# Atmospheric Disturbance Modelling for a Piloted Flight Simulation Study of Airplane Safety Envelope over Complex Terrain

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Stochastic Method of Atmospheric Turbulence Modelling

- low-altitude $h<1000$ $\mathrm{ft}$, where$$\begin{array}{cc}\hfill \phantom{\rule{1.em}{0ex}}& {L}_{w}=h,\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& {L}_{u}={L}_{v}=\frac{h}{{(0.177+0.000823h)}^{1.2}},\hfill \end{array}$$$$\begin{array}{cc}\hfill \phantom{\rule{1.em}{0ex}}& {\sigma}_{w}=0.1{W}_{20},\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& \frac{{\sigma}_{u}}{{\sigma}_{w}}=\frac{{\sigma}_{v}}{{\sigma}_{w}}=\frac{1}{{(0.177+0.000823h)}^{0.4}},\hfill \end{array}$$
- between low and medium/high altitudes 1000 $\mathrm{ft}$$<h<$ 2000 $\mathrm{ft}$, where turbulence quantities are determined by linearly interpolating between the values from the low altitude model at 1000 $\mathrm{ft}$ and the values from the high altitude model at 2000 $\mathrm{ft}$ [47].

## 3. Numerical Procedure

#### 3.1. Governing Equations

#### 3.2. Turbulence Closure

#### 3.2.1. Deardorff Subgrid-Scale Model

#### 3.2.2. Dynamic Subgrid-Scale Model

#### 3.3. Discretization and Numerics

#### 3.3.1. Numerical Grid

#### 3.3.2. Numerical Scheme

#### 3.3.3. Pressure Solver

#### 3.4. Boundary Conditions

#### 3.4.1. Topography and Surface Boundary Condition

- (i)
- grid cells in free atmosphere without adjacent solid surfaces,
- (ii)
- grid cells within orography,
- (iii)
- grid cells adjacent to solid surfaces, where a local surface layer is assumed.

#### 3.4.2. Mesoscale Nesting and Synthetic Turbulence Generation

#### 3.5. Grid Nesting and Computational Domain

^{3}in the x, y and z direction, with an equidistant grid spacing of 32 m. The x direction follows E-W axis and the y direction is parallel to S-N axis in the global coordinate system. In the vertical z direction, the bottom of the parent domain locates at 1746 m AMSL, which is determined by the topography information included in the dynamic driver. Further, two child domains of 2048 m × 2048 m × 3584 m were nested in the parent domain, The both child domains start from the parent domain bottom in the z direction and have a grid resolution of 8 m. We simulated the weather conditions of a summer day from UTC 06:00–12:00. Table 2 lists the information of the computational domain configuration.

## 4. Flight Simulation Test Campaign

#### 4.1. Concept of Flight Simulation Test Environment

- (i)
- by importing PALM instantaneous data with high temporal resolution with local mesh refinements (hereafter called turbulence case PALM),
- (ii)
- by activating Dryden turbulence model plus temporally mean data from PALM simulations without local mesh refinements (hereafter called turbulence case Dryden).

#### 4.2. Summary of Test Procedure

## 5. Results and Discussion

#### 5.1. PALM Simulation Evaluation

#### 5.1.1. Vertical Profiles

^{−1}. The low range of vertical speed indicates that the vertical motions of air parcels within the boundary layer are relatively slow. The stably stratified layer is confirmed by the vertical temperature profile as well. During the temporal evolution, due to the heating of the surface, the boundary layer continuously warms up and the potential temperature profiles shift to the right with a quasi-constant temperature gradient in vertical direction. In the first three hours (UTC 06:00–UTC 09:00), the negative temperature gradients indicate an unstable stratification near the surface, where turbulent wind can be induced.

#### 5.1.2. Temporal Evolution

#### 5.2. Results of Flight Simulation Test

#### 5.2.1. Spectral Analysis

#### 5.2.2. Results of Pilot Questionnaire

- (i)
- the mean value of case PALM must lie outside the $95\%$ confidence interval of case Dryden;
- (ii)
- the mean value of case Dryden must lie outside the $95\%$ confidence of case PALM.

## 6. Conclusions and Outlook

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ABL | Atmospheric Boundary Layer |

AMSL | Above Mean Sea Level |

BEH | Passo del Bernina |

COV | Piz Corvatsch |

COSMO | Consortium for Small-scale Modeling |

CFD | Computational Fluid Dynamics |

CLS | Control Loading System |

COV | Piz Corvatsch |

DNS | Direct Numerical Simulation |

FEAST | Finite Element Aircraft Simulation of Turbulence |

FFT | Fast Fourier Transform |

GUI | Graphic User Interface |

IMIS | Intercantonal Measurement and Information System |

INIFOR | Initialization and Forcing |

LES | Large Eddy Simulations |

LiDAR | Light Detection And Ranging |

NetCDF | Network Common Data |

PALM | Parallelized Large-Eddy Simulation |

PPL | Private Pilot License |

QGIS | Quantum Geographic Information System |

RANS | Reynolds-averaged Navier–Stokes |

SOBERT | Rotor Blade Element Turbulence |

SLEVE | Smooth LEvel VErtical |

SMN | SwissMetNet |

SRTM | Shuttle Radar Topography Mission |

STSB | Swiss Transportation Safety Investigation Board |

SGS | Sub-grid scale |

TKE | Turbulence Kinetic Energy |

UTC | Coordinated Universal Time |

WSL | Swiss Federal Institute for Forest, Snow and Landscape Research |

ZAV | Centre for Aviation |

ZHAW | Zurich University of Applied Sciences |

## Appendix A. Flight Simulation Test Campaign

#### Appendix A.1. Weight and Balance

MASS | ARM | ||||
---|---|---|---|---|---|

$\mathbf{Jb}.$ | $\mathbf{kg}$ | in | $\mathbf{m}$ | ||

Empty Mass | 1500 | $680.4$ | $85.9$ | $2.18$ | |

Position 1 | $176.4$ | 80 | $80.5$ | $2.04$ | |

Position 2 | $110.2$ | 50 | $80.5$ | $2.04$ | |

Position 3 | $110.2$ | 50 | $118.1$ | $3.00$ | |

Position 4 | $110.2$ | 50 | $142.8$ | $3.63$ | |

Fuel | $176.5$ | 80 | $95.0$ | $2.41$ | |

Overall | $2183.5$ | $990.4$ | $90.6$ | $2.30$ | $18.64\%$ M.A.C. |

#### Appendix A.2. Flight Test Card

#### Appendix A.3. Question Sheet

**Figure A2.**Cooper-Harper [69] handling qualities rating scale.

#### Appendix A.4. Pilot’s Experience

Pilot | Total No. of Hours | Hours under Similar Conditions | Technical Background |
---|---|---|---|

Pilot A | 95 | 10 | Aeronautical engineer |

Pilot B | 175 | 25 | Aeronautical engineer |

Pilot C | 55 | 5 | Aeronautical engineer |

Pilot D | 155 | 20 | Meteorologist |

#### Appendix A.5. Questionnaire Results

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**Figure 2.**Sketch of the Cartesian topography in PALM. The yellow cells represent orography, the white cells indicate fluid cells and the surface layer adjacent to orography are displayed in green on xz plane. The light blue lines represent the inner surface boundary of the surface layer on xz plane, while the orange lines defines the outer boundary on xz plane. According to the definition of the staggered C-grid, the black points on xy plane represent cell centres, where scalar variables are masked. The locations of u and v wind components displayed in red and blue define the location of impermeable orography surface.

**Figure 4.**PALM simulation domain for the mountainous region Samedan indicated in (

**a**) national map of Switzerland with relief, in (

**b**) SWISSIMAGE (source of the original images: the Federal Office of Topography in Switzerland). The border between Switzerland and Italy is displayed in green in (

**a**). The black frame in each subfigure represents the parent domain defined in the present case. The red frames in (

**b**) indicate the child domains of the parent domain.

**Figure 5.**Overview of the piloted flight simulation environment. The green blocks represent modules associated with the model of atmospheric disturbance, which is a submodel of the flight simulation model. The yellow blocks represent the energy management system’s subsystems.

**Figure 6.**Test scenarios marked in the Swiss federal 3D map viewer for (

**a**) the offline flight simulation and (

**b**) the piloted flight simulation (source of the original images: the Federal Office of Topography in Switzerland). The green curve in each subfigure represents the hypothetical flight path. The red shadowed zones represent the fluid cells of the child domains of the PALM simulation, which are defined in Figure 4 and Table 2. The black stars indicate the weather stations Piz Corvatsch 3294 m and Passo del Bernina 2260 m Bernina.

**Figure 7.**Horizontal mean vertical profiles of (

**a**) horizontal wind speed, (

**b**) vertical wind speed and (

**c**) potential temperature at the whole domain in time after the start of the simulation at 06:00 UTC.

**Figure 8.**Horizontal mean vertical profiles of (

**a**) total heat flux, (

**b**) sub-grid scale (SGS) heat flux and (

**c**) resolved-scale heat flux at the whole domain in time after the start of the simulation at 06:00 UTC.

**Figure 9.**Horizontal mean vertical profiles of (

**a**) flux component $wu$, (

**b**) flux component v and (

**c**) subgrid-scale (SGS) turbulent kinetic energy e at the whole domain in time after the start of the simulation at 06:00 UTC. The dashed curves indicate the simulated values by using Deardorff SGS model. The continuous curves present the simulated values by using the dynamic SGS model.

**Figure 10.**Horizontal mean variances of (

**a**) wind component u, (

**b**) wind component v and (

**c**) wind component w at the whole domain in time after the start of the simulation at 06:00 UTC. The dashed curves indicate the simulated values by using Deardorff SGS model. The continuous curves present the simulated values by using the dynamic SGS model.

**Figure 11.**Temporal evolutions of 10 min time-averaged horizontal wind speed ${u}_{h}$ at (

**a**) weather station Piz Corvatsch (COV) and (

**b**) weather station Passo del Bernina BEH over 21,600 s simulation time. The red lines present the measured data. The simulated data of Dynamic SGS model and Deardorff model (dashed) are displayed in black. The box in both subfigures in light blue shading indicate the time frame of interest for the flight simulation experiment, from 9000 s to 12,600 s after the start of the simulation at 06:00 UTC.

**Figure 12.**Temporal evolutions of wind direction at (

**a**) weather station Piz Corvatsch (COV) and (

**b**) weather station Passo del Bernina (BEH) over 21,600 s simulation time. The red scattered points solid lines present the hourly time-averaged measured data at COV and the 10-min averaged data at BEH. The solid lines represented 10 min time-averaged wind direction derived from the simulation. The box in both subfigures in light blue shading indicate the time frame of interest for the flight simulation experiment, from 9000 s to 12,600 s after the start of the simulation at 06:00 UTC.

**Figure 13.**Instantaneous vertical wind speed over the whole 3D domain with the original located at 10,800 s after start of the simulation at 06:00 UTC. The 3D volume rendering is displayed over the landsat satellite image of the computation domain (source of the original images: the Federal Office of Topography in Switzerland). The solid black lines denote the locations the y-z cross-section plots shown in Figure 14, at x = 8704 m (position 1) and x = 23,840 m (position 2) in the local simulation coordinate.

**Figure 14.**Instantaneous y-z cross-sections of vertical wind speed w and potential temperature $\theta $ (contours) at 10,800 s after the start of the simulation at 06:00 UTC, taken at (

**a**) x = 8704 m (position 1) and (

**b**) x = 23,840 m (position 2) in the local simulation coordinate. The green dashed line in (

**b**) indicated the position of x-y cross sections shown in Figure 15.

**Figure 15.**Instantaneous x-y cross-sections of potential temperature and horizontal flow fields (vector plots) at (

**a**) UTC 09:00, (

**b**) UTC 09:10, (

**c**) UTC 09:20 and (

**d**) UTC 09:30 at the altitude of 3200 m.

**Figure 16.**Spectra of wind velocity component (

**a**) u, (

**b**) v and (

**c**) w, derived from flight simulation output data of scenario Piz Corvatsch at an average altitude of 7500 ft (2280 m). The grey dashed line represents the reference $-3/5$-slope according to Kolmogorov’s law [71]. The $-2$-slope is plotted in green. The box in light blue shading indicates the time frame of interest for the flight simulation experiment, which is determined by the lower limit wave number ${k}_{min}$ of 2$\pi $/50 m${}^{-1}$ and the high limit wave number ${k}_{max}$ of 2$\pi $/5 m${}^{-1}$.

**Figure 17.**Spectra of airplane angular rate responses: (

**a**) roll rate p, (

**b**) pitch rate q and (

**c**) yaw rate r, derived from flight simulation output data of scenario Piz Corvatsch at an average altitude of 7500 ft (2280 m). The grey dashed line represents the reference $-3/5$-slope according to Kolmogorov’s law [71]. The $-2$-slope is plotted in green. The box in light blue shading indicates the time frame of interest for the flight simulation experiment, which is determined by the lower limit wave number ${k}_{min}$ of 2$\pi $/50 m${}^{-1}$ and the high limit wave number ${k}_{max}$ of 2$\pi $/5 m${}^{-1}$.

**Figure 18.**Spectra of wind velocity component (

**a**) u, (

**b**) v and (

**c**) w, derived from flight simulation output data of scenario Passo del Bernina at an average altitude of 10,500 ft (3200 m). The grey dashed line represents the reference $-3/5$-slope according to Kolmogorov’s law [71]. The dashed dot green line denotes the reference $-1$-slope. The box in light blue shading indicates the time frame of interest for the flight simulation experiment, which is determined by the lower limit wave number ${k}_{min}$ of 2$\pi $/50 m${}^{-1}$ and the high limit wave number ${k}_{max}$ of 2$\pi $/5 m${}^{-1}$.

**Figure 19.**Spectra of airplane angular rate responses: (

**a**) roll rate p, (

**b**) pitch rate q and (

**c**) yaw rate r, derived from flight simulation output data of scenario Passo del Bernina at an average altitude of 10,500 ft (3200 m). The grey dashed line represents the reference $-3/5$-slope according to Kolmogorov’s law [71]. The dashed green line denotes the reference $-1$-slope. The box in light blue shading indicates the time frame of interest for the flight simulation experiment, which is determined by the lower limit wave number ${k}_{min}$ of 2$\pi $/50 m${}^{-1}$ and the high limit wave number ${k}_{max}$ of 2$\pi $/5 m${}^{-1}$.

Symbol | Value | Description |
---|---|---|

${c}_{\mathrm{m}}$ | $0.1$ | SGS model constant |

${c}_{\mathrm{p}}$ | $1005\phantom{\rule{3.33333pt}{0ex}}\mathrm{J}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{kg}}^{-1}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{K}}^{-1}$ | Heat capacity of dry air at constant pressure |

g | $9.81\phantom{\rule{3.33333pt}{0ex}}{\mathrm{ms}}^{-2}$ | Gravitational acceleration |

${p}_{0}$ | $1000\phantom{\rule{3.33333pt}{0ex}}\mathrm{hPa}$ | Reference pressure |

${R}_{\mathrm{d}}$ | $287\phantom{\rule{3.33333pt}{0ex}}\mathrm{J}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{kg}}^{-1}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{K}}^{-1}$ | Specific gas constant for dry air |

${R}_{\mathrm{v}}$ | $461.51\phantom{\rule{3.33333pt}{0ex}}\mathrm{J}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{kg}}^{-1}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{K}}^{-1}$ | Specific gas constant for water vapor |

$\kappa $ | $0.4$ | Von Kármán constant |

$\mathsf{\Omega}$ | $\mathsf{\Omega}=0.729\times {10}^{-4}$$\mathrm{rad}{\mathrm{s}}^{-1}$ | Angular velocity of the Earth |

Spatial Domain | Number of Grid | Grid Resolution | Domain Origin in Coordinates System | Time Domain | |
---|---|---|---|---|---|

$({\mathit{n}}_{\mathbf{x}},{\mathit{n}}_{\mathbf{y}},{\mathit{n}}_{\mathbf{z}})\phantom{\rule{3.33333pt}{0ex}}[-]$ | $({\mathit{d}}_{\mathbf{x}},{\mathit{d}}_{\mathbf{y}},{\mathit{d}}_{\mathbf{z}})\phantom{\rule{3.33333pt}{0ex}}\left[\mathit{m}\right]$ | $\mathit{CH}\mathbf{1903}+$ | $\mathit{WGS}\mathbf{84}$ | ||

Parent domain | $\left(\mathrm{768,576,128}\right)$ | $\left(\mathrm{32,32,32}\right)$ | (774,572 E, 133,915 N) | $({9.71}^{\circ}$ E, ${46.33}^{\circ}$ N) | |

Child domain 1 | $\left(\mathrm{256,256,448}\right)$ | $\left(\mathrm{8,8,8}\right)$ | (778,864 E, 140,087 N) | $({9.76}^{\circ}$ E, ${46.39}^{\circ}$ N) | UTC 06:00–UTC 12:00 |

Child domain 2 | $\left(\mathrm{256,256,448}\right)$ | $\left(\mathrm{8,8,8}\right)$ | (793,612 E, 141,947 N) | $({9.96}^{\circ}$ E, ${46.40}^{\circ}$ N) |

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## Share and Cite

**MDPI and ACS Style**

Liu, X.; Abà, A.; Capone, P.; Manfriani, L.; Fu, Y.
Atmospheric Disturbance Modelling for a Piloted Flight Simulation Study of Airplane Safety Envelope over Complex Terrain. *Aerospace* **2022**, *9*, 103.
https://doi.org/10.3390/aerospace9020103

**AMA Style**

Liu X, Abà A, Capone P, Manfriani L, Fu Y.
Atmospheric Disturbance Modelling for a Piloted Flight Simulation Study of Airplane Safety Envelope over Complex Terrain. *Aerospace*. 2022; 9(2):103.
https://doi.org/10.3390/aerospace9020103

**Chicago/Turabian Style**

Liu, Xinying, Anna Abà, Pierluigi Capone, Leonardo Manfriani, and Yongling Fu.
2022. "Atmospheric Disturbance Modelling for a Piloted Flight Simulation Study of Airplane Safety Envelope over Complex Terrain" *Aerospace* 9, no. 2: 103.
https://doi.org/10.3390/aerospace9020103