Analysis of Supersonic Flow in a Converging-Diverging Nozzle with Geometry Variation

Abstract

propulsion systems, and high-speed fluid transport applications due to their ability to accelerate compressible flow from subsonic to supersonic conditions. The performance of a C-D nozzle is strongly influenced by its geometric configuration, which affects important flow characteristics such as Mach number distribution, velocity, and pressure variation. However, improper nozzle expansion may lead to unstable flow behavior and reduced acceleration efficiency, making geometry optimization an important aspect of nozzle design. This study aims to investigate the effect of nozzle geometry variation on supersonic flow behavior in a converging-diverging nozzle using Computational Fluid Dynamics (CFD). A two-dimensional axisymmetric model was developed and simulated using ANSYS Fluent with a density-based solver under steady-state conditions. Air was treated as a compressible fluid, while the energy equation and Shear Stress Transport (SST) k-ω turbulence model was applied to improve solution accuracy for high-speed flow analysis. A grid independence test was first conducted using six mesh cases with different element sizes to ensure that the numerical results were independent of mesh resolution. Outlet velocity was selected as the primary parameter for convergence assessment. The results showed that the percentage difference in outlet velocity between the finer mesh cases was less than 5%, confirming grid independence. The mesh with an element size of 1.5 mm and approximately 168,000 nodes was selected for further analysis. Three different nozzle geometries were then compared by modifying the curvature of the nozzle profile equation. Among the tested configurations, Geometry 1, defined by A=0.1+0.5x², produced the highest outlet Mach number of 1.8885 and the highest outlet velocity of 447.86 m/s, indicating the best supersonic performance. In contrast, the steeper expansion profile of Geometry 3 resulted in lower Mach number and weaker acceleration. It can be concluded that nozzle geometry has a significant influence on supersonic flow performance, where a smoother and more gradual diverging section improves pressure distribution and enhances flow acceleration. CFD proved to be an effective tool for evaluating nozzle performance and supporting nozzle design optimization.