An innovative method for the design of high energy performance building envelopes

Abstract

In this paper, an innovative method to minimise energy losses through building envelopes is presented, using the Proper Generalised Decomposition (PGD), written in terms of space x, time t, thermal diffusivity α and envelope thickness L. The physical phenomenon is solved at once, contrarily to classical numerical methods that cannot create a parameter dependent model. First, the PGD solution is validated with an analytical solution to prove its accuracy. Then a complex case study of a multi-layer wall submitted to transient boundary conditions is investigated. The parametric solution is computed as a function of the space and time coordinates, as well as the thermal insulation thickness and the load material thermal diffusivity. Physical behaviour and conduction loads are analysed for 76 values of thermal insulation thickness and 100 types of load material properties. Furthermore, the reduced computational cost of the PGD is highlighted. The method computes the solution 100 times faster than standard numerical approaches. In addition, the PGD solution has a low storage cost, providing interesting development of parametric solutions for real-time applications of energy management in buildings.