Motivation

In light of global warming and considering that in developed countries, buildings account for almost half of the total energy consumption (U.S. Department of Energy, 2015; European Commission Energy dept., 2020), it is essential to increase the energy efficiency of buildings. Solar-induced energy flows through the building envelope, particularly solar inputs through transparent surfaces, are highly relevant in this context. Due to the constantly rising proportions of glazed surfaces in modern buildings, the significance of this energy component has dramatically increased in recent decades. Solar gains through transparent surfaces can considerably lower the demand for heating and lighting energy in winter (Zirnhelt et al., 2015; Marino, Nucara et al., 2017a; Ménard and Souviron, 2020) while often representing the predominant heat source in summer. Therefore, solar inputs are also directly linked to increased cooling energy demand, indoor discomfort or potentially hazardous overheating (Hamdy et al., 2017; Marino et al., 2017b; McLeod et al., 2017).
In order to increase the energy efficiency of buildings, it is essential to have suitable models for solarinduced energy flows available. Accurate and physically valid models can, on the one hand, be used to develop and optimise the energetic performance of glazings and shadings at the component level. On the other hand, they are essential to enhance the accuracy of building performance simulation (BPS) for the entire building. BPS is applied to improve the energy efficiency of buildings on various levels ranging from the early design phase over design development to operation. Hence, the quality of the models used to determine solar energy flows has impacts on many levels ranging from cooling and heating capacity design over energy demand determination and optimisation to the assessment of the building’s user comfort.
However, in contrast to the detailed and elaborate calculation methods currently applied to describe heat transmission through the building envelope, the currently used methods to model solar-induced energy flows lack accuracy. The inaccuracies can be attributed to the fact that the related energy flows are linked to a large number of complex and multifaceted optical processes. Addressing this challenge with simple models requires a high level of abstraction that involves potentially significant errors.
Performing full-system measurements of windows, shading devices or façade elements instead of using models is no viable alternative. The available empirical methods are time-consuming and costly on the one hand and can only be carried out for specific, individual configurations on the other hand. Due to the variety and a large number of potential combinations of materials and systems, it is virtually impossible to cover all relevant products empirically.
The currently most applied methods to model the energetic performance of shaded or unshaded glazed components have been laid down in international standards. These calculation methods are based on severe simplifications. E.g., the commonly used Venetian blinds are still modelled assuming indefinitely thin, planar and ideally diffuse reflecting elements (ISO 15099, 2003; ISO 52022 part 1, 2018), performance values of glazings are calculated on the assumption of normal incidence and significant angular and spectral dependencies of light scattering processes are not considered (ISO 9050, 2003; EN 410, 2011). Based on these simplifications, calculating solar gains of shaded and unshaded glazings can involve significant errors (Platzer, 2001; Kuhn, 2006; Wermke, 2021).
Research performed in the last two decades focused mainly on directional dependence, which was disregarded in previous approaches, and led to novel, more complex approaches. The most commonly Introduction RadiCal, D. Rüdisser 2 used modern methods to determine the optical properties and energetic performance of glazings rely on scientific models that are implemented in the Window software by Lawrence Berkeley National Laboratory (LBNL Windows and Daylighting Group, 2022b). The method allows excellent modelling of multi-layered glazing components based on an extensive database containing product-specific, measured spectral data for normal incidence. However, it utilizes two simple models to approximate the directional behaviour for incidence at oblique angles (Curcija et al., 2018) and features only a few specific and simplified models for considering shading devices. In order to model shading elements with higher accuracy, additional raytracing software, mostly Radiance (Radiance Community, 2022), is used to provide directional scattering information (BSDF) in the form of Klems’ matrices (Klems, 1994b). The resulting combined optical model is then commonly applied in an energy balance model to derive directional solar heat gain coefficients (DSHGC); see, e.g., the two-layer model (Kuhn et al., 2011; Bueno et al., 2017). The derived DSHGC values can finally be used in energy performance simulation tools to determine the total transmitted power based on solar irradiance parameters. The modelled heat gains comprise directly transmitted radiation and secondary, transmissive heat flows. The entire workflow is complex, and its fragmentation causes inaccuracies that can be divided into two groups: on the one hand, the layered BSDF approach involves substantial limitations regarding its optical accuracy, particularly regarding spectral and angular selectivity, spatial information and polarisation. On the other hand, the derivation of DSHGC values requires the assumption of predefined thermal boundary conditions and thermal properties of all components. These parameters are mostly assumed as constant. However, they are, in fact, dynamic by nature and depend on the results of the final building simulation.
As a consequence of the limitations of the existing methods for modelling solar gains of transparent surfaces in the building envelope, the calculated energy performance of the entire building may be significantly inaccurate. This involves potentially wrong planning decisions in all phases of the building’s life cycle, ranging from early design to operation. Beyond that, the limitations of the currently applied models have adverse impacts on the evaluation and optimisation of existing shading or glazing elements and the development of innovative, new systems.
The scientific work in the recent two decades has mostly focused on combining and enhancing the approaches described above and, in particular, on providing ways to integrate them into existing building performance simulation methods. In recent years, dedicated, stand-alone tools to dynamically simulate energy demand and daylighting aspects based on the approaches discussed above were added by research teams working in this field, see the Comfen tool by LBNL (Mitchel et al., 2019) or the Fener tool (Bueno et al., 2015). However, the fragmented DSHGC workflow and the underlying fundamental optical models, which mostly date back to the eighties, are rarely questioned, representing a current research gap. On the one hand, a more universal modelling approach must be able to consider the three-dimensional structure of building components with a high level of detail. On the other hand, it has to be able to model light scattering processes with the precision of microscopic laboratory tests, considering the spectral, angular and polarisation properties of the incidence light and the target. This high level of modelling is required to accurately model the interaction of light with objects combining coated or uncoated transparent and opaque materials. The thesis’s main target is to develop a universal and unified method that meets these requirements to allow for accurate modelling of solar-induced energy flows for building science applications. The proposed method is based on a more fundamental level of light modelling, but is still able to provide its functionality in a comprehensible, robust and practical way.