# Computational Investigations and Control of Shock Interference +
## 4 Shock Interference in Modified Shock-Tube
### Results  
In order to assess the ability of URANS and LES to capture the transient shock-physics evolution, first comparisons between the calculated results from URANS and LES for the first 0.6 ms of the flow have been made in terms of static temperature, density, and shadow-graph contours. As this modified shock-tube has a square cross-section, only centerplane (or symmetry plane) contours are shown for comparison between the two computational approaches. The static temperature contours at the symmetry plane calculated with URANS and LES are shown below in Figures 16 and 17 at various times, respectively. There are several differences between URANS and LES results that can be observed from these plots. LES results show higher static temperature values as well as faster progression of the left-to-right waves in comparison to the URANS results. It can also be observed that a thicker boundary-layer development in URANS calculations results in larger curvature of shocks on both right and left sides as compared to the LES results, where the left shock remains planar. The shock-shock interference was greatly developed after approximately 4.228 \(\times\)\(10^{-4}\) seconds in the URANS results in comparison to the LES results at the same time. As mentioned in an earlier section, the LES results show a more detailed shock-shock interference as well as shock-boundary-layer interaction as compared to URANS results. Figure 15: Computational Domain: Modified shock-tube with a velocity inlet and pressure outlet. The dimensionless \(y^{+}\) values along the solid walls are shown below in Figure 21. This contour displays that the \(y+\) value at a given point becomes significantly higher as the incoming flow develops over that area. In addition to this, Figure 22 shows the ratio of the  
Figure 19: Density contours at the wall: adiabatic walls with URANS-SA. Figure 20: Reynolds number contours at the centerplane: adiabatic walls with URANS-SA. Figure 18: Density contours at the wall: adiabatic walls with LES. grid resolution to the Kolmogorov scale, \(\eta\). The Kolmogorov scale will not be resolved with LES, so being within 100 times \(\eta\) is adequate for this simulation. This plot shows that the Kolmogorov scale does change with time, but not so drastically that the physics cannot be resolved. These images provide justification for the mesh resolution used in this study. To observe how the density and static temperature evolve, the results at a later time are shown. Figure 23 shows the comparison of URANS and LES results at a later time. This shows the flow after the shocks had interacted with each other in the LES case. The density was lower in this area in the LES case compared to RANS. Richtmyer-Meshkov instability can also be observed in the LES results in comparison to the URANS results. The temperature contours also showed significant differences between the URANS and LES results. These differences include a higher temperature zone appearing near the wall, shown in the LES results. The Richtmyer-Meshkov instability was shown in both density and temperature contours. These contours displayed the advantages of LES simulations, as they showed significantly more details that are not captured by URANS. Contours of shadowgraphs were created for the LES and URANS cases to compare the two techniques. These are shown below in Figures 24 and 25, respectively. These plots further demonstrate the significant differences in results obtained with URANS and LES methods over the identical mesh. The RANS results showed only major features, while the LES results showed much finer details of the flowfield. LES calculations showed smaller structures within the larger structures--something that was not captured by the URANS calculations. In addition to this, the rotational effects are shown in the LES case, but not in the URANS case.