Revision as of 09:14, 12 August 2013

Planar shock-wave boundary-layer interaction

Semi-confined Flows

Underlying Flow Regime 3-32

Evaluation

Comparison of CFD Calculations with Experiments

LES versus experiment at shock generator angle of 8 degrees

Velocity fluctuations in a plane parallel to the wall evidence the presence of low and high velocity streaks that populates canonical boundary layers. After the separation (identified by the first dashed line), the size of turbulent structures in the spanwise direction significantly increases and further downstream the turbulence slowly relaxes toward its canonical state. This figure illustrates the fact that the simulation is capable of capturing most of the finest turbulent structures present in a supersonic boundary layer.

Quantitative comparisons in the symmetry plane are shown in Figure 6. The agreement between experiment and simulation is very good in the symmetry plane for the longitudinal velocity except in the separation bubble region. Nevertheless, it is important to mention that this region is very sensitive to the nature of inflow perturbations since a large variability of the results in this area has already been observed in the experiment, the 2006 data differing from the 2007 one, specifically in this region. The agreement with the experiment is also generally satisfactory for the Reynolds shear stress.

Longitudinal evolution of turbulence spectra in the spanwise direction are presented in Figure 7 for both large and narrow span simulations. In the separation region, it appears that a large part of the energy is contained in the small wave numbers in the large span computation. The cutoff wave number imposed by the finite span is too large in the narrow span simulation. This forces the energy to concentrate at smaller scale and affects the results.

Low frequency movements of the reflected shock are clearly observed in Figure 8. As in the experiment the frequency of the power spectral density maximum is located at St=0.03. The agreement on the energy distribution between the narrow span computation and the experiment is very good.

6.2 DES versus experiment at shock generator angle of 9.5 degrees

This section describes only the comparison the SDES computation with the experiments. The reader is referred to Doerffer et al. 2010 for a presentation of RANS results.

The chosen technique of inflow turbulence generation is the Synthetic Eddy Method (SEM) (Garnier, 2009). Figure 9 illustrates clearly the fact that LES content (resolved eddies) is introduced at the entrance of the computational domain over the entire boundary layer height. Nevertheless, lateral boundary layers are treated in RANS mode.

It is found (Figure 10) that even if some improvement is observed with respect to RANS computations performed on the same grid (Doerffer et al. 2010), it seems that the extent of the predicted corner flows is too small. This is tentatively attributed to the fact that lateral walls are treated with RANS at the inflow.

The agreement between SDES and PIV is generally better in the symmetry plane (see Figure 11) even if the bubble aspect ratio is larger in the SDES computation than in the experiment. According to the model proposed in Piponniau et al (2009), this should lead to an increase of the frequency of the reflected shock movement.

Even if the averaged results of this SDES simulation are far from being perfect, it is the only one that exists for the 9.5 degrees case carried out on the full geometry. Some work has then been performed to analyze the unsteady data hoping that it could complement the experimental results in a useful way.

Figure 12 presents isocontours of wall pressure fluctuations and streamlines which visualizes the flow topology. Streamlines should not be compared with those provided in Figure 10 since the flow topology changes drastically between the wall and 1.2 mm from the wall. Upstream of the interaction, pressure fluctuations are weak and they are due to turbulent fluctuations present in the boundary layer. A local pressure fluctuation maximum is observable near the separation at x=0.25. This quantity is used in the experiments to identify the beginning of the interaction zone. Nevertheless, it can be observed that the maxima of pressure fluctuations can be found in the corner flows and downstream from the interaction. In the latter case, these fluctuations are associated to Kelvin-Helmholtz type vortices which are generated in the shear layer above the separation bubble. More generally, these results indicate that the unsteady movements of highest intensity are localized in corner flows and a possible statistical link between these corner flows and the main separation area must be investigated.

Contributed by: Jean-Paul Dussauge — Orange