# Computational Investigations and Control of Shock Interference +
## 4 Shock Interference in Modified Shock-Tube
### Effect of Wall Temperature on Shock Interference  
Comparisons of wall pressure contours with adiabatic and isothermal walls (at 200 K) calculated with LES are shown in Figure 29. The results with isothermal walls show differences from the results with adiabatic walls, including lower overall wall pressure with isothermal walls. These results also show that isothermal walls result in a reduction of lower pressures at the wall corners where both the y- and z-walls meet. In addition, the pressure peak at the centerline is reduced significantly as well. Figure 30 displays temperature and pressure line plots at a time of 4.228 \(\times\) 10\({}^{-4}\) s. These variables were plotted at the wall and the centerline of the modified shock-tube. As shown in Figure 29, the pressure at the wall has lower peaks in the case with isothermal walls due to cooling. The pressure peaks were also at different locations within the shock structure. The centerline temperature distribution with isothermal wall appears to be heated at some locations while cooled in the region where shock interference is occurring. This is due to the fact that the air entering from the inlet is at 150 K, whereas the wall temperature is higher at 200 K. The centerline pressure shows that the case with the cooled walls actually had a substantially higher peak pressure. In this case, the pressure at the wall was reduced, but the pressure at the centerline increased. Figure 28: Eddy viscosity ratio contours at the wall: adiabatic walls with LES. Figure 27: Pressure contours at symmetry plane: adiabatic walls with LES. Figure 31 shows the same quantities as discussed above except at a time of \(4.909\times 10^{-4}\) s. Again, the walls were obviously cooler with the isothermal walls than they were with the adiabatic walls. The pressure at the wall also had a lower peak and less variation in the cooled walls case. The centerline was heated in some portions as mentioned above. At this time, however, the shock-train was dampened at the centerline in the cooled walls case. At the previous time, the pressure peak was noticeably higher. The shock-train near the wall is also shorter in the cooled wall case. Figure 30: Static temperature and pressure distribution at t \(\approx\) 4.228 \(\times\) 10\({}^{-4}\) s.  
Figure 29: Wall pressure contours with adiabatic (**top**) and isothermal (**bottom**) walls calculated with LES. Theoretically, wall cooling results in boundary-layer thickness reduction, resulting in less compression of the core flow due to thinner boundary-layer and therefore, weaker and/or shorter pseudo-shock-train. Figure 32 shows two plots. One is the u-velocity at z = 0, which was the centerline of the \(z\)-axis (width). The other plot shows the u-velocity at z = 0.0075, which was halfway between the centerline of the \(z\)-axis and the front wall of the modified shock-tube. These data were extracted at the same x-location within the shock structure, after it had developed. The boundary layer at the centerline of the \(z\)-axis was slightly thicker in the cooled walls case. This helps to provide an explanation as to why the pressure in the cooled walls case is not very different than the adiabatic case, at the centerline. It was observed previously that the effects of the wall cooling were significantly more prevalent at the wall. The plot in Figure 32b further supports this as the boundary layer in the cooled case was much thinner than that of the adiabatic case. This shows that the technique of cooling the walls does reduce the thickness of the boundary layer, as expected. The LES calculations were again performed with a higher inflow temperature to observe if the cooling effects were amplified with a higher temperature difference between the inflow and walls. Results with 300 K inflow are shown in Figure 33.  
These plots were from approximately the same time as the previous calculations.