Ventilation heat loss in a multifamily building under varying air density

: Standards related to calculation methods used in building energy performance simulation tools usually impose constant volumetric heat capacity of air. However, this simplification may result in errors if the actual conditions differ from the assumptions made. The paper presents the problem of dry air density and specific heat capacity variation and their influence on calculated energy use for space heating in a multifamily building. The monthly calculation method of PN-EN ISO 13790 was used. Simulations were performed in five cities, each in one climatic zone according to PN-EN 12831. Variation of the air density caused by air temperature and elevation resulted in differences in calculated heating demand from -4.5% to 4.5% in relation to that at constant volumetric heat capacity assumed in PN-EN ISO 13790. specific heat capacity. But varying outdoor conditions cause these parameters to change. This paper presents an assessment of the impact of the air density on the ventilation heat loss and resulting heating demand of a multifamily residential building in five cities, each in different Polish climatic zone. Calculations were performed using the monthly method of [10]. The ventilation heat loss was determined at capacity of of 1200 3 ∙ K, imposed in that and comparatively at monthly outdoor air temperatures from monthly weather data.


INTRODUCTION
Poland is the country with heating dominated climate [1][2][3]. Thus, energy use for space heating has significant share in total energy consumption in Polish buildings. One of the elements influencing heating demand is the ventilation (including ventilation and infiltration) heat loss [4][5][6]. Its importance increases with new standards [7], both in low-energy and passive [8] as well as in thermally refurbished objects [9]. This is so, because the main task of ventilation is to provide fresh air and to remove used air independently on the energy standard of a building.
Mathematical models applied in simulation tools used in energy auditing, design or certification of buildings commonly assume constant air density and specific heat capacity. But varying outdoor conditions cause these parameters to change.
This paper presents an assessment of the impact of the air density on the ventilation heat loss and resulting heating demand of a multifamily residential building in five cities, each in different Polish climatic zone. Calculations were performed using the monthly method of PN-EN ISO 13790 [10]. The ventilation heat loss was determined at constant volumetric heat capacity of air of 1200 J/m 3 •K, imposed in that standard, and comparatively at monthly outdoor air temperatures from monthly weather data.

Introduction
Calculation methods of PN-EN ISO 13790 to assess thermal performance of buildings don't take into account humidification or dehumidification processes. Hence, basic properties of dry air are described briefly in the following paragraphs.

Air density
Within the air temperature and atmospheric pressure variation met in climatic conditions of Europe it is sufficient to treat atmospheric air as ideal gas [11]. Hence, assuming current recommendations [12][13][14], it can be calculated that the density of dry air at standard conditions (T0 = 273.15 K, p0 = 100 kPa) is ρ0 = 1.27540 kg/m 3 and varies from 1.43276 kg/m 3 at -30°C to 1.14918 kg/m 3 at +30°C, i.e. decreases by 20%.
Atmospheric pressure has slightly less significant, but still noticeable, impact on air density. At 0°C ρa rises from 1.21163 kg/m 3 at 950 hPa to 1.33917 kg/m 3 at 1050 hPa, i.e. by 11% (Fig. 1). If only temperature measurements are available, the air density at the known elevation can be calculated from the barometric formula [15,16] at constant temperature (isothermal atmosphere): As a reference point typically standard conditions are used. From this: In such a case the air density depends only on the air temperature (T) on site:

Specific heat capacity
Specific heat capacity of dry air in the temperature range from -50°C to +50°C at p = 100 kPa changes from ca = 1006.1 J/kg·K to 1007.7 J/kg·K, with the minimum of 1005.7 J/kg·K at -20°C (Fig. 2).  [17] Atmospheric pressure has negligible effect on ca. For example, at 0°C ca = 1005.9 J/kg·K and 1013.9 J/kg·K at 100 kPa and 500 kPa, respectively. Hence, it seems appropriate to accept ca = 1006 J/kg·K for energy simulations of buildings.

Monthly method of PN-EN ISO 13790
To assess the thermal performance of buildings in Poland commonly monthly method of PN-EN ISO 13790 is used. This standard has been replaced by PN-EN ISO 52016 recently [18] but the monthly calculation method remained the same in essence [19]. In spite of its simplicity that method provides correct results [20] and therefore was commonly introduced in national regulations [21].
Thermal balance of a building zone consists of heat losses and heat gains. Heat losses include heat transfer by transmission and by ventilation: Heat gains include solar gains and heat gains from internal sources (occupants, appliances, lighting, tap water and recoverable system thermal losses): Calculation of thermal balance over one month takes into account dynamic effects by means of the gain utilization factor for heating. The monthly energy demand for space heating, QH,nd, is given by: For a given month the gain utilisation factor for heating, ηH,gn, depends on the relation between heat gains and heat losses: If γH > 0 and γH ≠ 1: If γH = 1: else if γH < 1: with: In Poland normative default values of αH,0 = 1 h and τH,0 = 15 h are used.
The time constant of a building depends on its internal heat capacity and overall heat transfer coefficients by transmission and by ventilation:

Ventilation heat loss
For a given thermal zone and time period the total heat loss by ventilation (including air infiltration and ventilation) for heating is calculated from the formula: with: PN-EN ISO 13790 imposed ρa·ca=1200 J/m 3 ·K. Assuming ca = 1006 J/kg·K (see Section 2.3.) at the pressure of 100 kPa the resulting air temperature is 18.9°C. It differs significantly from the average annual outdoor air temperature in Poland [22,23] of about 8°C, at which fresh air is delivered to interior of buildings via infiltration and ventilation.

Typical meteorological years
Files with typical meteorological years [24] (TMYs) were introduced in Poland in 2008 for building simulations along with the implementation of the Directive on Energy Performance of Buildings (EPBD). They have been prepared for 61 weather stations in Poland in hourly and monthly formats. Monthly data include month number, minimum, maximum and average air temperature (dry bulb), sky temperature, global solar irradiance on a horizontal surface and on sloped surfaces (30°, 45°, 60° and 90°) oriented in eight basic directions (N, NE, E, SE, S, SW, W and NW), the code and the name of the World Meteorological Organization (WMO) station. Hourly data include also day, hour (UTC time), relative humidity, moisture content, wind speed and wind direction. In addition north latitude, east longitude, elevation above sea level, time zone from 0 to east, number of days of meteorological data and the version number of a file are also given.

Building
To perform necessary simulations a model of a multifamily building was used (Fig. 3). Its main parameters are shown in Table 1. The design ventilation airflow was set in standard conditions. The thermal capacity of the building, Cm, was obtained from physical properties of materials using simple method from PN-EN ISO 13786 [25]. Additional data were given in [2].

Test locations
The PN-EN 12831 standard [26] defines five zones for calculation of the design heat load in Poland [27,28]. Five locations were chosen for further simulations, one in each zone, as listed in Table 2. Results presented in Table 3 show differences between volumetric heat capacities from two methods. Thus, further calculations of heating demand of the described building in subsequent months of a year were performed in each location.

Heating demand of the building
Applying the monthly method described in Section 3.1. with proper weather data monthly energy use for space heating of the building was calculated.
Using PN-EN ISO 13790 (first method) at constant ρa·ca = 1200 J/m 3 ·K annual heating demand (Fig. 4) was from 880.41 GJ in Koszalin to 1059.91 GJ in Zakopane. The second method provided results from 923.00 GJ to 1012.43 GJ. In three cases (1, 2, 4) the new method gave higher values of QH,nd, by 4.5% on average. Relatively low elevations of these cities didn't significantly reduce the air density. Air temperature in cold half year, from X to III, was lower than 18.9 °C (see Section 3.2.) and finally volumetric heat capacity was higher than 1200 J/m3·K resulting in greater ventilation heat loss.
Different situation was observed in locations 3 and 5. The air density calculated in Zakopane (5-th case) at elevation of 857 m (Eq. 2) and T0 was ρa,h = 1.1458 kg/m 3 , i.e. lower by 10.2% from ρ0.
In case of the 3-rd location reduction of air density due to elevation was compensated by lower temperature during heating season. That's why the difference in QH amounted only 1.5%.
Differences in QH,nd should be also considered in terms of heating energy consumption per floor area (EA). This is very important indicator from the point of view of energy certification of buildings [29,30]. The second method resulted in EA from 4.0 kWh/m 2 higher (Koszalin) to 4.4 kWh/m 2 lower (Zakopane) than the first one.

CONCLUSIONS
Varying environmental conditions, especially air temperature and barometric pressure, influence air density and ventilation heat loss in each building.
The monthly calculation method of PN-EN ISO 13790 was used to determine heating demand of a multifamily building in five Polish cities. Air density variation caused by changes in air temperature and elevation above sea level was described by the ideal gas law and barometric formulas, respectively.
Performed calculations revealed differences in the annual heating demand between two methods and confirmed its dependence on the aforementioned factors. In addition, previous works [2,31] indicated strong impact of the new PN-EN ISO 52010 standard on calculated solar gains in buildings, comparing to the method used so far, influencing values of heating and cooling demand without any physical changes in the building's structure. This is a premise for a detailed study about the calculation procedures used in the energy calculations of buildings.