# 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. Fan-curve explorer, before its controls load: the datasheet curve of one ebm-papst W2G115-AD15-13 fan at 12 V against a system that needs 12 Pa at 100 m³/h; they cross at 150 m³/h at 26.9 Pa, clear of the stall region below 132 m³/h, which is shaded 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. ```mermaid flowchart TD D["datasheet points
cadagent.thermal.fans"] --> C["fans_in_series
fans_in_parallel"] S["system: a test, CFD,
or heatsink pressure_drop"] --> K["system_coefficient
k in Δp = k Q²"] C --> O["fan_operating_point
flow · pressure · stable"] K --> O O --> T{"below
fan_stall_flow?"} T -->|"no"| G["the flow for the
heatsink and CFD"] T -->|"yes"| B["stalled: more fans in series,
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. ```python 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](formulas.md#what-it-computes). ## 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.
What we looked at before building the explorer, and the tests that keep it honest - **[fluids](https://github.com/CalebBell/fluids)** by Caleb Bell (MIT): duct and fitting losses to build a system curve from parts. Use it for the k of a real duct run. It pulls in SciPy, so it cannot run in the page, and the page must compute what agents get. - **Fan makers' selection tools** match their own fans to a system curve. They are the place to choose a fan, but they are the makers' software, not code we can test or embed. - **So the solver is built**, on the existing `fan_operating_point` (exact roots on each straight segment of the curve), with the fan data read from the datasheet's vector chart rather than digitised from a picture. - **Tests:** - `tests/test_formulas.py` solves one fan, two in series and two in parallel on a straight-line curve by hand (in a restrictive system, (√17 − 1)/8, 1/2 and (√65 − 1)/16 of the free-air flow), and the crossover where series and parallel give the same air. - It also finds every operating point the datasheet tabulates, on the datasheet's own system curves, within its rounding (5 m³/h, 1 Pa), and checks that the table lies right of the stall peak at every voltage. - `tests/webkit-formulas.test.mjs` runs the port on the golden vectors, including the stall dip with three crossings. They match bit for bit. - `tests/website-browser.mjs` runs the explorer at 360 and 1366 px under the site's security policy, in Chromium and WebKit, with the fan vectors run again in each engine.
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).