11.2. Key findings

The work performed in the PhD demonstrates that more accurate modelling of solar-induced energy flows in building science is possible if optical processes are modelled on a more fundamental level, and a strict separation of optical modelling and thermal simulation is maintained. In detail, the most significant findings are:

11.2.1. Physical optics approach

In order to accurately determine solar-related energy flows, a detailed and spectrally resolved modelling of all relevant optical processes is required. The optical model needs to consider detailed threedimensional geometry and the materials’ optical properties object. Hence, a raytracing process is required. Currently used raytracers are data-driven, as the optical properties of surfaces are mostly modelled based on empirical BSDF data. For building science applications, it is of essential importance that comprehensive and accurate models are available for the transparent surface, particularly for uncoated and coated glasses. Accurate modelling of such surfaces requires the consideration of the fundamental nature of light, i.e. its electrodynamic character. This can be performed most efficiently by solving Fresnel’s equations in complex-valued form. Compared to currently applied Conclusion RadiCal, D. Rüdisser 232 methods, the approach relies on a different type of material specification. This information is often not readily available, which can hamper the application of the method. However, the use of physical optics models leads to significant advantages as many significant dependencies are intrinsically contained and do not require additional assumptions or models. These are, in particular, the angular and spectral dependencies of scattering processes, i.e. reflection, transmittance/refraction and absorption. Since the models are based on fundamental physical principles, they generally require less input data than data-driven models. Their application potentially leads to plausible and realistic approximations for the case that limited material data is available or generic values are used.

11.2.2. Modelling of coatings

Accurate modelling of coatings applied on surfaces is a challenging but essential task, as they are an integral component of modern glazings (e.g. low-E or solar protection layers). Interference effects in coatings are responsible for intended and unintended spectrally and directionally selective properties of these coatings. In order to model the related optical properties efficiently, it is necessary to apply an extended Fresnel approach that is able to consider thin-films.

11.2.3. Additionally required models

In order to model practically relevant surfaces, it is essential to additionally consider the surface’s roughness as well as subsurface scattering processes. Two generic models are currently part of the method. The integrated parameters allow their adaptation for modelling a wide range of surfaces. However, it will be necessary to develop additional models to consider specific surfaces, e.g. microor nanostructured surfaces and metallic paints.

11.2.4. Consideration of polarisation

Polarisation is a fundamental, yet often neglected, property of light. Polarisation generally occurs on every scattering event at oblique incidence angles. In order to fully apply the Fresnel approach, the consideration of polarisation is a requirement. For the intended application, the concepts of the fourdimensional Stokes vectors and Müller matrices are well suited, as they allow efficient and straightforward integration of polarisation into the raytracing process and scattering models.

11.2.5. Inversion methods to determine optical properties

As the optical properties of materials are commonly not available in the required form, two inversion methods were implemented to derive them from available data. Although the methods rely on a stochastic optimisation of models with a relatively high degree of freedom, the results are consistent and indicate a plausible physical behaviour. The ambiguity of the results depends on the amount of input information provided. Spectral measurements at non-normal directions a rarely performed but would significantly increase the quality of the inversion results. If only near-normal measurements are available for the inversions, the results have to be treated cautiously. However, they potentially lead to an increased quality of the overall simulation results, as plausible spectral, angular and polarisation dependencies are intrinsically contained in the models.

11.2.6. Separation of optical and thermal domain

The concept of directional solar heat gain coefficients (DSHGC) is regarded as problematic, and its application should be questioned. The derivation of DSHGC values requires anticipation of results and boundary conditions of the dynamic thermal simulations that they will be applied to in later Conclusion RadiCal, D. Rüdisser 233 simulations. This constitutes a circular reference. From a fundamental point of view, it can be stated that the energy flows induced by solar radiation have significant thermal impacts, while temperatures or temperature gradients generally have little to no impact on the related solar processes. Based on this unilateral interaction, it is appropriate to separate the two domains entirely. The optical evaluations must be solved first, independent of any thermal considerations. The results of the optical model characterising only transmitted and absorbed energy flows induced by solar radiation should then be deployed to dynamic thermal simulation in an appropriate form.

11.2.7. SIOPs – representation of optical properties

The currently applied form to provide the results of the optical calculations in the form of 145 discrete values cannot satisfactorily cover the entire hemisphere. A smooth and continuous angular representation of the results is favourable as the temporal and spatial integrations and differentiations required in the evaluation processes also result in smooth and continuous functions. This increases both the accuracy and performance of the related dynamic thermal simulations. A method that provides smooth and continuous functions on the hemisphere is proposed in this work. The representation is based on spherical harmonics expansion and allows a flexible and efficient way to store, deploy and evaluate the results of the optical calculations.

11.2.8. Variability and dependencies of solar-induced energy flows

The performed full-system validation cases and application examples demonstrate the remarkable variability of solar-induced energy flows, thus demonstrating the need for accurate modelling. Even for the supposedly trivial case of an unshaded triple-glazed window, the optical and solar total transmittance values generally exhibit diurnal and seasonal variations in the double-digit percentage range. The most significant dependencies are those on the solar angles and on the sky condition. However, the results also demonstrate that a more refined modelling of the local environment is necessary to increase the accuracy of solar calculations further.

11.2.9. Usefulness of rendering

While initially not an objective of the thesis, rendering via backward raytracing turned out to be a substantial component of the method. Creating visual representations of the target objects allows for validating and demonstrating the quality of light modelling and the level of detail the method achieves. The quality of the backward raytracing used for the renderings represents the quality of the forward raytracing applied for the energetic calculations. Creating a single rendering requires evaluating billions of scattering events covering an extensive range of spectral and directional cases. Hence, the creation of renderings is a valuable validation step regarding the models’ accuracy, the implementation’s functionality and the correctness of material assignments.