Research on 2D SDE Method of Fluid Field Effect above Airfoil at Transonic Speed

Abstract

In this research, a Python-centric approach is proposed for simulating fluid dynamics over transonic airfoils. The study employs the finite difference method to solve the small disturbance equation (SDE), incorporating Newman boundary conditions. Iterative computations are adeptly managed using the successive over-relaxation (SOR) method. These methodologies, as validated through rigorous code testing, enable precise calculations of velocity distributions and vivid visualizations of fluid velocity streamlines. For this investigation, the airfoil is conceptualized as a minor obstruction and is abstracted into a trigonometric function. A pivotal aspect of this study is the exploration of the interplay between the Mach number and the 'shark angle'—a critical determinant in aerodynamic performance. Simulation outcomes reveal an inverse relationship between the Mach number and the airfoil's shark angle; a surge in the Mach number corresponds to a reduction in the shark angle. These findings, encapsulated in flow field diagrams, offer invaluable insights for the strategic design and optimization of airfoils, aiming to maximize lift while concurrently curtailing drag, thereby enhancing overall aerodynamic efficiency.