PSI - Issue 64

Mahdi M.K. Zanjani et al. / Procedia Structural Integrity 64 (2024) 1134–1141 Zanjani et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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Using sequential quadratic programming (SQP) to this end (Colabella et al., 2019), we find the optimal solution shown in Fig. 5, for which the energy consumption for cooling, heating and total is: = 1159.40 kWh, ℋ = 599.32 kWh, ℐ = 1758.72 kWh. (14)

Fig. 5. Optimal solution giving the porosity and mPCM content of the NRG&STRUCT-foams in the layers of the external walls of the BESTEST-NRGF 900 building at Bilbao. Compared to and ℋ , = 0.809 and ℋ = 1.030 ℋ , we can conclude that the BESTEST NRGF 900 building performs sensibly better for cooling and slightly worse for heating than the original BESTEST 900. Globally, +ℋ = 0.873 ( +ℋ ) , i.e., the optimal BESTEST-NRGF 900 requires 12.7% less energy than the reference BESTEST 900. This is to keep the indoor thermal comfort all along the year at Bilbao. As seen in Fig. 5, the minimum total energy consumption is achieved for a multilayer wall having the three outermost layers made of the same NRG&STRUCT-foam: i.e., having the highest allowed porosity max( )=0.9 and mPCM fraction =0.02 . It is important to remind that is the volume of mPCM per unit volume of the matrix of the NRG&STRUCT foam, hence consisting in hardened cement paste with embedded mPCM, whose volume is at its turn =1− per unit volume of NRG&STRUCT-foam. Therefore, in the 6.06 cm-thick outermost part of the optimal wall, the volume of mPCM per unit volume of NRG&STRUCT-foam is just 0.002 , almost negligible. Therefore, this part of the optimal wall plays, almost exclusively, an insulation role. On the other hand, the five innermost layers of the optimal wall have zero porosity, but a mPCM content gradually increasing from 0.11 to max( )=0.2 amount, especially at the outermost layer. These layers form the 10.09 cm-thick innermost part of the wall, which plays two roles: structural as well as TES. The optimal solution is close to that of the original BESTEST 900 concerning relative position and thickness of the insulation and structural walls, but the optimal structural wall contributes with extra TES thanks to the mPCM inclusions. Note that this is a structurally admissible solution, with the structural constraint of Eq. (8) satisfied in the limit, i.e.: ( 1 ) +⋯+ ( ) = ̅ = 870.68 kg/m 3 (15) Considering the structural layers = 4,5,6,7,8, the reduced density ( i ) gradually decreases from 1475 to 1295 kg/m 3 because of increase, but it remains high enough for structural aims. 5. Conclusions In this study, we introduce an optimization approach to analyze the energy performance of a building envelope while considering structural limitations. Key conclusions are: • We proposed the NRG&STRUCT-foam, a metamaterial balancing insulation, thermal energy storage (TES), and structural integrity, achieved through a combination of foamed concrete and mmPCM.