LES of shock wave / turbulent boundary layer interaction

29
directions are 45.8 and 17.7. Here the friction velocity u τ = √ τ w /ρ w
and the kinematic viscosity at the wall ν w = µ w /ρ w are based on mean
flow quantities. The boundary layer is resolved by 58 gridpoints in wallnormal
direction, and by 2 points in the viscous sublayer. Such a resolution
is found to be sufficient for the considered flow parameters (Stolz
& Adams, 2003).
As initial data an instantaneous solution was taken from the previous
flat plate simulations of Stolz & Adams (2003) and rescaled to match the
required Mach number and domain size. Since in the previous simulation
the domain width was only one third of the current, the initial field was
composed by repeating this field three times in spanwise direction. The
simulation was run long enough, so that a statistically stationary state
was reached. Sequentially it was continued for 55.7δ 0 /U ∞ characteristic
time-scales. Of all conservative variables (density, momentum and
total energy) 400 samples were taken at evenly spaced consecutive time
increments roughly spaced by 0.14δ 0 /U ∞ at the downstream position
x r = 11.15. for the estimation of mean and statistical quantities and for
inflow preparation. In the following we distinguish between Favre, i.e.
density-weighted statistical averages and Reynolds averages. The former
is indicated by a double prime f ′′ = f − 〈ρf〉 / 〈ρ〉 = f − {f}, the latter
by a single prime f ′ = f − 〈f〉.
3.1 Instantaneous structures
The instantaneous flow field can be visualized in terms of the density
field. Figure 3.1 reveals the existence of organized motions in the outer
layer, which is characterized by the occurrence of large-scale intermittently
appearing structures. These structures are separated from the
surrounding essentially irrotational fluid by sharp interfaces having a
three-dimensional character. Unlike the DNS, the LES resolution is not
sufficient to show them clearly. The angle of the structures agrees with
the values 45 − 60 ◦ reported by Spina et al. (1994). They move downstream
at approximately 90% of the freestream velocity. The average
spanwise extent of the largest eddies is approximately 1/2δ in the outer
layer, and decreases towards the wall.
The near-wall resolution is sufficient to capture fine structures. The
existence of elongated streaky structures of alternating high and low
speed near the wall is illustrated in figure 3.2 by the wall-normal component
of vorticity ω z . The wall-parallel plane is located at x + 3 = 8.5.