11. Conclusion

11.1. Summary

In order to improve the modelling of solar-related energy flows for building applications, a novel method has been developed, implemented and tested. First, the potential inaccuracies and limitations of the currently available and applied models and methods were analysed. Currently applied approaches to model solar gains through transparent surfaces of buildings mostly rely on combinations of at least two methods. Limitations are related to the individual methods but also arise from combining the methods. In order to overcome these restrictions, a unified approach that applies models of physical optics based on a single, detailed 3D CAD model was developed. Energetically significant optical processes were identified, and the related advanced optical models, primarily used in material science and astronomy, were adopted for their use in the building science context. A Monte Carlo raytracing method has been developed to incorporate the implemented optical models. While the propagation of light is still modelled based on the principles of geometrical optics, the scattering events, i.e. reflection, absorption and transmission, are modelled based on the relevant electrodynamic models. In order to do this, light’s polarisation state and spectral distribution must be considered in all modelled processes. Further, a matrix-based thin-film method allows modelling interference effects on surfaces covered with one or multiple thin layers of different materials. The feature is essential to the method, as modern glazings rely on such spectrally selective coatings. In addition to the physical optics approach, which fundamentally relies on solving Fresnel’s equations in their complex-valued form, a statistical roughness model and a generic subsurface-scattering model had to be added to allow for modelling of practically relevant surfaces. All optical models were implemented by applying the concepts of object-oriented programming. This allows straightforward future adaptation or extension of the models for specific surfaces or refined modelling.
In the applied physical optics models, the materials are characterised by their electrodynamic properties in the form of the spectrally resolved complex-valued index of refraction (cRI). Although the underlying physical quantities forming the cRI are accessible to measurement, they are often not readily available. To address this issue, two approaches allowing the application of the method if the required material data is initially unavailable were implemented. Firstly, two inversion methods were developed that allow deriving cRI functions of measured reflection, transmission or absorption spectra. Additionally, a fallback approach has been implemented if the required optical properties remain unavailable. It allows a gradual downgrading of the optical models to generic versions relying only on a single or a few parameters.
The combination of in-depth optical modelling of different materials and consideration of detailed geometry constitutes a complex and multifaceted model that cannot be evaluated in analytical closedform. Nonetheless, it can still be solved efficiently by means of stochastic approaches. For this reason, a raytracer fundamentally based on Monte Carlo methods was developed, implemented and tested in the course of the PhD.
In addition to the novel method proposed for optical modelling, a new interface for deploying the detailed raytracing data to building performance simulation was developed. The method is called SIOP (solar incidence operator) and is based on spherical harmonics, known from quantum physics. The SIOP concept allows providing the detailed optical data gathered in the raytracing process to thermal simulation in an efficient and comprehensive manner. Hence, SIOPs effectively enable sim- Conclusion RadiCal, D. Rüdisser 231 ulation tools to perform solar calculations with raytracing accuracy, but virtually at no computational costs. SIOPs are not only used to model solar gains resulting from irradiance directly transmitted through transparent surfaces but also provide information on the power absorbed in any relevant component of the façade or window. The combined information allows accurate dynamic simulation of all relevant temperatures and energy flows within a building component for any given boundary conditions. Thus, all temperature-related or thermal-mass-related dependencies can be modelled accurately.
Many validation and test cases are contained throughout the work. The tests are performed at different levels of the model to prove and demonstrate the validity, not only of the models and equations but also of their algorithmic implementation. In an essential validation, advanced virtual optical measurements, e.g. ellipsometry, are compared against available empirical data. Further, the evaluation of the SIOP based on the Perez diffuse sky model is validated against the standard calculation performed with a building performance simulation tool. At the highest level, the entire RadiCal workflow is applied to perform virtual measurements of a triple-glazed window equipped with four different shading devices. Real-world measurements performed over several months with varying solar incidence profiles are compared with virtual measurements performed on the modelled window. A dedicated measurement device and method were developed in the course of the PhD specifically for this purpose. This was necessary in order to be able to measure the spatially highly inhomogeneous irradiance field behind the shaded window under real-world conditions. Considering the generally higher error level linked to such measurements, the comparison shows a good level of agreement. The deviation of the calculated from the measured effective transmittances for 22 different shading configurations with variable irradiance profiles is in the range of a few per cent and below. Finally, the application of the method is demonstrated in a typical use case. The thermal performance of a triple-glazed window is accurately determined for different locations and orientations.
The established novel method can be used to address a wide range of research and industrial applications, reaching beyond the standard task of building performance simulations. Its full potential must be explored in further studies.