ONERA M6 wing Drag and Lift Coefficients - Review

In this article I will discuss about the valid drag and lift coefficients for ONERA M6 wing. More specifically I will talk about test run 2308.

The ONERA M6 wing was designed in 1972 by the ONERA Aerodynamics Department as an experimental geometry for studying three-dimensional, high Reynolds number flows with some complex flow phenomena (transonic shocks, shock-boundary layer interaction, separated flow).

The wind tunnel tests are documented by Schmitt and Charpin in the AGARD Report AR-138 published in 1979. This data is mainly consists of pressure coefficients at different span locations.

Pressure coefficient plot at location y/b = 0.65

The flow conditions for the test case 2308 is given below:

But the issue is that drag and lift coefficients are not published by ONERA and therefore we dont have any experimental data to compare with in first place. Therefore many people have done numrical studies and published data with different softwares, mesh types, flow schemes etc. Therefore we dont have one fixed value of drag and lift coefficients, but rather range of values for both. One of the table is given below from reference [2].

And NASA also published extensive data base on same case and here is the graph of CD, CL and CM graphs vs mesh size [3].

From above graphs we can lift down lift coefficient, drag coefficient and moment coefficient when element mesh element size is approaching zero (CFL3D, Structured) .

Now the funny part. Some people have quoted (non authentic papers/articles) that NASA's drag and lift coefficients are follows:

Above table is quite misleading and creating confusion in the CFD community. Interstig thing is that, this data is quoted by many people and even I have used same data to compare my results when I did project on ONERA M6 wing in 2016.

In my point of view data in table 4 is not completely wrong, but it has to do with the reference values. For example for the aerodynamic coefficient we have following formulas:

In pitching moment coefficient, we also need mean aerodynamic chord lenght which is 0.64607 meters for ONERA M6 wing.

While the reference area can we be found out using three methods:

1. using simple formula that reference area is product of mean aerodynamic chord and semi span.
2. Based on trapezdoil area formula
3. projected area from Fluent's built-in features. You can also solidworks (where we have made same model) features to get projected area in Y direction

We have also other reference conditions as follows (detailed derivation is available in my courses on ONERA M6 wing):

Mesh generated in ICEMCFD Hexa:

Using data discussed above and mesh as shown in Fig. 7, case was solved using Fluent 2022 R1 using density based solver.

Here is data for CD, CL and CM for three turbulence models by the author. Please note CM is takes at (0,0,0) and is around Z axis.

Now, concerning to the data presented in table 4, my guess is that, they have used the surface area instead of projected area. Which is roughly speaking twice the projected area.

Convergence plot for wj-bsl-earsm-kw. Convergence is achieved using solution steering in automatic mode in AERO features of ANSYS Fluent 2022 R1,

Convergence plot for SA model

Convergence plot for SST model

References :

1. Schmitt, V. and F. Charpin, "Pressure Distributions on the ONERA-M6-Wing at Transonic Mach Numbers," Experimental Data Base for Computer Program Assessment. Report of the Fluid Dynamics Panel Working Group 04, AGARD AR 138, May 1979.
2. Naveed Durrani1 and Ning Qin. "Comparison of RANS, DES and DDES results for ONERA M-6 Wing at transonic flow speed using an in-house parallel code" AIAA 2011-190. 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition 4 - 7 January 2011, Orlando, Florid
3. https://turbmodels.larc.nasa.gov/onerawingnumerics_val_sa.html

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