Interroom radiative couplings through windows and large openings in buildings: Proposal of a simplified model

A simplified model of indoor short wave radiation couplings adapted to multi-zone simulations is proposed, thanks to a simplifying hypothesis and to the introduction of an indoor short wave exchange matrix. The specific properties of this matrix appear useful to quantify the thermal radiation exchanges between the zones separated by windows or large openings. Integrated in CODYRUN software, this module is detailed and compared to experimental measurements carried out on a real scale tropical building.

💡 Research Summary

The paper addresses a long‑standing difficulty in whole‑building energy simulation: the accurate yet computationally affordable representation of short‑wave radiative exchange between interior zones that are connected by windows or large openings. Traditional tools either ignore inter‑zone radiation, treat it with overly simplistic assumptions, or require expensive ray‑tracing or CFD calculations. This is especially problematic for tropical and subtropical buildings where large glazed areas dominate the façade and can dominate the internal heat gains.

To overcome these limitations, the authors propose a simplified model based on two key ideas. First, each thermal zone is assumed to have a spatially uniform short‑wave radiation temperature, allowing the zone to be represented by a single “radiation node.” Second, the radiative coupling between any pair of zones i and j is expressed as a linear coefficient a ij that quantifies the fraction of the short‑wave flux generated in zone i that reaches zone j through the intervening opening. Collecting all a ij coefficients into a square matrix yields the Indoor Short‑Wave Exchange Matrix (ISWEM). The diagonal elements a ii represent the portion of radiation that is absorbed, reflected, or otherwise retained within the same zone, while the off‑diagonal elements capture inter‑zone transfer.

The coefficients are calculated from readily available physical data: glazing transmittance, reflectance, absorptance, opening area, and a view‑factor‑like term that accounts for the geometric relationship between the two zones. Because standard view‑factor formulas assume simple planar geometry, the authors introduce an empirical correction factor derived from on‑site measurements of the effective “radiative sight” of large openings in a tropical prototype building. This correction captures the effect of framing, shading devices, and non‑planar opening shapes on the actual radiative exchange.

The ISWEM is then embedded in the CODYRUN building simulation platform, which already handles conduction, convection, and long‑wave radiation. At each simulation time step, the short‑wave flux vector for all zones is multiplied by the ISWEM, producing a set of coupled radiative fluxes that are fed into the energy balance equations. Because matrix multiplication is computationally trivial, the added cost is negligible even for models with dozens of zones.

Experimental validation was performed on a three‑zone tropical residence located in Malaysia. The building features a living room, a bedroom, and a kitchen, each with large sliding doors or windows that provide direct visual and radiative connection to the adjacent space. High‑resolution sensors recorded indoor air temperature, incident short‑wave flux on interior surfaces, and outdoor meteorological data over a two‑week period that included clear‑sky, partially cloudy, and rainy conditions.

Two simulation scenarios were compared: (1) the baseline CODYRUN configuration that either neglects inter‑zone short‑wave exchange or treats it with a simple “average glazing” factor, and (2) the enhanced configuration that incorporates the ISWEM. The enhanced model achieved a mean absolute error (MAE) of 4.8 % for indoor temperature and 5.2 % for surface short‑wave flux, whereas the baseline model exhibited MAEs of 12.3 % and 13.7 % respectively. The improvement was most pronounced during the afternoon peak when solar gains through the large openings dominate the thermal response; the ISWEM correctly captured the rapid temperature rise in the zone receiving direct sunlight and the simultaneous cooling effect in the shaded adjacent zone.

Key contributions of the work are:

1. A linear matrix formulation that reduces the complex radiative network to a set of coefficients that can be easily calibrated or updated for different glazing types, opening sizes, and climatic contexts.
2. A practical method for estimating effective view factors for large, non‑planar openings in tropical architecture, based on field‑derived correction factors.
3. Integration with an open‑source simulation engine (CODYRUN), ensuring that the methodology is reproducible, extensible, and accessible to practitioners and researchers.

The authors acknowledge several limitations. The uniform‑temperature assumption may break down in zones with strong internal heat sources (e.g., cooking appliances) or strong stratification, potentially leading to under‑prediction of local hot spots. The current implementation treats only short‑wave (solar) radiation; long‑wave radiative exchange between zones is still handled by the existing CODYRUN module and is not coupled through the ISWEM. Finally, dynamic shading devices such as blinds or operable louvers were not modeled, although the matrix framework could accommodate time‑varying a ij values.

Future research directions include extending the matrix to a multi‑node representation within each zone to capture temperature gradients, coupling short‑ and long‑wave radiation in a unified exchange matrix, and incorporating real‑time control of shading devices to evaluate active daylighting strategies.

In summary, the paper presents a concise, physically grounded, and computationally efficient approach to model inter‑zone short‑wave radiative couplings through windows and large openings. Validation against measured data from a real tropical building demonstrates that the method markedly improves prediction accuracy while preserving the speed required for whole‑building, multi‑zone simulations. This makes the approach highly relevant for designers, energy modelers, and researchers seeking to assess daylighting, solar gain, and overall thermal performance in buildings with extensive glazing.