Turbulent flows, characterized by their complex and chaotic nature, play a pivotal role in various engineering and natural systems. Understanding and analyzing these phenomena is essential for optimizing design, predicting crucial outcomes, and addressing real-world challenges. Therefore, obtaining accurate, efficient, and rapid predictions of turbulent behaviors is of utmost importance. Data-driven methods such as deep learning algorithms are being increasingly implemented to speed up flow predictions compared to numerical solvers. However, these models often tend to be restricted to simple geometries on structured grids. Hence, a Graph Neural Network (GNN)-based surrogate model is proposed to handle unstructured mesh data of turbulent flow simulations in the context of a High-speed Orienting Momentum with Enhanced Reversibility (HOMER) nozzle. Additionally, dimensional reduction and clustering techniques are employed to classify the various cases and phenomena occurring in this application, enhancing our understanding of turbulent nozzle flow dynamics.