# Computational Evaluation of Turbulent Supersonic Jet Impinging on Inclined Plate
## 4 Results  
As a preliminary step, the grid convergence analysis presented in Section 2.2 is demonstrated in Figure 3 by comparing the pressure distributions on the plate mid-section for the different mesh resolutions with each other, as well as against the experimental data in [12]. The three different FV grids are made of 0.66 (coarse), 2.7 (medium), and 6.8 (fine) million cells for the whole computational domain. In this plot, the spatial coordinate along the plate is non-dimensionalized by the nozzle exit radius (\(R_{j}\equiv D_{j}/2\)), whereas the pressure variable is non-dimensionalized by the nozzle chamber (stagnation) pressure that is \(P_{c}=100\) kPa. By inspection of these data, the numerical resolution corresponding to the finest grid can be regarded, a posteriori, as adequate for capturing most of the complex flow features. Therefore, the various calculations for the two different turbulence modeling approaches were conducted using this particular grid. The pressure contours over the plate surface predicted by the two different methods are presented in Figure 4. These results have been obtained once the statistically steady state is reached, for different inclination angles that are \(\theta=30^{\circ}\), \(40^{\circ}\), and \(50^{\circ}\), respectively. Note, that practically since the near-wall region is modeled using the RANS approach for both turbulence models the shape of the pressure pattern of impingement is pretty similar for the two solutions, particularly at low plate incidences. As the inclination angle increases, slight differences start appearing. In fact, the higher the inclination angle, the stronger the jet deviation imposed by the plate (where \(\theta=90^{\circ}\) would correspond to perpendicular jet impingement), and the more complex is the separated compressible flow field. This way, the LES capability of the hybrid model leads to a better description of the resolved pressure field with increasing plate incidence. Apparently, at higher inclinashows a more elongated impingement zone over the plate, with the stagnation flow region being slightly larger, compared to RANS. The present qualitative results show a good agreement with reference numerical data in [16], which were obtained using a commercial code. Expectedly, since the plate center is perfectly aligned to the nozzle axis, the maximum pressure level is achieved at the mid-section of the plate, as illustrated in Figure 4. This way, when performing a quantitative analysis and comparison of pressure load using different methods, the plate section at \(Z=0\) is selected. Figure 5 shows the pressure distribution on the mid-section of the plate for the two different solutions, and varying plate incidence. Making a comparison with reference experimental data [12], both models result in quite correctly reproducing the  
Figure 4: Normalized surface pressure contours for unsteady RANS (**top**) and DES (**bottom**), for different plate angles that are \(\theta=30^{\circ}\), \(40^{\circ}\), and \(50^{\circ}\) (from left to right). The pressure level is non-dimensionalized by the stagnation pressure \(P_{c}\). Figure 3: Surface pressure distribution on the plate for varying numerical resolution, compared to experimental data [12]. pressure peak and its location on the plate. At the lowest inclination angle, the numerical solutions are able to predict the pressure oscillations away from the high-pressure region, even though the values and locations of local extrema are not well captured. The two different CFD solutions are further analyzed by looking at the resolved velocity and temperature fields, for varying plate inclination. Figure 6 shows the normalized speed contours in the mid-plane \(Z=0\) for the space region between the nozzle exit and the plate surface, while the corresponding thermal contours are depicted in Figure 7. In any case, a stagnation zone is visible in the impingement region, together with the consequent boundary layers development in both directions along the solid surface.