Reconsideration of the Fan Scaling Laws: Part II — Applications

The entire approach to the scaling of fan performance was reconsidered in Part I from first principles using the Navier-Stokes equations appropriate to rotating and swirling (incompressible) flows. Generalized fan scaling laws (GFSL) were derived, consistent with the fact that both Strouhal and Reynolds number must be maintained constant for full dynamical similarity to be possible. As a consequence, dynamic similarity is only possible if ΩD²/ν = const. (in addition to U/ΩD = constant, or equivalently, Q/ΩD³ = constant). This can be contrasted with the classical fan laws (CFSL) which for the same flow rate coefficient would imply that Q/ΩD³ = const. The differences in fan scaling laws between GFSL and CFSL lead to very different fan pressure and fan power scaling criteria. For example, using the GFSL, the pressure coefficient (or Euler number), similarity between the model and prototype fan results in ΔP_m/ΔP_p = 1/(L_m/L_p)² (for constant kinematic viscosity), whereas the CFSL pressure scaling criteria lead to ΔP_m/ΔP_p = (Ω_m/Ω_p)² (L_m/L_p)². Clearly these are very different scaling results and affect the scaling of all the relevant fan performance parameters. In this paper, several applications will be described of experimental programs which utilized these GFSL to design dynamically similar scale models of automotive fans, and these designs are contrasted with what might have been done had the classical laws been used. Three of the facilities were built, and each allowed detailed flow measurements, which would not otherwise have been possible. In addition, the implications and advantages of making tests in a high-pressure facility are explored. Some suggestions will also be made as to how the generalized scaling laws can be applied in design practice.