# Computational Evaluation of Turbulent Supersonic Jet Impinging on Inclined Plate
## 1 Introduction  
Despite decades of research and progress, accurate and efficient computational fluid dynamics (CFD) simulation of wall-bounded compressible turbulent flows still represents a challenging task, e.g., [1]. Within this framework, impinging supersonic jet flows continue to receive great attention, due to their technological importance as well as high complexity, in both theoretical and applied engineering research. In particular, the impingement of a turbulent supersonic jet on an inclined flat plate appears in various aerospace engineering applications, including rocket launchers, vertical/short-takeoff-and-landing aircraft operation, and jet-engine thrust control [2, 3]. Moreover, this particular jet flow configuration has been also employed in gas-liquid separators, heat exchanges, and mixing devices. In all these cases, the jet flow characteristics play a crucial role in enhancing mixing, as well as heat and mass transfer between the fluid phases, e.g., [4]. Generally, using applied CFD techniques makes it less expensive to examine a wide range of flow parameters and configurations, compared to experimental works. In this particular case, notwithstanding the geometric simplicity, the interaction between the jet flow and the inclined solid surface results in highly intricate fluid dynamic phenomena, such as flow separation, reattachment, vortex dynamics, and complex interactions between shocks and boundary layers. The significant computational complexity has directed research efforts primarily towards the examination of perpendicular jet impingement, e.g., [5]. However, recent advancements in computational power accessible to industrial research, coupled with the evolution of sophisticated numerical methods for applied CFD, have ledto an increased focus on supersonic jet flow dynamics, including more complex configurations, e.g., [6]. Specifically, engineering research has taken into account the variations in nozzle-to-wall distance, nozzle exit diameter, and impingement angle [7]. In fact, these geometric parameters, in conjunction with the nozzle pressure ratio, play a crucial role in determining the characteristics of impinging jet flow. For instance, an increase in the angle of inclination of the plate results in heightened surface pressure oscillations, due to more pronounced flow separation and reattachment phenomena, e.g., [8]. The present study specifically examines the scenario of near-wall impingement, characterized by a ratio of \(L/D_{j}<5\), where \(L\) denotes the distance from the nozzle to the plate (measured along the centerline of the nozzle) and \(D_{j}\) refers to the diameter of the nozzle exit section. In this context, the pressure exerted on the plate is significantly augmented, owing to the intricate flow structures that emerge from the intensified interactions between shock waves and expansion waves. Indeed, experimental research indicates that the pressure load resulting from the supersonic jet striking an inclined solid surface can exceed that observed at normal incidence, primarily due to the presence of multiple shock waves between the nozzle exit and the plate [9]. Furthermore, various studies have emphasized that the compressible flow structures formed at the zone of impingement are also affected by the fluid turbulence, e.g., [10]. In the initial experimental studies focused on near-wall impingement, pressure taps were employed to assess the pressure distribution on the plate. Typically, these measurements yield pressure fields characterized by low spatial resolution, which restricts further analysis, particularly in small-scale experiments. Additionally, in certain instances, the use of physical probes for measurement is not feasible, as they may significantly modify the flow field. In response to these limitations, the pressure-sensitive paint (PSP) technique was introduced to ascertain the pressure distribution with relatively high spatial resolution, thus serving as an effective tool for the examination of jet impingement [11].