Airfoil design with computational fluid dynamics

Abstract

In many industries, there is a need to model the flow of air over structural components. With sufficient information from these models, engineers can better implement these parts into a complete design. The purpose of this paper is to provide a model of specific airfoils using computational fluid dynamics (CFD). With computational fluid dynamics, the characteristics of air around an airfoil can be modeled, providing useful data to engineers who could be designing an airfoil or airplane. The CFD calculations are performed using Python, along with the two packages Numpy and Matplotlib. The governing equations of CFD, including Newton's Second Law, small disturbance equation (SDE), wave propagation, etc. are discretized and transformed into partial differentiation equations (PDE). Using the second order derivative of the wave propagation PDE, the SDE can be solved in iterations and plotted on a graph showing the velocity distributions for a particular airfoil. The results from the CFD calculations show general trends in velocity distributions, regardless of airfoil shape. These include a decrease in x-direction velocity at the ends of an airfoil with an increase at the midsection of the airfoil. Also, y-direction velocity is generally positive and increasing at the front of the airfoil, but negative and decreasing at the end of the airfoil. What is important to understand is how different airfoil shapes can change velocity distributions, moving to using 3D CFD calculations, and the possibility of using CFD for modeling airflow over a multitude of objects.[ Henry Bao, the first author, participated in the Illinois junior academy of science state fair, and abstracts of the regional winners' presentations were posted online. (ilacadofsci.com)]