### Applications

- Supersonic Aerodynamics
- Transonic Aerodynamics
- External Aircraft Component Design

### Models active in this Validation Case

- Compressible flow
- Energy models
- Ideal gases
- Double Precision

### Objective

To understand the accuracy of Envenio’s EXN/AERO manycore CFD solver in the context of an aerospace wing study.

### Reference Case Description - ONERA Wing

The ONERA M6 wing geometry is based on a scale wind tunnel model and is referenced by NASA and ONERA as a validation case for CFD codes with compressible / transonic flow capability -- in particular their ability to resolve normal shocks on the surface of the wing. According to documentation on the ONERA website, the model and range of experimental conditions are meant to reflect conditions seen in both military and civil aviation scenarios.

Figure 1: ONERA wing geometry

### Mesh Description

#### Table of Geometric Specifications (NASA):

Span, B 1.1963 meters

Mean Aerodynamic Chord, c 0.64607

Aspect Ratio 3.8

Taper Ratio 0.562

Leading-edge Sweep 30.0 degrees

Trailing-edge Sweep 15.8 degrees

#### Domain & Position of Model:

Domain Size

Streamwise 16.5 m

Vertical 9.86 m

Horizontal 8.82 m

Leading edge (at root) relative to inlet: 7.62 m

Centered vertically

Airfoil root on domain boundary

#### Mesh Resolution in the vicinity of the ONERA wing:

CV Thickness Wall 5e-4 m

Surface Aspect Ratio (wing) ~1.5 (max)

Horizontal Aspect Ratio (all) ~14 (max)

Vertical Aspect Ratio (all) ~1000 (max)

#### Total Mesh Size: ~9 Million

### Simulation Completion Criteria

The simulation should be run for at least two ‘wash throughs’ of initial conditions in order to obtain accurate surface pressure values. For cases where far-field values are constant and equal to the initial conditions it is appropriate to use body length (i.e. wing chord) as the reference length. The number of iterations N for a washthrough is calculated using the equation below:

where c is chord, is the mean velocity magnitude and is the time step duration. After time step N is reached, the engineer monitored the total body forces and stopped the simulation when the cumulative average force reached a statistically steady value in time.

### Simulation Setup

#### Solver Control

Time Step 0.000002 seconds

EXN GPU Allocation 2 Nvidia K80

EXN CPU Allocation 3 Intel Xeon 2.6GHz

Stop Condition Convergence of body forces (Lift & Drag)

X-axis orientation Positive downstream

Y-axis orientation Positive upward, normal to ground plane

Z-axis orientation Positive to the right of the body, looking downstream

#### Boundary Conditions

Velocity [x,y,z] [268.666, 14.3623, 0]

Kinetic Energy 0.0001

K Dissipation 0.0003

Wall model Smooth wall

Outlet Constant Total Pressure = 315980 Pa

Temperature Total Temperature = 255.556 K

#### Domain Settings

Turbulence Model RANS SST

Flow type Compressible; Air, Ideal Gas

Precision Double

#### Other notes

Wash through time 0.0024 seconds (1200 time steps)

Total simulated time 0.023 seconds (11500 time steps, 9.6 washthroughs)

Mesh Topology Structured multiblock, one-to-one connections at block interfaces, data written as structured arrays in CGNS format

### Simulation Outcomes, Timing, and External Factors

Reporting Item |
EXN/Aero |

Time to 1st wash-through |
Simulated time of 0.0024 sec requires 1200 time steps. This is equivalent to real-time = |

Time to completion |
Simulated time of 0.023 sec requires 11500 time steps This is equivalent to real time = |

Real time per time step | 21 sec |

CPU type | Intel Xeon E5-2630 v2 @ 2.60GHz |

CPU cores | 3 |

GPU type | NVIDIA Tesla K80 |

GPU cores | 2 x 2496 CUDA core per card |

Available Memory | 128GB system, 24GB each K80 card |

### Results

The pressure coefficient profiles are shown for span-normalized positions along the wing, including y/B = 0.2, y/B = 0.44, y/b = 0.65, y/B = 0.80, y/B = 0.9 and y/B = 0.95, presented in Figures 2 thru 7. The merging of two shock profiles creates a v-shaped pressue distribution above the wing surface, shown in pressure iso-contours in Figure 8. The pressure coefficient contours for the cross section at y/b=0.44 is presented in Figure 9.

Figure 2: Comparison of EXN/Aero simulation and experimental results at y/B=0.20

Figure 3: Comparison of EXN/Aero simulation and experimental results at y/B=0.44

Figure 4: Comparison of EXN/Aero simulation and experimental results at y/B=0.65

Figure 5: Comparison of EXN/Aero simulation and experimental results at y/B=0.80

Figure 6: Comparison of EXN/Aero simulation and experimental results at y/B=0.90

Figure 7: Comparison of EXN/Aero simulation and experimental results at y/B=0.95

Figure 8: Pressure coefficient distribution across the wing span for different Mach numbers

Figure 9: Pressure coefficient contours at the cross section y/B=0.44

Results are based on a 9 million element k-omega RANS simulation done in EXN/Aero. The simulation ran for 11,500 time steps of 2 x 10^{-6} s with an average CPU time of 21 seconds per time step. Total simulation time was approximately 67 hours.

The comparison of pressure coefficient profiles show that EXN/Aero resolves the location of the forward shock more accurately than the rear shock. The experimental data also shows a more abrupt change in Cp at the shocks than do the simulation results. In subsonic regions, the simulation results track closely with experimental data. Spalart-Almaras computational results from a Cobalt simulation are shown inset in Figures 2 thru 7 and reveal similar discrepancies at the shocks. It is expected that mesh refinement at the shock locations can improve resolution and sharpness of shocks. This refinement work is planned as part of the Envenio QA process.

### Keywords

- External Flow
- SST-RANS
- Compressibility
- Energy Models
- Double Precision
- Integrated Boundary Values
- External Flow
- Supersonic Flow
- Lift & Drag
- Vehicle Maneuvering
- Transonic Flow

### References

- NPARC Alliance Validation Archive ONERA M6 Wing https://www.grc.nasa.gov/WWW/wind/valid/m6wing/m6wing.html
- ONERA-M6 Wing, Star of CFD http://www.onera.fr/en/actualites/image-du-mois/onera-m6-wing-star-cfd