R290 Heat Pump Charge, Room Size and Leak Concentration

Charge sizing. IEC 60335-2-40:2022 Ed. 7, Annex GG: GG.1–GG.2 establish applicability, thresholds and the basic unventilated-room route; GG.3–GG.5 concern ventilated enclosures and machinery rooms; GG.13–GG.14 concern A2/A3 circulation airflow and enhanced tightness. Annex LL addresses detection and Annex QQ tested releasable charge. Clause-level applicability and test details were not checked against licensed text.

The published basic relation is $m_{max}=2.5\,LFL^{5/4}h_0\sqrt A$, inverted for minimum area. For R290, $m_1=4LFL$, $m_2=26LFL$, $m_3=130LFL$. GIZ (2025, printed p.35) supplies the basic, $0.35LFLh_0A$ enhanced-tightness and $0.50LFLH_{eff}A$ integral-airflow relations. Here $H_{eff}=2.2$ m. The direct indoor routes are capped at $m_2$; below $m_1$ there is no area criterion from these equations. GIZ’s heat-pump report (2022, pp.23–24) describes $m_3$ for a qualifying ventilated enclosure. Zero area in that row means no area equation is evaluated. The total circuit cap remains independent of any tested releasable mass.

R32 uses $LFL=0.307$ kg/m³ and threshold multipliers 6, 52 and 260; its basic minimum area also satisfies $m_c/(0.75LFLh_0)$ (EMSD 2020, printed pp.6–7).

Hole release. Liquid feed uses $\dot m=C_dA_o\sqrt{2\rho_u(p_u-p_a)}$. Vapour feed uses the ideal-gas isentropic nozzle relation, switching at the critical pressure ratio (NASA Glenn). Density, molar mass and heat-capacity ratio come from CoolProp at the entered states. Source pressure and temperature remain fixed during the release.

Room transport, derived here. Let $S(z)=e^{-z/h_s}/[h_s(1-e^{-H/h_s})]$. Solve $\partial_t c=K_z\partial_{zz}c-\lambda c+\dot m S(z)/A$, with zero diffusive flux at floor and ceiling. A cosine expansion integrates each linear mode analytically over constant-source/removal intervals. The zero mode is the well-mixed comparison, $d\bar c/dt=\dot m/V-\lambda\bar c$. Its analytical ventilation integral independently accounts for exhausted mass.

Before release completion, the rising analytical sensor solution is searched by bisection. After release completion, a chronological interval search bounds the analytical exponential sum and its derivatives, locates interior sensor maxima, and refines the earliest threshold crossing. This detector search is independent of chart sampling. Exhaust changes the uniform removal rate after the response delay. Isolation limits the source to the mass released before closure plus the specified trapped tail. Both room models use that same release and control history. Threshold durations are interpolated between time samples. LFL and UFL heights are roots of the modal profile, bisected to the specified height tolerance independently of the drawing grid; the flammable band excludes concentrations above UFL.

One closed room, initially free of refrigerant, with constant air temperature, atmospheric pressure and floor area. Lateral spreading to the floor is assumed immediate; the exponential floor source and prescribed vertical diffusivity represent stratification without resolving the gravity current. Outdoor-air removal acts uniformly at each height with clean makeup air. Recirculation alone removes no mass.

The transient is a dilute, isothermal dispersion model derived here, separate from the Annex GG charge equations. The 2.1–9.5 vol% propane flammability interval is from NIOSH; ambient vapour density converts it to mass concentrations. The standard sizing LFL remains the prescribed 0.038 kg/m³. Temperature-dependent combustion limits are not modelled.

Liquid release neglects flashing restrictions and boiling delay; vapour release neglects real-gas nozzle corrections. Neither is a refrigerant-circuit blowdown calculation. Automatic exhaust remains active after triggering; no detector reset, fault probability or valve leakage is modelled. The section drawing has a schematic horizontal width because floor area alone does not define a room aspect ratio.

The diffusivity input is displayed in cm²/s and explicitly converted to m²/s before evaluating the transport modes.

This implements the requested 2022 Edition 7 framework, not a complete installation conformity assessment. IEC lists a later edition. The paywalled Annex GG text, detailed airflow and outlet-velocity requirements, sensor qualification, enclosure pressure/duct tests, enhanced-tightness construction, compressor location restrictions and Annex QQ release tests were not independently verified. Conditional sizing paths apply only to a product documented for them; adding room ventilation or a detector does not create eligibility. A ventilated enclosure requires separation from the occupied room, monitored discharge outdoors and its applicable product tests; the $m_3$ number alone is insufficient.

EN 378-1:2016+A1:2020 Annex C also requires installation/access and location classification; that full selection is outside this calculator. Check against the standard in force, national adoption and manufacturer instructions. For an intact ventilated enclosure, gas is discharged outside: the room leak simulation instead represents an escape into the room or containment failure.

Floor concentration depends strongly on the assumed source-depth scale and mixing diffusivity. This vertically resolved screening model cannot exclude more severe local concentrations, especially near a jet or in a pit. Above 10 vol% the dilute assumption is flagged. The LFL-equivalent layer height is a mass/threshold-volume measure; it is distinct from the computed LFL contour and the LFL-to-UFL flammable band.

Default resolution is 128 vertical harmonics and 1,800 time intervals; both are exposed for refinement. Modes and detector events use analytical solutions; peak sampling and time above threshold still depend on chart time resolution. The below-LFL verdict applies only to the simulated window, and an unfinished release prompts extending that window. Contour-height roots use an independent absolute tolerance, entered in mm. Small negative spectral tails are clipped only in reconstructed profiles; conservation uses the unmodified mean mode. Animation interpolates modal states in time and displays a smooth vertical colour field. A coarse source representation or a release shorter than ten sampling intervals is flagged.