Calculation Methods

Simulation is the prediction of a real process by the use of a model. Of the many parameters which influence this process, some must be included in the

Model because they are interdependent (e. g., temperatures); others are little af­fected by other model parameters or by the results of the simulation and thus can be assumed as a preset parameter (e. g., dimensions, material properties, outdoor conditions). Such parameters form the boundary conditions for the model.

This section does not contain any fundamentals or mathematics but tries to describe the basic energy flows and the methods used in thermal building— dynamics simulation codes to model these. Also, the methods are described without stating the underlying algorithms and equations, for which the reader is referred to the literature and references. A short outline of how these models affect the application possibilities and limits is given at the end of this section and also in Section 11.3.7.

! 1.3.3.1 Outdoor Conditions

In thermal building-dynamics simulation codes, outdoor conditions are mostly input by the so-called weather data file, containing (usually hourly) data for air temperature, wind speed and direction, air humidity, and global and diffuse solar radiation on horizontal surfaces.

Data are provided as measured data or prepared data, representing typical data for a period of several years. Design reference years (DRY) established using methods developed with the framework of the IEA (International En­ergy Agency) represent characteristic data for a period of 10 years, condensed into a one-year data set. Internal coherence, e. g., between solar irradiation and air temperature, is maintained. For the United States, typical meteorologi­cal year (TMY) files are based on measurements in the period 1954 through 1972.

I 1.3.3.2 Heat Transfer through the Building Envelope

Conduction

Basically, two kinds of heat conduction are distinguished:

• Steady-state conduction

• Unsteady or dynamic conduction

Under steady-state conditions, the temperature distribution in the wall is only spatial and not time dependent. This is the case, e. g., if the boundary condi­tions on both sides of the wall are kept constant over a longer time period. The time to achieve such a steady-state condition is dependent on the thick­ness, conductivity, and specific heat of the material. If this time is much shorter than the change in time of the boundary conditions on the wall sur­face, then this is termed a quasi-steady-state condition. On the contrary, if this time is longer, the temperature distribution and the heat fluxes in the wall are not constant in time, and therefore the dynamic heat transfer must be ana­lyzed (Fig. 11.32).

Calculation Methods for Dynamic Conduction

In reality, heat is conducted in all three spatial dimensions. While specific building simulation codes can model the transient and steady-state two-di­mensional temperature distribution in building structures using finite-differ — ence or finite-elements methods, conduction is normally modeled one —

Calculation Methods

Dimensionally. In-plane conduction is neglected, and cold bridge effects are therefore not considered. However, with the increasing level of building insu­lation, these effects become more important. They have to be accounted for by setting the material properties and surface areas accordingly.

To describe the dynamic thermal behavior of the envelope and internal structural elements, the following two methods are most often used in thermal building simulation codes:

• Finite differences

• Response factors

In the Finite-difference approach, the partial differential equation for the conduction of heat in solids is replaced by a set of algebraic equations of tem­perature differences between discrete points in the slab. Actually, the wall is divided into a number of individual layers, and for each, the energy conserva­tion equation is applied. This leads to a set of linear equations, which are ex­plicitly or implicitly solved. This approach allows the calculation of the time evolution of temperatures in the wall, surface temperatures, and heat fluxes. The temporal and spatial resolution can be selected individually, although the computation time increases linearly for high resolutions. The method easily can be expanded to the two — and three-dimensional cases by dividing the wall into individual elements rather than layers.

The Response-factor approach is based on a method in which the response factors represent the transfer functions of the wall due to unit impulse excita­tions. The real excitation is approximated by a superposition of such impulses (mostly of triangular shape), and the real response is determined by the super­position of the impulse responses (see Figs. 11.33 and 11.34).5

The response factors are characteristic for the layer buildup of the selected wall and are calculated before (by a preprocessor program) or at the beginning of the simulation. Numerical reasons limit the time step to approximately 10 to 60 min, depending on the thickness and material properties of the wall lay­ers. The method allows the calculation of surface temperatures and heat fluxes bur not the determination of the temperature distribution within the wall. Due to the precalculation of these response factors, the computer time for the sim­ulation might be significantly reduced.

Calculation Methods

| FIGURE 11.33 Typical response function to a unit pulse of the temperature or heat flux boundary.

If energy is supplied to or extracted from a layer within the component, finite — difference models or problem-adapted one-dimensional response-factor — based models have to be used.

Although the method is expandable, it is normally used for the one­dimensional case (wall defined by layers).

Heat Loss to The Ground

The computation time for calculations of energy losses to the ground can be quite significant because of the three-dimensional heat conduction problem. Sim­plified methods are given in ISO/FDIS 13370: 1998.4

Heat Transfer through Windows

Each pane of a window absorbs and reflects a part of the incoming solar ra­diation in relation to the incident angle and the wavelength band, depending on the properties of the glazing material and coatings if applied (Fig. 11.35). Only a part of the insolation penetrates directly into the room. Energy is also transmit­ted from one side of the glazing to the other by other means of heat transfer.

For single glazing, the determination of the absorbed and transmitted radia­tion and of the heat transfer is quite straightforward, but for a window with multipane glazing, the calculation is more complex. Besides conduction in the panes, convection in the gaps as well as multiple reflections between the individ­ual panes must be considered.

Temperature

1.4

1.2

1

0.8

0.6

0.4

0.2

H-9“

-0.2

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подпись: temperature

4 6

Time

 

10 12

 

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(FIGURE 11.34 Determination of the real evolution of the heat flux at the inside wall surface: The tem­perature condition at the exterior surface is approximated by triangular pulses, and the heat flux response at the interior surface is determined by superposition of the heat flux responses of the individual pulses.

Solar

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Reflected solar radiation

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Long-wave

Radiation

подпись: long-wave
radiation

Transmitted solar radiation

подпись: transmitted solar radiation Calculation Methods

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FIGURE 11.35 The solar radiation on a window is partly transmitted directly into the room. Another part of the energy is absorbed in the glaring and released as long-wave radiation, The lower fig­ure shows the individual energy fluxes for a window glazing. The solar radiation is transmitted, reflected, and absorbed in the individual panes of the glazing, from where the energy is released by convection and long-wave radiation both to the room and to the outside.

For the calculation of such glazing in building-dynamics simulation codes, each pane is considered as a layer, exchanging energy with the other panes, with the room, and with the exterior.

For each layer the energy conservation equation is solved. The individual terms are the absorbed radiation in the layer and the radiative and convective heat exchange to the adjacent panes, to the room, or to the exterior.

The absorption is dependent on several parameters. This absorption can be calculated by specific window analysis programs such as WINDOW,5 using standardized data such as that provided by the program GLAD.6 These pro­grams calculate coefficients which are available to the users of building dy­namics programs in the form of libraries. Data for the calculation of the hear transfer through the window frame are included in these libraries.

Solar Shading and Solar Protection Devices

Shading by massive, fixed elements on the facade such as overhangs or sunscreens are treated as shading by parts of the building. Any solar protec­tion devices in front, in between, or behind a window’ need a more sophisti­cated model due to the interaction with the window glazing. It has to be noted that a device might give 100% shading to direct solar radiation while still transmitting diffuse radiation and thus light (diffuse light or beams reflected from the ground).

Simple models for louvers and other solar protection devices are based on a statement of constant reduction of the solar radiation flux on the window. A common assumption is that a louver is controlled so that no direct light can penetrate into the room.

Shading systems become an important factor for thermal behavior in cases of buildings with low internal loads. The analysis of energy-efficient buildings with advanced facade systems also require advanced models tor the solar protection system. Basically the whole system—shading device, glazing, spacers, and window frame—must be integrally modeled, taking into account the direct and indirect transmission (including multiple reflections) of direct and diffuse solar radiation and the solar absorption in the individual panes or slats (considering conduction, convection, and infrared radiation exchange). CEN has issued a reference calculation method.7 More advanced models also consider the effect of ventilation in the gap between individual glass panes or solar protection blinds.8

11.3.3.3 Room Models

In thermal building simulation, a thermal zone can be a part of a room, a room, or a combination of rooms defined as a part of the conditioned space, throughout which the internal temperature is assumed to have negligible spa­tial variations. The zone is enclosed by the surrounding walls (floor, ceiling, roof, wall elements) and windows.

For the numerical treatment, the energy exchange processes in a zone, as outlined earlier, are incorporated into a so-called room model.9’10

The room model consists of nodes, which are interconnected by heat ex­change paths (Fig. 11.36). The nodes represent either surface temperatures of the individual walls or the zone air temperature. For each node, an energy bal­ance is formulated. From the resulting set of equations, the temperatures and heat fluxes can be determined.

Most room models contain only one zone air node, thus assuming perfect mixing of the zone air and a homogenous temperature distribution in the space. Spatial temperature variations, such as vertical temperature gradients, are not considered. For specific applications such as displacement ventilation or atria, models with several zone air nodes in the vertical direction have been developed.11

The room models implemented in the codes can be distinguished further by how detailed the models of the energy exchange processes are. Simple mod­els use a combined convective-radiative heat exchange. More complex models use separate paths for these effects. Mixed forms also exist. The different models can also be distinguished by how the problem is solved. The energy balance for the zone is calculated in each time step of the simulation.

Moisture Transport

Moisture-transport simulation includes transport as well as storage phe­nomena, quite similar to the thermal dynamic analysis, where heat transfer and heat storage in the building elements are modeled. The moisture content in the building construction can influence the thermal behavior, because ma­terial properties like conductance or specific heat depend on moisture con­tent. In thermal building-dynamics simulation codes, however, these

^ Radiative ^ Of internal heat gam

+

О

Boundary condition Heat conductance

Convective

Part of internal heat gain

 

Convection Long-wave radiation

Convective energy transport by infiltration and/or ventilation

Short — and/or long-wave radiation on surface node (wall gain WG)

 

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W(‘,AA

 

Internal heat gain

 

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| FIGURE 11.36 The room model characterizes the individual energy flux paths as thermal resis­tances, which are connected to the individual surfaces and to the room air node.

Material properties are mostly constant input values. Therefore, variable material properties or even phase-change effects cannot readily be consid­ered.

Moisture is also transported by ventilation airflows. This is dealt with in more detail in Section 11.4.

11.3.3.4 Modeling of HVAC Systems

Depending on the program, HVAC systems must be defined either by se­lecting individual components and defining their parameters and their connec­tions or by choosing one of the systems available in the program.

Different modeling techniques are used, from empirical formulations us­ing polynomial approximations, to process definition (e. g., on the basis of psychrometrics as depicted in the H-x or Mollier diagram), and finally to de­tailed physical modeling including all kinds of energy exchange and control processes. Directly related to the modeling used is the kind and amount of in­put data required. In principle, three application fields can be distinguished for the use of HVAC models:

• Development of HVAC components: design and optimization

• Selection of size of HVAC components in the planning process (dimensioning) and simulation of the behavior of the system under partial load

• Energy-demand calculations

For the first kind of application, the focus is on certain elements of the HVAC component under consideration. The simulation is used to study and optimize design-specific aspects such as the pipe size and spacing or wetted area and fin geometry in a heat exchanger. This kind of modeling requires de­tailed knowledge on many input parameters and the related physical processes.

The second kind of modeling is focused on the needs of the planner and HVAC engineer, who has to comply with certain criteria for heat delivery or removal for comfort and energy efficiency and from this has to select a certain type of component available on the market. Once the component is selected, only the performance of this component under variable load is of interest. This kind of modeling normally requires much less input, because actually only the change in performance from a given design point to a point for the actual load has to be determined.12

Systems and control configurations as required may not be available in the simulation code or may not be able to be described and modeled in the re­quired detail. Depending on the application, an optional system extension or change can be defined using the existing model. Otherwise, a new’ model has to be developed and integrated into the code. In these cases, it is decisive for the selection of code used whether and how easily such an extension can be implemented.

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