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Ventilation, Internal Gains and Transmission Heat Transfer between Adjacent Zones

This module implements methods for evaluating heat transfer by ventilation and internal heat gains in thermally conditioned and unconditioned zones.

It also includes an auxiliary function for computing transmission heat transfer coefficients between conditioned and adjacent zones, following EN 13789.

Overview

The module covers three main components:

  1. Ventilation heat transfer coefficient (VentilationInternalGains.heat_transfer_coefficient_by_ventilation):
  2. Evaluates the natural ventilation rate and corresponding heat transfer coefficient (H_ve_nat) using EN 16798‑7 (wind and temperature-driven airflow).

  3. Supports a simplified occupancy-based ventilation model.

  4. Internal heat gains (VentilationInternalGains.internal_gains):

  5. Computes total internal heat gains from occupants, appliances, and optionally nearby unconditioned zones, using EN 16798‑1 and EN 15316‑1 formulations.

  6. Transmission between zones (transmission_heat_transfer_coefficient_ISO13789):

  7. Calculates inter-zone transmission coefficients (H_ztu_tot, b_ztu_m) according to EN 13789, accounting for heat exchanges between conditioned, unconditioned, and external environments.

Calculation of heat transfer coefficient by ventilation

@staticmethod
def heat_transfer_coefficient_by_ventilation(
    building_object, Tz, Te, u_site, Rw_arg_i=None, c_air=1006, 
    rho_air=1.204, C_wnd=0.001, C_st=0.0035, rho_a_ref=1.204, altitude=None,
    type_ventilation="temp_wind", flowrate_person=1.4
) -> h_natural_vent:

Inputs (main)

  • Tz [°C] indoor air temperature (zone).
  • Te [°C] outdoor air temperature.
  • u_site [m·s⁻¹] local wind speed at site height (as per EN 16798-7 assumptions).
  • Rw_arg_i [-] array of opening ratios per window (0…1). If None, defaults to 0.9.
  • C_wnd = 0.001 [(m·s⁻¹)⁻¹] wind coefficient (EN 16798-7 Table 11).
  • C_st = 0.0035 [(m·s⁻¹)/(m·K)] stack coefficient (EN 16798-7 Table 11).
  • rho_a_ref [kg·m⁻³] reference air density at ~20 °C; corrected with altitude if provided.
  • type_ventilation: "temp_wind" (ISO airing) or "occupancy" (area-based volumetric rule).
  • flowrate_person [L·s⁻¹·m⁻²] used only in "occupancy" branch.

Purpose

Physical purpose: compute the ventilation heat transfer coefficient \(H_{ve}\) [W·K⁻¹] of the thermal zone either: - from natural ventilation (EN 16798-7:2017, single-sided airing via windows, wind/stack), or - from occupancy-driven flow (simplified volumetric rate per floor area).

Physics

Step A — Effective opening height (stack path)
For each transparent surface: - parapet height \(h_p\) [m],
- window height \(h_w\) [m],
- path height (vertical center): \(h_{path,i} = h_p + \frac{h_w}{2}\), - fa height: \(h_{fa,i} = \frac{h_w}{2}\).

The useful stack height:

\[ h_{w,st} = \max_i\!\left(h_{path,i} + \frac{h_{fa,i}}{2}\right) - \min_i\!\left(h_{path,i} - \frac{h_{fa,i}}{2}\right) \tag{4.1} \]

Step B — Density correction
If altitude present, a standard atmosphere relation updates \(\rho_{a,ref}\). Outdoor density:

\[ \rho_{a,e} = \rho_{a,ref}\,\frac{291.15}{273.15 + T_e} \tag{4.2} \]

Step C — Effective openable area

For each window \(i\), geometric area \(A_{w,i} = h_{w,i}\,w_i\).
Open area \(A_{w,i}^{open} = A_{w,i}\,R_{w,i}\) with \(R_{w,i}\in[0,1]\). If Rw_arg_i is missing or length mismatches the number of windows, default \(R_{w,i}=0.9\).

\[ A_{w,tot} = \sum_i A_{w,i}^{open} \tag{4.3} \]

Step D — Airing volumetric flow (single-sided)

Using EN 16798-7 §6.4.3.5.4:

\[ q_v = 3600\;\frac{\rho_{a,ref}}{\rho_{a,e}}\;\frac{A_{w,tot}}{2}\, \left[\max\!\Big(C_{wnd}\,u_{site}^2,\; C_{st}\,h_{w,st}\,\lvert T_z-T_e\rvert\Big)\right]^{1/2} \quad [\text{m}^3/\text{h}] \tag{4.4} \]

Step E — Ventilation conductance

\[ H_{ve} = \frac{c_{air}\,\rho_{air}}{3600}\;q_v \quad [\text{W·K}^{-1}] \tag{4.5} \]

Occupancy branch: area-based simplified rule (constant per hour)

\[ H_{ve} = A_{use}\cdot (3.6\,\dot v_{pers})\cdot \frac{c_{air}\,\rho_{air}}{3600} \tag{4.6} \]

with \(\dot v_{pers}\) in [L·s⁻¹·m⁻²] and 3.6 converting L·s⁻¹·m⁻² to m³·h⁻¹·m⁻².

Outputs

  • np.ndarray of H_ve_k_t [W·K⁻¹] (scalar or time-series depending on inputs).

Example

if type_ventilation == "temp_wind":
    extract all windows -> {height, width, parapet}
    compute hw_path_i, hw_fa_i -> hw_st  # Eq. (4.1)
    density correction -> rho_a_e        # Eq. (4.2)
    aw_tot -> Eq. (4.3)
    qv -> Eq. (4.4)
    Hve -> Eq. (4.5)
else:  # occupancy
    A_use <- building_object["building"]["net_floor_area"]
    Hve  <- Eq. (4.6)
return np.array(Hve)

Edge Cases & Validation

  • No transparent surfaces → \(A_{w,tot}=0\) → \(H_{ve}=0\).
  • Rw_arg_i length mismatch → warning + default 0.9.
  • Negative or null u_site accepted; max(·) ensures stack/wind pick the dominant driver.

Internal gains calculation

def internal_gains(
    cls, building_type_class, a_use, unconditioned_zones_nearby=False,
    list_adj_zones=None, Fztc_ztu_m: float=1, b_ztu: float=1,
    h_occup: float=1, h_app: float=1, h_light: float=1, h_dhw: float=1,
    h_hvac: float=1, h_proc: float=1
) -> float:

Inputs (main)

  • building_type_class: key for the lookup table internal_gains_occupants (imported from source.table_iso_16798_1).
  • a_use [m²]: useful area of the conditioned zone.
  • h_* [-]: hourly multipliers (profiles) for each sub-component (currently occupants and appliances are used).
  • Coupling params for unconditioned zones:
    • b_ztu [-]: adjustment factor of the adjacent unconditioned zone (see §4.4, Eq. (4.13)).
    • Fztc_ztu_m [-]: fractional path factor conditioned→unconditioned in month m (lumped path coefficient).
    • list_adj_zones: number of adjacent zones (note: the current signature expects an int; see note below).

Note: The code uses for zones in range(list_adj_zones) — pass an int. If a list is desired in the future, change to for z in list_adj_zones:.

Purpose

Physical purpose: compute internal sensible gains \(\Phi_{int}\) [W] in the thermally conditioned zone, possibly accounting for spillover to adjacent unconditioned zones.

Physics

Let \(q_{occ}\) and \(q_{app}\) be the nominal density of internal gains [W·m⁻²] for occupants/equipment per building_type_class.

Base internal gains in the conditioned zone:

\[ \Phi_{int,z}(t) = \big(q_{occ}\,h_{occup}(t) + q_{app}\,h_{app}(t)\big)\;A_{use} \tag{4.7} \]

Optional spillover to unconditioned adjacent zones (unconditioned_zones_nearby = True):
The code currently adds a further term per adjacent zone combining a direct duplicated contribution and a fractional transfer modulated by \((1-b_{ztu})\,F_{ztc{\text -}ztu,m}\):

\[ \Phi_{int,z}^{eff}(t) = \Phi_{int,z}(t) + \sum_{j=1}^{N_{adj}} \left[\Phi_{int,z}(t) + \big(1-b_{ztu}\big)\,F_{ztc{\text -}ztu,m}\,\Phi_{int,z}(t)\right] \tag{4.8} \]

Output

  • float [W] — instantaneous internal sensible gains for the conditioned zone with the current coupling rule.

Example

q_occ = internal_gains_occupants[building_type_class]['occupants']
q_app = internal_gains_occupants[building_type_class]['appliances']
Phi_base = (q_occ*h_occup + q_app*h_app) * a_use        # Eq. (4.7)
if unconditioned_zones_nearby:
    Phi_eff = Phi_base
    for _ in range(list_adj_zones):
        Phi_eff += Phi_base + (1-b_ztu)*Fztc_ztu_m * Phi_base
    return float(Phi_eff)
else:
    return float(Phi_base)

Integration Roadmap (Future Enhancements)

  • Air leaks: integrate infiltration losses for cracks and envelope leakage tests.
  • Cross ventilation: include simultaneous airflow paths between opposite façades.
  • Mechanical ventilation: handle forced air systems with user‑defined flow rates and recovery efficiency.

References

  • ISO 52016‑1:2017, § 6.5.10 Ventilation and Heat Transfer Coefficients
  • ISO 16798‑7:2017, § 6.4.3.5 Natural Ventilation Airflow
  • ISO 16798‑1:2019, § M1–M10 Internal Gains
  • ISO 13789:2017, § 7 Transmission Heat Transfer Coefficients through Adjacent Spaces