LES of shock wave / turbulent boundary layer interaction

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extended to the compressible case as:
C finc = F C C f ,
Re θinc = F θ Re θ .
The van-Driest-II transformation for coefficients F C and F θ
with
F C =
α =
F θ = µ ∞
µ w
κ−1
2 M 2 ∞r
(arcsin α + arcsinβ) 2 ,
2A 2 − B
√
4A2 + B 2 ,
β =
A =
B =
B
√
4A2 + B 2 ,
√
κ − 1
(
2
M 2 ∞r T ∞
T w
,
1 + κ − 1 M 2
2
∞r − T )
w T∞
T ∞ T w
is found to be superior to others by Hopkins & Inouye (1971). Here
r = 0.9 is the temperature recovery factor. Obviously, the considered
case (Re δ2 ≈ 2000) is in the region of the rapid change of C f , where data
are much more scattered than at higher Reynolds number (Re δ2 > 4000).
The calculated skin friction coefficient lies close to the upper limit of this
scatter, the referenced experiment at the lower, but both of them agree
well with established data from Fernholz & Finley (1977, 1981) and
empirical correlations.
The wall normal distributions of mean Mach number, temperature,
velocity, and density are compared with the experimental data in figure
3.4. In the bulk, the computed velocity profiles agree well with the
experimental data, minor discrepancies can be observed for the density
and temperature profiles. These differences are well within the experimental
error margin. The computed van-Driest-transformed velocity
profiles, shown in figure 3.5, agree well with the logarithmic law of the
wall U + VD = lnx+ 3 /0.4 + 5.1. Wall-law constants are taken for adiabatic
walls, since our temperature at the wall is equal to the adiabatic one, this