Evaluation of building heating loads with dimensional analysis: application of the Buckingham π theorem

A detailed assessment of building energy performance requires a large amount of input data concerning building typology, environmental conditions, envelope thermophysical properties, geometry, control strategies, and several other parameters. Notwithstanding, the use of specialized software tools poses many challenges in regards to the retrieval of reliable and detailed information, setting a steep learning curve for engineers and energy managers. To speed up the preliminary assessment phase, it might be more convenient to resort to a simplified model that allows the evaluation of heating energy demand with a good level of accuracy and without excessive computational cost or user expertise. Dimensional analysis is a means of simplifying a physical problem by appealing to dimensional homogeneity to reduce the number of relevant variables. In this work, the authors investigated an alternative approach to assess the thermal energy demand of a high-performance-non-residential building. It was possible to define some dimensionless numbers that synthetically describe the links between the main characteristic parameters of the thermal balance by applying the Buckingham π theorem. After a detailed description of the Buckingham π theorem and of its application concerning the evaluation of the building energy balance, the authors identified nine “ad hoc” dimensionless numbers. The proposed methodology has been validated by the comparison of the heating energy demand calculated by detailed dynamic simulations carried out in TRNSYS according to the standards and laws of building energy requirements in seven different European countries. Applying a set of criteria, it was possible to employ a dimensionless number to determine, immediately and without any calculation or use of steady/dynamic software, the heating energy demand with an reliability >90%.