Effects on Induced Drag Prediction of Staggered Boxwings" *Aerospace* 5, no. 1: 14.
https://doi.org/10.3390/aerospace5010014