Viscous Scaling Phenomena in Miniature Centrifugal Flow Cooling Fans: Theory, Experiments and Correlation

This paper analyzes the scale effects that occur in miniature centrifugal flow fans and investigates the possibility of optimizing blade geometry so that performance can be enhanced. Such fans are typically employed in small scale heat sinks such as those used for processor cooling applications or in portable electronics. The specific design parameter varied is the blade chord length, and the resulting fan performance is gauged by examining the flow rate, pressure rise, and power consumption characteristics. The former two are measured using a BS 848 fan characterization rig and the latter, by directly measuring the power consumed. These characteristics are studied for three sets of scaled fans with diameters of 15 mm, 24 mm, and 30 mm, and each set considers six individual blade chord lengths. A novel theory is put forward to explain the anticipated effect of changing this parameter, and the results are analyzed in terms of the relevant dimensionless parameters: Reynolds number, chord length to diameter of fan ratio, flow coefficient, pressure coefficient, and power coefficient. When these characteristic parameters are plotted against the Reynolds number, similar trends are observed as the chord length is varied in all sets of scaled fans. The results show that the flow coefficient for all the miniature fans degrade at low Re values, but the onset of this degradation was observed at higher Re values for longer blade chord designs. Conversely, it was found that the pressure coefficient is elevated at low Re, and the onset Re for this phenomenon correlates well with the drop off in flow coefficient. Finally, the trend in power coefficient data is similar to that for the flow coefficient. The derived theory is used to correlate this data for which all data points fall within 6% of the correlation. Overall, the findings reported herein provide a good understanding of how changing the blade chord length affects the performance of miniature centrifugal fans; hence, providing fan designers with guidelines to aid in developing optimum blade designs, which minimize adverse scaling phenomena.