Fan affinity laws from a collision model

TL;DR

This paper derives the fan affinity laws using a kinetic theory approach with a collision model, providing a simpler alternative to hydrodynamical methods and offering numerical estimates for fan performance.

Contribution

It introduces a kinetic theory-based collision model to derive and validate the fan affinity laws, including numerical estimates for key performance metrics.

Findings

Proves the validity of the fan affinity laws

Provides numerical estimates for air delivery, thrust, and drag

Offers a kinetic theory approach as an alternative to hydrodynamical calculations

Abstract

The performance of a fan is usually estimated from hydrodynamical considerations. The calculations are long and involved and the results are expressed in terms of three affinity laws. In this work we use kinetic theory to attack this problem. A hard sphere collision model is used, and subsequently a correction to account for the flow behaviour of air is incorporated. Our calculations prove the affinity laws and provide numerical estimates of the air delivery, thrust and drag on a rotating fan.