TP-06: Ventilation and Infiltration

Overview

Ventilation and infiltration determine the rate at which outdoor air enters and conditioned air leaves a dwelling. This air exchange drives a heat loss (or gain) that, alongside fabric losses, determines the space heating demand.

The calculation follows Method 1 of BS EN 16798-7:2017, which uses a pressure-based airflow network to compute mass flow rates through each airflow path: envelope leaks, purpose-built vents, openable windows, combustion appliances, and mechanical ventilation systems. The internal reference pressure is solved iteratively to satisfy mass balance at each timestep.

The resulting ventilation heat transfer coefficient $H_{ve}$ W/K enters the zone heat balance directly, coupling the ventilation calculation to the space heating demand solver.

Inputs

Calculation

Air Density Correction

Air density is adjusted for the site altitude above sea level:

${\rho }_{alt}={\rho }_{a,ref}{\left(1-\frac{0.00651\cdot h_{alt}}{293}\right)}^{4.255}$

where ${\rho }_{a,ref}=1.204$ kg/m³ is the reference air density at sea level and 20 °C.

At a given temperature $T$ (in Kelvin), the local air density is:

$\rho (T)=\frac{T_{e,ref}}{T}\cdot {\rho }_{alt}$

where $T_{e,ref}=293.15$ K.

Wind Speed at Zone Level

The meteorological wind speed is corrected for terrain roughness to obtain the wind speed at the building zone level:

$u_{site}=\frac{C_{rgh,site}\cdot C_{top,site}}{C_{rgh,met}\cdot C_{top,met}}\cdot u_{10}$

where:

• $C_{rgh,site}$ is the roughness coefficient at the building site
• $C_{top,site}$ is the topography coefficient at the building site (default 1.0)
• $C_{rgh,met}$ is the roughness coefficient at the meteorological station (default 1.0)
• $C_{top,met}$ is the topography coefficient at the meteorological station (default 1.0)

Terrain Roughness Coefficient

The roughness coefficient depends on terrain class and height of the airflow path $z$:

$C_{rgh}=K_R\cdot \ln \left(\frac{z}{z_0}\right)$

where $z$ is clamped to a minimum value $z_{min}$. The terrain parameters are:

Pressure Difference at an Airflow Path

The pressure difference between exterior and interior at a given airflow path height $h_{path}$ drives airflow through each opening. From BS EN 16798-7, Equations 4, 5, and 6:

$p_{e,path}={\rho }_{a,ref}\frac{T_{e,ref}}{T_e}\left(\frac{1}{2}{C}_{p,path}\cdot u_{site}^2-h_{path}\cdot g\right)$

$p_{z,path}=p_{z,ref}-{\rho }_{a,ref}\cdot h_{path}\cdot g\cdot \frac{T_{e,ref}}{T_z}$

$\Delta p_{path}=p_{e,path}-p_{z,path}$

where:

• $p_{z,ref}$ is the internal reference pressure (Pa), solved iteratively
• $C_{p,path}$ is the wind pressure coefficient for the airflow path
• $g=9.81$ m/s² is the gravitational acceleration
• $T_e$ and $T_z$ are external and zone air temperatures in Kelvin

Wind Pressure Coefficients

Wind pressure coefficients $C_p$ are determined from BS EN 16798-7, Table B.7. The coefficient depends on facade direction (windward, leeward, or neither), shield class, height, and whether cross-ventilation is possible.

Facade Direction

For elements with pitch $\ge$ 60° (walls), the facade direction is determined by comparing the element orientation with the wind direction:

• Windward: orientation difference $\le$ 60°
• Neither: orientation difference between 60° and 120°
• Leeward: orientation difference $\ge$ 120°

For elements with pitch < 60° (roofs), further classification applies when cross-ventilation is possible: Roof10 (pitch < 10°), Roof10_30 (10° to 30°), and Roof30 (30° to 60°).

Cross-Ventilation Coefficients

When cross-ventilation is possible ($f_{cross}=\text{true}$), the wind pressure coefficients for walls vary with height and shield class:

Non-Cross-Ventilation Coefficients

When cross-ventilation is not possible, reduced coefficients apply: windward = 0.05, leeward = $-0.05$, roof = 0, neither = 0.

Airflow Through Envelope Leaks

Envelope leakage is distributed across five notional leak paths (BS EN 16798-7, Table B.12):

1. Windward facade at 0.25 $h_z$
2. Leeward facade at 0.25 $h_z$
3. Windward facade at 0.75 $h_z$
4. Leeward facade at 0.75 $h_z$
5. Roof at $h_z$

Leakage Coefficient

The overall leakage coefficient is derived from the pressurisation test result:

$C_{leak}=\frac{q_{v,\Delta p,leak,ref}\cdot A_{leak}}{\Delta p_{leak,ref}^{n_{leak}}}$

where $n_{leak}=0.667$ is the flow exponent for leaks (BS EN 16798-7, Section B.3.3.14).

This is distributed between facades and roof in proportion to their areas:

$C_{leak,facades}=C_{leak}\cdot \frac{A_{facades}}{A_{facades}+A_{roof}}$

$C_{leak,roof}=C_{leak}\cdot \frac{A_{roof}}{A_{facades}+A_{roof}}$

Each facade leak path receives 0.25 of the facade leakage coefficient (four paths share the facade leakage), while the single roof path receives the full roof leakage coefficient.

Leak Airflow

The volume flow rate through each leak path is (Equation 62):

$q_{v,leak,path}=C_{leak,path}\cdot \text{sign}(\Delta p_{path})\cdot |\Delta p_{path}{|}^{n_{leak}}$

Airflow Through Vents

Purpose-built vents (trickle vents, air bricks) are modelled as openings with adjustable position $R_v$ (0 = closed, 1 = fully open).

Vent Flow Coefficient

The airflow coefficient is calculated from the equivalent area (Equation 59):

$C_{vent,path}=\frac{3600}{10000}\cdot C_{D,vent}\cdot A_{vent}\cdot {\left(\frac{2}{{\rho }_{a,ref}}\right)}^{0.5}\cdot {\left(\frac{1}{\Delta p_{vent,ref}}\right)}^{n_{vent}-0.5}$

where:

• $C_{D,vent}=0.6$ is the discharge coefficient (BS EN 16798-7, Section B.3.2.1)
• $n_{vent}=0.5$ is the flow exponent (BS EN 16798-7, Section B.3.2.2)
• $A_{vent}$ is the effective opening area $R_v\cdot A_{vent,max}$

Vent Airflow

The volume flow rate through each vent is (Equation 58):

$q_{v,vent,path}=C_{vent,path}\cdot \text{sign}(\Delta p_{path})\cdot |\Delta p_{path}{|}^{n_{vent}}$

Airflow Through Windows

Openable windows are modelled using Section 6.4.3.5 of BS EN 16798-7. Each window may be divided into multiple parts to capture vertical pressure gradients across the window height.

Window Opening Free Area

The window opening free area depends on the opening ratio $R_w$ (Equation 40):

$A_w=R_w\cdot A_{w,max}$

Windows are treated as closed ($R_w=0$) if no window-opening control is defined or if the control signal is off.

Window Flow Coefficient

The flow coefficient for a window is (Equation 54):

$C_{w,path}=3600\cdot C_{D,w}\cdot A_w\cdot {\left(\frac{2}{{\rho }_{a,ref}}\right)}^{n_w}$

where:

• $C_{D,w}=0.67$ is the window discharge coefficient (BS EN 16798-7, Section B.3.2.1)
• $n_w=0.5$ is the window flow exponent (BS EN 16798-7, Section B.3.2.2)

Window Part Heights

For a window divided into $N_{w,div}$ divisions, the height for pressure difference calculation at the $j$-th part is (Equation 55):

$h_{w,div,path,j}=h_{w,path}-\frac{h_{w,fa}}{2}+\frac{h_{w,fa}}{2(N_{w,div}+1)}+\frac{h_{w,fa}}{N_{w,div}+1}\cdot (j-1)$

Window Part Airflow

The airflow through each window division is (Equation 53):

$q_{v,w,div,path}=\frac{C_{w,path}}{N_{w,div}+1}\cdot \text{sign}(\Delta p_{path})\cdot |\Delta p_{path}{|}^{n_w}$

Airflows through all window parts are summed to give total inflow and outflow through the window (Equations 56 and 57).

Combustion Appliances

Combustion appliances that draw room air for combustion create an additional extract airflow. The volume flow rate is (Equation 35):

$q_{v,comb}=3.6\cdot f_{op,comb}\cdot f_{as}\cdot f_{ff}\cdot P_{h,fi}$

where:

• $f_{op,comb}$ is the operation signal (0 = off, 1 = on)
• $f_{as}$ is the appliance system factor (Table B.2)
• $f_{ff}$ is the fuel flow factor (Table B.3)
• $P_{h,fi}$ is the fuel input power kW

The appliance system factor $f_{as}$ depends on the combustion air supply and flue gas exhaust arrangements:

Fuel flow factors $f_{ff}$ from Table B.3:

This flow is treated as outgoing (extract) from the zone (Equations 37 and 38).

Mechanical Ventilation

Mechanical ventilation systems provide controlled air supply and/or extraction. The model supports five system types:

• MVHR (Mechanical Ventilation with Heat Recovery): balanced supply and extract with heat recovery
• Centralised continuous MEV (Mechanical Extract Ventilation): extract only, continuous operation
• Decentralised continuous MEV: extract only, continuous, individual fans per wet room
• Intermittent MEV: extract only, operating on a timed schedule
• PIV (Positive Input Ventilation): supply only

Required Outdoor Air Flow Rate

The design outdoor air flow rate is adjusted for system and control factors (Equation 9):

$q_{v,ODA,req}=\frac{f_{ctrl}\cdot f_{sys}}{E_v}\cdot q_{v,ODA,design}$

where:

• $f_{ctrl}=1.0$ (Table B.4, residential default)
• $f_{sys}=1.1$ (Table B.5)
• $E_v=1.0$ (Section B.3.3.7, assuming perfect mixing)

Air Flow at Terminal Devices

The required supply and extract flow rates at the air terminal devices depend on system type (Equations 10 to 17):

The actual flow rates to the zone are scaled by the operational fraction $f_{op,V}$:

$q_{v,SUP,dis}=f_{op,V}\cdot q_{v,SUP,req}$

$q_{v,ETA,dis}=f_{op,V}\cdot q_{v,ETA,req}$

For continuous systems (MVHR, centralised and decentralised MEV), $f_{op,V}=1$. For intermittent MEV, $f_{op,V}$ is determined by the control schedule.

Heat Recovery

For MVHR systems, the effective heat recovery saving is represented as a reduction in the incoming air flow rate rather than a supply temperature increase. This avoids coupling the heat recovery calculation to the internal temperature solver:

$q_{v,hr,saving}=q_{v,SUP,dis}\cdot {\eta }_{hr}$

This effective saving is subtracted from the total incoming mass flow rate when computing the ventilation heat transfer coefficient.

Fan Energy

Fan power is calculated from the specific fan power and the design flow rate, apportioned to the zone by volume fraction:

$P_{fan}=SFP\cdot \frac{q_{v,ODA,req}}{3600}\cdot 1000\cdot \frac{V_{zone}}{V_{total}}$

where $P_{fan}$ is in watts, the factor of 3600 converts m³/h to m³/s, and 1000 converts m³ to litres. Fan energy per timestep is:

$E_{fan}=\frac{P_{fan}}{1000}\cdot \Delta t\cdot f_{op,V}$

where $\Delta t$ is the timestep duration in hours.

For MVHR, fan energy is split equally between supply and extract fans. For MEV systems, all fan energy is attributed to the extract fan. For PIV, all fan energy is attributed to the supply fan. The supply fan energy contributes to internal heat gains within the zone.

Mass Balance and Internal Reference Pressure

At each timestep, the internal reference pressure $p_{z,ref}$ is determined by solving the mass balance equation (Equation 67):

$\sum {\dot{m}}_{in}+\sum {\dot{m}}_{out}=0$

The total incoming and outgoing mass flow rates include contributions from all airflow paths:

${\dot{m}}_{in}={\dot{m}}_{in,windows}+{\dot{m}}_{in,vents}+{\dot{m}}_{in,leaks}+{\dot{m}}_{in,comb}+{\dot{m}}_{SUP}$

${\dot{m}}_{out}={\dot{m}}_{out,windows}+{\dot{m}}_{out,vents}+{\dot{m}}_{out,leaks}+{\dot{m}}_{out,comb}+{\dot{m}}_{ETA}$

Volume and mass flow rates are related by:

$\dot{m}=q_v\cdot \rho (T)$

where incoming air is at external temperature and outgoing air at zone temperature (Equations 65 and 66).

The solver uses Brent's method to find the root of the mass balance equation, expanding the search interval progressively through the sequence $\pm$1, $\pm$5, $\pm$10, $\pm$15, $\pm$20, $\pm$40, $\pm$50, $\pm$100, $\pm$200 Pa around an initial guess until a valid bracket is found.

Vent Opening Control

When minimum and maximum air change rate limits are specified, the vent opening ratio $R_v$ is adjusted to bring the air change rate within bounds.

The procedure is:

1. Calculate ACH at the current $R_v$ from the previous timestep.
2. If ACH is within $[AC{H}_{min},AC{H}_{max}]$, retain the current $R_v$.
3. If ACH is below $AC{H}_{min}$, check whether fully opening vents ($R_v=1$) can reach the minimum. If not, set $R_v=1$. Otherwise, find the $R_v$ that achieves $AC{H}_{min}$.
4. If ACH exceeds $AC{H}_{max}$, check whether fully closing vents ($R_v=0$) can reach the maximum. If not, set $R_v=0$. Otherwise, find the $R_v$ that achieves $AC{H}_{max}$.

The target $R_v$ is found using golden section minimisation on $[0,1]$, minimising the residual:

$\text{residual}(R_v)=\text{round}\left(|ACH(R_v)-AC{H}_{target}|,10\right)-10^{-10}\cdot R_v$

The small gradient term $-10^{-10}\cdot R_v$ prevents the solver from stalling on flat regions at low vent openings where leakage and mechanical flows dominate.

Ventilation Heat Transfer Coefficient

The total incoming volume flow rate, after accounting for heat recovery savings, is converted to an air change rate:

$ACH=\frac{q_{v,in,effective}}{V_{zone}}$

where $q_{v,in,effective}$ is in m³/h and $V_{zone}$ is the zone volume.

The ventilation heat transfer coefficient is then:

$H_{ve}={\rho }_{a,ref}\cdot c_a\cdot \frac{ACH\cdot V_{zone}}{3600}$

where:

• ${\rho }_{a,ref}=1.204$ kg/m³
• $c_a=1012$ J/(kg·K) is the specific heat capacity of air
• The factor of 3600 converts m³/h to m³/s

$H_{ve}$ is in W/K and represents the rate of heat loss per degree temperature difference between the zone and the external air.

Ductwork Heat Loss

For MVHR systems, ductwork connecting the heat recovery unit to the building envelope introduces additional heat losses. Ductwork insulation is modelled per ISO 12241:2022 for steady-state radial heat flow.

Duct Thermal Resistance

Each duct has three resistances in series: internal surface, insulation, and external surface.

Circular ducts:

$R_{int}=\frac{1}{h_{int}\cdot \pi \cdot d_{int}}$

$R_{ins}=\frac{\ln (D_{ins}/d_{int})}{2\pi \cdot k_{ins}}$

$R_{ext}=\frac{1}{h_{ext}\cdot \pi \cdot D_{ins}}$

where:

• $d_{int}$ is the internal diameter m
• $D_{ins}=d_{ext}+2\cdot t_{ins}$ is the outer diameter including insulation m
• $k_{ins}$ is the thermal conductivity of the insulation W/(m·K)
• $t_{ins}$ is the insulation thickness m

Rectangular ducts:

$R_{int}=\frac{1}{h_{int}\cdot P_{int}}$

$R_{ins}=\frac{2\cdot t_{ins}}{k_{ins}\cdot (P_{int}+P_{ext})}$

$R_{ext}=\frac{1}{h_{ext}\cdot P_{ext}}$

where:

• $P_{int}$ is the internal perimeter m
• $P_{ext}=P_{int}+8\cdot t_{ins}$ is the external perimeter including insulation m

All linear resistances have units of K·m/W. The heat transfer coefficients are:

Duct Heat Loss

The heat loss through a duct of length $L$ is:

$Q_{duct}=\frac{T_{in}-T_{out}}{R_{int}+R_{ins}+R_{ext}}\cdot L$

where $T_{in}$ is the temperature of the air inside the duct and $T_{out}$ is the temperature of the environment surrounding the duct.

MVHR Duct Heat Loss by Segment

An MVHR system has four duct segments: intake, supply, extract, and exhaust. Whether a duct segment contributes to the dwelling heat loss depends on the location of the MVHR unit (inside or outside the thermal envelope).

MVHR unit outside the thermal envelope:

MVHR unit inside the thermal envelope:

The heat recovery efficiency ${\eta }_{hr}$ modifies certain duct losses because the thermal benefit of recovered heat is proportional to the efficiency.

Outputs

Assumptions

• Flow exponents are fixed at $n_w=0.5$ (windows), $n_{vent}=0.5$ (vents), and $n_{leak}=0.667$ (leaks), per BS EN 16798-7.
• Discharge coefficients are $C_{D,w}=0.67$ for windows and $C_{D,vent}=0.6$ for vents and air terminal devices, per BS EN 16798-7, Section B.3.2.1.
• The ventilation zone is modelled as a single well-mixed volume with ventilation effectiveness $E_v=1.0$.
• The control factor $f_{ctrl}=1.0$ and system factor $f_{sys}=1.1$ are fixed defaults for residential buildings (Tables B.4 and B.5).
• Topography coefficients at both the building site and the meteorological station default to 1.0.
• Heat recovery is represented as an effective reduction in incoming air flow rather than a supply temperature increase. This avoids coupling the MVHR calculation to the zone temperature solver.
• MVHR supply and extract are assumed to be perfectly balanced at equal flow rates.
• Duct internal heat transfer coefficient is fixed at 15.5 W/(m²·K), corresponding to air velocity of approximately 3 m/s.
• Combustion appliance fuel input power $P_{h,fi}$ and operational status are provided externally; no combustion modelling is performed within this module.

Cross-references

• TP-01: Overview and Climate Data -- wind speed, wind direction, and external temperature from climate data
• TP-03: External Conditions -- external air temperature used in pressure and density calculations
• TP-04: Space Heating Demand -- ventilation heat transfer coefficient $H_{ve}$ feeds into the zone heat balance matrix
• TP-05: Fabric Heat Loss -- facade and roof areas used for leak distribution; combined with $H_{ve}$ for total heat loss
• TP-10: Pipework and Ductwork Losses -- ductwork thermal resistance calculations for MVHR systems