Various Flow in a Slender Tube: Mach Number and Domain Shape Influenced by Boundary Obstacles Via Small Disturbance Equations

Abstract

With the exponential advancements in computer hardware and software in recent years, computational fluid dynamics (CFD) has emerged as a highly efficient alternative to traditional fluid mechanics studies. Its prowess in accurately predicting and analyzing flow mechanics has led to widespread adoption across diverse engineering disciplines. This research delves into a numerical analysis of flow conditions utilizing the small disturbance equation (SDE). The study bridges the gap between mathematical formulations and computational language, exemplified through Python code, by harnessing the successive over-relaxation (SOR) method, Neumann boundary conditions (BC), and the ghost point technique. The research underscores its predictions' precision in subsonic and supersonic scenarios by meticulously evaluating the resultant errors. This accuracy is further corroborated by examining overarching flow patterns and Mach number distributions. However, the program's outputs indicate a discernible lack of precision in the transonic case, with errors surpassing acceptable thresholds. This discrepancy is hypothesized to stem from potential mischaracterizations of points at the inflow and outflow boundaries. This study, thus, offers invaluable insights while also highlighting areas necessitating further refinement.