# Computational Evaluation of Turbulent Supersonic Jet Impinging on Inclined Plate
## 4 Results
It is worth noting  
Figure 5: Surface pressure distribution on the plate for different inclinations that are \(\theta=30^{\circ}\), \(40^{\circ}\), and \(50^{\circ}\) (from top to bottom), compared to experimental data [12]. that both solutions are able to capture the jet boundary and the jet shock away from the wall with acceptably high fidelity. However, a slower and more consistent velocity field along the plate is obtained with DES, as the RANS computation seems to overpredict the fluid velocity in the wall jet region. Moreover, the DES approach is able to more clearly reveal the presence of the expansion waves that are produced at the exit of the under-expanded nozzle and their reflection from the jet boundary. Such waves turn into compression waves that coalesce to form a barrel-shaped shock. Increasing the plate angle, in accordance with the experimental findings, the flow structure changes and the flow complexity grows. Apparently, as the jet spreads along the plate, the fluid velocity tends to decrease, while the boundary layer thickness increases. Moreover, the stagnation zone tends to shift slightly upwards. This flow scenario is in agreement with previous numerical investigations, where more sophisticated, and more costly, LES techniques were adopted [30]. However, the drift of the stagnation bubble should be further investigated, due to its crucial impact on the evaluation of heat transfer and wall shear stress over the plate. By inspection of the temperature contours in Figure 7, it seems that unsteady RANS tends to over-predict the temperature in the jet core region, as well as in the wall proximity, while the thermal field exhibits a more uniform behavior for DES. Moreover, the temperature in the far-field region appears slightly higher for the RANS solution. Figure 6: Normalized speed contours in the plane \(Z=0\) for unsteady RANS (**left**) and DES (**right**), for different plate angles that are \(\theta=30^{\circ}\), \(40^{\circ}\), and \(50^{\circ}\) (from top to bottom). The speed level is non-dimensionalized by the inlet velocity \(U^{*}\). In accordance with previous investigations, the pure RANS solution is shown to provide too slow decay of the mean velocity profile along the jet axis, including the core region, which can be attributed to the underprediction of the turbulence mixing in the shear layer. The nearby temperature field is overestimated, leading to the misrepresentation of the heat transfer rate in the impingement zone. On the contrary, the hybrid RANS/LES approach produces faster mixing, due to the capability to take into account the vortex breakup process in the shear layer of the jet and in the near-wall region, which leads to a more correct estimation of the thermal field in the proximity of the plate [31]. A more detailed description of the complex flow structures arising from the jet impingement is presented in the following, using the numerical Schlieren technique. In Figure 8, the various flow scenarios associated with different plate inclinations are visualized by reporting the contour maps of the density gradient modulus, making a direct comparison against experimental Schlieren images provided by [PERSON] et al. [12]. For the numerical data, the contour level varies between zero (white color) and 0.053 (yellow color). Indeed, based on the experimental findings, it was found that the complex flow patterns can be classified into different types, namely: Type I (with/without bubble), Type II (with/without bubble), and Type III, as discussed in [13; 14]. The actual flow type can be predicted in advance, once the plate angle, the nozzle-to-plate distance, and the shock cell length are given and known. Apparently, at \(\theta=30^{\circ}\), both solutions correctly resemble the  
Figure 7: Normalized temperature contours in the plane \(Z=0\) for unsteady RANS (**left**) and DES (**right**), for different plate angles that are \(\theta=\)30\({}^{\circ}\), 40\({}^{\circ}\), and 50\({}^{\circ}\) (from top to bottom).