Numerical wind tunnels

TL;DR

This paper introduces a computer simulation tool for wind tunnels that solves the Navier-Stokes equations to visualize vortex formation and calculate drag, aiding education in viscous fluid dynamics.

Contribution

It presents a set of programs for simulating wind tunnel flows around arbitrary objects, enhancing teaching and understanding of viscous fluid behavior.

Findings

Visualization of von Kármán vortices behind objects

Calculation of drag forces on simplified wing models

Demonstration of flow patterns at different angles of attack

Abstract

Flow of viscous fluids are not usually discussed in detail in general and basic courses of physics. This is due in part to the fact that the Navier-Stokes equation has analytical solution only for a few restricted cases, while more sophisticated problems can only be solved by numerical methods. In this text, we present a computer simulation of wind tunnel, i.e., we present a set of programs to solve the Navier-Stokes equation for an arbitrary object inserted in a wind tunnel. The tunnel enables us to visualize the formation of vortices behind object, the so-called von K\'arm\'an vortices, and calculate the drag force on the object. We believe that this numerical wind tunnel can support the teacher and allow a more elaborate discussion of viscous flow. The potential of the tunnel is exemplified by the study of the drag on a simplified model of wing whose angle of attack can be controlled. A link to download the programs that make up the tunnel appears at the end.