Modelling approach and description

User related inputs

The aim of building the multi-zone model was to enable taking user profiles better into account when calculating the energy demand for space heating while still using simplified and computationally light models. The surveys and measurements supplied regarding three user related aspects whose zonal modelling implementations are analysed: the heating profiles (heating hours and set-point temperatures), the ventilation profiles (the use of windows) and the internal heat gains (defined in part by the presence of people). The modelling implementations of these three parameters are discussed in the following paragraphs, distinguishing single-zone modelling approaches from multi-zone modelling approaches where each room is modelled as a separate zone. One user related parameter influencing the multi-zone model is added to this list: the opening of doors between rooms.

HEATING PROFILES

LIVING AREA: DIRECTLY HEATED AREA

To distinguish variations in simulation results due to different modelling approaches from variations due to different heating profiles (heating hours and set-point temperatures), the different models are used with their respective standard heating profiles and with the same set of real heating profiles. Figure 6.5 summarizes the different heating profiles of the living area. The heating profile considered in the Flemish approach [80] is not shown in Figure 6.5

because it consists of a time and space average equivalent set-point temperature of 18°C that applies on the building level, without specification of the underlying assumption regarding the living area. The multi-zone method is applied only in combination with the real heating profiles, as the predefined heating area fractions from the regulation frameworks (GE: 75% or NL: 50%) do not fit with the multi-zone models. On the opposite, the Flemish approach includes all assumptions about the heating profile implicitly within the official equivalent set point temperature of 18°C, thus making it impossible to consider the other standard or real heating profiles.

Figure 6.5: Real versus standard heating profiles from DIN 18599 (GE) and NEN 7120 (NL): heating set point temperatures and daily heating hours in the living area

OTHER ROOMS

The households barely heated the other rooms (see 3.3.2 and 4.3.1). The circulation area and the toilet were heated in none of the analysed cases. The small bathrooms were heated using electric heaters, but only for short durations, with only four households reporting to heat their bathroom for more than one hour per day but still for less than two hours per day. Only two of the 23 households included in the analysis on the heating demand and five of the 30 households included in the analysis on the indoor temperatures reported using an electric heater in one of their bedrooms. Four of them heated only one bedroom and only in the evening before going to sleep, for less than three hours per day.

The fifth household reported heating two bedrooms for 11 hours but the measurements showed the target temperature was 5°C lower than in their living room. Therefore, when considering the real heating profiles in the modelling approaches of NEN 7120 [78] (from the Netherlands, further indicated as ‘NL’) and DIN 18599 [176] (from Germany, further indicate as ‘GE’), the considered fraction of directly heated spaces (see 5.2.2) is defined as being 40%, consisting only of the 32% and 8% of the floor area taken by the living room and the

kitchen, respectively. While the kitchen had no electric heater, it is also considered as a part of the directly heated area because of the large permanent opening between the kitchen and the living room (see further in this section).

DIN 18599 makes a strict distinction between the directly heated building area and the indirectly heated area, but NEN 7120 differentiates the main heated living area from the remaining moderately heated area, considering that this moderately heated area is also heated directly, but only for 20% of the time or thus for 4.8 hours per day (see 5.2.2). This time fraction (parameter fmod,t in Eq.(5.15)) can be overridden when considering the real profiles, but the underlying assumption of the Dutch approach is that this time fraction applies to the whole of the area that is not included in the main heated living area, thus including all bedrooms, the circulation area etc. Because for most cases the bathroom is the only of those rooms that is heated, it would be an significant overestimation of the real heating profile to take the heating time fraction of the bathroom as fmod,t. Instead, when considering the real heating profiles, fmod,t is defined for this study as the area weighed heating time fraction of the moderately heated area, using Eq.(6.6).

ft,heat,mhz,r = heating time fraction of room ‘r’ of the moderately heated zone (= 0 if never heated directly) [-]

Afl,mhz,r = floor area of room ‘r’ of the moderately heated zone [m²]

Afl,mhz,tot = total floor area of the moderately heated zone [m²]

HYGIENIC VENTILATION FLOW RATES

The energy performance calculation method in Belgium considers the same hygienic ventilation flow rates in a house without ventilation system as in a house with a ventilation system [122,148], using Eq. (6.7). For the analysed houses, this results in an air change rate (ACH) of 0.77. However, as discussed in Chapter 3 (see 3.3.3 and 3.4.1) the analysed houses had no ventilation system and the inhabitants stated to rarely open their windows during winter (Table 6.1).

Therefore, based on literature, the real air change rate is expected to be much lower (see 3.3.3, [57,151,152]). Furthermore, windows were not opened to the same extent in all rooms, with mainly the bedroom windows and the bathroom windows being used. To take more realistic air change rates into account in the models and to take into account the differentiation between rooms in the multi-zone model, the air flows through windows were calculated based on the data from the surveys. The simplified approach considered single-sided ventilation and was based on Eq.(6.9), Eq.(6.10), Eq.(6.11) and Eq.(6.12) from EN 15242

[184]. These formulas allow calculating the average air flows through open windows taking into account wind speed, stack effect and wind turbulence.

Based on these calculated air flows, the corresponding heat transfer coefficients were calculated using Eq.(6.8), at room level or at building level for the multi-zone models and the single-multi-zone models, respectively. Using these equations in combination with a monthly quasi-steady state model simplifies the dynamics of air flows by assuming that the average temperature difference and wind speeds when the windows are open equal the monthly average temperature differences and wind speeds.

𝑞𝑣,𝑎𝑖𝑟𝑖𝑛𝑔,𝐸𝑃𝐵 = 𝑚ℎ𝑒𝑎𝑡 [0.2 + 0.5 𝑒^{−𝑉⁄500}] V _(6.7)

With

m_heat = a multiplication factor, related to the type of ventilation system and the quality of the workmanship [80]. When assessing the energy performance of houses, using the default value (=1.5) is allowed for new houses and it is the only approach for existing houses [122] [-]

V = the volume of the building [m³]

𝐻𝑣,𝑎𝑖𝑟𝑖𝑛𝑔,𝑤𝑖𝑛𝑑𝑜𝑤𝑠= ∑ 𝜌_𝑎 𝑐_𝑎 𝑓_{𝑜𝑝𝑒𝑛,𝑤} 𝑞_{𝑣,𝑎𝑖𝑟𝑖𝑛𝑔,𝑤}

𝑤 (6.8)

𝑞𝑣,𝑎𝑖𝑟𝑖𝑛𝑔,𝑤= 3.6 500 𝐴𝑜𝑤𝑉^0.5 _(6.9)

𝑉 = 𝐶𝑡+ 𝐶𝑤 𝑣𝑚𝑒𝑡2 + 𝐶𝑠𝑡 𝐻𝑤𝑖𝑛𝑑𝑜𝑤 𝑎𝑏𝑠(𝑇𝑖− 𝑇𝑒) _(6.10)

𝐴𝑜𝑤= 𝐶𝑘(𝛼) 𝐴_{𝑤 (6.11)}

𝐶𝑘(𝛼) = 2.6 10⁻⁷ 𝛼³− 1.19 10⁻⁴ 𝛼²+ 1.86 10⁻² 𝛼 _(6.12)

With

Hv,airing,windows = time averaged heat loss coefficient caused by window openings [W/K]

ρa = density of air [kg/m³]

ca = specific heat capacity of air [J/(kg.K)]

fopen,w = opening time fraction of window ‘w’ [-]

qv,airing,w = air flow rate through the open window ‘w’ [m³/h]

Aow = window opening area [m²]