# Computational Evaluation of Turbulent Supersonic Jet Impinging on Inclined Plate
## 1 Introduction
For example, [PERSON] and collaborators [12] explored the behavior of supersonic jets impacting inclined flat plates at various nozzle-to-plate distances (\(L/D_{j}\)), impingement angles (\(\theta\)), and nozzle pressure ratios (\(PR\)). The latter parameter is defined as \(PR=P_{j}/P_{\infty}\), where \(P_{j}\) and \(P_{\infty}\) represent nozzle exit and ambient pressures, respectively. By integrating the high-resolution pressure maps obtained from PSP technology with Schlieren imaging, a methodology was developed to anticipate the overall impinging jet configuration. These experimental findings revealed the existence of various flow patterns, which are dependent on the characteristics of the impinging jet [13]. Additionally, [PERSON] et al. [14] conducted experiments on jet impingement at elevated plate angles, systematically varying the position and inclination of the plate within the ranges of \(1\leq L/D_{j}\leq 4.5\) and \(60^{\circ}\leq\theta\leq 90^{\circ}\), respectively. It is crucial to note that CFD analysis effectively replicates the surface pressure distribution over the plate with the desired spatial resolution. The precise assessment of the pressure field greatly enhances flow diagnostics and, thus, industrial design, particularly in predicting and mitigating pressure loading and improving system reliability, which is especially vital for aerospace and defense applications. For example, considering the particular application to the takeoff of an aircraft (or a missile), the local increase in velocity results in a decrease in local pressure near the impingement area, which can lead to diminished lift. This reduction in lift may result in either a failed takeoff or increased fuel consumption. In recent years, several experimental studies have been conducted to explore the lift loss induced by this phenomenon, utilizing a simplified test configuration that includes a baffle plate surrounding a single air jet. For instance, a series of experiments examining various nozzle-to-ground heights were presented in [15], indicating that a closer proximity to the ground surface correlates with a greater loss of lift. In this demanding context, the primary objective of this work is to conduct a computational investigation of the impinging jet flow field utilizing a modern turbulence model. Unlike earlier numerical investigations, such as those presented in [16], which relied on conventional unsteady Reynolds-averaged Navier-Stokes (RANS) models, this research also employs a hybrid turbulence modeling procedure known as detached-eddy simulation (DES). Indeed, traditional RANS simulations are limited in their ability to capture spectral content in the flow field, even when sufficient spatio-temporal resolution is achieved, as they compute the (statistical) mean flow, thereby eliminating all turbulence information from the resolved flow field through the averaging process. Although multi-scale RANS models that can accurately predict flow separation details and anisotropic turbulence are still in development, e.g., [17], the growing accessibility of high-performance computing (HPC) resources for industrial research enables more precise evaluation of turbulent supersonic jet impingement. Specifically, the current DES formulation, which is based on the hybridization of the two-equation eddy-viscosity \(k-\omega\) shear-stress transport (SST) model [18], akin to large-eddy simulation (LES), facilitates the emergence of a resolved turbulent spectrum, allowing for partial resolution of turbulent fluctuations. To examine the capability of the two different techniques to reproduce the complex flow physics arising from the jet impingement, various computations are conducted for varying inclination angles. Furthermore, contrasting with similar investigations where commercial proprietary software is usually employed, the use of an open-source CFD solver allows us to overcome a couple of significant limitations.