Presets
Playback
Machine
Power setting, floor, nozzle block and the HEPA filter.
Dust
How fast dust is picked up and how fast time runs.
Layers
Model checks
The science
Fan, system and operating point
The fan follows the affinity laws: Pfan(Q) = P0 s2 (1 − (Q/(Qmax s))2), with s the speed ratio. The air path is a series of turbulent resistances (nozzle, hose, cyclone, pre-motor foam, HEPA, exhaust), ΔP = Σ ki Q2. Setting the two equal gives the operating point in closed form, Q = s √(P0/(ktot + P0/Qmax2)). Clogging raises kpre and kHEPA (a cubic term at high load), a blocked nozzle raises knozzle enormously: flow collapses while suction at the inlet peaks.
Cyclone separation
Each cyclone stage follows a Lapple-type grade efficiency η(d) = 1/(1 + (d50/d)2), exactly 50 % at the cut size d50. The cut size scales with 1/√(inlet velocity), i.e. as √(Qref/Q), and rises when the bin is nearly full because dust is re-entrained. The downstream foam and HEPA filters have their own grade efficiencies; a HEPA filter is weakest near the most penetrating particle size (about 0.3 µm) and stops at least 99.97 % there when clean.
Power and noise
Air power is Pfan Q; fan efficiency has a parabola in Q/Qmax, shaft power adds windage s3, electrical power divides by the motor efficiency. Noise follows a tip-speed law, about 50 log10(speed) plus a small flow term.
Honest simplifications
- Lumped parameters with typical canister-vacuum figures; no CFD. Efficiencies, resistances and capacities are illustrative, not those of any product.
- Three dust size classes (300, 12 and 1 µm) carry the mass; the drawn particles are samples of the model's capture fractions, not tracked trajectories.
- Nozzle pick-up is a simple function of flow, and carpet is only a different nozzle resistance and pick-up factor.
What to try
- Press "Blocked nozzle": flow almost vanishes while suction at the nozzle is at its maximum, and the fan runs in the starved region of its curve.
- Press "Clogged filters" and see the system curve steepen and the operating point slide left on the fan curve.
- Press "No HEPA filter": the fine particles (pink) start escaping through the exhaust.
- Press "Bin nearly full": the cyclone cut size rises and coarse dust passes on to the filters.
- Compare eco and boost: air power grows much faster than airflow.