A second, more detailed approach to modelling the air flows through a building is to establish an Air Flow Network (AFN). The AFN consists of a number of nodes connected by air flow components through surface linkages (Gu, 2007). Each heat
119 transfer surface in a building, with both faces exposed to air, works as a surface linkage through which air flows (Gu, 2007).The associated air flow component for each surface can be one crack (or surface effective leakage area) at the average height of the surface, one opening in an exterior or interior window or door, or a horizontal opening. In EnergyPlus, each linkage surface specifies two connected nodes: two zone nodes based on inside and outside face environment for an interior surface, or a zone node based on inside face environment and an external node (US Department of Energy, 2013c). Since AFN assumes that air flows from one node to another, it simplifies airflows through its pathways and cannot predict internal air circulation within a thermal zone (Gu, 2007).
DesignBuilder was employed in this study to facilitate the process of defining the nodes and linkage surfaces via its “calculated natural ventilation” simulation option. The air flow through cracks in the walls, floors and the roof is calculated by AFN model as a function of the pressure difference across the crack according to power law in form of equation ( 5-3) (US Department of Energy, 2013c).
𝑄𝑄 = (𝐶𝐶𝐼𝐼𝐼𝐼𝐶𝐶𝑘𝑘 𝐹𝐹𝐼𝐼𝐶𝐶𝐼𝐼𝐼𝐼𝐼𝐼) ∗ 𝐶𝐶𝑇𝑇∗ 𝐶𝐶𝑄𝑄 (∆𝑃𝑃)𝑑𝑑 ( 5-3)
Where:
𝑄𝑄 = air mass flow rate (kg/s) Crack factor = multiplier for a crack
𝐶𝐶𝑇𝑇 = reference condition temperature correction factor (dimensionless)
𝐶𝐶𝑄𝑄 = air mass flow coefficient (kg/sat1 Pa)
∆𝑃𝑃 = pressure difference across crack (Pa)
n = Air flow exponent (dimensionless): The valid range is 0.5 for fully turbulent flow to 1.0, for fully laminar flow (US Department of Energy, 2013c).
Air flows through doors, windows and vents when they are open or closed are calculated by a similar method. When these openings are closed, AFN model
120 flow coefficient (𝐶𝐶𝑄𝑄) (kg/s at1 Pa) is calculated by multiplying the air mass flow
coefficient (kg/s. crack length at1 Pa) by the length of the crack (i.e. the perimeter of the opening).
When these openings are open another form of the power law equation in form of equation ( 5-4) is used:
𝑄𝑄 = 𝐶𝐶𝑑𝑑𝐴𝐴�2∆𝑃𝑃𝜌𝜌 ( 5-4)
Where:
𝑄𝑄 = volume flow rate across the opening (m3/s)
𝐶𝐶𝑑𝑑 = discharge coefficient (dimensionless); depends on the geometry of the opening
and the Reynolds number of the flow
A = surface area of the opening (m2); defined using an opening factor which defines the fraction of total surface area of an opening which is opened
ΔP = pressure difference across the opening (Pa) ρ = air density (kg/m3)
The air mass flow rate (kg/s) is then calculated by multiplying the volume flow rate by the air density. Bi-directional flows can be modelled for vertical openings when air is simultaneously moving in two directions depending on stack effects and wind
conditions (US Department of Energy, 2013c).
EnergyPlus can also use AFN to model air flows through horizontal openings such as staircase. Horizontal openings can produce two-way flow when forced and buoyancy flows co- exists, however, AFN cannot model bi-directional flows at a given time step (US Department of Energy, 2013c)
The input variables required for establishing the AFN were: wind pressure
121 each crack, air mass flow coefficient (𝐶𝐶𝑄𝑄) (kg/s. m crack length) and flow exponent (n) for the doors and windows when they are closed and discharge coefficient (𝐶𝐶𝑑𝑑) for each opening at each opening factor. These are discussed in more detail below.
• Wind pressure coefficients (𝑪𝑪𝒑𝒑)
AFN uses wind pressure coefficients (𝐶𝐶𝑝𝑝) to calculate the wind driven pressure on the external surfaces of a building. Wind pressure coefficient values are required for each wind direction at an interval (for example: every 45 degrees) on each external surface. Sensitivity analysis by Cóstola et al. (2010) has shown 𝐶𝐶𝑝𝑝 as one of the most influential input parameters on air change rate and thus several building performance indicators such as energy consumption and thermal comfort (Cóstola, Blocken & Hensen, 2009). The wind pressure coefficient is dependent on a number of factors including building geometry, facade detailing, position on the facade, the degree of exposure, wind speed and wind direction (Cóstola, Blocken & Hensen, 2009). Therefore, wind pressure coefficients are generally unknown, except in the case of very simple structures or extremely well studied buildings, and must be assumed which could significantly influence the accuracy of the air change rate calculations (ASHRAE, 2009).
Wind pressure coefficients could be obtained from full scale measurements or wind tunnel model tests of the specific site and building or via CFD (ASHRAE, 2009). However, full scale experiments are very complex and expensive. Alternatively, there are databases of 𝐶𝐶𝑝𝑝 values which could be used as secondary sources of data. DesignBuilder is supplied with a database of wind pressure coefficients based on data from Liddament (1986) which is also reported in CIBSE guide A (CIBSE, 2006a) and is often used as a “good first level of approximation for basic design purposes” (DesignBuilder, 2014). The 𝐶𝐶𝑝𝑝 data is for low rise buildings (i.e. buildings of 3 storeys or less) with square surfaces (aspect ratio 1:1) and for 3 levels of site exposure to wind: sheltered, normal and exposed. The data is given in 45° increments. In this study, 𝐶𝐶𝑝𝑝 data was chosen from DesignBuilder’s database considering normal site exposure. Figure 5-5 was adopted from CIBSE guide A (CIBSE, 2006) and shows the definition of surfaces in determining wind pressure coefficients.
122 Figure 5-5: definition of surfaces in determining wind pressure coefficients (CIBSE, 2006)
Example of wind pressure coefficients over façade 1 and roof (front) for wind angels in 45º increments were presented in Table 5-6 (DesignBuilder, 2014). They were based on the slope of surfaces considering normal exposure of the site to wind and aspect ratio 1:1.
Table 5-6: Wind pressure coefficients over façade 1 and roof (front) for wind angles in 45º increments based on the slope of surfaces considering normal exposure of the site to wind and aspect ratio 1:1 (DesignBuilder, 2014)
Wind angel to surface Vertical Slope<=10º Slope 11-30º Slope 31-89º
0º 0.4 -0.6 -0.35 0.3 45º 0.1 -0.5 -0.45 -0.5 90º -0.3 -0.4 -0.55 -0.6 135º -0.35 -0.5 -0.45 -0.5 180º -0.2 -0.6 -0.35 -0.5 225º -0.35 -0.5 -0.45 -0.5 270º -0.3 -0.4 -0.55 -0.6 315º -0.1 -0.5 -0.45 -0.5
123 • Air mass flow coefficient (𝑪𝑪𝑸𝑸) (kg/s at 1 Pa) and flow exponent (n) for
each crack
AFN requires air mass flow coefficient (𝐶𝐶𝑄𝑄) (kg/s) at a reference condition
(temperature, pressure and humidity) for each crack in internal and external walls, floor/ceiling and roof defined at 1 pa pressure difference across the crack. Gaps and cracks in the building fabric cannot be accurately characterized by visual inspection as the leakage paths are often obscured by internal finishes or external cladding and are hard to follow (ATTMA, 2010). Although the air tightness of the test houses were measured at 50 Pa, it was not possible to use these values directly in the model when using AFN.
DesignBuilder uses a simplified approach which defines one crack for each surface of the building. The characteristics of these cracks are defined in DesignBuilder crack templates. There are five crack templates in DesignBuilder: Very poor, poor, medium, good and excellent which can be selected according to the leakiness level of the building under study. Since the air permeability test proven an indication of poor air tightness of the test houses (see section 3.3.6), data corresponding to “poor” crack template was chosen for the model. The crack templates has air mass flow coefficient per square meter of each surface (kg/s.𝑚𝑚2) at1 Pa (Table 5-7) which provides the air mass flow coefficient (𝐶𝐶𝑄𝑄) (kg/s) required in EnergyPlus by
multiplying the flow coefficient per square meter of the surface by the surface area (Table 5-7). In addition, DesignBuilder’s crack templates have flow exponents (n) (equation ( 5-3)) for internal and external walls, floor/ceiling and roof (Table 5-7).
124 Table 5-7: Crack characteristics according to DesignBuilder’s “poor” crack template used in the model for walls, floors and the roof
Building element
Air mass flow coefficient (𝑪𝑪𝑸𝑸) (Kg/s.𝒎𝒎𝟐𝟐) at 1Pa Flow exponent (n) External walls 0.0002 0.7 Internal walls 0.005 0.75 Internal floors 0.002 0.7 External floors 0.001 1.0 Roof 0.00015 0.7
• Air mass flow coefficient (𝑪𝑪𝑸𝑸) (kg/s. m crack length) and flow exponent
(n) for the doors and windows when they are closed
DesignBuilder also provides the air mass flow coefficient (𝐶𝐶𝑄𝑄) (kg/s. m crack) at1 Pa and flow exponent (n) for the cracks around the perimeter of these openings on the same five point scale (Table 5-8).
Table 5-8: Crack characteristics according to DesignBuilder’s “poor” crack template used in the model for the doors, windows and vents
Building element
Air mass flow coefficient (𝑪𝑪𝑸𝑸) (Kg/s. m) at 1Pa Flow exponent (n) External windows 0.001 0.6 External doors 0.0018 0.66 Internal doors 0.02 0.6 External vents 0.01 0.66 • Discharge coefficients (𝑪𝑪𝒅𝒅)
Discharge coefficient is difficult to determine and experimental values which has found for discharge coefficient varies from 0.3 to 0.8 and without a clear
125 CONTAMW which is a multi-zone air flow and contaminant transport analysis
software developed by US department of commerce (Dols & Walton, 2002) suggests a discharge coefficient of 0.6 for orifices and slightly higher for large openings in buildings. ASHRAE (ASHRAE, 2009) propose the correlation based on inter zone temperature differences as in equation ( 5-5) for the range of ΔTs from 0.5 to 40ºC:
Cd = 0.4 + 0.0045 ΔT ( 5-5) DesignBuilder’s help documentation notes that “given other uncertainties in natural
ventilation calculations (wind pressure coefficients, effective areas of real-world openings and crack flows etc.), using a discharge coefficient between 0.60 and 0.65 should provide sufficient accuracy” (DesignBuilder, 2014). Discharge coefficient of
0.65 was selected for all the openings including the horizontal openings and both opening factors.