# Computational Evaluation of Turbulent Supersonic Jet Impinging on Inclined Plate
## 2 Computational Model
### Flow Domain and Boundary Conditions  
The flow geometry consists of a diverging axisymmetric nozzle, generating the turbulent supersonic jet, together with a large receiver chamber containing the inclined flat plate. The large computational domain was prescribed in order to accurately capture most of the complex flow field features. It extends up to 100 \(D_{j}\), 64 \(D_{j}\), 64 \(D_{j}\), and 71 \(D_{j}\) in the longitudinal, upper, lower, and lateral directions, respectively, where the nozzle exit diameter \(D_{j}\) is assumed as the reference length. The nozzle geometry is designed to ensure the desired Mach number at the exit section that is \(M_{j}=2.2\). The rectangular flat plate has the following extents: 10 \(D_{j}\) (length), 10 \(D_{j}\) (width), and 0.28 \(D_{j}\) (thickness). Some important data are summarized in Table 1, while a schematic view of the computational domain is presented in Figure 1, where the \(X\)-axis direction is aligned with the nozzle centerline. The flow region of particular interest between the nozzle exit and the plate surface is depicted in the zoomed-in picture. Note, that the size of the present computational domain is actually reduced compared to reference numerical simulations in [16].  
At the inlet section, corresponding to the nozzle throat, since the nozzle geometry is given and known, pressure, temperature, and velocity are directly imposed using Dirichlet boundary conditions, with the thermodynamic state being determined by means of isentropic flow relations. Both the impingement plate and nozzle surfaces are treated as adiabatic walls so that corresponding homogeneous Neumann boundary conditions are adopted for the thermal field. In addition, no-slip boundary conditions are imposed on the walls. Importantly, the wave transmissive boundary condition is imposed for both pressure and velocity, in order to avoid the propagation of transmissive and reflective acoustic waves through the computational domain. Following [19], such a particular boundary condition enables the CFD solution to capture the propagation of acoustic and pressure waves with minimal artificial reflections, ensuring that unbounded flow domains are realistically represented. Note, that in this study in contrast with the pure RANS analysis performed in [16], where the symmetry boundary condition at the plane \(Z=0\) was imposed for the mean flow solution, the (partial) resolution of the fluctuating turbulent flow component makes this condition inadequate. Indeed, owing to the adoption of a hybrid RANS/LES formulation, the jet flow was simulated in the entire computational domain, without resorting to any simplification. The different types of boundary conditions are summarized in Table 2, while the associated values for the field variables are given in Table 3. Note, that the far-field values for the turbulent kinetic energy (\(k\)) and the specific dissipation rate (\(\omega\)) were determined by setting the initial level of turbulence intensity to 1%.  
\begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Symbol** & **Value** \\ \hline Nozzle exit Mach number & \(M_{j}\) & 2.2 \\ Nozzle exit diameter & \(D_{j}\) & 7.08 mm \\ Nozzle throat diameter & \(D^{*}\) & 5.0 mm \\ Nozzle pressure ratio & PR = \(P_{j}/P_{\infty}\) & 7 \\ Nozzle-to-plate distance & \(L/D_{j}\) & 2 \\ Plate inclination angle & \(\theta\) & \(30^{\circ},40^{\circ},50^{\circ}\) \\ \hline \end{tabular}
\end{table}
Table 1: Jet flow configuration parameters.  
Figure 1: Sketch of computational domain, with zoomed-in picture of the space region of primary interest.