Experimental Validation of a Theoretical Model for Sphere Levitation in a Vertical Turbulent Air Jet

Abstract

The study focuses on the levitation of a sphere in a vertical turbulent air jet, a well-known phenomenon involving the balance between the fluid drag force and gravitational weight. The purpose of measuring the equilibrium levitation height was to experimentally confirm the predictions made by the theoretical model. This model combines turbulent jet theory with existing drag coefficient equations. Spheres of different masses were suspended in the jet of a hair dryer, and their positions were measured using video analysis. By solving the force balance equation, the theoretical model was constructed. The drag force was determined using the centerline velocity of the jet, which follows a decay law from a virtual origin. The results confirmed the expected trend that the levitation height decreases as the sphere’s weight increases. However, the measured heights were lower than the predicted values. The variations in results were mainly due to flow instabilities at the jet source and the assumed location of the virtual origin, both of which affect the velocity profile. According to the thesis, while ideal models provide a qualitative understanding, their quantitative accuracy is limited by the complexity of real-world flow. To improve the experiments, a more stable flow source should be used. Additionally, direct measurement of the flow field using Particle Image Velocimetry (PIV) and the use of Computational Fluid Dynamics (CFD) simulations may be explored.