Best Practice Advice AC1-02
RAE M2155 Wing
Application Challenge 1-02 © copyright ERCOFTAC 2004
Best Practice Advice for the AC
Key Fluid Physics
The wing RAE M2155 has been the subject of many numerical simulations, has been chosen to validate and assess turbulence models in E.C. funded project AVTAC . The experiments [2,3] were performed at the DERA 8ft x 6ft transonic wind tunnel in the Mach number range 06 - 0.87 and at a Reynolds number (based on the geometric mean chord) of 4 x 106.
The wing RAE M2155 is swept, of low-aspect ratio, and has the plantform reported in Figure 1 with the following reference dimensions :
• Root chord = 914.4 mm.
• Geometric mean chord = 629.1 mm.
• Aerodynamic mean chord = 677.0 mm.
• Half-span = 1028.7 mm.
Figure1: Geometry of the wing RAE M2155
The wing presents a complex flow field with three-dimensional separations and triple shock waves structure. The boundary layers are subjected to strong adverse pressure gradients (the trailing edges being heavily loaded), a regime which is difficult for numerical methods but of great importance in wing design.
Two forms of separation have been found in the experiments; a trailing-edge separation and a shock-induced separation. The cases with shock-induced separation has reattachment upstream of the trailing edge. Four conditions at Reynolds number 4.1 x 106 have been chosen for a more detailed study :
• CASE 1
The Mach number is 0.744 and the angle of incidence is 2.5o. Flow separation does not occur and there are no strong shock waves. The boundary layer on the lower surface experiences significant skew aft of mid-chord.
• CASE 2
The Mach number is 0.806 and the angle of incidence is 2.5 o. A triple shock wave occurs over the inner half-span of the upper surface. Outboard of this there is a single shock which provokes local separation. The lower surface flow is similar to Case 1 but with greater skew. On the lower surface no shock waves are present, and the adverse pressure gradient and the sweep of the wing causes a deviation of the flow from the free-stream direction up to 45 o degrees.
• CASE 3
The Mach number is 0.843 and the angle of incidence is 1.5o. A triple shock wave occurs over the 80% of span., although the flow remains attached everywhere. A shock wave forms on the lower surface at ~80% span.
• CASE 4
The Mach number is 0.854 and the angle of incidence is 1.5 °. The upper surface boundary layer separates at the trailing edge (between 30% and 55% span) and is close to separation behind the outboard leg of the triple shock. On the lower surface in the region of the outboard shock, the boundary layer is extremely skewed (the angle between the flow direction and the wing generator is less than 10 °).
The flow is characterized by the following underlying regimes :
• Boundary layers subject to adverse pressure gradients
• Shock - boundary layer interaction
Possible uncertainities are :
• Tunnel wall interference effects that, during the experiments, were found to be significant particularly at the higher free stream Mach numbers.
• Length of the computational domain, and in particular the location of the inflow plane.
• The interaction between the boundary layers developing on the wing surface and on the tunnel wall where the wing is mounted on.
Computational Domain and Boundary Conditions
The computational domain should include the tunnel walls. The inflow plane needs to be located at 3-5 times the root chord of the wing, and the outflow plane at least at 5 times the wing root chord.
The wing was mounted directly on the tunnel wall, so that the wall boundary layer and wing boundary layer interact. It is advisable therefore to model both the boundary layer developing on the wing and on the tunnel wall where the wing in mounted on.
The following boundary conditions should be used :
• Inflow : Velocity and density prescribed, pressure extrapolated from interior
• Outflow : Pressure prescribed, velocity and density extrapolated from interior
• Tunnel walls where the wing is mounted on : No slip
• Tunnel walls not connected to the wing : Slip
• Wing surfaces : No slip
At the inflow, the turbulent kinetic energy should be in the range 0.01%<k<0.2%
Discretisation and Grid Resolution
Based on the comparison between numerical and experimental results presented in the D30 and on the BPA drawn in the associated UFR3-03 and UFR 3-05, the following advices can be given :
• Discretisation method
Use at least a second order accurate scheme with as little as numerical dissipation possible.
• Grid and grid resolution
For low Reynolds number turbulence models, use a y+ of O(1) for the first layer of cells.
For a wall function approach, use a mesh with wall adjacent heights 50 < y+ < 100
Use 5-10 grid points within a distance y+=20 from the wall
Use 30-60 grid points inside the boundary layer
Use at least 10 grid points in the stream-wise direction across the shock
Between the four flow conditions studied in more detail during the experiments, the case 2 seems to be the most severe and relevant to assess a CFD method. At the case 2 condition (Figure 2), the flow on the upper surface of the wing presents a triple shock wave system from the root to about 50% of the span, and a single shock wave from about the 50% to the tip. A flow separation starts where the three shocks join together and ends at about 90% of the span. The flow is very close to separate also in the trailing edge zone being subject to a strong adverse pressure gradient. The prediction of the shock waves system, of the separation and reattachment lines and of the pressure recovery behind the shock and in the trailing edge zone are the challenges for the turbulence models. In fact, the turbulence model should be able to simulate a flow in conditions of rapid change of its mean characteristics, in order to reproduce the shock boundary layer interaction, and the interaction between a developing boundary layer and a re-attaching shear layer in the zone of pressure recovery.
Figure 2: Wing RAE M2155 – case 2 Oil flow visualization
Based on the results achieved by QinetiQ  and CIRA , and on the conclusions drawn in the related UFR documents, the following BPA can be given • Turbulence modelling:
Use turbulence models with a non linear constitutive relation or the Menter SST k-ω to better predict the position of the shocks. Linear turbulence models provide shocks located more downstream than the experimental data (figure 3).
Use turbulence models with a non linear constitutive relation or the Menter SST k-ω to better predict the pressure recovery behind the shocks (figure 3).
Use turbulence models with a non linear constitutive relation or the Menter SST k-ω to better predict the velocities in the zones where the flow is separated or very close to separate (Figure 4).
• Transition modelling:
Nothing can be said about transition modelling because transition was fixed in the experiments and in the numerical simulations at 5% of the local chord.
Figure 3 : Wing RAE M2155 Case 2 – Pressure Coefficient
Figure 4: Wing RAE M2155 –case 2
Velocity profile at x/c=0.40 y/b=0.77
Recommendations for Future Work
Turbulence modelling plays a key role for the simulation of the flow over the wing RAE M2155. Further simulations of this flow using other turbulence models like the the Durbin v2-f model  are hopefully to be performed. A numerical experiment to evaluate the effect that key features of turbulence models, like realisability, near-wall behaviour, Reynolds stresses anisotropy, turbulent length scale, have on the simulation of this kind of flow would be of interest.
 Gould A., Courty J.C., Sillen M., Elsholz E., Abbas A. The AVTAC project – a review of European aerospace CFD. ECCOMAS 2000 Congress, September 11th – 14th 2000, Barcelona Spain
 M.C.P. Firmin, M.A. McDonald. Measurements of the flow over a low-aspect ratio wing in the Mach number range 0.6 to 0.87 for the purpose of validation of computational methods. Part 1: wing design, model construction, surface flow. Vols. 1 & 2, D.R.A. Technical Reports 92016, 1992.
 AGARD-AR-303, Vol II, Test Case B1.1, 1994
 Peshkin D. A. Non-linear Reynolds stress relations and the RAE M2155 test cases. Technical Report: DERA/MSS/MSFC1/TR004301. Strictly limited circulation.
 Catalano P., Amato M. An evaluation of RANS turbulence modelling for aerodynamic applications. Aerospace Science and Technology J., Vol. 7, Issue 7, pp. 493 – 509, 2003
Durbin P.A. Near-wall turbulence closure modelling without damping functions. Theoretical and Computational Fluid Dynamics, Vol. 3, pp 1-13, 1991.
© copyright ERCOFTAC 2004
Contributors: Pietro Catalano - CIRA; QinetiQ