Airflow and fans

A fan does not deliver the airflow printed on its box. It delivers what its pressure-flow curve gives where that curve meets the enclosure's own curve, the pressure the air needs to get through vents, boards and fins at each flow. That crossing is the operating point. cadagent.formulas finds it, for one fan or several in series or in parallel, and says when it falls in the fan's stall region. cadagent.thermal.fans holds fan curves read from datasheets. The explorer below runs the browser port of the same functions, tested against the Python on shared vectors.

Try it: the fan-curve explorer

The teal line is the datasheet curve of an ebm-papst W2G115-AD15-13, a 115 mm axial fan, at the supply voltage you pick. The rust parabola is the system: set how much pressure the enclosure needs at 100 m³/h, which fixes k in Δp = k Q². The dot is where they cross. The shaded band is the stall region: the dip and flat top left of the curve's last peak. The default runs at 150 m³/h, clear of the stall region, which is below 132 m³/h.

Try these:

• Make the enclosure tighter: 25 Pa at 100 m³/h (smaller vents, a denser grille). The point drops to 112 m³/h and into the stall region. On that flat stretch a little more resistance costs a lot of air, and the fan gets loud.
• Add a second fan in parallel. At 25 Pa you get 140 m³/h, and each fan still stalls at 70 m³/h. Switch to series and the pair gives 148 m³/h, clear of the stall region: in a restrictive system, fans in series win.
• Open the enclosure up: 4 Pa at 100 m³/h. Now two fans in parallel give 275 m³/h and two in series only 186 m³/h. In an open system, fans in parallel win.
• Change the voltage. The same fan at 8 V and 16 V is a smaller and a larger curve, each with its own stall region.

How to read it

The stall region is left of the peak that ends the curve's last rise in pressure. The maker's own table of measured points lies right of that peak at every voltage, which is the range the fan is meant to run in. In the stall region the fan is louder and less efficient. On a flat or rising stretch of the curve, its flow also swings with small changes in the system. Further left, where the curve falls steeply again, the point is steady but still stalled.

A system curve can also cross a deep dip two or three times. The fan can then settle at any of the crossings, and fan_operating_point flags the result unstable. That needs a dip where pressure divided by flow rises: a system Δp = r Q + k Q² has Δp / Q = r + k Q, which never falls, so a curve whose Δp / Q falls all the way is crossed only once. This fan's dips are that shallow at all three voltages, in series and in parallel too, so the explorer never shows "Unstable". The Python tests the check on a curve with a deeper dip, which a system crosses three times.

flowchart TD
    D["datasheet points<br/>cadagent.thermal.fans"] --> C["fans_in_series<br/>fans_in_parallel"]
    S["system: a test, CFD,<br/>or heatsink pressure_drop"] --> K["system_coefficient<br/>k in Δp = k Q²"]
    C --> O["fan_operating_point<br/>flow · pressure · stable"]
    K --> O
    O --> T{"below<br/>fan_stall_flow?"}
    T -->|"no"| G["the flow for the<br/>heatsink and CFD"]
    T -->|"yes"| B["stalled: more fans in series,<br/>larger vents, another fan"]
    classDef here fill:#fffdf5,stroke:#173d3c,color:#173d3c
    classDef near fill:#eef1e4,stroke:#6f8a80,color:#173d3c
    classDef out fill:#ffe1cc,stroke:#bd3a12,color:#173d3c
    class C,K,O,T here
    class D,S near
    class G,B out

From Python

SI units: flow in m³/s, pressure in Pa, k in Pa·s²/m⁶.

from cadagent import formulas as fx
from cadagent.thermal.fans import FANS
fan = FANS["w2g115-ad15-13-12v"].curve()                 # [(Q m3/s, dp Pa)] from the datasheet
k = fx.system_coefficient(12.0, 100 / 3600)              # 12 Pa at 100 m3/h
op = fx.fan_operating_point(fan, k)                      # flow 0.0416 m3/s (150 m3/h), 26.9 Pa
op["stable"], op["stall"]                                # True, False
fx.fan_stall_flow(fan) * 3600                            # 132.2 m3/h: below it, the stall region
fx.fan_operating_point(fx.fans_in_series(fan, 2), fx.system_coefficient(25.0, 100 / 3600))

For a plate-fin heatsink, cadagent.thermal.heatsink gives the pressure drop and the thermal resistance at a flow. For where the air really goes inside an enclosure, cadagent.simulation.cfd models the fan as an actuator disc. Each formula states its units, limits and source in fx.catalogue(), and they are listed with the others on Engineering formulas.

Limits

• Steady flow at one air density. The datasheet's pressures are for 1.2 kg/m³ of air. Hot or thin air moves less mass for the same curve.
• The maker's test rig, not your enclosure. The curve is measured with a free inlet and a free outlet (ISO 5801, installation category A), so its pressure is the fan's static rise, with the outlet's velocity pressure counted as lost. A grille, a finger guard or a board close to the fan costs pressure that the curve does not show.
• The system curve is the hard part. A real one comes from a test or from CFD (cadagent.simulation.cfd), not from a guessed k. Δp = k Q² is turbulent loss; filters and fin channels add a linear part, r in fan_operating_point.
• Identical fans, sharing evenly. Series fans close together lose pressure to swirl. In the stall region, fans in parallel can share unevenly: one stalls and the others carry more. Neither is modelled.
• The curve is read from the datasheet's chart to about 1 m³/h and 1 Pa. The stall peak is found from its points, so a dip shallower than that reading still counts.

Sources: F. M. White, Fluid Mechanics, 7th ed., McGraw-Hill, 2011, Section 11.5 (matching pumps and fans to system characteristics, in series and in parallel); ebm-papst Mulfingen, data sheet W2G115-AD15-13, item no. 50788-5-9980, approved 2016-05-09, p. 5 (air performance curves and measured values).