Drum regimes. A drum of radius R turning at ω has Froude number Fr = ω²R/g. Low Fr: the load rolls and cascades down the surface; Fr of about 0.4 to 1: items are carried over the top and drop in a cataract through the air (best tumbling for drying); Fr ≥ 1: the wall pushes harder than gravity pulls, so items cling and ride round.
Cling speed. An item pressed to the wall at the very top has contact force N = m(ω²rc - g), where rc = R - r is the radius of its centre. It stays pinned only when N ≥ 0, so ωc = √(g/R) for a point item and √(g/(R - r)) for a bundle of radius r. For R = 0.30 m: 54.6 rpm (point) and about 60 rpm (towel-sized bundle). The speed does not depend on the mass of the load. Grip matters too: at the side of the drum friction must carry the weight, so μ of roughly 1 or more is needed near Fr = 1. A real tumble dryer runs just below the cling speed on purpose.
Air and water. Saturation pressure from the Magnus formula ps = 611.2 exp(17.62T/(243.12+T)) Pa; humidity ratio w = 0.622 p/(P - p). The wet fabric settles at the adiabatic-saturation (wet-bulb) temperature, where cp(Tair - Twb) = L (ws(Twb) - win).
Evaporation. Mass transfer: dm/dt = η · ṁair · (ws(Tfabric) - win) with contact effectiveness η = 1 - e-NTU, NTU ∝ mdry · exposure / ṁair. The exposure factor comes from the particle simulation: items in free flight are well exposed, items clinging to the wall or buried in the pile are not. Above the critical moisture Xc the rate is constant (surface water); below it the rate falls linearly to the equilibrium moisture Xeq (water must diffuse out of the fibres).
Energy. Evaporating 1 kg of water needs at least L = 2.26 MJ = 0.628 kWh. Electric energy per kg is higher because the air leaves warm and the fabric, drum and cabinet are heated too. The heater power equals ṁair cp (Tair - Troom) up to an element limit. A heat pump recycles heat (COP about 3), so it can go below 0.63 kWh per kg of electric energy.
Simplifications, honestly. The pile is modelled as 2D soft discs in the drum cross-section (no cloth bending, no depth); item sizes, grip, NTU coefficient, Xc and the fan curve are typical round numbers, not a specific machine. The lint-filter model scales airflow by 1 - 0.65 c; in this model the heater power follows the airflow, so a clogged filter mainly makes the cycle longer, while real machines also lose extra energy to thermostat cycling (not modelled). The sock loss is a toy, not a measured rate. Cost and CO2 use the sliders you set. Generic machine: no brand is modelled.