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 = (thermal conductivity of air), =1.5 (for spherical air bubbles) and =0.7405 (value for hexagonal close and face-centered packings); the adopted values of and are those in Fachinotti et al. (2023b). The matrix of an NRG&STRUCT-foam is also a composite with the cement paste as matrix and mPCM as dispersed spherical inclusions. To compute its effective conductivity ≡ & , let us call Eq. (3) with ≡ (thermal conductivity of cement paste), ≡ , ≡ (thermal conductivity of the mPCM), =1.5 and =0.7405 . 3. BESTEST 900 demo-building Let´s consider the energy simulation of the BESTEST 900 (ANSI/ASHRAE Std 140-2017) as our reference point for the analysis (Fig. 2). Within the BESTEST 900, the indoor thermal environment is fixed between 20 °C and 27 °C via proper conditioning. Its external walls have three layers: wood siding, foam insulation, and concrete, each one detailed with the respective thicknesses and material properties in Table 2. 1137 4

Fig. 2. Geometry of the buildings BESTEST 900 and respective layouts of their external walls.

Table 2. Layers in the external walls of the BESTEST 900. Layer Thickness Density

Specific heat Thermal conductivity

Concrete (interior) Foam insulation Wood siding (exterior)

10 cm 6.15 cm 0.9 cm

1400 kg/m 3 1000 J/kg/°C 1.225 kg/m 3 1000 J/kg/°C

0.51 W/m/°C 0.026 W/m/°C

530 kg/m 3 0.14 W/m/°C Now, we define a new building, namely BESTEST-NRGF 900, like the BESTEST 900 except that its -layers of NRG&STRUCT-foams replace the insulation and the structural layers in the external walls of the BESTEST 900. Each NRG&STRUCT-foam layer has thickness ( + )/ , being =6.15 cm and =10 cm the thicknesses of the insulation and structural layers. The NRG&STRUCT-foam in layer = 1,2, … , is characterized by the porosity ( ) , the mPCM content ( ) ; the whole multilayered wall of functionally graded NRG&STRUCT-foams wall is determined by: = [ ( 1 ) , ( 1 ) ,…, ( ) , ( ) ] , (4) which is the vector of design variables in the context of mathematical optimization. The optimal wall is given by the solution of the optimization problem: min ℐ( ), (5) where the objective function ℐ is a building energy performance index, the lower the better. We adopt: ℐ = + ℋ, (6) where is the energy consumed for cooling when the indoor temperature is above 27°C and ℋ is the energy ℋ consumed for heating when the indoor temperature is below 20°C. To preserve the stability of the hardened NRG&STRUCT-foam, the optimization problem is subject to the bound constraints: 0≤ ≤max( ) = 0.9, 0 ≤ ≤max( )=0.2. (7) 900 J/kg/°C