Set ONERA M6 Wing Initial Condition
 

Dear all,

For ONERA M6 Wing case at http://www.grc.nasa.gov/WWW/wind/val.../m6wing01.html, it sets the Initial Conditions to be:

Mach=0.8395, Pressure (psia)=45.82899 Temperature (R)=460.0 Angle-of-Attack (deg)=3.06 Angle-of-Sideslip (deg)=0.0

And in the document, it says that:

These corresond to a Reynolds number of 11.72 million based on the mean aerodynamic chord length. These conditions match the Mach number, Reynolds number, and angle-of-attack of test 2308 from the paper by Schmitt and Charpin in AGARD Report AR-138 referenced below. The static temperature was selected to be 460 degrees Rankine, which with the Mach and Reynolds number yielded a static pressure of 45.82899 psi.

My questions are:

1). How the Reynolds number of 11.72 million was calculated based on the mean aerodynamic chord length? What is the density is used in calculation? Simply air? and the Velocity =?

Note that the mean aerodynamic chord is 0.64607 meters.

2). Why the static temperature was selected to be 460 degrees Rankine? And how to yield a static pressure of 45.82899 psi. I tried to use 460 degrees Rankine, but could not get the answer.

3). The input uses the wall function keyword, which is to invoke wall function boundary conditions on viscous walls, using the White-Christoph law of the wall.

Any one knows what is the meaning of White-Christoph law of the wall?

Thanks!

I know I'm bringing a thread back from the dead, but if I've managed to find it while searching for the answer - someone else might, too. M6 is a popular enough case anyway to clarify this a bit.

1) In the NASA WIND simulation they actually non-dimensionalized the wing semi-span from 1.1963 m to 1 [unitless] but they also switched to feet (without ever mentioning this anywhere on the site). So, the mean chord is 0.54 (feet - for Re number calculation purposes). Otherwise, if you try to calculate Re based on 0.64607 m, the density goes up to ~4.30 kg/m3 for 255.6 K (460 R) and you get a Re of ~46 million instead of 11.72 mil.

2) It's used because of the reason listed above. Since they decreased the reference length value used to calculate Re, they had to change the temperature (with it the density, viscosity & speed of sound) in order to keep flow similarity. Basically, since they wanted to have a 1 foot semi-span wing for their simulation - they had to fuck up all the other conditions too. Why? BECAUSE! #murica number 1! And it makes perfect sense to measure things based on lengths of body parts and barley corn.

3) This law-of-the-wall formulation has something to do with the fact that changes in density (which are there because of transonic flow) affect the compressible boundary layer near the wall region. You shouldn't really worry about this unless you're using their exact software (WIND), as today's y+ independent wall treatments with viscous heating options and other things take care of this without you having to worry about it explicitly.