Thermal model calculation method

Apart from the previously discussed air change rates, which directly influence air quality, thermal comfort is a crucial indicator in the evaluation of natural ventilation concepts. If thermal comfort can be guaranteed, then significant cooling and ventilation energy conservation can be achieved. The dynamic design day heat transfer model aims to provide guidance for the design, especially the system sizing of passive ventilated buildings by relating the system dimensions (Tool ‘Step 1’) to the comfort requirements reached (Tool ‘Step 2’). It dynamically reflects the climate, the internal and solar heat gains, the passive air driving forces, the thermal mass, the conduction through the envelope, and the impact of these parameters on internal temperatures and humidity. A matter of particular interest is the interaction of natural ventilation potentials and the diurnal cooling capacity of thermal mass with different sizing parameters, levels of heat gains, and simple control strategies for night-time ventilation only. This is in combination with fresh air for indoor air quality issues or with a strategy that allows increased air change rates even during daytime.

In this section, only a brief overview of the heat transfer models involved is given;

the in-depth model description including equations is given in Appendix B. The ‘pre-processed’ summer design days referred to here are calculated according to the methodology described in § 5.3.3. A procedure with three iterations assumes that the design day is preceded by an infinite number of identical days of the same idealised weather.

3.2.2.1 Model components

Heat transfer in the model consists of a radiant share, a convective share, and a ventilative share. The radiant fraction is added to the thermal mass, which increases the surface temperature.

Internal air

The interior air space is treated as well-mixed with uniform air temperature distribution. For simplicity of the model, all heat gains or losses to the internal air are treated as sensible heat. The dynamic internal room air temperature includes the reservoir effect of the volumetric heat capacity of the cell air. The ventilative and convective fractions of the heat transfer are added to the air heat capacity, which results in the raising or lowering of internal air temperature.

Figure 3.15: Schematic of the internal air heat balance.

Ventilation

In the dynamic thermal model of ‘Tool Step 2’, the flow rate is calculated according to fixed opening areas pre-calculated in ‘Tool Step 1’ for only one storey. Heat gains and losses due to ventilation per timestep (Δt = 60 s) are a function of the mass flow rate multiplied by the enthalpy difference between the external and the internal air.

The mass flow rate per timestep is the volume flow rate multiplied by the mean air density between inside and outside.

Convection from inside surfaces

Air heat balance

Ventilation enthalpy

Convection from internal sources

External wall

The external wall is the opaque façade area depending on the façade’s glazing ratio.

A lumped capacity model manages the wall internal heat conduction and storage process, and is described below. The construction’s heat gains and losses are treated according to Figure 3.16.

Figure 3.16: Schematic of the external wall heat balance model.

External window

All windows are combined to a single glazing model, where the window’s total area is the façade area multiplied by the glazing ratio. Radiation incident on the external envelope is backcalculated from the ‘pre-processed’ transmitted solar radiation according to simple window indices. The construction’s heat gains and losses are treated according to Figure 3.17.

Figure 3.17: Schematic of the external window heat balance model.

The lumped capacity model for the glazing shown in Figure 3.18 has only two capacities, one for each pane. This is due to the material properties, which are high conductivity and low heat capacity of thin glass. A resistance was added between the panes to account for the thermal resistance of the gas fill, which is calculated according the U-Value of the window minus the film coefficients on both sides of the window.

Figure 3.18: RC-model for the windows.

Internal floor / ceiling

The internal floor and ceiling of one storey are combined to one single construction with equal adjacent inside air conditions on both sides (and hence treated adiabatic).

Again, a five layer lumped capacity model manages the internal heat conduction and storage process. The construction’s heat gains and losses are treated according to Figure 3.19.

Figure 3.19: Schematic of the internal floor / ceiling adiabatic construction heat balance model.

Internal ‘additional’ mass

The tool developed also includes two ‘extra’ surfaces of one construction, which is called the ‘extra’ or ‘additional’ thermal mass construction. As an example, one of the uses of this construction would be to account for the heavyweight partitions within a space. As a general definition, the ‘extra’ thermal mass should be sized to represent all fabric within the space that is exposed to air, except the walls, the ceiling, the floor, and the windows. Figure 3.20 gives a schematic overview of the

‘extra’ mass model heat balance.

Figure 3.20: Schematic of the internal ‘extra’ mass construction heat balance model.

3.2.2.2 Heat transfer calculation methods Convection

The surfaces’ convective heat transfer is realised by Newton’s law of cooling, which includes a constant heat transfer coefficient. The law states that the rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings. In contrast, the convection model allows heat flow from the surroundings into the body, if the ambient air temperature is higher than the construction’s surface temperature. The external heat transfer coefficient is calculated for each timestep according to the Mobile Window Thermal Test (MoWiTT) method [127], and the internal heat transfer coefficient for each surface is a constant input value.

Radiation

Contrary to convective or conductive heat transfer, radiative heat transfer does not require any material medium for transport. The emitting rate depends on the absolute surface temperature and the surface emissivity. In the model, the grey body equation for two parallel surfaces is the governing equation, which approximates that the interaction between a given surface of a construction and the rest of the surfaces of an enclosure can be described as the interaction between the two surface elements.

One of these two surfaces has the surface temperature of the construction element, and the other surface has the mean radiant temperature of the surrounding elements, which here is the mean radiant temperature of a half sphere facing the surface. For internal heat exchange, the half sphere consists of all other construction surfaces facing the surface; for external heat exchange, the half sphere consists of the ground, the sky, and the atmosphere.

Figure 3.21: Long wave radiation exchange at the interior surfaces.

Figure 3.22: Long wave radiation exchange at the exterior surfaces.

Solar heat gains

The solar radiation incident on the construction surfaces has a direct component and a diffuse component. Surfaces either absorb or reflect a fraction of incident radiation.

The transmitted solar radiation entering the cell is a ‘pre-processed’ hourly input value, which a user may gather from auxiliary building simulation programs like EnergyPlus (for inputs for the Kanyon building, see Appendix B). This is to avoid a time consuming and comprehensive calculation that includes the position of sun at each moment. Based on the position and optical properties of windows in the space, and with the consideration of multiple angular reflections, the fraction of the solar radiation entering the space that is incident on each surface is determined. 90% of the

‘pre-processed’ transmitted direct solar radiation is assumed to irradiate the floor surface. The other 10% direct solar radiation is uniformly distributed to the other internal surfaces facing the windows together with the diffuse transmitted solar radiation share. The diffuse transmitted solar radiation share is absorbed or reflected by all internal surfaces facing the windows depending on their areas and absorptance values.

construction

surface _si

Q̇_{si ∞}

q_sky q_envelope

q_atmosphere q_ground

envelope

ground

surface _se

Figure 3.23: Direct solar beam distribution on interior surfaces.

Figure 3.24: Diffuse solar beam distribution on interior surfaces.

Exterior solar radiation is absorbed, reflected, or if the surface is a window also transmitted by the surface. Values incident on the external envelope are backcalculated from the transmitted solar radiation according to simple window indices.

Internal heat gains

The internal heat sources are occupants, lights and equipment. Internal heat gains are a direct input to the design tool based on hourly value schedules, consisting of both convective and radiative shares. Internal heat gains are considered to be grey bodies that participate in the thermal radiation exchange, and sources of sensible heat for the heat and moisture balance in the room air module.

Figure 3.25: Internal heat gains distribution.

Thermal mass

Thermal mass is equivalent to thermal capacitance of a body, which is the ability to store thermal energy. Thermal mass can serve to flatten out the daily temperature

surroundings are cooler. Thus, thermal mass has the capability to time shift and lower the amplitude of indoor air peak temperatures.

The Lumped Capacitance Model (LCM) was utilised for the prediction of dynamic thermal behaviour. The model strongly reduces the complexity in the thermal model that is needed to represent the thermal response of multi-layered constructions. The LCM is however able to keep the overall accuracy of the full model, and is therefore utilised to facilitate the transient heat transfer process within a construction including mass. The LCM is an analytical one-dimensional network model, which employs the well-known analogies between the thermal and the electrical laws. With this analogy, the conductivity of the materials is interpreted as electric conductivity of a resistor, and the thermal mass as electrical capacity of a capacitor. The simple RC-network aims to solve the heat conduction/storage equation for solid layers by connecting construction layers to each other via a number of nodes (Figure 3.26).

Figure 3.26: Layers of the Lumped Capacity Model (LCM) construction.

Figure 3.27: The heat flux balance at the surface node.

3.2.2.3 Adaptive comfort assessment Operative temperature

With rising ambient air temperatures, the operative temperature is allowed to increase in naturally ventilated, non air-conditioned buildings. The average internal operative temperature of the space is the average of the internal mean air temperature and the internal mean radiant temperature [41,128]. It is a rough approximation as the influence of direct sunlight and air velocity is not reflected. Recommended operative temperatures are calculated for different comfort categories according to EN 15251 (for more details, see § 2.6.3). Because the design tool considers only one summer design day, which is out of the running timeframe context, the upper comfort limits are calculated only according to the mean external dry-bulb temperature of the design day itself. Figure 3.5 shows the adaptive comfort limits of EN 15251 category II for a typical summer design day.

q_c q_{si ∞} q_int,r

qτ,dir

qτ,dif

T_si

Psychrometrics

The most widely used thermal comfort standards including air humidity account for the occupants of air-conditioned buildings, and have narrow thermal limits. They discourage the use of naturally ventilated passive solar buildings, where occupants have more relaxed expectations and can tolerate a wider temperature swing. The EN 15251 standard [41] accounts for personal adaptation by extending the thermal comfort limits depending on external conditions, but does not include the effect of humidity and air velocity.

To fill this gap, the design tool developed also includes psychrometric charts. A psychrometric chart graphically represents the thermodynamic properties of moist air. Humidity affects which temperatures are comfortable for the building occupants.

People are most comfortable within appropriate ranges of temperature, relative humidity, and airflow. Daytime ventilation with higher indoor airspeeds directly affects the cooling sensation of building occupants when the temperature is felt as too warm. People naturally cool themselves by evaporation; higher humidity levels are more stressful.

Martinez et al. [129] developed extended comfort boundaries for hot summer conditions in office buildings. The occupants’ adaptive behaviour has been investigated considering changes in airspeed, clothing level and transmitted solar radiation. It was found that the presence of diffuse solar radiation shifts the comfort limits towards cooler air temperatures by about 2 °C. Contrarily, increasing airspeed leads to an acceptance of warmer conditions, but this effect becomes less effective as the air velocity continues to rise. Moreover, increasing air velocities were found to be more effective in the presence of solar radiation. Figure 3.28 and Figure 3.29 show psychrometric adaptive comfort assessment limits of the tool developed according to Martinez et al. along with an exemplarily calculated diurnal course of internal moist air properties for a typical summer design day in Istanbul.

Figure 3.28: Exemplary indoor air conditions together with predicted comfort limits for 0 W/m² of solar radiation and different air velocities [129].

Figure 3.29: Exemplarily indoor air conditions together with predicted comfort limits for 50 W/m² of solar radiation and different air velocities [129].

3.2.2.4 Setting amounts of air for opening dimensioning

Natural ventilation serves to guarantee good indoor air quality and passive cooling in warm periods in order to achieve good thermal comfort without mechanical cooling systems. Therefore, the minimum design air change rate for a passive approach must be intense enough to guarantee the criteria defined for both IAQ and comfort (e.g., 95% of the occupied time in the category IDA II).

100% 90% 80%

In terms of IAQ and according to the EN 13779 standard [55], 12,5 litres per second per person is sufficient to achieve medium air quality (IDA 2). To guarantee this hygienic volume flow rate during occupancy, the flow must also occur during the absence of wind, and design conditions are thus purely buoyancy driven.

High summer air change rates are desirable for passive ventilative cooling, e.g., removal of heat and cooling the building structure at night (according to Figure 2.19 up to 20 h^-1 or more based on the volume of the building [43]). Here, combined wind and buoyancy forces can be assumed for the design. The amount of colder external air needed for cooling is not a fixed value but is dependent on the building, the usage, the operation, and the climate the building is located in. Therefore, to

‘fast-forward’ analyse the ventilative cooling potential of the natural ventilation system, in the ‘Tool Step 1’, the flow path is sized for a specific air change rate with unchanging boundary conditions including average local wind velocities for the hottest 91 days of the year. In the ‘Tool Step 2’, the dynamic thermal response of the building is investigated. The aim is to size the natural ventilation system in a way to stay within acceptable comfort boundaries since thermal comfort is a crucial indicator for evaluating the natural ventilation concepts. Based on the summer design days defined before (see SWMD approach in § 5.3.3), for this sizing-design assessment two requirements need to be achieved, as follows:

• The internal operative temperature stays within the category III comfort boundaries during the local climate extreme summer design day.

• The internal operative temperature stays within the category II comfort boundaries during the local climate typical summer design day.

Results of the tool can be found in passive cooling case-study application section § 6.2.