Reconsideration of the Fan Scaling Laws: Part I — Theory

Generalized Fan Scaling Laws (GSFL) are derived for the scaling of fan performance. These follow from first principles using the Navier-Stokes equations appropriate to rotating and swirling flows. Not surprisingly, both Strouhal and Reynolds number similarity must be maintained. Thus for a geometrically similar family of fans, dynamic similarity is only possible if ΩD/U = constandUD/ν = const. If the second relation is solved for U and substituted into the first, it follows that full dynamic similarity is possible only if ΩD²/ν = const. This can be contrasted with the classical fan laws (CFSL) which for the same flow rate coefficient would imply that Q/ΩD³ (or U/ΩD) = const, implying that both fan size ratio and fan speed ratio are independent fan scaling parameters. Clearly for dynamic similarity to be maintained, the velocity and fan speed can not be varied independently (i.e. fan size and fan speed are not independent scaling parameters), contrary to the implications of the classical fan scaling laws. Further implications of the differences between the classical and generalized scaling laws for fan performance testing and design will be explored. Also several examples will be given in Part II as to how the generalized scaling laws can be applied in design practice.