Statistical data

In this section the relevant statistical data for the flow around the wing-body junction computed with MIGALE is given. The reported data is the one mentioned in Table 1 of the list of desirable quantities (PDF).

The data is available as:

In .vtu (ASCII) format for statistical data.
In .csv (text) format as vertical profiles at various locations.

This database is a first attempt of DNS for the present wing-body junction flow problem. Although affected by some spatial under-resolution and the need of a larger time window for the collection of the statistics, the information provided is of primary importance for future computational studies. The database will be further studied in the near future and additional results added later.

Volume data

Volumetric data of the statistics are provided here. For more information regarding the stored quantities and the storage format, please refer to the storage format guidelines.

The available files are:

Surface data

Surface data of the statistics are provided here. For more information regarding the stored quantities and the storage format, please refer to the storage format guidelines.

The available files are:

The pressure coefficient contour on the bottom surface is reported in Fig. 13. Due to the configuration geometry, a favourable pressure gradient is generated downstream of the leading edge, where the flow goes around the wing profile, resulting in a reduction of $C_{p}$ (blue area). This reduction attenuates when moving away from the airfoil, but it is still appreciable along the lateral boundaries, i.e., $\max {(C_{p,lateral})}=-0.15$ . Accordingly, although small, a blockage effect on the flow due to the lateral boundaries is present. As expected for a flow in the incompressible regime (here $Ma=0.078$ ), the maximum value of $C_{p}$ is close to 1 at the leading edge of the wing.

Fig. 14 shows the time averaged dimensionless wall shear stress distribution on the floor. It is conceivable that the streaky behaviour of the wall shear stress can be ascribed to the need of a larger time window to collect averages.

The favourable pressure gradient on the side of the airfoil nose induces a flow acceleration, which is the main cause of the increase of the wall shear stress. Downstream the wing, in the wake region, the traces of the horseshoe vortexes on the floor can also be observed. Vortices are also visible by the streamlines at selected planes shown in Fig. 15.


Figure 13: Wing-body junction. Contour of pressure coefficient on the bottom surface for $-3<x/T<10$


Figure 14: Wing-body junction. Contour of averaged dimensionless wall shear stress on the bottom surface for $-12.75<x/T<10$


Figure 15: Wing-body junction. Streamlines at selected planes, i.e., symmetry plane (streamlines generated with $x$ - and $y$ - components of the averaged velocity field) and cross section planes (streamlines generated with $y$ - and $z$ - components of the averaged velocity field) at $x/T=0.75$ and $x/T=4.46$ , superimposed on contour of averaged dimensionless wall shear stress

Profile data

Profile data have been extracted from the symmetry plane $z/T=0$ at different streamwise locations ( $x/T=-0.45,-0.40,-0.35,-0.30,-0.25,-0.20,-0.15,-0.10,-0.05,-0.01$ ) and made dimensionless with respect to reference quantities ( $u_{ref}$ , $\rho _{ref}$ ). The data stored in each file are:

vertical location $y/T$
average velocity components $U_{i}/u_{ref}$
Reynolds stress components $R_{ij}/(\rho _{ref}u_{ref}^{2})$
turbulent kinetic energy $k/u_{ref}^{2}$

Profiles at selected streamwise locations are reported in Fig. 16.

profile_midplane_-0.45.csv

profile_midplane_-0.40.csv

profile_midplane_-0.35.csv

profile_midplane_-0.30.csv

profile_midplane_-0.25.csv

profile_midplane_-0.20.csv

profile_midplane_-0.15.csv

profile_midplane_-0.10.csv

profile_midplane_-0.05.csv

profile_midplane_-0.01.csv

Table 4: Wing-body junction. Profiles on symmetry plane at different streamwise locations

Figure 16: Wing-body junction. Profiles at symmetry plane at different stremwise locations

Contour data

Contour data of the averaged velocity components $U$ and $V$ , the three normal stresses $R_{xx}$ , $R_{yy}$ and $R_{zz}$ , the turbulent kinetic energy $k$ , and the shear stress $R_{xy}$ in the symmetry plane are provided in Fig. 17. As the region depicted is in front of the leading edge, it is visible the effect of the horse-shoe vortex: while the streamwise component of the velocity becomes negative above the horizontal solid wall, the normalwise one presents a large negative region close to the leading edge. This results in a clockwise rotating vortex. Within this vortex the Reynolds stresses as well as the turbulent kinetic energy show the maximum intensity. Moreover, looking more in detail, it is possible to notice the presence of a tiny vortex in anticlockwise rotation clinging to the leading edge of the wing, near the wing-body junction. All contours are normalized with respect to the reference quantities.

Figure 17: Wing-body junction. Contours of average velocity compoents, Reynolds normal stresses, turbulent kinetic energy and Reynolds shear stress at symmetry plane

Contributed by: Francesco Bassi (UNIBG), Alessandro Colombo (UNIBG), Francesco Carlo Massa (UNIBG), Michael Leschziner (ICL/ERCOFTAC), Jean-Baptiste Chapelier (ONERA) — University of Bergamo (UNIBG), ICL (Imperial College London), ONERA

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Computational Details

Quantification of Resolution

Statistical Data

Instantaneous Data

Storage Format