# Simulation and Modeling of Rigid Aircraft Aerodynamic Responses to Arbitrary Gust Distributions

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## Abstract

**:**

## 1. Introduction

## 2. Gust Modeling Methods

## 3. Flow Solver

## 4. Test Cases

#### 4.1. Two-Dimensional NACA0012 Airfoil

#### 4.2. The HIRENASD Model

## 5. Results and Discussions

#### 5.1. Validation and Verification of User-Defined Codes

#### 5.2. Simulation Results of NACA0012 Airfoil

#### 5.3. Simulation Results of HIRENASD Configuration

#### 5.4. Computational Costs

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

a | acoustic speed, m s${}^{-1}$ |

c | chord length |

CFD | computational fluid dynamics |

CPU | central processing unit |

${C}_{L}$ | lift coefficient |

${C}_{L\alpha}$ | lift curve slope |

${C}_{{L}_{wg}}$ | lift-gust curve slope |

$Cp$ | pressure coefficient, $(p-{p}_{\infty})/{q}_{\infty}$ |

CREATE | Computational Research and Engineering Acquisition Tools and Environments |

DDES | Delayed Detached Eddy Simulation |

DoD | Department of Defense |

ETW | European Transonic Windtunnel |

H | gust gradient distance, m |

HIRENASD | high Reynolds number aero-structural dynamics |

HPC | High Performance Computing |

$\Delta L$ | incremental lift |

M | Mach number, V/a |

$\Delta n$ | vertical acceleration increment |

p | static pressure, N/m${}^{2}$ |

${p}_{\infty}$ | free-stream pressure, N/m${}^{2}$ |

$\mathsf{\Psi}\left(s\right)$ | Küssner exponential series approximation or sharp edge gust data |

${q}_{\infty}$ | free-stream dynamic pressure, N/m${}^{2}$ |

s | normalized time |

S | wing area |

SA | Spalart–Allmaras |

SARC | Spalart–Allmaras with rotational and curvature correction |

RANS | Reynolds Averaged Navier Stokes |

t | time, s |

USAFA | United States Air Force Academy |

${V}_{\infty}$ | free-stream velocity, m s${}^{-1}$ |

u,v,w | velocity components, m s${}^{-1}$ |

${w}_{g}$ | gust vertical velocity, m s${}^{-1}$ |

${w}_{g,max}$ | maximum gust vertical velocity, m s${}^{-1}$ |

X | gust penetration distance, m |

x,y,z | grid coordinates, m |

$y+$ | non-dimensional wall normal distance |

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**Figure 1.**A continuous gust being singled out with a ramp and a one-minus-cosine gust profile. This figure was adapted from [36].

**Figure 2.**NACA0012 grid. Grid consists of 72,852 cells. Grid has pismatic sublayers around airfoil and tetrahedral cells in the outer region.

**Figure 5.**Validation of HIRENASD CFD models with experimental data. For section position, refer to [32]. In the figures, solid lines show Cobalt predictions using SARC turbulence models. The upper surfaces are shown with yellow-filled markers. The black-filled markers show the bottom surface. Simulations and experimental data correspond to Mach 0.7, a Reynolds per length of 7 millions, and an angle of attack of 1.5${}^{\circ}$.

**Figure 6.**Verification of user-defined codes. In (

**a**), lift coefficient values are plotted vs. the angle of attack using the far-field boundary condition of Cobalt and the user-defined scripts of calm conditions. In (

**b**), a 1-cosine vertical gust profile is simulated using the analytical function and tabulated data. The 1-cosine function has an amplitude of 1 m/s, one cycle, and a gust gradient distance of about 17c.

**Figure 7.**CFD and analytical data of the lift-gust curve slope due to a unit sharp-edge gust at M = 0.1 and 0.5. The test case is a flat plate 1 m long. C

_{Lwg}, the lift-gust curve slope, is defined as $\frac{2\pi}{V.wg}[{C}_{L}(wg\ne 0,t)-{C}_{L}(wg=0,t=0)]$ and has units of per radian. M = 0 analytical data are from Jones approximation function [4]; analytical data at M = 0.5 are from Mazelsky and Drischle [5].

**Figure 8.**NACA0012 airfoil responses to a unit sharp-edge gust at Mach numbers of 0.1, 0.3, and 0.5.

**Figure 9.**NACA0012 airfoil responses to a 1-cosine gust at Mach numbers of 0.1, 0.3, and 0.5. ΔC

_{L}is defined as C

_{L}(wg ≠ 0, t) − C

_{L}(wg = 0, t = 0).

**Figure 10.**NACA0012 airfoil responses to a ramp gust at Mach numbers of 0.1, 0.3, and 0.5. ΔC

_{L}is defined as C

_{L}(wg ≠ 0, t) − C

_{L}(wg = 0, t = 0).

**Figure 12.**HIRENASD and NACA0012 airfoil responses to a unit sharp-edge gust at Mach numbers of 0.1 and 0.7.

**Figure 13.**HIRENASD responses to a unit sharp-edge gust at Mach number of 0.1. Symmetry plane is colored by vertical velocity. Wing is colored by pressure coefficient.

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**MDPI and ACS Style**

Ghoreyshi, M.; Greisz, I.; Jirasek, A.; Satchell, M.
Simulation and Modeling of Rigid Aircraft Aerodynamic Responses to Arbitrary Gust Distributions. *Aerospace* **2018**, *5*, 43.
https://doi.org/10.3390/aerospace5020043

**AMA Style**

Ghoreyshi M, Greisz I, Jirasek A, Satchell M.
Simulation and Modeling of Rigid Aircraft Aerodynamic Responses to Arbitrary Gust Distributions. *Aerospace*. 2018; 5(2):43.
https://doi.org/10.3390/aerospace5020043

**Chicago/Turabian Style**

Ghoreyshi, Mehdi, Ivan Greisz, Adam Jirasek, and Matthew Satchell.
2018. "Simulation and Modeling of Rigid Aircraft Aerodynamic Responses to Arbitrary Gust Distributions" *Aerospace* 5, no. 2: 43.
https://doi.org/10.3390/aerospace5020043