Introduction

This test case features wing mounted on a flat plate, which is representative of the wing-body junction flow problems encountered in applications of aeronautical interest. The flow features the interaction between the incipient turbulent boundary layer and the mounted airfoil and the main physical phenomenon of interest is the horseshoe vortex developing at the junction and the corner separation. This flow is also highly 3D and anisotropic regarding the turbulent stresses. Establishing a DNS database of this flow is of crucial interest since it has been shown that RANS models (both Boussinesq and Reynolds stresses-based models) display strong difficulties in recovering data from the available experiments. Such a database allows for a more thorough availability of the flow field with respect to the experiments and gives the possibility of using Machine Learning or data-assimilation techniques to improve standard RANS models.

Review of previous studies and choice of test case

A thorough listing of existing experimental and numerical studies regarding wing-body junction flows can be found in Gand et al. (2010). The present DNS is based on the configuration considered in the simulations by Apsley & Leschziner (2001), who were based themselves on the experimental studies by Devenport and Simpson (1990) and Fleming et al. (1995). The Reynolds number based on the airfoil thickness is similar to the experiment and its value is 115,000 and the flow is almost incompressible with a Mach number based on the freestream velocity of 0.078. The uDNS setup reproduces the experimental conditions but with half the experimental impacting boundary layer thickness. Therefore a direct comparison with the experimental results is not possible for the present uDNS.

Description of the test case

Geometry and flow parameters

Fig. 2 displays a view of the computational domain and flow configuration geometry. The reference length scale is the wing thickness $T=71.7\,{\text{mm}}$ , and the corresponding Reynolds number $Re=115\,000$ . The wing is formed by a 3:2 semi-elliptic nose with a NACA0020 tail profile. The resulting chord-to-thickness ratio is $4.254$ . The computational domain size is $62.75T$ in the stream direction, $8T$ in the span direction and $3T$ in the wall-normal direction. The coordinates origin is located at the root leading edge of the airfoil. The is no flow incidence relatively to the wing, corresponding to an angle of attack of $0$ degrees. Parameters of the flow (air with $\gamma =1.4$ , $MM=28.96\,{\text{kg/kmol}}$ , $\mu =1.716\cdot 10^{-5}\,{\text{Pa s}}$ ) are reported in Tab. 1.

Figure 2: Wing-body junction. Domain for the DNS simulation

${Ma}$	${Re}$	${T_{ref}}$	${u_{ref}}$	${\rho _{ref}}$	${p_{ref}}$
${0.078}$	${115\,000}$	${298.15\,{\text{K}}}$	${27.00\,{\text{m/s}}}$	${1.019\,{\text{kg/m}}^{3}}$	${87251\,{\text{Pa}}}$

Table 1: Wing-body junction. Flow parameters

Boundary conditions | TO UPDATE !!!

Although for DNS the inflow boundary conditions are different than RANS, to allow a valid comparison they must guarantee the same boundary layer properties at a given point, hereinafter referred to as checkpoint, upstream of the rounded step, i.e., ${x_{ckp}/H=-3.5}$ . At this position ${x_{ckp}}$ , the properties to be matched are the Reynolds number based on the momentum thickness ${Re_{\theta }=1,780}$ , the Reynolds number based on the friction velocity ${Re_{\tau }=700}$ and the boundary layer thickness $\delta _{99}/H=0.241$ . As a technique to promote the laminar-turbulent transition of the boundary layer and reduce the upstream length of the domain, a local tripping term inspired by the work of Housseini et al. (2016) and Schlatter and Örlü (2012) is used. To define the mesh density and the computational domain size that ensure the target boundary layer integral parameters at ${x_{chp}}$ , a precursory computational campaign for the turbulent flow over a flat plate was performed. According to the outcomes of this campaign, the inlet boundary is located at ${x/H=-12.7}$ , where the Blasius laminar velocity profile computed at ${Re_{x}=650,000}$ , the uniform static pressure ${P_{s,ref}}$ and the uniform total temperature ${T_{t,inflow}}$ are imposed, see UFR 3-36: Table 2 for dimensional values of each quantity. At location ${x/H=-12.1}$ , within the laminar boundary layer region, the tripping source term is activated to promote the transition to turbulence, see Fig. 2. At the outlet boundary, placed at $x/H=24.0$ , the static pressure ${P_{s,ref}}$ is imposed with an exit-pressure outflow boundary condition. To mitigate spurious perturbations possibly originating at the outlet boundary, the mesh is coarsened in the streamwise direction for ${x/H>13.82}$ . The upper boundary is a permeable far-field Riemann boundary condition located $180.0H$ from the no-slip adiabatic wall downstream the smooth step and computed via the exact Riemann solver. Finally, side planes are considered as periodic with a distance from each other of ${\Delta z=3H}$ .

For this particular flow configuration, we aim at simulating a transitional boundary layer in order to replicate the flow conditions of the experiment. To do so, a Blasius velocity profile is imposed at the inlet corresponding to $Re_{x}=900,000$ with a uniform temperature. A laminar boundary layer is then established, and a flow perturbation is introduced at $Re_{x}=950,000$ with amplitude $A_{T}={\frac {\rho _{ref}U_{ref}^{2}}{T}}$ to trigger transition to turbulence. The total length of the boundary layer was determined such that the turbulent boundary layer thickness upwind the airfoil reaches half of the experimental value. Symmetry conditions are imposed at the lateral boundary conditions ( $z=\pm 4T$ ). The bottom boundary is a no-slip adiabatic wall type for $xz$ planes at $y=0$ between $x=-12.75T$ and $x=17T$ , and symmetry type between $x=17T$ and $x=67T$ . The outlet is located away from the profile at $x=67T$ , and the zone between $x=17T$ and $x=67T$ acts as a sponge layer, featuring increasingly coarse elements such that a constant flow field is recovered when reaching the outlet.

References

Apsley, D.D. and Leschziner, M. (2001): Investigation of Advanced Turbulence Models for the Flow in a Generic Wing-Body Junction. Flow, Turbulence and Combustion, Vol. 67, pp. 25–55
Gand, F., Deck, S., Brunet, V., and Sagaut, P. (2010): Flow dynamics past a simplified wing body junction. Physics of Fluids, Vol. 22, 115111
Devenport W.J. and Simpson R.L. (1990): Time-dependent and time-averaged turbulence structure near the nose of a wing-body junction. Journal Fluid Mechanics, Vol. 67, pp. 23–55
Fleming, J.L., Simpson, R.L., Cowling, J.E. and Devenport, W.J. (1993): An experimental study of wing-body junction and wake flow. Exp. Fluids Vol. 14, pp. 366–378
S. Hosseini, R. Vinuesa, P. Schlatter, A. Hanifia and D. Henningson (2016): Direct numerical simulation of the flow around a wing section at moderate Reynolds number, International Journal of Heat and Fluid Flow, 61:117–128
Schlatter, P. and Örlü, R. (2012): Turbulent boundary layers at moderate Reynolds numbers: inflow length and tripping effects,Journal of Fluid Mechanics, 710:5–34

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

Front Page

Description

Computational Details

Quantification of Resolution

Statistical Data

Instantaneous Data

Storage Format