In this section the basic physical models for the simulation of the dynamic thermal behavior of a building are given. The description starts with the transfer of heat and solar radiation through the building envelope, then summarizes the various ways that this energy is distributed in the room, shows the methods to calculate the instantaneous space sensible load (in other words, the cooling or heating load of the room), and finally deals with the outdoor conditions. In addition, a short overview of the modeling of HVAC components and systems is given.
Heat is transferred by means of three quite different mechanisms:
• Thermal conduction
• Thermal convection
• Thermal radiation
Conduction is the heat transfer due to spatial temperature differences (temperature gradient) without any macroscopic material movement. Conduction is important in solids and depends essentially on the material properties (Fig. 11.27).
Convection is the heat transfer in the fluid from or to a surface (Fig. 11.28) or within the fluid itself. Convective heat transport from a solid is combined with a conductive heat transfer in the solid itself. We distinguish between free and forced convection. If the fluid flow is generated internally by density differences (buoyancy forces), the heat transfer is termed Free convection. Typical examples are the cold down-draft along a cold wall or the thermal plume upward along a warm verrical surface. Forced convection takes place when fluid movement is produced by applied pressure differences due to external means such as a pump. A typical example is the flow in a duct or a pipe.
Radiative Heat Transfer
Kach body having a temperate above absolute zero radiates energy in the form of electromagnetic waves. The amount of energy emitted is dependent on the temperature and on the emissivity of the material. The wavelength or frequency distribution (the spectrum) of the emitted radiation is dependent on the absolute temperature of the body and on the surface properties.
Long-wave radiation (infrared radiation) is in the range of 0.8-100 |xm, short-wave radiation (visible as light) is in the range 0.4-0.8 p. m, and solar radiation is in the range 0.3-3.0 |i, m.
18.104.22.168 Heat-Exchange Processes in the Room
The air temperature of a room at any given time is given by a hear-balance equation which includes the heat flux exchanged by convection at each wall element (A • Qc), the heat flow exchanged by ventilation (<&„), the convective part of hear flow due to internal heat gains (<!>„;), the convective part of heat flow due to the HVAC system (<I>hc)T and the variation of energy in the room air(c M dffa/dt):
+ + = (1L13)
I =■ i
The individual hear fluxes in (Eq. 11.13)—<7r. ^c^Hc—are a^so time —
The convection term Qc is given by (hc, convective heat transfer coefficient; fls, inside surface temperature of wall element J; 0^, room air temperature):
<tc, = h40‘-9*>- <ll-14>
The internal surface temperature of each wall element / is given by a heat — balance equation:
Tfh,/’ *7sr./ A X ‘ ’Pit,/ — 0 , (11.15)
Where Qlr is the heat flux by long-wave radiation exchange with other internal surfaces, QSr is the heat flux due to the absorbed short-wave radiation, Qt is the heat flux by convection, Qcd is heat flux by conduction, is the heat flux
Due to rhe radiative component of the internal heat gains, and <piu is the view factor between source and surface / (Figs. 11.29 and 11.30).
The humidity ratio of a room at any given time is given by a latent hear balance equation including the water vapor flows due to infiltration F), To ventilation to moisture transport through envelope elements
(Mw D), to internal sources (Mw j), and to the HVAC system (MK,;,), and the variation of moisture content in the zone air mass M (M dxa/dt):
AW+ + + = M (11.16)
All heat flux and moisture flux elements in Eqs. (11.13) To (11.16) Are also time-dependent.
The heat transferred into a room by solar radiation (short-wave radiation) strongly influences the room climate. Direct and diffuse solar radiation are generally considered separately (Fig. 11.31). Reflections normally are not considered in building simulation codes. According to this assumption, the direct radiation is attributed to the surfaces hit by the beam, while diffuse radiation is distributed to the individual surfaces in the room either according to the area of each surface (area-weighted approach) or according to the geometric situation as seen from the transparent surface (view-factor method, see also long-wave radiation exchange later). At the wall surface, the energy balance is
H Solar F-y
Short-wave «w——————- radiation
FIGURE 11.31 Radiation fluxes at the building facade: the solar radiation components (direct or beam, diffuse, and reflected radiation from the ground or other buildings) and the components of the radiation back from the building facade (reflected solar and thermal infrared radiation from the building envelope).
Established by long-wave radiation exchange to other surfaces, by convection to the room air, and by heat conduction into the wall construction.
Proper consideration of solar radiation exchange between two rooms through a transparent element is important when analyzing atria, sun — spaces, or glazed double facades.
Convective Heat Transfer at Surfaces
The kind of convective heat transfer—forced convection or natural (at floor, wall, or ceiling)—must be considered and taken into account by- selecting appropriate values for the convective heat transfer coefficient H( (see Eq. (11.14)). Thus, the heat transfer coefficient implicitly assumes the flow situation at the surface. Normally, coefficients for convective heat transfer are considered as a preset constant parameter (the coefficient may be defined as variable, however, depending on other parameters). Therefore, the selection of appropriate values is crucial. Values for heat transfer coefficients can be found in several references; a comprehensive summary is given in Daskalaki.1
Long-Wave Radiation Exchange
All surfaces in a zone exchange long-wave radiation with each other. The net energy transmitted from one surface to another is dependent on the surface temperatures, the surface emissivity, the area, and the orientation of the two surfaces relative to each other. For long-wave radiation, the surface emissivity is assumed to be angle independent. The geometric relation of the two surfaces is described by the view factor. If multireflections are taken into account, the net radiation heat exchange is calculated using exchange factors (e. g., according to Gebhart2).
Internal Heat Gains (Casual Gains)
In industrial applications, internal heat gains are very often the most important factor affecting the thermal indoor climate. Typical heat sources are machines, appliances and equipment, and all kind of processes taking place in the room. Artificial lighting and people further contribute to the internal heai load in the room.
In the simulation, the time dependency of the energy release of such sources is defined in so-called schedules. The heat sources transfer energy to the room air by convection and to the surfaces by long-wave radiation. In principle, heat sources can be modeled by two kinds of parameterization!
• Heat source with defined surface temperature and area
• Heat source with predefined total gain and the split between convective and radiative heat release
In the case of a given surface temperature, the amount of energy released is determined by the parameters for the convective and radiative heat exchange. As far as convection is concerned, these are the temperatures of the heat source surface and room air, respectively, and the heat transfer coefficient. The radiative heat exchange is determined by the view factors and the temperatures of the surrounding surfaces.
In the second approach, the energy release is split by a predefined (mostly constant) factor between convection and radiation. The convective part is directly transferred as energy gain to the room air, while the radiative part is distributed to the surrounding walls by the area-weighted method or the view-factor method.
Heat gains from internal loads normally are sensible heat. Nevertheless, many processes release a significant amount of moisture. Also, occupants produce relevant amounts of latent heat, especially at high metabolic rates and at high air temperatures.
When air flows at a certain rate through the space, energy is transported in relation to the difference between supply and extract air temperature. Such airflow can be induced by natural or mechanical ventilation. See Section 11.5 on the interaction between naturally induced airflows and the thermal behavior of the room.
Heat Storage In the Room
Normally, the heat storage capacity of the air in the space can be neglected. Machines, tools, equipment, etc. situated in the room may have a significant influence on the thermal behavior of the room and must be considered in the simulation.
22.214.171.124 Outdoor Conditions
Outdoor Air Temperature
Outdoor air temperature is an important factor regarding the building energy balance. Outdoor air temperature affects the heat transfer through external walls and roofs and the heat transfer by ventilation. Moreover, outdoor air
Temperature is a driving force for natural ventilation, as the difference between indoor and outdoor air temperature causes the stack effect.
Outdoor Air Humidity
Outdoor air humidity strongly affects the latent cooling load and energy requirements during summer season. Year-round outdoor air humidity must be considered when studying condensation conditions.
Wind affects the convective heat transfer on external walls and is a driving force for natural ventilation.
Solar Radiation (Short-Wave Radiation)
The total or global solar radiation has a direct part (beam radiation) and a diffuse part (Fig. 11.31). In the simulation, solar radiation input values must be converted to radiation values for each surface of the building. For nonhorizontal surfaces, the diffuse radiation is composed of (a) the contribution from the diffuse sky and (b) reflections from the ground. The diffuse sky radiation is not uniform. It is composed of three parts, referred to as Isotropic, circumsolar, and Horizontal brightening. Several diffuse sky models are available. Depending on the model used, discrepancies for the boundary conditions may occur with the same basic set of solar radiation data, thus leading to differences in the simulation results.
The solar radiation absorbed on external building surfaces increases the wall surface temperature, thus leading to a change in the heat conducted through the component. In low-wind conditions, free convective flows drift up the warm external wall surface. This changes the convective heat transfer and leads to increased temperatures of supply air for natural ventilation.
Neither effect normally is accounted for in building simulation programs. Normally, for energy analysis, this is not critical, but it may have a significant effect ori natural ventilation of multistory buildings.
Since insolation often has a very significant effect on the heat balance of a building, shading by buildings or other objects in the surroundings of the building must be taken into account. Also, certain wings or parts of the building itself may shade the part under investigation permanently or over certain time periods. Normally, thermal building-dynamics simulation programs allow for the consideration of such shading.
A fictive sky temperature, dependent on ambient temperature, emissivity, and cloudiness, is introduced to account for the long-wave radiative heat exchange between the building envelope and the sky.
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