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planning:calculating_energy_efficiency:dynamic_simulation

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Dynamic simulation of a building's thermal performance


Fig. 1 A typical room model used in instationary simulation of a buildings
thermal performance; this is the model-type used
in the program DYNBIL [Feist 1994]


Models used for Simulation

The actual task in dealing with the questions of indoor climate and energy balance results from the high level of complexity which the “house and heating” system exhibits in combination with the respective physical theories of the subsystems.

The mathematical models for mapping the subsystems are largely “simple” and proven: the heat conduction in solids and non-flowing fluids can be described by Fourier's dynamic heat conduction equation, convection in space is dealt with by the equations of Navier-Stokes, radiation is determined according to Planck's law of radiation - etc. The respective basic equations mentioned here generally result in coupled, non-linear, partial differential equations of 2nd order in space and time, taking into account the temperature dependence of the coefficients. However, boundary conditions encountered in buildings require considerable effort even for a single subsystem (e.g. the gas space of a double-pane insulation glazing). This has its cause

  • on the one hand in the complexity of the basic equilibria involved (e.g. with Navier Stokes),
  • on the other hand especially in the present boundary conditions, e.g. the generally not simple geometries of components.

While a solution to the flow problem for a room in a stationary case can be tackled numerically with some effort today using the Navier-Stokes equations, a solution to the overall problem “building & heating” in the coupling of all appropriate physical theories (“first principles”) today still exceeds every reasonable computation capacity.

On the contrary, the task is to reduce the complexity again by decisive simplifications in the parts constituting the overall model to such an extent that treatment with reasonable effort is always the path to take.

It is clear from the task that the model must map all the essential, interacting components of the building and the heating system: each sub-model must be dealt with under the boundary conditions that are significantly determined by the other components. This is one of the theses that will be substantiated at various points in this publication - two examples:

  • The energy balance of a window surface depends not only on the component “window” itself, but also on the other components of the room (in particular their insulation and their storage capacity on the room side) and on the operation of ventilation and heating systems,
  • The assessment of components for solar energy use (such as transparent heat insulation) with regard to the energy balance to be achieved all year round depends on the (insulation) standard of the building in which the subsystem is used.

An image of the overall “Building & Heating” system is therefore indispensable for the investigations provided here. However, in order to reduce the complexity of the model, it is conceivable to reduce the level of detail of the model formation for the individual components: it only has to be guaranteed that the interactions between the components are adequately represented stay. As a result, for any desired, more precise detailed examinations, it remains at liberty to extract the boundary conditions for individual components from the (coarser) overall model and to use them for detailed individual models of components.

Special features of the computer-aided simulation

The mathematical model for the treatment of the thermal behavior of buildings is characterized by a high level of complexity as shown in the last section: a whole series of partial models for

  • Instationary heat conduction (Fourier equation),
  • The flow of air in space (Navier-Stokes equations),
  • The radiation exchange between components (Planck law),
  • The reflection, transmission and absorption of solar radiation,
  • Control of heating,
  • Free heat sources in the room,
  • Infiltration and ventilation

are to be treated and linked. This is done geometrically with generally omplex boundary conditions (geometry of a building) and the climate as an inhomogeneity.

Even with simple sub-models (such as the connections of different components, e.g. on the eaves), the mathematical sub-model (e.g. Fourier problem with boundary conditions) can no longer be solved analytically. Already here you have to rely on numerical methods for the solution. To implement such numerical methods, computer algorithms are expediently used today.

Such a computer algorithm can also be understood as a (program-based) model of the mathematical model: in this respect the use of computer simulation does not mean a pr

References

[Feist 1994] Thermische Gebäudesimulation; 1. Auflage, 366 Seiten, 1994 Thermal building simulation, first edition,1994

planning/calculating_energy_efficiency/dynamic_simulation.1596620693.txt.gz · Last modified: 2020/08/05 11:44 by wfeist