Fan Laws for Rack Systems

As datacenter aisle noise levels approach OSHA workplace limits, air-cooled server racks share with desktop workstations the ultimate problem of being thermally constrained within a finite packaging volume by acoustic emission restrictions. The primary source of noise in most scalable 1 and 2 EIA rack drawers is an air moving device. Multiple compact dual stage counter-rotating bladed tubeaxial devices are being adopted to overcome the pressure drop of increasingly densely packed electronics. The design problem of maximizing hydraulic output within space and noise constraints naturally leads to the question of whether these many smaller fans could be gainfully replaced by fewer but larger fans. To examine this question, the fan laws for single devices are extended to equivalent systems of multiple parallel and series fans. The principle of impedance matching is applied to hydraulic sources and loads to maximize pumping power. A novel method is introduced to map fan speed, size, and hydraulic performance. The paper provides a proof that equal-staged noise-neutral space-filling planar arrays of parallel homologous devices must deliver the same net rack flow and pressure, and it shows that series arrangements of multiple stages of planar parallel fan arrays will always, under acoustic parity conditions, yield increased pressure at diminishing flow with each successive stage. At equivalent system hydraulic output, larger fans in series are shown to consume greater packaging volume while achieving lower overall acoustic output. Net rack flow and pressure relationships are also quantified for systems of equal total rack fan shaft power input. Examination of actual unit level fan noise measurements suggests that in practice, systems of small fans typically output 4 to 9 dB higher noise levels than larger fans operated at the same net flow and pressure. Finally, a survey of unit level airflow and power input measurements reveals that larger fans exhibit higher total efficiency than smaller fans.