LES of shock wave / turbulent boundary layer interaction

Chapter 3
Flat plate boundary layer
A well known problem in the simulation of turbulent boundary layers
is that realistic inflow data are needed. Recently Xu & Martin (2004)
have reviewed different inflow generation techniques. Following them,
the inflow generation techniques can be organized into three categories:
1 spatially evolving boundary layer simulating the full transition process;
2 using data from previous simulations (or data combined with those
from experiment);
3 various techniques using an instantaneous downstream flow field
(streamwise periodic boundary conditions, extended temporal approach,
rescaling and recycling method, etc.).
A brief summary of available simulations can be found in appendix A.
A DNS of a spatially evolving turbulent supersonic flat-plate boundary
layer is conducted by Rai et al. (1995). A developed turbulent boundary
layer with a momentum thickness of Re θ ≈ 4500 was obtained by the
simulation of laminar-turbulent transition initiated by a blowing/suction
strip. This case is close to an experiment by Shutts et al. (case 55010501
in Fernholz & Finley (1977)) with Re θ ≈ 6000 and M ∞ = 2.25. Later
Gatski & Erlebacher (2002) and Pirozzoli et al. (2004) repeated this DNS
on a finer grid. Their results showed that both the near-wall asymptotic
behavior and the log-law exhibit similarities with the incompressible case
when the van-Driest velocity transformation is applied. Similarly, the
Reynolds stresses also are independent of Mach number when scaled with
the mean density ratio as suggested by Morkovin (1962). The results also
showed that the total temperature fluctuations were not negligible. LES
of this case was performed by Spyropoulos & Blaisdell (1998) using a
dynamic Smagorinsky model and by Rizzetta & Visbal (2004), using
Smagorinsky, dynamic Smagorinsky and MILES approaches.
Guarini et al. (2000) employed a ”slow growth” assumption to simulate
a turbulent boundary layer at Re θ = 1577. It is assumed that the
boundary layer grows slowly in the streamwise direction so that the turbulence
can be treated as approximately homogeneous in this direction.